Document [original]

Interactions and Structures of the Exopolysaccharide Levan

and β-lactoglobulin in binary and ternary Systems

vorgelegt von

M.Sc.

Christoph Simon Hundschell

ORCID: 0000-0003-4468-921X

an der Fakultät III – Prozesswissenschaften

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften

– Dr. rer. nat. –

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Hajo Haase

Gutachterin: Prof. Dr. Anja M. Wagemans

Gutachter: Prof. Dr. Stephan Drusch

Gutachter: Prof. Dr. Rudi F. Vogel

Tag der wissenschaftlichen Aussprache: 22. Juni 2023

Berlin 2023

Acknowledgments

First and foremost, I would like to express my heartfelt gratitude to Prof. Dr. Anja Maria

Wagemans for her invaluable guidance, mentorship, and unwavering support throughout my

academic journey. Her profound knowledge, insights and expertise have been instrumental in

shaping my research and intellectual growth. Her optimism, constructive feedback and

numerous scientific discussions and meetings have been pivotal in the successful completion

of this thesis.

I would also like to thank Prof. Dr. Stephan Drusch, whose guidance and feedback have been

an essential source of motivation and inspiration for me throughout my academic journey at

TU-Berlin. His astute insights and constructive feedback have been critical in shaping my

academic and professional growth.

Additionally, I am thankful to Prof. Dr. Rudi Vogel for his flexibility and willingness to

evaluate my thesis. I appreciate his time and effort in providing feedback on my work.

I am grateful to the students I supervised, Hannes, Sabrina, Juliane and Linda, as well as the

tutors Thu and Thanh. Their contributions and work in the laboratory were invaluable and

helped to significantly to advance this thesis.

I would also like to express my gratitude to my colleagues at the Department of Food Colloids

and the Department of Food Technology and Food Material Science. You were always helpful,

supportive and made work a fun place to be. A special thanks goes to Sabrina Bäther for

proofreading this thesis.

Last but not least, I would like to express my deepest gratitude to my beloved family, my

friends and my loving partner. Your unwavering support and encouragement have been a

constant source of strength and inspiration throughout my journey. I am truly blessed to have

you in my life and I cannot thank you enough for all that you have done for me. Your

presence has made all the difference and I am honored to have you by my side.

Abstract

Exopolysaccharides are carbohydrate polymers produced by a variety of microorganisms.

Depending on the microorganism and environmental conditions, they can differ in their

monosaccharide structure, molecular weight and degree of branching. Despite this great

diversity, only a few exopolysaccharides are used in a targeted manner in food products. An

exopolysaccharide with great potential as a thickening, texturing and clouding agent is levan.

In addition to these techno-functional properties, levan has health-promoting effects as a source

of dietary fiber. This β-2,6-linked fructose polymer can be produced in situ by food-grade lactic

acid and acetic acid bacteria. Moreover, its molecular weight and thus its functionality can be

tailored by controlling the pH during fermentation. Despite the outstanding properties of levan,

the macromolecular structure in dependence on the molecular weight has not yet been fully

elucidated, and little is known about the behavior of levan in food-related protein-containing

systems. A well-studied model protein for such systems with many applications in food

products is β-lactoglobulin. It is a globular protein obtained from whey and has various

functional properties such as gel formation or interfacial stabilization.

Therefore, this thesis investigates the fundamental mechanism of structure formation of levan

in food-related protein-containing systems to establish levan as a functional polymer. For this

purpose, the structures and interactions of levan, β-lactoglobulin and levan-β-lactoglobulin

mixtures were systematically investigated on three levels (dilute – binary, dilute – ternary,

concentrated – ternary). On the first level, the macromolecular structure and molecular

interaction of the individual polymers in dilute systems were analyzed. It was shown that the

macromolecular structure of levan shifted from a random coil to a compact spherical molecule

with increasing molecular weight. Furthermore, a negative Mark-Houwink-Sakurada

coefficient was found for the first time for biopolymers and could be attributed to an increase

in molecular density with molecular weight. To determine the specific and non-specific

interactions of β-lactoglobulin a new measurement protocol was established combining

analytical ultracentrifugation and membrane osmometry. Specific molecular interactions were

determined in terms of the dimer dissociation constant from analytical ultracentrifugation. The

second virial coefficient corresponding to the non-specific interactions was measured by

membrane osmometry and calculated considering the dimer dissociation. These measurements

confirmed a strong contribution of electrostatic interactions on both kinds of interactions for β-

lactoglobulin. On the second level, the molecular interactions and the phase behavior of dilute

ternary levan-β-lactoglobulin mixtures were characterized. Repulsive pair interactions due to

the excluded volume effect were found between levan and β-lactoglobulin. These were more

pronounced for high molecular weight levan. In addition, it was shown that electrostatic

interactions between the β-lactoglobulin molecules did not affect the pair interactions between

levan and β-lactoglobulin but were decisive for the phase behavior of the mixtures. These

results were confirmed on the third level, where the phase behavior and the gel network

structure of concentrated ternary levan-β-lactoglobulin were analyzed. On the one hand, high

molecular weights of levan and/or weak repulsive electrostatic interactions between the

Abstract

III

β-lactoglobulin molecules caused the formation of phase-separated gels. On the other hand,

strong repulsive electrostatic interactions combined with low molecular weights of levan

favored the formation of swollen gels. In both cases, a strengthening of the gel network structure

due to the local accumulation of β-lactoglobulin could be ascribed to the excluded volume

effect. However, this effect was reversed when high levan concentrations sterically interfered

with the gel formation of β-lactoglobulin.

Finally, this thesis contributes to a deeper understanding of levan in food-relevant, protein-rich

systems. In general, interactions between levan and β-lactoglobulin are dominated by the

excluded volume effect. These observations can be generalized for globular proteins and enable

the understanding of structure-function relationships in various levan-containing food systems.

Kurzfassung

Exopolysaccharide sind hochmolekulare Kohlenhydrate, die von einer Vielzahl an

Mikroorganismen produziert werden. In Abhängigkeit der Art des Mikroorganismus und der

Milieubedingungen können sie sich in ihrer Monosaccharidstruktur, ihrem Molekulargewicht

und der Anzahl an Seitenketten unterscheiden. Trotz der großen Vielfalt an Exopolysacchariden

werden nur wenige dieser Polymere gezielt in Lebensmitteln eingesetzt. Ein Exopolysaccharid

mit großem Potential als Verdickungsmittel, Strukturbildner und Trübungsmittel ist Levan.

Neben den genannten technofunktionellen Eigenschaften weist es als Ballaststoff auch eine

gesundheitsfördernde Wirkung auf. Zudem ist es möglich, dieses β-2,6-verknüpfte

Fruktosepolymer von Milchsäure- und Essigsäurebakterien in situ in Lebensmitteln zu

produzieren. Darüber hinaus kann das Molekulargewicht von Levan und damit seine

Funktionalität durch die Kontrolle des pH-Werts während der Fermentierung angepasst werden.

Trotz dieser herausragenden Eigenschaften ist die makromolekulare Struktur von Levan in

Abhängigkeit des Molekulargewichts noch nicht vollständig aufgeklärt. Zudem ist nur wenig

über die Eigenschaften von Levan in lebensmittelrelevanten proteinhaltigen Systemen bekannt.

Ein bestens charakterisiertes Modelprotein für diese Systeme mit zahlreichen Anwendungen in

der Lebensmittelindustrie ist β-Lactoglobulin. Dieses globuläre Protein wird aus Molke

gewonnen und hat zahlreiche technofunktionelle Eigenschaften, wie die Ausbildung von

Gelnetzwerken oder die Stabilisierung von Grenzflächen.

Um Levan als funktionelles Polymer zu etablieren, wird in dieser Arbeit der grundlegende

Mechanismus der Strukturbildung von Levan in lebensmittelrelevanten proteinhaltigen

Systemen untersucht. Hierzu wurden die Strukturen und Interaktionen von Levan,

β-Lactoglobulin und Levan-β-Lactoglobulin Mischungen systematisch auf drei Ebenen

(verdünnt – binär, verdünnt – tenär, konzentriert – tenär) untersucht. Auf der ersten Ebene

wurde die makromolekulare Struktur und die molekularen Interaktionen der einzelnen

Polymere in verdünnten Systemen untersucht. Dabei konnte gezeigt werden, dass die

makromolekulare Struktur von Levan mit zunehmenden Molekulargewicht von einer Random

Coil Struktur zu einer kompakten sphärischen Struktur übergeht. Darüber hinaus konnte für

Levan als erstes Biopolymer ein negativer Mark-Houwink-Sakurada Koeffizient gefunden

werden. Dies konnte auf eine Zunahme der Moleküldichte mit zunehmendem

Molekulargewicht zurückgeführt werden. Zur Bestimmung der spezifischen und

unspezifischen Wechselwirkungen von β-Lactoglobulin wurden analytische

Ultrazentrifugation und Membranosmometrie in einer neuen Methode kombiniert. Spezifische

molekulare Wechselwirkungen wurden anhand der Dimer-Dissoziationskonstante aus der

analytischen Ultrazentrifugation analysiert. Als Maß für unspezifische Wechselwirkungen

wurde der zweite Virialkoeffizient unter Berücksichtigung der Dimer-Dissoziation mittels

Membranosmometrie bestimmt. Diese Messungen bestätigten einen starken Beitrag der

elektrostatischen Wechselwirkungen zu den spezifischen und unspezifischen

Wechselwirkungen von β-Lactoglobulin. Auf der zweiten Ebene wurden die molekularen

Wechselwirkungen und das Phasenverhalten von Levan-β-Lactoglobulin Mischungen in

Kurzfassung

verdünnten ternären Systemen charakterisiert. Hierbei konnten repulsive Paar Interaktionen

zwischen beiden Polymerspezies auf den Excluded Volumen Effekt zurückgeführt werden.

Diese Interaktionen waren für hochmolekulares Levan stärker ausgeprägt. Darüber hinaus

konnte gezeigt werden, dass elektrostatische Wechselwirkungen zwischen β-Lactoglobulin

Molekülen die Paar Interaktionen zwischen Levan und β-Lactoglobulin nicht beeinflussten.

Allerdings waren diese für das Phasenverhalten der Mischungen entscheidend. Diese

Ergebnisse konnten durch die Analyse des Phasenverhaltens und der Gel-Netzwerkstruktur von

konzentrierten ternären Levan-β-Lactoglobulin Mischungen bestätigt werden. Die Ausbildung

von phasenseparierten Gelen wurde durch ein hohes Molekulargewicht des Levans sowie durch

geringe repulsive elektrostatische Interaktionen zwischen den β-Lactoglobulin Molekülen

begünstigt. Gequollene Netzwerke konnten im Fall eines niedrigen Molekulargewichts des

Levans in Kombination mit stark abstoßenden elektrostatischen Wechselwirkungen zwischen

den Proteinen beobachtet werden. In beiden Fällen wurde die Gel-Netzwerkstruktur durch die

lokale Aufkonzentrierung von β-Lactoglobulin aufgrund des Excluded Volume Effekts

verstärkt. Allerdings führte eine zu hohe Levankonzentration aufgrund sterischer Effekte zur

Behinderung der Gel-Netzwerkbildung des β-Lactoglobulin.

Letztendlich trägt diese Arbeit zu einem tieferen Verständnis von Levan in

lebensmittelrelevanten, proteinreichen Systemen bei. Mischungen aus Levan und

β-Lactoglobulin werden hauptsächlich durch den Excluded Volume Effekt dominiert. Diese

Ergebnisse können auf andere globuläre Proteine übertragen werden und ermöglichen so ein

tieferes Verständnis der Struktur-Funktions-Zusammenhänge von Levan in Lebensmittel-

systemen.

Table of Contents 
VI 
 
Table of Contents 
 
1.  Motivation and Objective ................................................................................................... 1 
2.  Theoretical Background ...................................................................................................... 9 
2.1  Molecular interactions and macromolecular conformation in binary systems ............ 9 
2.2  Molecular interactions and phase behavior in ternary systems ................................. 10 
2.3  Gelation of binary Systems........................................................................................ 12 
2.4  Gelation of ternary Systems ...................................................................................... 14 
2.5  Exopolysaccharides ................................................................................................... 16 
2.5.1  Food applications of Exopolysaccharides .......................................................... 17 
2.5.2  Levan .................................................................................................................. 19 
2.6  β-lactoglobulin ........................................................................................................... 21 
3.  Publications ....................................................................................................................... 25 
Manuscript I ............................................................................................................................. 26 
I-1 Abstract ........................................................................................................................... 27 
I-2 Introduction ..................................................................................................................... 28 
I-3 Material & Methods ........................................................................................................ 29 
I-3.1 Cultivation and Levan Production ............................................................................ 29 
I-3.2 Gradual Ethanol Precipitation .................................................................................. 29 
I-3.3 Sample Preparation .................................................................................................. 29 
I-3.4 Photometry ............................................................................................................... 29 
I-3.5 Viscometry ............................................................................................................... 30 
I-3.6 Dynamic Light Scattering ........................................................................................ 31 
I-3.7 Multi Angel Laser Light Scattering ......................................................................... 31 
I-4 Molecular Conformation and Shape Determination ....................................................... 32 
I-5 Results and Discussion ................................................................................................... 33 
I-5.1 Hydrodynamic radius RH.......................................................................................... 34 
I-5.3 Hydrodynamic coefficient ν ..................................................................................... 36 
I-5.4 Intrinsic viscosity ..................................................................................................... 37 
I-5.5 General Discussion ................................................................................................... 39 
I-6 Conclusion ...................................................................................................................... 40 
Manuscript II ............................................................................................................................ 41 
II-1 Abstract .......................................................................................................................... 42 
II-2 Introduction ................................................................................................................... 43 
II-3 Theoretical Background ................................................................................................ 46 

Table of Contents 
VII 
 
II-3.1 Dimer Dissociation ................................................................................................. 46 
II-3.2 Fundamentals of analytical ultracentrifugation ...................................................... 46 
II-3.3 Concentration-dependent sedimentation and diffusion coefficient ........................ 47 
II-3.4 Second virial coefficient from membrane osmometry measurements .................... 48 
II-3.5 Interaction potential from xDLVO-CG calculations .............................................. 49 
II-4 Materials and Methods .................................................................................................. 51 
II-4.1 Coarse-grained molecular calculations ................................................................... 51 
II-4.2 Umbrella sampling simulations .............................................................................. 52 
II-4.3 β-lactoglobulin ........................................................................................................ 53 
II-4.4 Protein sample preparation for analytical ultracentrifugation ................................ 53 
II-4.5 Analytical ultracentrifugation experiments ............................................................. 54 
II-4.6 Protein sample preparation for membrane osmometry experiments ...................... 54 
II-4.7 Membrane osmometry experiments ........................................................................ 55 
II-5 Results and Discussion .................................................................................................. 55 
II-5.1 Coarse-grained molecular B22 calculations ........................................................... 55 
II-5.2 Dimer dissociation constant from analytical ultracentrifugation ............................ 58 
II-5.3 Determination of the osmotic second virial coefficients from membrane 
osmometry experiments .................................................................................................... 61 
II-5.4 Relationship between the osmotic second virial coefficient and the dimer 
dissociation energy ............................................................................................................ 64 
II-6 Conclusions ................................................................................................................... 66 
Manuscript III ........................................................................................................................... 68 
III-1 Abstract ........................................................................................................................ 69 
III-2 Introduction .................................................................................................................. 70 
III-3 Theory .......................................................................................................................... 71 
III-3.1 Osmometry ............................................................................................................ 71 
III-3.2 Viscometry ............................................................................................................. 73 
III-4 Material and Methods ................................................................................................... 74 
III-4.1 β-lactoglobulin ....................................................................................................... 74 
III-4.2 Levan ..................................................................................................................... 74 
III-4.3 Osmometry ............................................................................................................ 75 
III-4.4 Viscometry ............................................................................................................. 76 
III-4.5 Dynamic Light Scattering ...................................................................................... 76 
III-5 Results and Discussion ................................................................................................. 77 
III-5.1 β-lactoglobulin ....................................................................................................... 77 
III-5.2 Levan ..................................................................................................................... 79 

Table of Contents 
VIII 
 
III-5.3 β-lactoglobulin Levan Mixtures ............................................................................ 80 
III-6 Conclusion .................................................................................................................... 83 
Manuscript IV .......................................................................................................................... 84 
IV-1 Abstract ........................................................................................................................ 85 
IV-2 Introduction .................................................................................................................. 86 
IV-3 Materials and Methods ................................................................................................. 88 
IV-3.1 β-lactoglobulin and levan production .................................................................... 88 
IV-3.2 Sample preparation ................................................................................................ 88 
IV-3.3 Rheological measurements .................................................................................... 88 
IV-3.4 Scanning electron microscopy (SEM) ................................................................... 89 
IV-3.5 NMR ...................................................................................................................... 89 
IV-4 Results and Discussion................................................................................................. 90 
IV-4.1 Heat-induced gelation ............................................................................................ 90 
IV-4.2 Water binding ........................................................................................................ 93 
IV-4.3 Phase behavior and network structure ................................................................... 94 
IV-5 Conclusion ................................................................................................................. 100 
4.  General Discussion ......................................................................................................... 102 
4.1  Levan in dilute binary systems ................................................................................ 102 
4.2  β-lactoglobulin in dilute binary systems .................................................................. 104 
4.3  Levan and β-lactoglobulin in dilute ternary systems ............................................... 106 
4.4  Levan and β-lactoglobulin in concentrated ternary systems ................................... 109 
5.  Concluding Remarks and Outlook .................................................................................. 112 
References .............................................................................................................................. 117 
Annex ..................................................................................................................................... 141 
List of Conference Contributions ....................................................................................... 141 
List of Additional Publications ........................................................................................... 142 
Supplementary Data Manuscript I ...................................................................................... 143 
Supplementary Data Manuscript II..................................................................................... 145 
Supplementary Data Manuscript IV ................................................................................... 151 
 
 
   

List of Figures

Figure 1: Schematic illustration of the possible phase states of a ternary polymer mixture.

Figure 2: Schematic illustration of the excluded volume effect. ………….………….……

Figure 3: Schematic representation of the gel types of a ternary polymer mixture. ……...….

Figure 4: Schematic phase diagram of a polymer mixture of a gelling and a non-gelling

polymer. …………………………………………………………………………...….…….

Figure 5: Cell aggregates of Gluconobacter albidus (TMW 2.1191) in a levan-containing

medium. ……………………………………………………………………………………..

Figure 6: Schematic representation of the monomer, dimer and octamer equilibrium of β-

lactoglobulin in respect of the pH, protein concentration and ionic strength. …………...…...

Figure 7: Schematic representation of the thermal denaturation and gel formation of β-

lactoglobulin. …………………………………………………………………………..……

Figure I-1: Structure of levan (A). Levan solution (8 g/L) with increasing polymer size (left

to right) (B). ………………………………………………………………………...……….

Figure I-2: Cumulative distribution of hydrodynamic radius from DLS of levan before

(black, unfilled symbols) and after (grey, filled symbols) ethanol fractionation. LevF

(squares), Lev4, (triangles), Lev5 (diamonds). ……………………………………………...

Figure I-3: Dependence of geometric Radius Rgeo (squares), hydrodynamic radius RH,DLS

from DLS (diamonds) and hydrodynamic radius RH,visc from viscometry (triangles) on levan

molecular weight. …………………………………………………………….……………..

Figure I-4: Dependence of RG/RH,DLS (triangle) and RG/RH,visc (diamonds) on levan

molecular weight (A). Dependence of Rgeo/RH,DLS (triangle) and Rgeo/RH,visc (diamonds) on

levan molecular weight (B). The dotted line at 0.774 (A) and 1.0 (B) represents the

represents the theoretical value for a compact sphere. ……………………………………….

Figure I-5: Dependence of geometric radius Rgeo, radius of gyration RG (lines, right axis)

and hydrodynamic coefficients (triangles νG; diamonds νgeo, left axis) on levan molecular

weight. The lines at 0.5 and 0.33 represents the theoretical hydrodynamic coefficients of a

random coil at theta conditions and a compact sphere respectively. ……………...………….

Figure I-6: Mark-Houwink-Sakurada Plot (A). Dependence of the Huggins constant on

levan molecular weight (B). …………………………………………………………………

Figure II-1: Graphical abstract of manuscript II. …………………………………………...

Figure II-2: Coarse-grained representation of β-lg monomer (A) and dimer (B) used to

calculate the second osmotic virial coefficient B22 by means of xDLVO-CG. ….…………...

List of Figures

Figure II-3: Graphical representation of the charge state of the β-lg monomer and dimer as

a function of the solution pH. The dimer binding site is indicated. The electrostatic potential

was calculated using an Adaptive Poisson-Boltzmann Solver (APBS) with a default grid

dimension, as implemented in the APBS software [1]. ……………………………………...

Figure II-4: Interaction potential W22(a) as a function of the protein-protein COM distance.

The electrostatic interaction potential (Wel) is shown for a salt concentration of 10 mM

sodium chloride (solid lines) and 100 mM sodium chloride (dashed lines) at pH 3.0 (in

green) and pH 7.0 (in blue) alongside the contribution from dispersion interactions (marked

in red). …………………………………………………………………………..…………...

Figure II-5: Osmotic second virial coefficient B22 as calculated using xDLVO-CG for β-lg

monomer-monomer, monomer-dimer and dimer-dimer interactions as a function of the salt

concentration at pH 3.0 (A) and at pH 7.0 (B). ………………………………………………

Figure II-6: (A) Exemplarily measured sedimentation profiles as obtained from AUC

experiments for a solution pH of 7.0 and a salt concentration of 100 mM sodium chloride

and a protein concentration of 18 µmol/L. Data acquisition was carried out at a wavelength

of 280 nm. The color code indicates the course of the sedimentation profile over time [2].

(B) Retrieved sedimentation coefficient distributions for β-lg in water at pH 7.0 and a salt

concentration of 100 mM sodium chloride at various protein loading concentrations. The

sedimentation data was analyzed using the c(s) model [3]. The plot was created using

GUSSI [2]. ………………………………………………………….……………………….

Figure II-7: Weight-averaged sedimentation coefficients as measured by AUC experiments

versus β-lg loading concentration. The isotherms are determined for different solution

conditions: (A) pH 3.0 with a salt concentration of 100 mM, (B) pH 7.0 with a sodium

chloride concentration of 100 mM and (C) pH 7.0 at a salt concentration of 10 mM sodium

chloride. Each isotherm is fitted using the software SEDPHAT in order to determine the

dimer dissociation constant. Notably, beyond protein concentrations of 10-4 M, the

influence of non-ideality phenomena is strongly increased, thus extrapolation of the

isotherms is not possible and cannot be interpreted in a physical manner. …………………

Figure II-8: (A) Experimentally determined molecular weight-corrected osmotic pressure

for concentration-dependent molecular weight for β-lg in sodium chloride solutions as a

function of protein loading concentration. Results are shown for different pH values and

salt concentrations. (B) The osmotic second virial coefficient B22 for different pH values

and sodium chloride concentrations. The coarse-grained xDLVO calculations provide

values for monomer-monomer (M-M), monomer-dimer (M-D) and dimer-dimer

interactions (D-D). Experimental values are retrieved from a combination of the results

from AUC and membrane osmometry (green bars). For a solution pH of 3.0 and a salt

concentration of 10 mM sodium chloride, the dimer dissociation constant for the calculation

of the osmotic second virial coefficient was taken from literature. …………………………..

List of Figures

Figure II-9: (A) Free energy of β-lg dimerization at different studied solution conditions

obtained from umbrella sampling simulations at 300 K and atmospheric pressure. (B)

Second virial coefficient from membrane osmometry as a function of the dissociation

energy as determined from SV-AUC (red circles). The experimental results are compared

with the theoretical results from xDLVO-CG (B22) for monomer-monomer interactions and

MD/US simulations for the Gibbs free energy (black circles). .……………………………...

Figure III-1: Graphical abstract of manuscript III. ………………….……………………...

Figure III-2: Molecular weight of β-lg in dependence of the sodium chloride concentration.

The dotted lines represent the molecular weight of the β-lg monomer and the β-lg dimer

(A). Second virial coefficients of β-lg in dependence of the sodium chloride concentration.

Filled and unfilled symbols represent one repetition each (B). ………………………………

Figure III-3: Intrinsic viscosity of β-lg in dependence of the sodium chloride concentration

(A). Huggins coefficients of β-lg in dependence of the sodium chloride concentration (B).

Filled and unfilled symbols represent one repetition each. ………………………………….

Figure III-4: Average molecular weight of levan-β-lg mixtures at 2.5 and 100 mM NaCl.

Diamonds represent molecular weights calculated from the individual polymer

measurements according to equation 5. Triangles show the molecular weichts meausred in

the polymer mixtures (A). Cross-virialcoefficient of levan-β-lg mixtures at 2.5 and 100 mM

NaCl. Filled and unfilled symbols represent one repetition each (B). ……………...………..

Figure III-5: Interaction coefficient α from viscometry of levan-β-lg mixtures at 2.5 and

100 mM NaCl. Filled and unfilled symbols represent on repetition each. …………………...

Figure IV-1: Graphical abstract of manuscript V. …………………………………………..

Figure IV-2: Development of the storage modulus in the temperature sweeps of gels

containing different contents of Lev4 (A and B), different molecular weights (C and D) at

10 mM NaCl (left panel) and 100 mM NaCl (right panel). The temperature ramp ranged

from 20 °C to 90 °C. Shown is the range from 45 °C to 90 °C and the holding phase at 90

°C, where gelation takes place. ……………………………………………………………...

Figure IV-3: Gel point temperature of samples containing different Lev4 contents (left

side) and different molecular weights of levan (right side). *Sample gelled after a holding

time of 2.9 ± 0.9 min at 90 °C. ……………………………………………………………….

Figure IV-4: Relaxation times T2 of gels containing different Lev4 contents (left side) and

different molecular weights of levan (right side). …………………...……………………….

Figure IV-5: Frequency sweep of the pure β-lg gel (lighter colors) and the β-lg gel

containing 3.0 wt% Lev4 (darker colors) at 10 mM (A) and 100 mM (B) NaCl. Filled

List of Figures

XII

symbols indicate the loss modulus (Gʹʹ) and open symbols indicate the storage modulus

(Gʹ). …………...…………………………………………………………………………….

Figure IV-6: SEM images and photographs of the mixed β-lg gels containing different

Lev4 contents in 10 mM and 100 mM NaCl. SEM images at 100× magnification focus on

phase-separated regions, if present, and SEM images at 1000× magnification are focused

on the continuous phase. …………………………………………….………………………

Figure IV-7: SEM images and photographs of the mixed β-lg gels containing levan of

different molecular weight in 10 mM and 100 mM NaCl. SEM images at 100×

magnification focus on phase-separated regions, if present, and SEM images at 1000×

magnification are focused on the continuous β-lg network. …………………………………

100

Figure 8: Schematic representation of the macromolecular conformation of levan from G.

albidus in dependence of the molecular weight. ………………………….………………….

103

Supplementary data S I-2: Dependence of the specific extinction coefficient on the

geometric radius of levan. …………………………………………………………………...

143

Supplementary data S I-3: Polymer concentration as a function of the retention time

during the aF4-MALLS measurement. Solid line RI detection, dashed line UV detection,

dotted line corrected UV detection. Lev4 F6 (A), Lev4 F5 (B). ……………………………..

144

Supplementary data S I-4: Cumulative molecular weight distribution as a function of the

molecular weight. Solid line RI detection, dashed line UV detection, dotted line corrected

UV detection. Lev4 F6 (A), Lev4 F5 (B). ……………………………………...……………

144

Supplementary data S II-1: Dispersion potential derived from the Hamaker constant and

the Lennard-Jones potential between the β-lg monomers (A) and BLG dimers (B). Potential

was calculated using xDLVO-CG method, described in literature. …………………………

145

Supplementary data S II-2: The osmotic second virial coefficient B22 for different pH

values and sodium chloride concentrations as calculated from xDLVO-calculations and the

2-sphere DLVO approach. Values are provided for monomer-monomer (M-M), monomer-

dimer (M-D) and dimer-dimer interactions (D-D). ………………………………………….

145

Supplementary data S II-3: Anisotropy of the total charge of β-lg proteins in xDLVO-CG

model. …………………………………………………………………..…………………...

146

Supplementary data S II-2: Measured extinction at a wavelength of 280 nm for various

protein concentrations in water at pH 7.0 and salt concentration of 10 mM sodium chloride.

The linear slope provides the extinction coefficient. ………………………………………...

146

Supplementary data S II-4: (A): Sedimentation coefficient distribution as retrieved from

data analysis in SEDFIT for a protein mass loading concentration of 1.0 g/L. The solution

pH and the salt concentration are indicated in the legend. (B) Weight averaged

List of Figures

XIII

sedimentation coefficient for varying protein concentration at a solution pH of 3.0 and a salt

concentration of 10 mM sodium chloride. ………………………………...…………………

147

Supplementary data S II-5: Reduced osmotic pressure for β-lg in sodium chloride

solutions as a function of protein loading concentration. Results are shown for different pH

values and salt concentrations. ……………………..………………………………………..

148

Supplementary data S II-6: Second virial coefficient as calculated from equation 15 for

different protein loading concentrations. (Right): Theoretical calculated molecular weight-

corrected osmotic pressure from equation 16 for concentration-dependent molecular weight

for β-lg in sodium chloride solutions as a function of protein loading concentration. ……….

148

Supplementary data S II-7: Theoretical weight fraction of monomers and dimers for an

equilibrium constant of 39.7 µM. This corresponds to a solution pH of 3.0 and a salt

concentration of 10 mM NaCl. ………………...……………………………………………

149

Supplementary data S II-8: Umbrella sampling histograms obtained from molecular

dynamics simulations of 61 US windows of β-lg dimer at pH 3.0 and 7.0 with the salt

concentration of 10 mM and 100 mM sodium chloride. …..…………………………………

149

Supplementary data S II-9: Potential of mean force showing the free energy of β-lg

dimerization at different solution conditions. ……………………………………………..

150

Supplementary data S III-3: Cumulative distribution of the Z-average hydrodynamic

radius of LevCoil (black lines) and LevSphere (grey lines) at 2.5 mM (solid lines) and 100 mM

(dashed lines) NaCl. …………………………………………………………………………

155

List of Tables

XIV

List of Tables

Table 1: Food industrial application of functional EPS. …………………………………...

Table 2: Amino acid composition of β-lactoglobulin [4]. ……………………………….

Table I-1: Ethanol concentrations and levan amounts of the fractionation process. ……….

Table II-1: The dimer dissociation constant as obtained from fitting of the isotherms,

which are determined from AUC experiments. The dimer dissociation constants are

provided as a function of solution pH and salt concentration. At a solution pH of 3.0 and

a salt concentration of 10 mM sodium chloride, the AUC experiments are influenced by

charge effects. The values for the dimer dissociation constant based on a confidence

interval of 68 % are provided. ……………..……………………………………………….

Table III-1: Number average molecular weight, osmotic second virial coefficient,

intrinsic viscosity, Huggins coefficient and Z-average hydrodynamic Radius of LevCoil and

LevSphere at 2.5 mM and 100mM. …………………………………………………………...

Table IV-1: Storage modulus (Gʹ), Loss modulus (Gʹʹ), tan(δ) and n of the heat-induced

β-lg with different levan contents or with different levan molecular weights during the

frequency sweeps. ……………………………..…………………………………………...

Supplementary data S I-1: Molecular Sizes of levan and its fractions. …………………...

143

Supplementary data S II-3: Osmotic second virial coefficients (in 10-3 mol/ (mL g2))

calculated using the dispersion potential based on the Hamaker constant and Lennard-

Jones potential (see equations 13-21). ……………..……………………………………….

147

Supplementary data S III-1: Raw data osmometry. …………….………………………..

151

Supplementary data S III-2: Raw data viscometry. ……………………………………...

153

List of Abbreviations and Symbols

Amplitude

aF4

Asymmetric flow field flow fractionation

AUC

analytical ultracentrifugation

Bʹ

Second virial coefficient

Concentration

coarse-grained

COM

center-of-mass

CPMG

Carr-Purcell-Meiboom-Gill

dn/dc

Refractive index increment

DVLO

Derjaguin, Landau, Verwey, and Overbeek

Frequency

Gʹ

Storage modulus

Gʹʹ

Loss modulus

Gluconobacter

Intensity

Huggins coefficient

Mass

Molar mass

MALLS

Multi-angle laser light scattering

molecular dynamics

number average molecular weight

weight average molecular weight

Avogadro constant

NaG

Sodium gluconate medium

PDI

Polydispersity index

List of Abbreviations and Symbols

XVI

PMF

potential of mean force

PPIs

protein-protein interactions

Gas constant

Radius of gyration

Rgeo

Geometrical radius

Hydrodynamic radius

Refractive index

SEM

Scanning electron microscopy

sedimentation velocity

Temperature

Time domain nuclear magnetic resonance

Transverse relaxation times

tan(δ)

Loss tangent

TD-NMR

Time domain nuclear magnetic resonance

Umbrella sampling simulations

Ultraviolet

vdW

van der Waals

Weight fractions

WHAM

weighted histogram analysis method

β-lg

β-lactoglobulin

extinction coefficient

Viscosity

Hydrodynamic coefficient

[η]

Intrinsic viscosity

3D-RISM

three-dimensional Reference Interaction Site Model

Motivation and Objective

1. Motivation and Objective

Exopolysaccharides with different molecular weights, monosaccharide compositions and

monosaccharide arrangements are formed by a variety of microorganisms. Due to this great

diversity, they represent a large reservoir of functional hydrocolloids [5]. Their abilities to bind

high amounts of water, form networks and interact with other components allow them to

texturize, gel or thicken [6]. Therefore, exopolysaccharides represent highly functional

ingredients in food, cosmetics and pharmaceuticals. However, with a few exceptions such as

xanthan, gellan or curdlan, which are commonly used as food additives, exopolysaccharides are

only used to a limited extent in the food industry [7]. In particular, the in situ formation of

exopolysaccharides in fermented foods has great potential for improving the functional

properties without the need for the declaration of food additives [8].

A promising exopolysaccharide that is produced by food-grade lactic acid bacteria and acetic

acid bacteria is levan. This fructan-type polysaccharide can be used as an opacifying agent and

improves the quality of various foods. For example, it is used to improve the loaf volume and

crumb hardness of gluten-free bread or the texture of fermented vegetable products [9,10].

Furthermore, it is a source of dietary fiber and is considered to be a prebiotic [9,11–14]. The

rheological properties of levan range from a Newtonian fluid to a viscoelastic solid, depending

on the polysaccharide concentration and molecular weight [11,15]. Since the molecular weight

of levan can be controlled by modifying the fermentation conditions, its properties can be

tailored for several potential applications in food products [16]. To exploit the full potential of

exopolysaccharides, their structures and interactions in food systems must be studied and

understood in defined model systems. Due to the high complexity of food matrices, it is useful

to analyze the properties of exopolysaccharides alone in binary model systems and in

combination with other food biopolymers in ternary model systems.

Besides polysaccharides, proteins are one of the most important groups of food biopolymers.

On the one hand, they play an important role in human nutrition, on the other hand, they have

techno-functional properties such as gelling properties which are crucial for the structure

formation of many food products. To effectively use exopolysaccharides in real food matrices,

their performance with proteins should be examined. Doing so, three levels of systematic

characterization should be considered: dilute – binary, dilute – ternary and concentrated –

ternary.

On the first level, the macromolecular conformation, polymer-solvent and polymer-polymer

interactions of the individual polymers need to be analyzed in dilute, binary systems. These

mutually dependent parameters determine the basic functional properties of the polymers. For

example, the formation of polysaccharide gel networks is often associated with the formation

of ordered secondary structures [17]. The formation of these structures in dilute systems cause

a change of macromolecular conformation and can be controlled by altering the polymer-

polymer and polymer-solvent interactions through a change in solvent properties [18].

Therefore, understanding the first level enables the optimization of the functional properties of

Motivation and Objective

exopolysaccharide-containing products. At the second level, the polymer-polymer interactions

between different polymers in dilute ternary systems should be studied. These interactions are

crucial for the phase behavior of polymer mixtures and therefore their potential applications.

While complexation between polysaccharides and proteins due to attractive interactions can be

used to stabilize oil-water interfaces, the same effect can weaken polysaccharide-protein gel

networks or prevent gel formation [19,20]. Similarly, repulsive interactions can result in

undesirable macroscopic phase separation of food products or improved gel properties due to

the local accumulation of gel network-forming polymers [21,22]. Therefore, understanding

these interactions and how to manipulate them can improve the comprehension of

exopolysaccharides in food applications. At the third level, to further approach a real food

system, molecular interactions and structures in a concentrated ternary system are analyzed.

Food-relevant phenomena such as segregative phase separation or the formation of different

gel network structures as well as their influence on the functional properties can be investigated

directly at this level [23]. Moreover, the characterization of binary and ternary systems at the

third level allows predictions about the texture properties and storage stability of food systems.

The macromolecular structure of polysaccharides in dilute binary systems is largely determined

by the flexibility of the polymer chain and the interplay between polymer-polymer and

polymer-solvent interactions [24,25]. The chain flexibility depends on the type of glycosidic

bond and the molecular interactions between individual neighboring polymer segments [26].

Glycosidic bonds can be alpha or beta, depending on the orientation of the linked

monosaccharides. The position of the carbon atoms involved in the bond can also affect the

flexibility of the carbohydrate chain. The molecular interactions contributing to chain flexibility

include hydrogen bonding, van der Waals interactions, electrostatic interactions, and steric

interactions. The polymer-polymer and polymer-solvent interactions are dependent on the

chemical structure of the polymer and the solvent. A low affinity to the solvent leads to stronger

polymer-polymer interactions and a more compact macromolecular structure. A high affinity

for the solvent results in strong polymer-solvent interactions and cause extended

macromolecular structures. The solvent affinity can be largely dependent on the molecular

weight. This can be attributed to different intensities of polymer-polymer and polymer-solvent

interactions. Especially uncharged polymers show a low affinity to aqueous solvents and thus

a more compact structure with increasing molecular weight [27]. The number and length of side

chains also influence the molecular conformation. In general, a higher degree of branching leads

to a more compact structure [17].

As with polysaccharides, the knowledge of the macromolecular conformation and molecular

interactions of proteins in dilute systems is essential to fully exploit their potential and

understand their techno-functionality function. These molecular properties determine whether

proteins form oligomers aggregate, gel or stabilize [28–31]. The macromolecular structure of

proteins depend on their ability to form oligomers. Some proteins, like β-lactoglobulin, exist

predominantly in specific oligomeric states [32]. These states exist in equilibrium with

monomers and oligomers, which is influenced by pH, ionic strength, temperature, and protein

Motivation and Objective

concentration [33]. The driving forces of this equilibrium are specific and non-specific protein

interactions. Specific interactions are attractive interactions, such as hydrogen bonds or ionic

bonds, between specific protein residues that stabilize oligomers. These interactions always

occur between certain functional groups of amino acids and are the same in all oligomers within

a protein species. Non-specific interactions are mainly repulsive, electrostatic in nature, and

result from the overall charge of the protein. In contrast to specific interactions, all charged

groups contribute to the repulsive interactions between proteins. In addition, these interactions

act independently of the orientation of the proteins to each other [34,35]. Due to the interplay

of these opposing interactions, stronger electrostatic repulsions due to more charges far from

the isoelectric point or less shielded repulsive charges at low ionic strength, favor the

monomeric state [36]. Even though the mechanism of the monomer-oligomer equilibrium of

proteins is well understood, the measurement of the involved specific and non-specific

interactions remains a challenge. This is not only true for β-lactoglobulin but dynamically

interacting monomer-oligomer systems in general. The difficulty results from the concentration

dependence of the monomer-oligomer equilibrium [37]. The shift of the monomer-oligomer

ratio with changing polymer concentration has a direct effect on the molecular interactions.

Therefore, monomer-monomer, dimer-oligomer and oligomer-oligomer interactions must be

considered to describe the non-specific interactions of such systems.

Analyzing ternary protein-polysaccharide mixtures in dilute model systems is a key step

towards the targeted use of new and promising exopolysaccharides in food systems. The

polymer-polymer and polymer-solvent interactions determine the phase behavior and thus the

structure and stability of such systems [19,38]. In general, mixtures of two or more polymers

can be miscible or immiscible depending on their interactions [39]. Miscible (or co-soluble)

systems are characterized by weak or non-existent interactions between the different polymer

species [40]. In the case of associative interactions, the formation of soluble complexes,

complex coacervation or precipitation may occur [39]. If repulsive interactions are predominant

segregative phase separation (also thermodynamic incompatibility) can take place. In this case,

two separate phases are formed, each containing primarily one of the two polymers and only

traces of the other polymer [41]. The type of interactions between two polymers and thus the

phase behavior depends not only on the polymers but also on the properties of the solvent. A

change in the solvent conditions such as pH, ionic strength or polarity can also alter the phase

behavior of a ternary system [21,42,43]. The interactions between polysaccharides and proteins

as well as the possibilities to influence them are the main area of interest for many research

areas. Electrostatic interactions between charged groups, hydrogen bonds or van der Waals

interactions can influence the polymer-polymer interactions [44]. Also, repulsive interactions

due to the excluded volume effect are very likely to have a significant impact on these

interactions. In addition, molecular interactions and changes in the macromolecular structure

within a polymer species must also be considered, as these can affect the interactions mentioned

above.

Motivation and Objective

Characterizing the structures and interactions in concentrated ternary systems is crucial for

understanding complex food systems. In particular, the gelation of biopolymers plays a central

role, resulting in a solid structure despite the high liquid content [45]. Here, the elastic

component results from a three-dimensional gel network of chemically or physically linked

polymers [46]. For many food systems, a single gel-forming polymer is not sufficient to produce

the desired structure. In addition, various food components interact with each other and

therefore strengthen or weaken the gel structures [47]. Depending on the molecular interactions

between two polymer species and their phase behavior different kinds of networks can be

formed in concentrated ternary systems. Attractive interacting polymers can form coupled

networks in which physical crosslinks between the polymer species form a network structure

[19]. No or weak interactions lead to interpenetrating networks or swollen networks. Each

polymer type forms its independent network in the case of interpenetrating networks [46]. In

swollen networks, one polymer forms the network while the other polymer is randomly

distributed throughout the system [48]. Repulsive interactions lead to the formation of phase-

separated networks where each polymer accumulates primarily in one phase [46,48]. The

formation of the above-mentioned networks can be partially predicted from the interactions in

dilute ternary systems [49]. However, the properties of the networks depend on many other

factors, such as the gelling rate, the polymer ratio or the total polymer concentration [50]. These

factors can antagonistically or synergistically modify the gel networks [19,43]. Furthermore,

molecular interactions change with the onset of gelation. Polymer-solvent interactions become

weaker and polymer-polymer interactions of the network-forming component become stronger,

thus enabling aggregation and network formation. This also affects the interactions between the

different polymer species. For example, the aggregation and therefore the gelation of polymers

can enhance the excluded volume effect, leading to a competition between network formation

and phase separation [20].

Levan is an exopolysaccharide composed of β-2→6-glycosidically linked β-D-fructofuranosyl

units and may also have some β-2→1-glycosidically linked side chains. It can be produced with

high molecular weights of up to 109 Da. [15]. Moreover, the molecular weight of levan can be

tailored over a wide range by adjusting the pH during enzymatic levan production [16].

Furthermore, it has been shown that the degree of branching of levan can be largely independent

of the fermentation conditions [15]. The β-2→6-glycosidically linked β-D-fructofuranosyl units

of levan confer high flexibility to the polymer chain of levan, thus enabling a compact structure

[51,52]. For polysaccharides with a large number of hydrophilic groups and no charges such as

levan, hydrogen bonds are probably the most important interaction type between neighboring

polymer segments, while electrostatic and hydrophobic interactions play a minor role. In

literature, low molecular weight levan is reported to have a random coil shape, while high

molecular weight levan is described to have a spherical structure [53,54]. However, studies on

the relationship between molecular weight, macromolecular conformation and molecular

interactions of levan are mainly limited to the molecular weight range from 104 to 107 Da

[55,56]. Furthermore, acid hydrolysis has often been used to produce different fractions

Motivation and Objective

[54,57,58]. However, this can not only change the molecular weight but also the degree of

branching. For molecular weights higher than 107 Da only a few studies are available. These

studies do not focus on the impact of molecular weight on the macromolecular conformation

[11,14,59]. Furthermore, the results are not necessarily comparable due to the varying

microbiological origin in different studies. In addition, the dispersity of the levan samples is not

always considered, which complicates the interpretation of the data. For these reasons, the

studies performed to date show an incomplete picture of dilute binary levan systems.

Therefore, it is necessary to study the macromolecular conformation and molecular

interactions of levan produced by a single organism without subsequent chemical

modifications and under consideration of dispersity over a large molecular weight range.

The protein β-lactoglobulin, which is derived from whey has been extensively studied as a

model protein and is found in numerous food products [60,61]. It contributes to the stabilization

of oil-water interfaces or the formation of gel structures. These functionalities are based on the

molecular interactions and the macromolecular structure of the protein. In binary systems

β-lactoglobulin exists predominantly in a monomer-dimer equilibrium [32]. Under specific

conditions, higher oligomers can be formed near the isoelectric point [35]. The monomer-dimer

equilibrium depends on pH, ionic strength, temperature, and protein concentration [33]. In the

case of β-lactoglobulin, specific interactions, i.e. hydrogen bonds between certain protein

residues of two monomers, stabilize the dimer state, while the monomer state is primarily

favored by nonspecific electrostatic repulsion [34,35]. Although β-lactoglobulin is a well-

studied model protein, the simultaneous measurement of specific and non-specific interactions

remains a challenge due to their mutual influence. A powerful method to quantify specific

interactions of dynamically interacting systems is analytical ultracentrifugation. The analysis

of the sedimentation profiles allows the determination of association and dissociation processes

in terms of the association or dissociation constant [62]. The quantification of non-specific

interactions between polymers can be quantified by determining the second cross-virial

coefficient using membrane osmometry [37,63]. Since the second cross-virial coefficient

depends on the osmotic pressure and thus on the number of particles, it is influenced directly

by the concentration-dependent association or dissociation in a monomer-dimer system.

Therefore, the dissociation process due to specific interactions must be known to study

nonspecific interactions. To address this challenge, a combination of analytical

ultracentrifugation and membrane osmometry must be established as a tool to

concurrently characterize both non-specific and specific interactions in a dynamically

interacting monomer-dimer system.

Considering ternary levan-protein systems, no studies are available that investigate the

molecular interactions and phase behavior of levan and β-lactoglobulin or proteins in general.

However, based on the chemical composition and macromolecular structure of levan, some

assumptions can be made. Since levan has many hydroxyl groups, hydrogen bonding could

influence the polymer-polymer interactions between levan and β-lactoglobulin [44]. This

potentially could lead to the formation of complexes. Due to the compact and spherical structure

Motivation and Objective

of levan and its lack of charges, the excluded volume effect may dominate the interactions

between both polymers. In this case, repulsive interactions could cause segregative phase

separation. Given the lack of charges, it is unlikely that electrostatic interactions between β-

lactoglobulin and levan affect the molecular interactions directly. However, in the case of β-

lactoglobulin, changes in electrostatic interactions due to a change in ionic strength or pH, can

alter the monomer-dimer equilibrium [36]. This is associated with a change in molecular weight

and macromolecular structure of the protein [33]. Since the excluded volume effect and the

probability of hydrogen bonding are influenced by molecular weight and macromolecular

structure, electrostatic interactions could indirectly affect the interactions between levan and β-

lactoglobulin. To test these claims, the influences of levan molecular weight, protein charge

and monomer-dimer equilibrium on the molecular interactions and phase behavior of

dilute ternary mixtures need to be investigated.

As with levan-β-lactoglobulin mixtures in diluted systems, little is known about concentrated

systems involving levan-β-lactoglobulin mixtures. However, some assumptions can be made

based on studies that have examined the effect of other polysaccharides on the gel formation of

β-lactoglobulin [64–67]. In general, the addition of polysaccharides can modify the gel network

either antagonistically or synergistically, depending on the chemical structure of the

polysaccharide, the mixing ratio, and the gelation mechanism [19,43]. Attractive interactions

due to hydrogen bonds could result in coupled networks. However, due to the compact spherical

structure and lack of charges of levan, it is more likely that the excluded volume effect will

dominate the interaction between levan and β-lactoglobulin. These interactions would result in

the formation of swollen gels or phase-separated gels, as seen in other neutral polysaccharide-

protein mixtures. Nevertheless, the prediction of the gel network type and the resulting

properties is difficult as network formation and phase separation occur simultaneously and

compete with each other [20]. In addition, repulsive interactions and phase separation can both

disrupt and promote gel network formation, leading to either weaker or stronger network

structures [21]. Furthermore, changes in composition, solvent conditions, or polymer properties

can alter the gel system. This is particularly relevant for β-lactoglobulin, which can form

different kinds of networks [68]. The formed network structure depends on the solvent

conditions, such as pH and ionic strength. If strong electrostatic repulsions are present, a

fibrillar gel is formed; if they are not present or screened, a particle gel is formed [68,69].

Furthermore, electrostatic interactions between proteins influence the gelation of β-

lactoglobulin, but also the phase behavior of a ternary system [70] Therefore, it is necessary

to analyze the network type and the resulting network properties of levan-β-lactoglobulin

mixtures in concentrated ternary systems regarding their weight fraction, levan

molecular weight and ionic strength.

Overall, this thesis focuses on the exopolysaccharide levan in food-related systems, to identify

possible areas of application and limitations, and thus establish levan as a functional

exopolysaccharide. Therefore, the aim of this thesis is the characterization and understanding

of the structures and the interactions of the exopolysaccharide levan. In addition to the

Motivation and Objective

exopolysaccharide itself, this thesis is focusing on the interactions and phase behavior of ternary

levan-β-lactoglobulin mixtures. Levan and the model protein β-lactoglobulin as well as their

mixtures are analyzed at three levels (dilute – binary, dilute – ternary, concentrated – ternary)

leading to four objectives.

Objective 1: Characterization of levan in binary dilute systems

The systematic investigation of polymers in diluted binary systems requires the controlled

modification of the molecular interaction. In the case of levan, the key parameter determining

polymer-polymer and polymer-solvent interaction and thus the macromolecular structure is the

molecular weight [53,54]. In this context, the following was proposed:

• The macromolecular conformation of levan in diluted binary systems is largely

dependent on the molecular weight. Due to an increased number of intersegmental

contacts with increasing chain length, the number of intramolecular interactions

increases. This results in a contraction of the macromolecular structure, which is

indicated by a more compact macromolecular structure with increasing molecular

weight.

To test the hypotheses, levan of different molecular weights and similar branching is produced

and further fractionated to obtain samples with a narrow dispersity over a broad range of

molecular weights. The characterization of the exopolysaccharide is performed using static

light scattering, dynamic light scattering and viscometry to obtain molecular radii, intrinsic

viscosity, molecular weights as well as structures and interaction-related parameters

(manuscript I). These variables are compared and combined to obtain a comprehensive

understanding of levan in binary systems.

Objective 2: Characterization of β-lactoglobulin in binary dilute systems

The monomer-dimer equilibrium of β-lactoglobulin is determined by specific and non-specific

molecular interactions. The simultaneous determination of these interactions remains a

challenge, as both affect the monomer-dimer equilibrium. Therefore, an experimental protocol

is developed using analytical ultracentrifugation and membrane osmometry to determine

specific and nonspecific interactions based on the dissociation constant and second virial

coefficient, respectively (manuscript II). To test the protocol under different conditions, the

pH and NaCl concentrations are varied and the results are compared with molecular dynamics

simulations. Since this objective was focused on the development of an experimental protocol,

no hypotheses were formulated.

Objective 3: Characterization of levan-β-lactoglobulin mixtures in ternary dilute systems

The third objective focuses on the molecular interactions of levan and β-lactoglobulin in dilute

ternary systems. An important parameter here is the molecular weight of the levan since the

effect of excluded volume often dominates in mixtures of neutral polysaccharides and proteins

[39]. Furthermore, the ionic strength affects the intermolecular interactions because the

Motivation and Objective

monomer-dimer equilibrium and thus the excluded volume of β-lactoglobulin changes due to

the charge shielding by the salt. In addition, the change in intermolecular interactions between

individual β-lactoglobulin molecules due to salt may affect the phase behavior of ternary

systems. These considerations result in the following hypotheses:

• Due to the absence of strong attractive interactions between the uncharged levan and

β-lactoglobulin, the excluded volume effect dominates the molecular interactions in

dilute ternary systems. This results in repulsive interactions between the two polymer

species. Due to the lack of electrostatic interactions between the polymers, the ionic

strength has no relevant effect on the interactions. However, higher ionic strength favors

segregative phase separation since the accumulation of β-lactoglobulin within a phase

is favored due to the shielding of repulsive electrostatic interactions between proteins.

To test this hypothesis, levan with different molecular weights is used to study the molecular

interaction with β-lactoglobulin at different salt concentrations (manuscript III). The second

(cross-)virial coefficient and viscosity interaction parameters are measured by membrane

osmometry and viscometry to determine the molecular interactions and predict the phase

behavior.

Objective 4: Characterization of levan-β-lactoglobulin mixtures in ternary concentrated

systems

At the third level, the heat-induced gel formation, gel structures and phase behavior of levan-

β-lactoglobulin mixtures in concentrated systems are addressed. Since the molecular weight of

levan and the ionic strength influence dilute ternary systems on the second level they are also

relevant in concentrated ternary systems. Especially, the molecular weight of levan and the

levan content should influence the gel type since they determine the strength of the excluded

volume effect and therefore the phase behavior. In this context, the following was hypothesized:

• Concentrated ternary levan-β-lactoglobulin systems are dominated by repulsive forces

due to the excluded volume effect. The heat-induced aggregation of β-lactoglobulin

increases the molecular weight difference between levan and β-lactoglobulin, thus

enhancing segregative forces. At sufficiently high levan concentrations, this results in

the formation of phase-separated networks. A higher molecular weight of levan results

in an enhancement of the excluded volume effect and therefore phase separation

becomes more likely. A higher ionic strength promotes phase separation since the

reduced electrostatic repulsion between the β-lactoglobulin molecules facilitates the

accumulation of the protein.

To prove these hypotheses, heat-induced levan-β-lactoglobulin gels at different salt

concentrations, levan molecular weights and levan contents are analyzed using rheology, time-

domain nuclear magnetic resonance and electron microscopy (manuscript IV). Gelation, water

binding, gel structure and gel type are investigated to characterize the gels.

Theoretical Background

2. Theoretical Background

2.1 Molecular interactions and macromolecular conformation in binary systems

The affinity between a solvent and a polymer results from polymer-solvent and polymer-

polymer interactions and describes the compatibility of a binary polymer-solvent mixture. The

solvent affinity is influenced by solvent characteristics such as polarity and temperature, as well

as by polymer characteristics such as its monomer structure, type of linkage between the

monomers, possible side chains, and molecular weight. The solvent affinity determines whether

a polymer dissolves completely (good solvent), partially (poor solvent), or is insoluble (non-

solvent) [25]. To dissolve an undissolved polymer, the clustered macromolecules must be

separated from each other. As a result, a single macromolecule is no longer surrounded by other

polymers, but by the solvent. In this process, the interactions between the polymers are replaced

by the interactions between the polymer and the solvent [71]. For this process to occur

spontaneously, the dissolved state must be energetically more favorable than the undissolved

state [25]. Thermodynamically, the free enthalpy of the system must decrease due to the

dissolution process as stated in equation 1 [27].

∆𝐺=∆𝐻−𝑇∆𝑆

(1)

ΔG: Free enthalpy, ΔH: Solution enthalpy, T: Temperature, ΔS: Solution entropy

The solution entropy results from the increase in disorder due to the mixing of polymer and

solvent and always has positive values [72]. The contribution of the solution entropy depends

on the molecular weight. The higher the molecular weight, the lower the solution entropy since

the possible molecular arrangements decrease with increasing chain length [27]. The solution

enthalpy results from the difference between the interaction energies in the dissolved and

undissolved state. During the dissolution process, polymer-polymer and solvent-solvent

contacts disappear and polymer-solvent bonds are formed. Therefore, the solution enthalpy can

be expressed as follows [73]:

∆𝐻=𝑓(𝑊12−𝑊11−𝑊22)

(2)

W: Interaction energy between the molecules, 1 = Solvent molecule, 2 = Polymer

Since the change in free enthalpy depends on the concentration of already dissolved substances,

a saturation of a polymer solution occurs with increasing concentration. The higher the polymer

concentration of the solution, the lower the gain in free energy due to additionally dissolved

macromolecules [71].

Similar to solubility, the macromolecular conformation of a polymer results from the polymer-

solvent and polymer-polymer interactions. The macromolecular conformation describes the

spatial expansion of a polymer in a solvent. In a good solvent, interactions between the polymer

and the solvent are favored [25]. Therefore, a polymer can expand and has an extended

Theoretical Background

molecular shape. In a poor solvent, polymer-polymer interactions dominate and the polymer

has a compact conformation [24]. Thus, a change in solvent properties, caused for example by

a change in temperature or salt concentration, can lead to a contraction or expansion of the

macromolecule [74].

In addition to the properties of the solvent, the macromolecular structure is also influenced by

the polymer itself. Most soluble proteins are composed of an irregular arrangement of amino

acids. The side chains of the amino acids differ in their affinity for the solvent. In aqueous

systems, hydrophobic side chains are oriented inward and hydrophilic side chains are oriented

outward. This results in a compact globular protein structure with a hydrophobic core and a

hydrophilic shell [75]. Proteins such as gelatin are an exception. They have a more regular

structure and fewer hydrophobic side chains, which allows them to adopt a helical

macromolecular structure [76]. In contrast to proteins, most polysaccharides are composed of

repeating monosaccharide units arranged in a regular pattern. Thus, the affinity to the solvent

does not change within the molecule. Polysaccharides can be differentiated in polymers with

an ordered secondary structure or a disordered random coil structure. For polymers such as

curdlan or xanthan gum, it can be thermodynamically favorable to adopt an ordered helical

structure [77,78]. Typically, these structures are stabilized by specific molecular interactions

between neighboring monomer units, which often result in an extended macromolecular

structure [79]. Random coils do not have a permanent structure, but constant fluctuations in the

local conformation of the polymer chain. The more flexible the bonds between the monomer

building blocks of random coils, the more compact it can arrange itself [52]. Also, an increasing

number of side chains results in a more compact random coil structure [17].

In general, all polymers can be classified into spheres, random coils and rod-like molecules,

depending on their macromolecular structure [80]. Sphere-like macromolecules result from the

domination of intramolecular polymer-polymer interactions over polymer-solvent. This is the

case for globular proteins with a hydrophobic core such as β-lactoglobulin or unordered

polysaccharides in poor solvents. The perfect random coil is formed by polymers without

secondary structure in theta solvents, where polymer-solvent and polymer-polymer interactions

are balanced. As the solvent affinity decreases, random coils become increasingly spherical and

as the solvent quality increases, they become more extended [74]. Rod-like molecules often

result from the inflexible structure of ordered secondary structures. In addition, electrostatic

repulsion between similar charged groups within a polymer can cause the formation of rod-like

macromolecular structures [80].

2.2 Molecular interactions and phase behavior in ternary systems

The phase behavior of ternary system (Fig. 1) is largely dependent on the type of interactions

between the polymers and the polymer concentration. In the presence of associative interactions

between biopolymers, the formation of soluble complexes, complex coacervation or

Theoretical Background

precipitation may occur [81]. In most cases, electrostatic interactions between two differently

charged polymers are responsible for these phenomena. The strength of the attractive

interactions, the mixing ratio and the affinity to the solvent determine which case occurs.

Soluble complexes are present in one phase and form if the ratio of oppositely charged

biopolymers is far from equivalent (assuming the charge ratio is equal). This causes the

formation of charged complexes, which remain in solution due to electrostatic repulsion [82].

Whether precipitates or complex coacervates form, depends on the charge density of the

polymers. Highly charged polyelectrolytes usually form precipitates, while weakly charged

polyelectrolytes promote the formation of complex coacervates [20,83]. In the case of

precipitation, a two-phase system is formed. The solvent phase is low in polymer and the

polymer phase is present as an insoluble solid. During complex coacervation, two liquid phases

are formed. A polymer-depleted phase and a high-viscosity phase containing both polymers

[84].The driving force for coacervation as well as precipitation is an entropy gain due to the

release of counterions by complexation [83]. While complex coacervation is favored by a

negative enthalpy change, precipitation is associated with a positive enthalpy change, because

precipitation requires more steric interactions to be overcome due to the higher packing density

of the polymers [20]. In compatible systems, also referred to as co-soluble systems, the

polymers in a biopolymer mixture are randomly distributed without the formation of complexes

or two separate phases. No or only very weak interactions (attractive or repulsive) occur

between the polymers [40]. In the case of repulsive interactions, segregative phase separation

(also referred to as thermodynamic incompatibility) may occur. Two separate phases are

Figure 1: Schematic illustration of the possible phase states of a ternary polymer mixture.

Theoretical Background

formed, each containing one of the two polymers and having only traces of the other polymer

species [81]. At low polymer concentration, both polymers are compatible, whereas at higher

concentration, the phase separation threshold is exceeded, causing the system to become

incompatible and leading to phase separation. The driving force for incompatibility are

repulsive interactions between the different polymer species, which can be caused by similar

charges or the excluded volume effect [42]. The excluded volume effect is a key mechanism in

incompatible systems. Here, the excluded volume (Fig. 2) is an area around a polymer that

cannot be occupied by the center of mass of a second polymer species. If the excluded volume

of one polymer species overlaps, an overlap volume is created. The solvent of the overlap

volume is now additionally available to the second polymer species. The second polymer

species thus has more space to distribute in the system, increasing the total entropy [39]. If the

polymer concentration is sufficiently high and the entropy gain sufficiently large, the excluded

volume effect can cause segregative phase separation. Whether segregative phase separation

occurs depends not only on the polymer concentration but also on the solvent affinity and the

size of the two polymers. The more the two polymer species differ in their affinity for the

solvent, the more likely segregative phase separation will occur. The same applies to the

polymer size. The greater the size of the two polymers, the greater the entropy gain due to the

excluded volume effect and the more likely phase separation will occur [40].

Figure 2: Schematic illustration of the excluded volume effect.

2.3 Gelation of binary Systems

The gelation of biopolymers is a key factor in the structuring of many food products. The gel-

like character results from a three-dimensional network of chemically or physically linked

polymers, which form a chemical or physical gel, respectively. The polymer network extends

continuously over the entire solvent volume and immobilizes the liquid [85]. For gel formation,

the balance between polymer-polymer interactions and polymer-solvent interactions is of great

importance. On the one hand, the polymer chains must interact sufficiently to form a stable

network, and on the other hand, the affinity between polymer and solvent must be high enough

to bind large amounts of solvent. If the interactions between the individual polymer chains are

too weak, no network will form. If the interactions between the polymer chains are too strong

and the affinity for the solvent too low, a precipitate will form instead of a gel [17]. Chemical

Theoretical Background

gels are formed by the covalent linkage of polymer molecules. This type of crosslinking is

important in the gel formation of synthetic polymers and to some extent also in the heat

denaturation of proteins or the enzymatic crosslinking of polymers [86,87]. Most gel-forming

biopolymers form physical gels, which are crosslinked via physical interactions such as

hydrogen bonds, ionic interactions, hydrophobic interactions or van der Waals forces [88].

Physical gels can be classified into fibrillar gels and particle gels depending on the network

structure. Fibrillar gels are formed by many polysaccharides and by proteins at pH values more

distant from the isoelectric point of the protein [47,68]. They have a fine network structure with

a pore size in the nanometer range. Since the pore size is far below the wavelength of visible

light, there is no light refraction and the gels appear clear [69]. Particle gels are formed by many

proteins near the isoelectric point or at sufficiently high salt concentrations. Initially, aggregates

of several proteins are formed [68]. These aggregates attach and form a three-dimensional

network. The pore size of these gels can be up to several 100 µm, well above the wavelength

of visible light. Therefore, these gels appear nontransparent [89].

To gain an understanding of gel formation and the properties of gels, it is necessary to

understand the interplay between polymer-polymer and polymer-solvent interactions during the

gelation process. Before gelation, polymers are dissolved or dispersed in the solvent. In this

state, there are no or only small associative forces between the individual polymers, which are

not sufficient for network formation [17]. To form a gel, the properties of the solvent and thus

the polymer-polymer and/or polymer-solvent interactions must be changed. Depending on the

polymer and solvent, changes in pH, ion concentration, or temperature are suitable to induce

gelation [90]. The pH and ion concentration are particularly important in the gelation of

polyelectrolytes. If a change in the pH of a polymer solution causes the total charge of a polymer

to decrease, the electrostatic repulsion between the chains decreases. This allows the polymer

chains to approach each other and interact via non-electrostatic interactions such as hydrogen

bonds [46]. The influence of ionic strength is also due to electrostatic forces. In general, as the

ion concentration increases, the electrostatic repulsion between similarly charged polymer

chains is reduced due to the shielding of the charges, thus enhancing chain association [91]. In

addition, some polysaccharides such as pectin or alginate can gel at suitable pH and ionic

strength by forming chelate complexes [92]. In this process, the polymer chains associate

through electrostatic interactions. The positively charged cations interact with the negatively

charged groups of two different polymer chains, enabling the polymers to associate [92].

Temperature plays an important role in the gel formation of globular proteins such as β-

lactoglobulin [93]. Heating the proteins weakens intramolecular interactions and irreversibly

changes the secondary and tertiary structure of the proteins [94]. The hydrophobic core regions

of the proteins become exposed and interact with the surrounding medium. As a result, the

affinity for the solvent decreases and protein-protein interactions increase, favoring protein

aggregation and gel formation [95].

Theoretical Background

2.4 Gelation of ternary Systems

In addition to gelling polymers, many foods also contain additional macromolecules as

ingredients. These interact with the gelling polymers and thus change the properties of the gel.

This can be intentional if a single polymer is not sufficient to achieve the desired functionality

or can cause problems like syneresis [96,97]. In a ternary system, different gel structures can

form depending on the interaction between the polymers. The four main gel types are coupled

networks, interpenetrated networks, swollen networks and phase-separated networks (Fig. 3)

[43].

Coupled networks also referred to as complex gels are formed when two different biopolymers

interact attractively with each other [48]. The interactions result in adhesion zones between the

two different polymers, forming a three-dimensional gel network [19]. In the case of positively

charged proteins and negatively charged polysaccharides, the responsible interactions are

mostly electrostatic. However, the formation of coupled networks between polysaccharides and

proteins is relatively rare. Instead of forming network-like structures, oppositely charged

polysaccharide-protein mixtures often tend to precipitate or coacervate [50]. Another example

of a coupled network occurs when galactomannans are mixed with helical polysaccharides such

as xanthan gum, carrageenan or agarose [98,99]. Here, hydrogen bonds are mainly responsible

for the formation of the adhesion zones between the polymers. The formation of coupled

networks can lead to structures that can have both positive and negative effects on gel properties

[46]. A positive effect is the formation of adhesion zones between two polymer species, which

cannot gel on their own. The additional adhesion zones form and stabilize the gel structure [41].

The same mechanism allows gelling polymers to form network structures at lower

concentrations [41]. In addition, the gelation temperature or gel strength can be controlled by

selecting suitable mixing ratios [66,100]. Negative effects often occur with differently charged

polymer species. Complex formation between the polymers reduces the adhesion zones for gel

formation. Therefore, the formation of a gel network is prevented, or higher polymer

concentrations are required [50].

Figure 3: Schematic representation of the gel types of a ternary polymer mixture. (Adapted

from Cairns et al. (1987) [101].

Theoretical Background

An uncommon gel type is an interpenetrating network, also known as mixed gel. It consists of

two separate gel networks which penetrate each other without the formation of adhesive zones

[46]. For an interpenetrating network to be formed, both polymers must be able to gel

independently. In addition, the polymers must be co-soluble, with no or only very weak

interactions between the polymer species. Otherwise, additional adhesion zones would form in

the case of attractive interactions or segregative phase separation would occur if repulsive

interactions dominate. However, since most polymers are thermodynamically incompatible or

tend to form complexes, this type of gel is very rare [19].

The gelation of thermodynamically incompatible systems leads to the formation of swollen

networks or phase-separated networks [46,48]. Which gel types are formed depends on whether

one or both polymers can gel. In addition, the gelation concentration, the gelation rate and the

phase separation threshold influence the gel type [50].

Figure 4 shows the phase states of a ternary system in which only one polymer can gel. The

light blue area indicates the range of co-solubility in which both polymers are dissolved. When

the gelation concentration of the gelling polymer is exceeded and the phase separation threshold

is not reached, a swollen network is formed [48]. Above the phase separation threshold,

depending on whether the liquid phase or the gel phase forms the continuous phase, a

suspension with gel particles or a phase-separated network is formed. In the latter case, the

liquid phase is dispersed over the gel [48]. When both polymers are gelled, a phase-separated

gel is formed in which the continuous and dispersed phases can be gelled [50]. Furthermore,

the presence of an additional polymer leads to a higher rate of gelation in a thermodynamically

incompatible system [19]. The effect arises from a reduction of the excess entropy of mixing

since different polymer species do not have access to the volume occupied by the other

species [48]. On the one hand, phase separation causes the accumulation of the polymers in

their respective phase. Therefore, the gelling concentration of phase-separated gels

Figure 4: Schematic phase diagram of a polymer mixture of a gelling and a non-gelling

polymer.

Theoretical Background

is lowered and the gel structure can be stronger [43]. On the other hand, the excluded volume

effect causes a local accumulation of the polymers in co-soluble systems. This results in a lower

gelation concentration and a reinforcement of the gel structure of swollen networks [48]. An

important factor influencing swollen networks and phase-separated gels by altering the

excluded volume effect is gelation itself [19]. With the onset of gelation, the polymers

aggregate, thus their excluded volume increases and the entropy gain due to segregation is more

pronounced. Therefore, phase separation can occur in systems that are co-soluble before

gelation [21].

2.5 Exopolysaccharides

Polysaccharides are high molecular weight compounds consisting of one or more different

sugar monomers linked by glycosidic bonds. These sugar monomers may also be esterified with

functional groups such as carboxyl or sulfate groups. They can be categorized into

heteropolysaccharides and homopolysaccharides. Heteropolysaccharides are composed of

constantly repeating units of at least two different sugar monomers. Galactose, glucose,

rhamnose and mannose are the most common monosaccharides [102]. Homopolysaccharides

consist of only one type of sugar monomer. Typically, this is glucose or fructose which is

derived from sucrose and polymerized by glycosyl or fructosyl transferases [103]. In nature,

they often contribute to structure formation, such as cellulose and pectin in plants, carrageenan

and agar in algae or chitin in insects. Polysaccharides like starch, glycogen and inulin as well

as plant seed polysaccharides like locust bean gum and guar gum, also serve as energy stores

[17,103]. Their properties are determined by their molecular weight, the arrangement and type

of monosaccharides, the number of side chains and the type of glycosidic bonds [5].

Polysaccharides, which are produced by microorganisms and secreted into their environment,

are referred to as exopolysaccharides. They can be distinguished in capsular and extracellular

microbial polysaccharides. Capsular polysaccharides are covalently bound to the cell wall and

form a cohesive layer around the cell [104]. If the polysaccharides are completely secreted into

the external environment or extracellularly synthesized, they can be referred to as extracellular

microbial polysaccharides [103]. Exopolysaccharides play a variety of roles in the cell and the

environment [105]. In addition to promoting adhesion to solid surfaces and contributing to

biofilm formation, extracellular polysaccharides are largely associated with protection against

environmental stressors. They protect cells from dehydration, osmotic stress, phagocytosis and

antibiotics or other toxic substances [106]. Furthermore, they may be involved in quorum

sensing in biofilms or serve as food reservoirs [107,108].

Theoretical Background

2.5.1 Food applications of Exopolysaccharides

EPS are used in the food industry as emulsifiers, stabilizers, thickeners, gelling agents as well

as for moisture retention and have numerous applications in other industries, such as the

chemical, pharmaceutical and cosmetic industries. Recent applications of dextran, levan and

curdlan in foods are summarized in table 1. Besides the ability to modify the rheological

properties of a product, some EPS have nutritional and health benefits. Curdlan, levan and

dextran are considered to be prebiotic [109–111]. Furthermore, EPS can have additional effects,

such as the anti-inflammatory, antitumor, antioxidant or cell proliferating effect of levan [110].

Dextran is produced by many food-grade organisms such as lactic acid bacteria. It is used to

improve the texture of products containing plant protein to produce vegan replacements for

dairy products. Weisella cibaria MG1 ferments wholemeal quinoa milk and produces high

amounts of a high molecular dextran [112]. Dextran increased the water holding capacity and

the quinoa yogurt viscosity, which is comparable to commercial dairy yogurt. The fermentation

of fava bean concentrates with different dextran-producing lactic acid bacteria allowed a texture

modification and stabilization of the final product. The addition of sucrose to the fava bean

concentrate enhanced the dextran formation and therefore the rheological and textural

properties of the ferments. The benefit of in situ dextran production in fava bean protein is

emphasized since the techno-functional properties of the ferments could not be mimicked by

simply mixing dextran, organic acids and the protein concentrate [113].

Table 1: Food industrial application of functional EPS.

Exopoly-

saccharide

EPS source

Function and Application

References

Dextran

Leuconostoc pseudomesen-

teroides, Weissella cibaria,

Weissella confusa

Stabilization, prevention of

protein aggregation, and texture

modification in fava bean protein

isolate and concentrate

[113,114]

Dextran

Leuconostoc

pseudomesenteroides,

Leuconostoc mesenteroides,

Leuconostoc citreum,

Weissella cibaria, Lacto-

bacillus plantarum

Gel structure strengthening and

texture modification in fava bean

doughs

[115]

Dextran

Leuconostoc mesenteroides,

Weissella cibaria

Viscosity enhancement in soy and

dairy milk

[116]

Dextran

Weissella cibaria

Viscosity enhancement and

increase of water holding capacity

in quinoa-based yogurt

[112]

Dextran

Improved dough elasticity,

decreased hardness of fresh and

[117]

This chapter is part of the following publication: Hundschell, C. S., Wagemans, A. M.; Rheology of common uncharged

exopolysaccharides for food applications, Current Opinion in Food Science (2019), 27, 1 – 7,

https://doi.org/10.1016/j.cofs.2019.02.011

Commercially available EPS, microbial stain unknown

Theoretical Background

Exopoly-

saccharide

EPS source

Function and Application

References

stored wheat bread, and improved

crumb softness after storage

Levan,

Dextran,

β-glucan

Lactococcus lactis,

Leuconostoc citreum,

Leuconostoc mesenteroides,

Pediococcus claussenii,

Weissella confusa

Increased viscosity and elasticity

in fermented vegetable products

(pureed carrots)

[9]

Levan

Gluconobacter albidus

Increased loaf volume and

decreased crumb hardness of

gluten-free buckwheat bread

[13]

Curdlan

Increased viscosity and

lubrication properties of protein

solutions

[118]

Curdlan

Improved texture and water-

holding capacity in low-salt pork

sausages

[119]

Curdlan

Increased gel strength, water

holding capacity, and gel

formation in heat-treated Alaska

Pollock surimi gels

[120]

Curdlan

Improved structural rigidity, gel

strength, water-holding capacity,

and sensory properties of

restructured ribbonfish

[121]

Curdlan

Reduced cooking loss, improved

textural, and cooking properties of

tofu noodles

[122]

Curdlan

Agrobacterium sp., 2

Reduced syneresis, increased

firmness, and viscosity of yogurts

[123]

The levan of Gluconobacter albidus improves the loaf volume and the crumb hardness of

gluten-free buckwheat bread [13,16]. The enhancement of the bread characteristics could be

caused by improved viscoelastic properties of levan-containing doughs, since high molecular

weight levan, with stronger viscoelastic properties, affected the bread characteristics more

positively than low molecular weight levan. The growth and levan production of Leuconostoc

citreum BD1707 in sucrose-supplemented tomato juice and the thickening capacity of in situ

produced levan of Leuconostoc mesenteroides E-91461 in pureed carrots is a promising

approach to replace texturizers in fermented vegetable-containing products [9,10]. Despite

these advances, the influence of levan on the rheological properties of foods has not been widely

studied in the last years.

Curdlan is used in the food industry because of its gelling and rheological properties. It is

tasteless, colorless, and odorless and can be used to replace fat, modify the texture and improve

the water-retention [124]. In foods, whose structures consist of heat-denatured protein, the

formation of a heat-irreversible high-set gel can be used to enhance food structure. This

Theoretical Background

property was used in low-salt pork sausages, heat-treated Alaska Pollock surimi and

restructured ribbonfish to improve the texture, gel strength and water-holding capacity [119–

121].

In general, not only the EPS quantity but also the type of EPS is important for the structuring

of fermented products. In the study of Grosu-Tudor et. al (2017) soymilk and dairy milk were

fermented with several EPS-producing lactic acid bacteria, with and without sucrose addition.

In experiments without sucrose addition, Leuconostoc mesenteroides 112 achieved the highest

viscosity, although the amount of EPS produced was the smallest of all tested microorganisms.

In dairy milk with sucrose addition, Leuconostoc mesenteroides 127 attained a low viscosity

although the EPS production was amongst the highest. These insights indicate that the type of

EPS, its conformation and its compatibility with other food ingredients are the main factors

influencing the rheological properties. Therefore, the measurement of the intrinsic viscosity and

the characterization of the flow and viscoelastic behavior of EPS and EPS-containing foods

reveals important information to exploit the benefits of EPS in food systems.

2.5.2 Levan

Levan is a fructan type homopolysaccharide. It consists of β-2,6 glycosidically linked fructose

monomers and may have β-2,1 linked side chains [125]. In addition, a glucose molecule may

be attached at the beginning of the chain due to its synthesis pathway [126]. Levan with a low

molecular weight (10 to 200 fructose monomers) is synthesized by some plants. It serves as a

storage carbohydrate or plays a role in protecting against cold or drought stress of the plants

[127]. As an exopolysaccharide, levan is produced by many different bacteria and fungi [128].

Here, levan is involved in biofilm formation and probably has a protective function against

stress factors such as drought or osmotic stress [51]. In addition, it can serve as an energy source

under starvation conditions [125]. Some levan-producing microorganisms interact with

eukaryotic hosts. In plants, they can act as symbionts, but also as pathogens. In the second case,

the levan may represent a virulence factor that favors the growth of the pathogens [51]. Some

Actinomyces and Streptococcus strains colonize the oral cavity. The levan they produce is

involved in plaque formation and thus in the development of caries [129]. Furthermore, levan-

producing microorganisms have also been isolated from soil and fermented foods [51,125].

Generally, microbial levan is produced extracellularly from sucrose by levansucrases from the

glycoside hydrolase 68 family. Depending on the acceptor molecule, levansucrase can catalyze

different reactions. The energy released during the cleavage of the glycosidic bond of sucrose

is used to attach a fructose molecule to an acceptor molecule. If the enzyme transfers the

fructose to water, the sucrose is hydrolyzed into glucose and fructose [126]. If a second sucrose

molecule is used as an acceptor, the enzyme catalyzes the formation of 6-kestose. The formation

of oligosaccharides and levan is catalyzed when the fructose residue is transferred to 6-kestose

or a growing fructose chain [126].

Theoretical Background

Depending on the microbial strain and environmental factors such as sucrose concentration,

pH, temperature and ionic strength, the production of levan and its molecular weight varies

[14,15,125,130]. In the literature, the molecular weight of levan is reported in the range of

105 Da to 109 Da [53,131,132]. The gyration radius ranges from 20 nm to several hundred nm

and the hydrodynamic radius from 2.5 nm to 151 nm [133,134]. The intrinsic viscosity of levan

is reported to be 7.0 mL/g to 45 mL/g [59,133,135]. This unusuall low intrinsic viscosity for

polysaccharides indicates a high density of levan molecules.

Gluconobacter albidus (TMW 2.1191), a species of acetic acid bacteria isolated from water

kefir, is a promising source of levan. (Fig. 5) [136]. The amount and molecular weight produced

by these organism can be controlled by adjusting the pH and sucrose concentration during

synthesis [15,16,137]. In addition, a method has been established that allows the production of

levan in a cell-free buffer system, which greatly improves the purity of the polysaccharide [15].

The rheological properties of levan are strongly dependent on the molecular weight and vary

from newton-like behavior at low concentrations and/or low molecular weights to gel-like

behavior at high molecular weights [11,14,59,133]. In the case of the levan of Gluconobacter

albidus, the molecular weight dependence of rheological properties was previously shown [15].

Levan of Gluconobacter albidus produced by uncontrolled fermentation and therefore at low

pH has a low molecular weight. This levan exhibits a low viscosity and Newtonian behavior at

concentrations up to 25% (w/v). Controlled enzymatic levan production in a cell-free buffer at

pH 5.0 and pH 6.0 yields high molecular weight levan. This levan shows a shear thinning

behavior in rotational tests at concentration of 3% (w/v) and a gel-like behavior in oscillation

tests at concentrations of 5% (w/v). Compared to the low molecular weight levan produced by

fermentation, it exhibits 100 to 1000 times higher viscosity at a concentration of 5% (w/v) [15].

A controlled enzymatically produced levan prepared at pH 4.0 shows less pronounced shear-

thinning behavior in the rotation test and the behavior of a viscoelastic fluid in the oscillation

test than the levan produced enzymatically at higher pH. The molecular weight of this levan is

in between the earlier mentioned levan [15]. These results suggest that the levan produced by

Gluconobacter and other organisms can interact other and form intermolecular networks when

Figure 5: Cell aggregates of Gluconobacter albidus (TMW 2.1191) in a levan-containing

medium.

Theoretical Background

a critical molecular size and polymer concentration are exceeded. These networks may consist

of highly entangled high molecular weight levan chains. In solutions of levan with small

molecular size, the number of entanglement points between different levan chains are probably

insufficient to stabilize a physical network. Therefore, no physical network is formed [15].

Another approach to explain the rheological properties is the compact structure of levan.

Therefore, levan may behave like a nanogel particle above a certain molecular weight. In this

case, the viscoelastic behavior of levan of a certain size could be explained by the interaction

of soft spheres forming a colloidal network [15].

2.6 β-Lactoglobulin

β-lactoglobulin is a globular protein and is found in the milk of many mammals. In bovine

whey, β-lactoglobulin is the major protein at about 7.0 to 12 g/L and accounts for about 50%

of the total protein [60]. It consists of 162 amino acids and has a molecular weight of

approximately 18.4 kDa [32]. β-lactoglobulin occurs in several different variants, with variants

A and B being the most common in bovine β-lactoglobulin. The amino acid sequence of both

variants differs at two positions. (A: Asp64, Val118; B: Gly64, Ala118) [36]. From table 2 the

composition of aromatic, hydrophobic, hydrophilic uncharged, positive and negative charged

amino acids according to Farrell et al. can be seen [4].

Table 2: Amino acid composition of β-lactoglobulin [4].

Amino acid

β-lg

Amino acid

β-lg

Aromatic

Phenylalanine

Positively

charged

Arginine

Tyrosine

Histidine

Tryptophan

Lysine

Hydrophilic

uncharged

Serine

Negatively

charged

Aspartic acid

Threonine

Glutamic acid

Asparagine

Hydrophobic

Alanine

Glutamine

Valine

Cysteine

Isoleucine

Glycine

Leucine

Proline

Methionine

The native structure of proteins such as β-lactoglobulin can be described at the primary,

secondary, tertiary, and quaternary levels [72]. The primary structure describes the arrangement

of amino acids shown in Table 2, which determines the secondary structure. Native β-

lactoglobulin is composed of approximately 15% α-helix, 51% β-sheet, 17% β-turns, and 17%

random coil [60]. These secondary structural elements (α-helix and β-sheet) are stabilized by

intramolecular hydrogen bonds between carbonyl and amino groups and linked by β-turns

[138]. Together with the random coils, these structural elements form the tertiary structure. It

describes the spatial arrangement of the secondary structures and is stabilized by intramolecular

Theoretical Background

hydrogen bonds, hydrophobic interactions, electrostatic interactions, van der Waals forces, and

disulfide bonds [139]. β-lactoglobulin has a total of fife cysteine residues, from which two

disulfide bonds originate [32]. In total, β-lactoglobulin consists of nine β-strands, eight of them

forming a central cavity known as the β-barrel. The interior of this cavity is hydrophobic, while

the opening is lined with hydrophilic amino acids [36]. The β-barrel is flanked by an α-helix,

and the final ninth β-strand forms most of the dimer interface [32].

The quaternary structure of β-lactoglobulin (Fig. 6) is mainly dominated by an equilibrium of

monomers and dimers as well as octamers [36]. The dimer state is stabilized by intermolecular

hydrogen bonds and electrostatic interactions. Hydrogen bonds between two monomers are

formed among the ninth β-strand (also referred to as intermolecular β-strand) as well as β-turns

[140,141]. Electrostatic interactions occur between the positively charged Arg40 and the

negatively charged Asp33 [142].

The equilibrium between the monomeric, dimeric and octameric forms of β-lactoglobulin can

be influenced by pH, ionic strength, temperature and protein concentration [143]. At a low ionic

strength and low pH of 2.0 to 3.0 or at high pH above 8.0 β-lactoglobulin is predominantly

monomeric. At these pH values far from the isoelectric point (IEP: 5.2), nonspecific

electrostatic repulsion dominates due to the high protein charge. The addition of salt screens

the electrostatic repulsion between the monomers and thus favors the dimer state [144]. Just

below the isoelectric point in the pH range of 3.7 to 5.2 with an optimum at 4.7, octamers can

form [35]. The octamers are in equilibrium with dimers and their formation is enhanced by a

decrease in temperature and a decrease in ionic strength [143]. Above the isoelectric point,

mainly dimers are formed, which increasingly change to the monomeric form at low ionic

strength and increasing pH value. In general, the equilibrium between monomer and dimer

shifts towards the monomeric form at higher temperatures, lower protein concentrations, lower

ionic strengths and at pH values further away from the isoelectric point [36,143–145].

Figure 6: Schematic representation of the monomer, dimer and octamer equilibrium of

β-lactoglobulin in respect of the pH, protein concentration and ionic strength.

Theoretical Background

The denaturation of β-lactoglobulin can be induced by various factors including temperature,

pressure, shear, pH, and chemical denaturating agents and causes protein aggregation and

gelation [146–148]. In this process, the native structure of the protein, including secondary,

tertiary and quaternary structure, is lost [149]. In terms of food processing, thermal denaturation

is the most relevant process and will be discussed further. The heat-induced gelation of

β-lactoglobulin is composed of several reversible and irreversible processes (Fig. 7) that can be

influenced by protein concentration and solvent conditions such as pH and ionic strength [33].

In the first step, existing dimers reversibly dissociate to monomers by an increase in temperature

[150]. A further increase in temperature causes a reversible change and therefore the formation

of denatured monomers. Thereby, the free thiol group Cys121 and hydrophobic regions of the

protein are exposed [150]. At 65 °C, the helical secondary structures are abruptly lost, and β-

lactoglobulin reaches the molten globule state, which is characterized by regions of local

disorder and increased flexibility [151,152]. At 75 °C reactive thiol groups and adhesive

hydrophobic surfaces cause the formation of denatured dimers. Two free thiol groups of Cys121

can form a disulfide bond, or a thiol group exchange occurs between the free thiol group of

Cys121 and the disulfide bond Cys66-Cys160 leaving a new free thiol group at Cys160 [149]. In the

further process, higher oligomers are formed through non-covalent interactions (hydrophobic

and salt-induced) and thiol/disulfide exchange reactions [153–155].

If the protein concentration is high enough, this aggregation causes the formation of three-

dimensional gel networks. Depending on the ionic strength and pH value, fibrillar gels or

particle gels can be formed (Fig. 7). A heat treatment at low ionic strength in combination with

a pH value away from the isoelectric point results in fibrillar gels, which appear transparent and

the gel strands have a diameter in the nm range [69]. Under these conditions, the proteins are

highly charged. Therefore, the electrostatic repulsion must be overcome by the long-range weak

attractive interactions which stabilize the network [47]. The structure resembling a chain

of beads results from the minimization of electrostatic repulsion by this arrangement. Reducing

Figure 7: Schematic representation of the thermal denaturation and gel formation of β-

lactoglobulin.

Theoretical Background

electrostatic repulsion by adjusting pH or increasing ionic strength results in more flexible gel

strands with more branching points [47]. At high ionic strengths and pH values around the

isoelectric point, particle gels are formed. These are nontransparent and the gel pores are in the

µm range [69]. The formation of these structures occurs in two steps under conditions, in which

charged protein groups are shielded by counterions or the total charge is low. According to

Aymard et al., spherical protein aggregates are formed first, which aggregate into fractal

networks in the second step [156].

Publications

3. Publications

This thesis includes the content of the following manuscripts I – IV, which have been published

in international peer-reviewed scientific journals:

Manuscript I

Hundschell C. S., Jakob F., Wagemans A. M.; Molecular weight dependent structure of the

exopolysaccharide levan. International Journal of Biological Macromolecules (2020), 161, 398-

405, https://doi.org/10.1016/j.ijbiomac.2020.06.019

Manuscript II

Uttinger M. J.*, Hundschell C. S.*, Lautenbach V., Pusara S., Bäther S., Heyn T. R., Keppler

J. K., Wenzel W., Walter J., Kozlowska M., Wagemans A. M., Peukert W.; Determination of

specific and non-specific protein-protein interactions for beta-lactoglobulin by analytical

ultracentrifugation and membrane osmometry experiments, Soft Matter (2022),

https://doi.org/10.1039/D2SM00908K

*These authors contributed equally to the manuscript

Manuscript III

Hundschell C. S., Bäther S., Drusch S., Wagemans A. M.; Osmometric and viscometric study

of levan, β-lactoglobulin and their mixtures. Food Hydrocolloids (2020), 101, 105580,

https://doi.org/10.1016/j.foodhyd.2019.105580

Manuscript IV

Hundschell C. S., Brühan J., Anzmann T., Kohlus R., Wagemans A. M.; Influence of levan on

the thermally induced gel formation of β-lactoglobulin, gels (2021), 8, 228,

https://doi.org/10.3390/gels8040228

Manuscript I

Molecular weight dependent structure of the

exopolysaccharide levan

International Journal of Biological Macromolecules (2020), accepted manuscript

The publication is online available at https://doi.org/10.1016/j.ijbiomac.2020.06.019

Authors

Christoph S. Hundschell1; Frank Jakob2; Anja M. Wagemans1

1: Food Colloids, Technische Universität Berlin, Germany

2: Chair of Technical Microbiology, Technische Universität München, Germany

Manuscript I

I-1 Abstract

Levan is a bacterial homopolysaccharide, which consists of β-2→6 linked β-(D)-fructose

monomers. Because of its structural properties and its health-promoting effects, levan is a

promising functional ingredient for food, cosmetic and pharmaceutical products. The properties

of levan have been reported to be linked to its molecular weight. For a better understanding of

how the molecular weight determines its polymer conformation in aqueous solution, levan

produced by the food-grade acetic acid bacterium Gluconobacter albidus TMW 2.1191 was

analyzed over a broad molecular weight range using dynamic and static light scattering and

viscometry. Levan, with low molecular weight, exhibited a compact random coil structure. As

the molecular weight increased, the structure transformed into a compact non-drained sphere.

The density of the sphere continued to increase with increasing molecular weight. This resulted

in a negative exponent in the Mark-Houwink-Sakurada Plot. For the first time, an increase in

molecular density with increasing molecular weight, as determined by a negative Mark-

Houwink-Sakurada exponent, could be shown for biopolymers. Our results reveal the unique

properties of high molecular weight levan and confirm the need of further systematic studies

on the structure-function relationship of levan for its targeted use in food, cosmetic and

pharmaceutical applications.

Manuscript I

I-2 Introduction

Levan (Fig. I-1A) is a β-2,1 linked fructan-type polysaccharide produced extracellularly by a

variety of microorganisms to promote the surface adhesion and biofilm formation [51]. In the

context of human consumption, positive effects such as prebiotic properties, lowering

cholesterol, as well as antiviral and antitumoral properties have been reported [12,157–159].

Besides the nutritional characteristics, levan has unique techno-functional properties. It can be

used as an in situ produced thickening agent in fermented foods or to improve the crumb

hardness and the specific volume of gluten-free buckwheat bread [9,13,16]. Moreover, levan

can be applied as opacifying agent due to the Tyndall effect (Fig. I-1B), which seems to be

more pronounced at a high molecular weight [14,160].

Literature discussing experiments on levan reveals varying physical properties. The radius of

gyration was found to be between 20 nm and several hundred nm [53,59,133,134], while the

hydrodynamic radius ranged between 2.5 and 151 nm [133,134]. The molecular weight of levan

was reported to range from 105 to 109 Da [53,129,161]. A compact and spherical molecular

structure was indicated by an unusual low intrinsic viscosity (7 to 45 mL/g) [14,55,58,135,162].

Viscosity studies of levan showed mixed results. While Newtonian flow behavior was observed

at concentrations up to 20 to 30 % in the studies of Arvidson et al. [133] and Kasapis et al. [59],

an onset of shear-thinning behavior was observed in the concentration range from 1.0 to 4.0 %

by Benigar et al. [14].

The apparent contradicting rheological properties in the studies mentioned above can be

explained by the microbiological origin, molecular weight and structural properties that varied.

Moreover, the dispersity of the levan samples was not always characterized, which may have a

large effect on the measured properties. In addition, to the best of our knowledge, the molecular

weight was not correlated with the levan properties – in particular, levan properties were not

investigated in the molecular weight range above 107 Da nor over a broad molecular weight

range using one type of levan produced by a specific microorganism and its secreted

levansucrase. Therefore, we aimed to characterize the structural properties of Gluconobacter

(G.) albidus levan fractions with a low dispersity in the molecular weight range of 104 to 109 Da

using dynamic light scattering, multi-angle light scattering and viscometry. Doing so, we

examined the molecular, intrinsic viscosity, hydrodynamic radius, radius of gyration and

Figure I-1: (A) Structure of levan. (B) Levan solution (8 g/L) with increasing polymer size (left

to right).

Manuscript I

geometric radius in order to investigate the change in molecular structure as a function of

molecular weight.

I-3 Materials & Methods

I-3.1 Cultivation and Levan Production

The cultivation of the acetic acid bacteria G. albidus as well as the levan production was carried

out as described in Hundschell et al. [163]. In total, three levan samples were produced under

different conditions. A low molecular levan (LevF) was produced by fermentation of a sucrose-

containing sodium gluconate medium. The high molecular weight samples Lev4 and Lev5 were

produced in a cell-free, enzyme-containing sodium acetate buffer at pH 4.0 and pH 5,

respectively. Different values of the buffer pH were chosen because the pH affects the enzyme

reaction and therefore the molecular weight [16].

I-3.2 Gradual Ethanol Precipitation

To reduce the dispersity of the samples and to obtain several levan fractions of different

molecular weight, gradual ethanol precipitation was used. 10 g of each levan was dissolved in

500 mL of distilled water and stirred overnight at 4.0 °C. Afterwards, ethanol was slowly added

while continuously stirring until a change in turbidity indicated that levan had precipitated.

Subsequently, the precipitated levan was separated from the solution by centrifugation

(10.000 g, 30 min, 4.0 °C). This procedure was repeated with the remaining supernatant until

no further precipitation was visible. Doing so, four to seven fractions were obtained for each

levan. The high molecular weight levans precipitated at ethanol concentrations of 52 to 56

vol.%, while the low molecular weight levans precipitated at significantly higher ethanol

concentrations (up to 70 vol.%). The values of the ethanol concentrations, sample yields and

the samples dispersity index are listed in table I-1. After centrifugation, the precipitate was

washed with ethanol and the remaining ethanol was evaporated at room temperature. Finally,

the levan fractions were redispersed in distilled water and freeze-dried.

I-3.3 Sample Preparation

For all experiments, levan was dissolved in distilled water using a magnetic stir plate. The

samples were stored overnight in the refrigerator to ensure complete hydration of the polymers.

All analyses described below were performed in triplicate at 20 °C unless otherwise noted.

I-3.4 Photometry

The specific extinction coefficient at 400 nm of levan was determined in a photometer (Helios

Omega UV-vis spectrophotometer, Thermo Fisher Scientific Germany BV & Co KG,

Germany). A standard curve with eight different concentrations was generated. Low molecular

weight levans (LevF, LevF F2 – F5) were measured at concentrations between 20 and 50 g/L,

medium molecular weight levans (LevF F1, Lev4 F7) at 3.0 to 5.0 g/L, and the higher molecular

weight levans (Lev4, Lev4 F1 – F6, Lev5, Lev5 F1 – F4) at 1.0 to 2.0 g/L.

Manuscript I

Table I-1: Ethanol concentrations and levan amounts of the fractionation process.

Fraction

Sample name

Ethanol (vol %)

Mass (g)

LevF

LevF F1

55.58

1.15

LevF F2

56.88

1.84

LevF F3

60.69

1.92

LevF F4

64.00

1.09

LevF F5

70.32

1.38

Lev4

Lev4 F1

53.88

0.67

Lev4 F2

54.88

1.10

Lev4 F3

55.29

1.19

Lev4 F4

55.30

1.29

Lev4 F5

55.62

1.66

Lev4 F6

55.97

0.98

Lev4 F7

66.50

1.46

Lev5

Lev5 F1

52.04

1.55

Lev5 F2

53.13

1.58

Lev5 F3

54.15

4.00

Lev5 F1

55.31

1.38

I-3.5 Viscometry

The viscosity of the solvent η0 and of the levan solution ηS was determined utilizing a rolling

ball micro viscometer (LOVIS 2000M, Anton Paar GmbH, Germany). A glass capillary with a

radius of 1.59 mm and a steel ball with a radius of 1.5 mm at an angle of 50 ° were used.

Viscosity was measured in triplicate at six concentrations in the range of 2.0 to 4.5 g/L. To

determine the density of the solutions a bending vibrator (DMA 38, Anton Paar GmbH,

Germany) was used. The intrinsic viscosity [η] was determined by plotting the measured

reduced viscosity ηred against the polymer concentration c and using the Huggins equation

[164].

𝜂𝑟𝑒𝑑 =𝜂𝑆−𝜂0

𝜂0𝑐=[𝜂]+𝑘𝐻[𝜂]2𝑐

(1)

The y-intercept represents the intrinsic viscosity, which gives a measure of the polymers

hydrodynamic volume, whereas the slope corresponds to the Huggins coefficient kH, which

describes the nature of interactions or the affinity in a polymer-solvent system. The

hydrodynamic radius from viscosity RH,visc was subsequently calculated using the viscosity law

according to Einstein:

𝑅𝐻,𝑣𝑖𝑠𝑐 =(3[𝜂]𝑀

10𝜋𝑁𝑎)1

(2)

where Na is the Avogadro constant and M is the molecular weight [165].

Manuscript I

I-3.6 Dynamic Light Scattering

The hydrodynamic radius RH,DLS of the levan fractions was measured with a ZetaSizer Nano ZS

(Malvern Instruments, UK) utilizing dynamic light scattering. Each sample was measured three

times with automatic measurement duration at an angle of 173°. The solvent refractive index

was 1.33, and the viscosity was 1.0031 mPas. Low molecular levans (LevF, LevF F2 – F5)

were measured at a concentration of 2.0 g/L while higher molecular weight levans (LevF F1,

Lev4, Lev4 F1 – F7, Lev5, Lev5 F1 – F4) were measured at 0.1 g/l. The volume distribution

and the mean of the volume distribution RH,DLS were determined. To convert the intensity

distribution into the volume distribution, a refractive index of 1.65 was determined for levan.

Doing so, a Horiba particle sizer (LA-950, Horiba Jobin Yvon GmbH, Bernsheim, Germany)

and the Method expert option within the LA-950 software were used as described by

Krzeminski et al. [166]. All data analysis was performed using the instrument software.

I-3.7 Multi Angel Laser Light Scattering

Levan fractions and the unfractionated levan were separated according to polymer size with

asymmetric flow field flow fractionation (aF4) (Wyatt Technology, Germany) and analyzed

with multi-angle laser light scattering (MALLS) (Dawn Heleos II, Wyatt Technology,

Germany). UV (Dionex Ultimate 3000, Thermo Fisher Scientific, USA) and RI (Refractomax

521, Thermo Fisher Scientific, USA) detection were used for concentration determination. The

injected volume was 100 µL, and the polysaccharide concentration was 0.1 to 1.0 g/L. For

separation, the method of Jakob et al. [53] was used with modification. An injection flow rate

of 0.2 mL/min and a constant elution flow rate of 1.0 mL/min were used. The crossflow was

reduced from 3.0 mL/min to 0.1 mL/min within the first 10 min of elution. Subsequently, the

crossflow was kept constant at 0.1 mL/min for 15 min before being set to 0 mL/min. The

separation was performed on 10 kDa regenerated cellulose membranes (Superon GmbH

Germany) using a 50 mM NaNO3 solution as eluent. Data are representative of two

measurements.

Concentration determination. Depending on the molecular size of the levan, either UV or RI

detection was used for concentration determination in the aF4-MALLS system. The RI detector

measures the difference in refractive index between solvent and polymer solution. Therefore, it

can be used for all substances that differ in refractive index from the solvent; however, it is not

as sensitive as the UV detector. Moreover, the refractive index is temperature and pressure-

dependent [167]. The quality of the aF4 separation and the accuracy of the concentration

determination are oppositely affected by the polymer concentration: The higher the

concentration, the worse the aF4 separation, but the better the concentration signal. The low

molecular weight levan was more efficiently separated at higher polymer concentrations than

the high molecular weight levan. Therefore, the RI detector was suitable for the concentration

determination of the low molecular weight levan (LevF, LevF F1 – F5, Lev4 F7). The UV

detector was used for levans with a higher molecular weight because they effectively scatter

light and cause a strong UV signal at low levan concentrations. For high molecular weight

Manuscript I

levans, the UV detector was therefore superior to the RI detector in terms of its concentration

sensitivity. In addition, no baseline subtraction was needed to compensate for the pressure

dependence as applied for the RI detector. Because the molecular size influences the extinction

coefficient ε, a fit (Fig. S I-2 supplementary data; equation 3) between the geometric radius Rgeo

and ε was applied to avoid errors due to the molecular size dependence:

𝜀=3.17∙10−6 𝑅𝑔𝑒𝑜2.23

(3)

Equation 3 enabled the assessment of the polymer concentration for each volume slice during

the aF4-MALLS UV measurement from Rgeo, which was determined in the particle mode (no

concentration signals needed for distribution analysis) and the UV detector signal. Figure S I-4

(supplementary data) shows the concentration curve during the aF4-MALLS measurement for

Lev4 F5 and Lev4 F6. For both fractions, a suitable UV and RI signal could be obtained. After

the correction for the size-dependent extinction coefficient, the concentration curves and

molecular weight distributions (Fig. S I-3 and S I-4, supplementary data) from the UV and RI

detection were found to be similar.

Data analysis. ASTRA 6 software (Wyatt Technology, Germany) was used for aF4-MALLS-

UV/RI data analysis. Different models were considered to determine the radius and the

molecular weight from MALLS experiments. In respect to polymer size and conformation, the

quality of the fit differed from model to model. The molecular weight, the dispersity index PDI

and Rgeo were determined via a sphere model since this model delivered the best fit over the

entire molecular weight range for all levan fractions. For the determination of the radius of

gyration RG MALLS data were analyzed through a Debye model with a third-order polynomial

fit. According to Andersson, Wittgren and Wahlund [168] and Baborowski and Friese [169],

this model is well suited for compact spherical colloids with a Rgeo of up to ~170 nm. Below 10

to 15 nm, the determination of the radii is impossible – regardless of the model – since the

scattering of these particles is not angle dependent. All radii were determined in the

concentration-independent particle mode. For molecular weight calculations, a refractive index

increment (dn/dc) of 0.146 mL/g (50 mM NaNO3) was used for G. albidus levan according to

Ua-Arak et al. [16]. In all calculations, the concentration is assumed to be sufficiently low to

neglect the second virial coefficient and higher terms. The samples should be sufficiently

diluted by aF4 separation to prevent errors from neglecting the second virial coefficients [168].

I-4 Molecular Conformation and Shape Determination

In this section, the theoretical background for the discussion of the molecular conformation and

shape determination of the levan samples is described.

The hydrodynamic radius RH of a polymer is an apparent measure and corresponds to the radius

of an equivalent hard sphere with the same diffusion properties as those observed for the

macromolecule. The geometric radius Rgeo represents the actual dimensions of spherical

macromolecules. For compact, spherical macromolecules, the value of RH and Rgeo is therefore

Manuscript I

essentially identical. For polymer conformations that differ from the compact spherical shape,

the values of both radii differ [170]. In a non-drained sphere, RH and Rgeo are equal and therefore

RH/Rgeo is 1.0 [170]. In a less compact polymer, the solvent can permeate through the coil,

resulting in different diffusion properties including a decrease in RH, which makes it virtually

smaller than Rgeo (RH/Rgeo < 1). Considering this behavior, RH/Rgeo decreases with increasing

polymer density.

The radius of gyration RG specifies the mean distance between the individual polymer segments

of a molecule and its center of gravity. The ratio of RG and RH provides information about the

investigated polymer’s shape. In theory, RG/RH for a compact sphere is 0.775 while less compact

polymers exhibit a higher RG/RH. According to Nilsson [80], for linear random coils under theta

conditions RG/RH = 1.5 and in good solvents is RG/RH = 1.78. A listing of RG/RH values for

some polysaccharides can be found in the publication by Nilsson [80]. A relationship between

RG and the molecular weight is generally assumed that can be used to describe the conformation

of polymers [80].

𝑅𝐺=𝑘𝐺𝑀𝜈𝐺

(4)

Here, the constant kG depends on the polymer and solvent, and the hydrodynamic coefficient

νG depends on the spatial structure and density of the macromolecules. For a compact sphere,

νG is 0.33, for a random coil 0.5 to 0.6 and for a rod 1.0 [80]. Thus, a smaller νG can be

interpreted to reflect a more compact (denser) molecule structure.

Besides the radii described above, information about a polymer conformation can be obtained

from the Mark-Houwink-Sakurada relation [25].

[𝜂]=𝑘𝜂𝑀𝛼

(5)

This is equivalent to equation 4, but instead of RG, the intrinsic viscosity is examined as a

function of the molecular weight. The constant kη, depends, like kG, on the polymer-solvent

system. The Mark-Houwink-Sakurada exponent α gives information about the molecule

structure. A compact sphere has an α of 0. Under theta conditions, α for a linear random coil is

0.5 and for a rigid rod is 1.0 [25]. Both exponents, νG and α, are linked by the following equation

[171].

𝛼=3𝜈𝐺−1

(6)

I-5 Results and Discussion

In this section, the experimental results for Rgeo, RG, and RH as well as the intrinsic viscosity

and shape quotients derived thereof are used to discuss the conformation of levan from G.

albidus as a function of molecular weight. The conformation of levan has been discussed in

earlier studies [14,53–55,134,162,172]. In most cases, only a limited range of molecular

weights was investigated or levan from various microorganisms was analyzed. In our study, the

Manuscript I

structure of levan from G. albidus was analyzed over a broad range of molecular weights (104

to 109 Da) by MALLS, DLS and viscometry.

I-5.1 Hydrodynamic radius RH

Assuming a spherical molecular shape, RH can be determined by DLS (Fig. I-2) or equation 2

leading to RH,DLS and RH,visc, respectively. The comparison of RH,DLS and RH,visc (Fig. I-3) allows

the evaluation of the accuracy of the data because two independent techniques were used to

determine RH either based on the particle motion detected by the DLS method or the intrinsic

viscosity determined utilizing the viscometry. In our study, the values for RH from DLS and

viscometry of levan from G. albidus were found to be almost equal. In the molecular weight

range between 107 and 5·108 Da (PDI: 1.2 to 2.5), the radii differed by less than 5.0 %,

suggesting a spherical molecular shape. Wolff et al. [173] showed similar results, studying a

high molecular weight inulin with a compact molecular structure. In their study, the difference

between RH from DLS (108 nm) and viscometry (109 nm) of the β-2,1 linked fructan was only

1.0 nm. In our study, below 107 Da, the deviation between both radii of the G. albidus levan

was larger (PDI: 2.0 to 8.1). This can be explained by a less compact molecular structure and

an increased PDI for these fractions. A high dispersity negatively affects the accuracy when

determining the effective RH from DLS results. Thus, the largest deviations between RH from

DLS and viscometry were found in the samples with the highest PDI (LevF and Lev4).

Figure I-2: Cumulative distribution of hydrodynamic radius from DLS of levan before (black,

unfilled symbols) and after (grey, filled symbols) ethanol fractionation. LevF (squares), Lev4,

(triangles), Lev5 (diamonds).

Manuscript I

Figure I-3: Dependence of geometric Radius Rgeo (squares), hydrodynamic radius RH,DLS from

DLS (diamonds) and hydrodynamic radius RH,visc from viscometry (triangles) on levan

molecular weight.

I-5.2 Shape quotients RG/RH and Rgeo/RH

The shape of a polymer can be estimated from the quotient of RG and RH from DLS (RG/RH,DLS)

or RG and RH from viscometry (RG/RH,visc). By replacing RG with Rgeo, the two quotients –

Rgeo/RH,DLS and Rgeo/RH,visc – are obtained. These quotients allow the differentiation between

compact spherical and less dense random coil structures. For a compact sphere the theoretical

value of Rgeo/RH is 1.0 and of RG/RH 0.775 and both increase for less dense random coil

structures [80]. For a linear random coil structure at theta conditions, a RG/RH value of 1.5 and

in a good solvent a RG/RH of 1.78 is expected [80]. The experimental values of the quotients are

plotted as a function of the molecular weight in figure I-4. Below 107 Da, the values of RG/RH,DLS

and RG/RH,visc were between 1.5 to 2.3 and 1.2 to 1.9, respectively, and tended to increase with

decreasing molecular weight. This suggests a random coil structure for molecular weights

below 107 Da, which contracted with increasing molecular weight. Above 107 Da (RH ≥ 33 nm),

Figure I-4: (A) Dependence of R

H,DLS

(triangle) and R

H,visc

(diamonds) on levan

molecular weight.

(B) Dependence of Rgeo/RH,DLS (triangle) and Rgeo/RH,visc

(diamonds) on levan

molecular weight. The dotted line at 0.774 (A) and 1.0 (B) represents the represents the

theoretical value for a compact sphere.

Manuscript I

an Rgeo/RH,DLS value between 0.95 and 1.07 and an Rgeo/RH,visc value between 0.98 and 1.10

indicate a spherical shape. Similarly, RG/RH,DLS ranged from 0.75 to 1.03 and RG/RH,visc from

0.69 to 1.03 above 107 Da, thus falling within the theoretical range of a compact spherical

polymer. Interestingly, a similar ‘spherical’ RG/RH range of 0.99 to 1.33 was reported for less

dense, hyperbranched polymers, such as amylopectin-rich starch [174]. The slight decrease of

RG/RH we observed above 108 Da (Fig. I-4A) was probably not related to the structure of levan

but might be caused by a lack of data points at low scattering angles. For molecular weights

above 108 Da, RG/RH was expected to be constant as observed for Rgeo/RH (Fig. I-4B). While the

sphere model which was used to determine Rgeo is predictive over the entire molecular weight

range, the resolution of the MALLS at small scattering angles is no longer sufficient to

accurately determine RG with the Debye model for levans larger than 150 nm. Accordingly, in

the publication of Baborowski and Friese [169], RG of a spherical colloid above 170 nm could

not be determined accurately using the Debye model with a third-order fit. In their study, the

model also underestimated RG. Runyon et al. [134] also used RG/RH to describe the structure of

a levan using two major size populations. Their results demonstrated the transition from a

random coil to a sphere conformation for levan in the same molecular size range as we observed

in our study. Below a RH of 32 nm (33 nm in our study), their RG/RH also increased from

approximately 0.775 to 1.8 with decreasing molecular weight. In the higher molecular weight

range of 32 to 129 nm, the shape factor corresponded approximately to the theoretical value of

a compact sphere.

I-5.3 Hydrodynamic coefficient ν

The hydrodynamic coefficient νG can be calculated from the slope of the double logarithmic

plot of the RG as a function of the molecular weight. Similarly, RH can be used, to obtain the

hydrodynamic coefficient νH, which can be interpreted equivalent to νG. [175,176]. Using the

same approach, in our study, Rgeo was used to obtain the hydrodynamic coefficient (νgeo). This

was allowed because Rgeo = RH was valid and the sphere model was predictive over the entire

molecular weight range tested (Fig. I-5). Therefore, we assumed that νgeo can be interpreted as

equivalent to νG. For molecular weights below 108 Da, νgeo and νG were largely in agreement

with slightly higher values for νG. Here, the values of v decreased from 0.5 to 0.33 with

increasing molecular weight suggesting structures that range from random coil/sphere

conformation to compact sphere conformation, respectively. At 107 Da, a ν of 0.33 implies a

spherical conformation. Above 108 Da, νG and νgeo decreased further with the molecular weight

indicating a spherical structure and an increasing polymer density. Here, νG decreased more

than νgeo, due to the limitations of the Debye model at small scattering angles as mentioned

above. Slightly higher values of νG (0.43) were reported for a levan from S. salivaris in the

molecular weight range of 18.5·106 to 57.1·106 Da [55]. Jakob et al. [53] also studied the

conformation of levans (from four different acetic acid bacteria) over a wide molecular weight

range using aF4-MALLS. A similar decrease in νG with increasing molecular weight was

observed. However, in the lower molecular weight range, νG was slightly higher than the values

Manuscript I

in our study. In the high molecular weight range, Jakob et al. reported a νG of less than 0.33 for

levans produced by Kozakia baliensis and Neoasaia chiangmaiensis [53]. Likewise, in a study

examining inulin, a similar low v was found for high molecular weights [173].

I-5.4 Intrinsic viscosity

The measured intrinsic viscosities are shown in Fig. I-6A. The intrinsic viscosity ranged from

14 mL/g to 50 mL/g. These values are unusually low for polysaccharides but are consistent with

literature values for levan, which ranged from 7.0 mL/g to 0.45 mL/g [14,54,55,58,135,162].

In contrast, other polysaccharides with a less dense structure such as dextran or xanthan have

intrinsic viscosities ranging from 100 mL/g to 50.000 mL/g [177,178]. In comparison to

dextran, the low intrinsic viscosity and compact molecular structure of levan might be due to

the D-fructofuranose ring having greater flexibility than the D-glucopyranose ring. The greater

flexibility may allow a tighter entanglement and therefore a more compact macromolecular

structure [133]. The intrinsic viscosity has been used to derive the exponent α from the Mark-

Figure I-5: Dependence of geometric radius R

geo

, radius of gyration R

(lines, right axis) and

hydrodynamic coefficients (triangles ν

G; diamonds νgeo, left axis) on levan molecular weight.

The lines at 0.5 and 0.33 represents the theoretical hydrodynamic coefficients of a random coil

at theta conditions and a compact sphere respectively.

Figure I-6: (A) Mark-Houwink-Sakurada Plot. (B) Dependence of the Huggins constant on

levan molecular weight.

Manuscript I

Houwink-Sakurada relation (Fig. I-6A; equation 5) and is linked to the molecular structure.

Below 5.5·105 Da, an α of 0.35 indicates a compact random coil structure for levan. In the range

between 106 to 108 Da, α seemed to be largely independent of the molecular weight and

indicates a compact spherical polymer structure. The two outliers in this range could be ascribed

to the high dispersity of the fractions LevF and Lev4 F7. Therefore, more data points would be

needed to obtain a significant prediction of α in this molecular weight range. Nevertheless, the

change of α at around 106 Da is evident indicating a shift from a compact random coil towards

a compact spherical levan. Similarly, Stivala and Zweig [54] found two different domains for

α: a random coil structure (α = 0.67) for 104 Da to 8.9·104 Da and a spherical structure (α = 0.05)

for 2.2·105 Da to 8.3·106 Da. Bahary and Stivala [58] also found two different domains in the

Mark-Houwink-Sakurada plot of acid-hydrolyzed levan indicating a random coil structure at

low molecular weights and a spherical shape at higher molecular weights. Comparably, the

molecular structure of inulin was reported to change at approximately 105 Da [173,179].

At molecular weights above 108 Da, an unusual behavior was observed: the intrinsic viscosity

decreased with increasing molecular weight, which resulted in a negative α (-0.12) in the Mark-

Houwink-Sakurada plot. This decrease in intrinsic viscosity at high molecular weights also

suggests an increase in the molecular density for the spherical levan molecules. Since the

intrinsic viscosity is a measure of the hydrodynamic volume and refers to a volume per gram,

the results are not in contradiction to the continuously increasing radii determined by DLS and

MALLS measurements. The radius of these polymers rises with molecular weight, but the

volume per gram decreases due to the rise in molecular density.

A negative α was also calculated using equation 6 since ν was found to be below 0.33 for

molecular weights above 108 Da [171]. To the best of our knowledge, a negative α has not yet

been reported for polysaccharides or biopolymers. Only synthetically produced, highly ordered

dendric macromolecules such as polyether dendrimers show a similar molecular weight

dependence for the intrinsic viscosity [180,181].

In addition to α, the intrinsic viscosity can be used to obtain the Huggins coefficient kH, which

describes the nature of interactions or the affinity in a polymer-solvent system using the second

term of the Huggins equation (equation 1). Moreover, kH is a measure of solvent quality and

can provide additional information about polymer-polymer interactions. Below 107 Da, kH was

found to be largely independent of the molecular weight with values of 0.75 to 0.95 (Fig I-6B).

Since the kH values of levan were located slightly above the theta value (~0.6), poor solvent

properties of distilled water at 20 °C for levan can be concluded [182]. Ehrlich et al. [162] found

similar values by measuring fractions of a S. salevarius levan at comparable molecular weights.

Above 108 Da, kH increased with increasing molecular weight indicating that polymer-solvent

or polymer-polymer interactions changed continuously. According to Dort [183], an increase

in the Huggins coefficient can be explained by associative inter- or intramolecular interactions.

Since positive second virial coefficients were found for the levan of G. albidus intramolecular

attraction can be excluded [163].

Manuscript I

I-5.5 General Discussion

The results of the DLS, MALLS and viscosity measurements indicate that the G. albidus levan

conformation can be divided into three domains. At low molecular weights (< 5.5·105 Da), the

shape quotients of the radii, α and ν suggest a compact random coil structure. In the intermediate

region around 107 Da, a v of approximately 0.33 and a largely molecular weight-independent

intrinsic viscosity suggest a compact spherical structure. Above 108 Da, this spherical-shaped

structure is retained, however, a ν < 0.33 and a negative α suggest an increasing sphere density

with increasing molecular weight. For the analysis of the results, three domains have been

discussed. However, the transitions between the domains are not sharply defined and it might

be seen as a continuous transition from a random coil into a spherical polymer whose density

increases with increasing molecular weight.

The reason for these conformational changes can be attributed to a higher density of

intramolecular interactions with increasing molecular weight. As the chain length increases, the

number of intersegmental contacts and therefore, the number of intramolecular interactions per

chain segment increases. This causes a restriction of movement of the individual fructose

segments in the molecule and a restricted rotation around the glycosidic bonds [179]. Benigar

et al. [14] also proposed that intermolecular attractions become stronger with increased

molecular weight due to greater entanglement probabilities. A further possible explanation for

the structural change to a more compact molecular structure could be an increasing number of

branches with increasing molecular weight. Previous methylation analysis of unfractionated

LevF, Lev4 and Lev5 showed a rather low degree of branching. Furthermore, the ratio between

2,6- and 1,2,6-linked fructose monomers was almost equal for all three samples [15]. Detailed

branching analyses of the fractionated levan samples obtained in the present study could hence

help to validate the latter theory.

Attractive intramolecular interactions are most likely based on hydrogen bonds, considering the

structure of the fructose molecule. Moreover, the molecular weight-dependent Huggins

coefficient, which was found at high molecular weights, indicates the presence of hydrogen

bonds: at a critical molecular weight (108 Da) an increased level of intramolecular hydrogen

bonds might alter the solvent affinity and therefore the macromolecular conformation of levan.

Because of these changes, which are progressively pronounced with increasing molecular

weight, the Huggins coefficient increases. This explanation is supported by Stivala and Bahary

[58] who detected an increase in levan intrinsic viscosity and RG in solution by adding urea and

increasing the temperature. Both actions interfere with the formation of the intramolecular

hydrogen bonds causing the polymer to swell.

The change in macromolecular conformation of G. albidus levan is furthermore supported by

experiments reported on inulin, which showed similar conformation changes in the same

molecular weight range [173,179]. Both β-2,6 linked levan and the β-2,1 linked fructose

polymer inulin exhibited a low intrinsic viscosity and a compact molecular structure, however,

no decrease in intrinsic viscosity of inulin at high molecular weights has yet been reported.

Manuscript I

I-6 Conclusion

The present study demonstrates the transformation of G. albidus levan from a compact random

coil structure to a dense sphere with increasing molecular weight. Moreover, the structure of

the spherical levan molecule becomes more and more compact with increasing molecular

weight indicated by a decline in intrinsic viscosity with increasing molecular weight (M > 108

Da). The structure of a polysaccharide in solution determines its techno-functional properties.

Therefore, the findings contribute to establishing the structure-function relationship of levan.

Moreover, the results contribute to the mechanistic understanding for the potential use of levan

in food, cosmetics and other industrial applications.

Manuscript II

Determination of specific and non-specific protein-protein

interactions for β-lactoglobulin by analytical

ultracentrifugation and membrane osmometry experiments

Soft matter (2022), accepted manuscript

The publication is online available at https://doi.org/10.1016/j.ijbiomac.2020.06.019

Authors

Maximilian J. Uttinger1*; Christoph S. Hundschell2*; Vanessa Lautenbach1; Srdjan Pusara3;

Sabrina Bäther2; Timon R. Heyn4; Julia K. Keppler5, Wolfgang Wenzel3; Johannes Walter1;

Mariana Kozlowska3; Anja M. Wagemans2; Wolfgang Peukert1

1: Interdisciplinary Center for Functional Particle Systems, Friedrich-Alexander-Universität

Erlangen-Nürnberg, Germany

2: Food Colloids, Technische Universität Berlin, Germany

3: Institute of Nanotechnology, Karlsruhe Institute of Technology, Germany

4: Institute of Human Nutrition and Food Science, Division of Food Technology, Kiel

University Germany

5: Food Process Engineering, Wageningen University, Netherlands

*: These authors equally contributed to the manuscript

Manuscript II

II-1 Abstract

Protein-protein interactions are essential for the understanding of biological processes. Specific

protein aggregation is an important aspect for many biological systems. In particular,

electrostatic interactions play the key role for protein-protein interactions, as many amino acids

have pH-dependent charge states. Moreover, protein dissociation is directly related to

the solution pH, ionic strength, temperature and protein concentration. The subtle interplay

between different specific and non-specific interactions is demonstrated for β-lactoglobulin

with a focus on low salt concentrations, thus mimicking technically relevant processing

conditions. β-lactoglobulin is a well-characterized model system, proven to attain its monomer-

dimer equilibrium strongly dependent upon the pH of the solution. In this manuscript, we

present a unique combination of analytical ultracentrifugation and membrane osmometry

experiments, which quantifies specific and non-specific interactions, i.e. in terms of the dimer

dissociation constants and the second osmotic virial coefficient, at pH 3.0 and 7.0 and sodium

chloride concentrations of 10 mM and 100 mM. This provides direct insight into protein-protein

interactions for a system with a concentration-dependent monomer-dimer equilibrium.

Moreover, using a coarse-grained extended DLVO model in combination with molecular

dynamics simulations, we quantify non-specific monomer-monomer, monomer-dimer

and dimer-dimer interactions as well as the binding free energy of β-lactoglobulin dimerization

from theoretical calculations. The experimentally determined interactions are shown to be

mainly governed by electrostatic interactions and further agree with free energy calculations.

Our experimental protocol aims to determine non-specific and specific interactions for a

dynamically interacting system and provides an understanding of protein-protein interactions

for β-lactoglobulin at low salt concentrations.

Figure II-1: Graphical abstract of manuscript II.

Manuscript II

II-2 Introduction

Understanding the nature of protein-protein interactions (PPIs) is essential to explain biological

systems and their function in biological processes. PPIs determine the properties of proteins,

such as protein aggregation, assembly, gel formation or stabilization, thus influencing their

subsequent biological function and commercial use [28–31]. Moreover, an essential aspect of

the systems behaviour is the statistical mechanics of the system, which can be described through

the chemical potential of the system [184,185]. Both, specific and non-specific interactions are

the driving force for the particular behavior of macromolecules. On the one hand, specific

interactions refer to a directed oligomerization, i.e. the formation of a new species [186–189].

On the other hand, non-specific interactions refer to van der Waals forces (vdW) and

electrostatic interactions, where the latter originate from dipole-dipole and charge-charge

interactions. In particular, non-specific interactions significantly affect transport properties such

as sedimentation and diffusion of proteins and their oligomers at finite particle concentrations,

which can be taken into account by respective interaction parameters, i.e. the Gralen coefficient

and the second virial coefficient [190]. In this context, electrostatic interactions are a central

aspect of PPIs, as many amino acids have pH-dependent charge states [191]. In aqueous

solution, especially upon changes of the ionic strength, controlled protein aggregation and

oligomerization are significantly pronounced in the proximity of the isoelectric point, hence for

a protein net charge of zero. Yet, protein aggregation and oligomerization also occur at pH

values dissimilar to the isoelectric point for changed solvent conditions or in different solvents

such as ethanol [192]. In this manuscript, we target the experimental determination of both,

association (specific PPIs) and concentration non-ideality (non-specific PPIs) for dynamically

interacting systems, which remains a great challenge and requires careful experimental

protocols [3]. The understanding of such systems is especially relevant with respect to

applications in food technology, where controlled protein oligomerization can be induced by

mechanical stress and can be controlled or prevented by adjusting the salt concentration

[35,193–195]. In particular, protein aggregation is a relevant mechanism in food applications

[196]. Moreover, β-lg is considered a protein relevant for applications as recombinantly

produced milk proteins [197].

In this context, β-lactoglobulin (β-lg) is one of the most relevant proteins, which shows different

oligomerization patterns and aggregate contributions upon changes of the solution pH [198].

The targeted β-lg aggregation was reported to result in amyloid and amyloid-like aggregates,

which is desired for various applications [199]. β-lg is a well-characterized model system,

which has also been studied with respect to recombinant modification within the amino-acid

sequence [197]. β-lg monomers, which carry a high charge apart from the isoelectric point, are

dominantly present for pH ≤ 3.0 and for pH > 8, otherwise, dimers and higher oligomers, such

as octamers, are present [35]. β-lg dimers are in equilibrium with monomers as a function of

salt concentration, temperature and protein concentration. In case of a sufficient screening or

absence of electrostatic interactions, e.g. by the addition of ions which suppresses the

electrostatic interactions or a change in the solution pH, the formation of hydrogen bonds is

Manuscript II

enabled, which stabilize the dimer states [192,198]. The monomer-dimer equilibrium of

recombinant β-lg with a modified N-terminus is not affected by the small changes within the

amino-acid sequence since no significant changes of the quaternary structure of the protein

were observed [197].

Monomer–dimer equilibria of β-lg can be explained from the PPIs at specific solution

conditions. They are described by the interaction potential between macromolecules in aqueous

dispersions, i.e. by the potential of mean force (PMF). Direct measurement of the PMF and the

PPIs contributions is limited. Information about the average effective interactions in a two-body

system is provided by the osmotic second virial coefficient B22 [200–202]. When considering

proteins as spherical particles, B22 is related to a PMF as given in equation 1:

𝐵22 =1

2𝑁𝐴

𝑀2∫(1−𝑒−𝑊22(𝑎)

𝑘𝐵𝑇)4𝜋𝑎2𝑑𝑎

∞

(1)

Here, a is the intermolecular center-to-center distance between two proteins and M is the protein

molar mass, W22(a) represents the PMF between two macromolecules. Equation 1 holds true

for dilute systems in which higher-order interactions are negligible and higher-order virial

coefficients can be excluded. Notably, it is possible to formulate a more generalized version of

equation 1, which is introduced within our manuscript [203].

From a theoretical point of view, the free energy of the salt-dependent binding of β-lg can be

investigated using molecular dynamics (MD) simulations, but sampling of protein-protein

configurations in the total PMF, in equation 1, beyond the β-lg dimer from the crystal structure,

was not yet reported [204]. According to the DLVO (Derjaguin, Landau, Verwey, and

Overbeek) theory, the PMF consists of the electric double-layer forces and vdW interactions

[205]. DLVO theory enables the basic understanding of forces between charged interacting

surfaces in aqueous solutions. It has been reported to predict B22 in good correlation with

available experimental measurements, however, traditional DLVO is an approximate method

with a set of limitations [188,206]. A better description of solution induction effects on the PPIs

between proteins was introduced by several post-DLVO theories, e.g. reported by Herhut et al.

(2016) or Kastelic et al. (2015), known as extended DLVO, i.e. xDLVO [207,208]. Recently,

the calculation of the PPIs beyond the spherical-shaped particles, as commonly used in DLVO,

was introduced within a xDLVO coarse-grained (CG) model [203]. Beyond the DLVO theory

and the extended models, W22(a) can be estimated using MD and Monte Carlo simulations with

both all-atom and CG protein representations [209–211]. The results of these computationally

intensive methods have shown that even if the detailed structural and charge characteristics of

the protein are properly preserved, other macroscopic features significantly affect the total

PMF. Therefore, all-atom simulations are limited for B22 predictions and a rescale of the PMFs

is necessary [211].

From an experimental point of view, analytical ultracentrifugation (AUC) is a well-established

technique for the analysis of individual macromolecules and (nano-)particles in solution, also

with respect to concentration-non-ideality [190,212,213]. From the acquired sedimentation

Manuscript II

profiles, the sedimentation and diffusion coefficients can be determined for each individual

species. From these parameters, the molar mass distribution of the sample is typically retrieved.

Moreover, the analysis of the sedimentation profiles allows for a determination of association

and dissociation processes for dynamically interacting systems, such as β-lg [62,214].

Furthermore, the determination of non-ideality parameters and protein self-association from the

analysis of AUC data has already been addressed by the work of Roark and Yphanties

[215,216]. Furthermore, recent software developments enabled the direct determination of non-

ideality from SV-AUC experiments via the software packages SEDANAL and SEDPHAT

[190,214,217].

Membrane osmometry serves as a powerful experimental tool for the determination of osmotic

second virial coefficients. However, the reduced osmotic pressure, as measured by membrane

osmometry at varying protein loading concentrations, is directly affected by the association or

dissociation constant of a monomer-dimer system [62]. Thus, the dissociation process must be

known in order to study non-specific PPIs (by B22). In this manuscript, we establish a

combination of AUC and membrane osmometry as a powerful tool to concurrently characterize

both non-specific and specific PPIs for a dynamically interacting system.

For the evaluation of the experimental protocol, the extent of the non-specific PPIs on the β-lg

monomer-dimer equilibrium as a function of pH and salt concentration is analyzed with a focus

on low salt concentration conditions in order to mimic conditions, which are often associated

with conditions in food processing [218]. In particular, we determine the extent of specific PPIs

in terms of the dimer dissociation constant for the system β-lg AB from AUC experiments, a

relevant variant of β-lg in food technology [197]. With the known dissociation constants of β-

lg, membrane osmometry measurements enable the experimental determination of the

molecular weight-corrected osmotic pressure, which provides the second virial coefficients for

the β-lg monomer-dimer equilibrium. In this way, we establish an experimental protocol for the

determination of PPIs for a system with a concentration-dependent monomer-dimer

equilibrium.

In order to support the experimental study with theoretical predictions, the osmotic second virial

coefficients are calculated using the recently reported xDLVO-CG method, with CG

representation of the protein [203]. xDLVO-CG calculations aim to estimate the impact of non-

specific interactions in β-lg monomer-dimer equilibria. Moreover, we relate the experimentally

measured dimer dissociation constant, which is directly converted to the Gibbs free energy, to

the extent of non-specific PPIs, i.e. the extent of electrostatic interactions. This is further

supported by the free energy calculations of the β-lg system using MD simulations in

combination with an umbrella sampling approach. Finally, based on our results from the

experimental protocol, we aim to provide a qualitative prediction for controlled protein

oligomerization through the osmotic second virial coefficient.

Manuscript II

II-3 Theoretical Background

II-3.1 Dimer Dissociation

Dimer dissociation is usually described by a chemical reaction of second order. Thus, a

monomer-dimer equilibrium is modeled according to [62,197]:

𝐴2 𝑘𝑓

↔

𝑘𝑏 2𝐴

(2)

The dimer and monomer are denoted as A2 and A. The reaction constants for the forward and

backward reaction are denoted kf and kb. These finally lead to the dimer dissociation constant

KD, which is provided by the ratio of the reaction constants and the concentrations of the

monomer and dimer A and A2, respectively, according to:

𝐾𝐷= 𝑘𝑓

𝑘𝑏=[𝐴]2

[𝐴2]

(3)

Here, the monomer and dimer concentration [A] and [A2] are provided in molar concentrations,

i.e. mol/m3.

II-3.2 Fundamentals of analytical ultracentrifugation

The sedimentation coefficient is defined as the velocity u acquired by a particle in a centrifugal

field



2r and is given by [212]:

𝑠= 𝑢



2𝑟=𝑚𝑝(1−𝑣𝜌𝑠)

𝑓

(4)

The mass of the sedimenting species is denoted as mP with its partial specific volume 𝑣 and

translational friction coefficient f. The solvent density is denoted



S. The diffusion coefficient

of a protein or particle is described by the Stokes-Einstein relation. For known hydrodynamic

diameter xH, the diffusion coefficient is given by [219]:

𝐷= 𝑘𝐵𝑇

𝑓=𝑘𝐵𝑇

3𝜋𝜂𝑥𝐻

(5)

The Boltzmann constant is denoted as kB, the temperature as T and the solvent viscosity is



The evolution of particle concentration c in a sector-shaped centrifugal cell is described by

Lamm’s equation, which is applied to evaluate the measured sedimentation profiles, from

which the sedimentation coefficient and the diffusion coefficient distribution are determined.

Lamm’s equation is derived from a mass conservation approach taking into account the

sedimentation flux and the local diffusive flux and is given by [213]:

𝜕𝑐

𝜕𝑡 =𝐷(𝜕2𝑐

𝜕𝑟2+1𝜕𝑐

𝑟𝜕𝑟)−



2𝑠(𝑟𝜕𝑐

𝜕𝑟+2𝑐)

(6)

The radial position within the centrifugal cell is denoted as r and the angular rotor velocity is



Manuscript II

II-3.3 Concentration-dependent sedimentation and diffusion coefficient

In the case of moderate and high molar concentrations, the translation friction coefficient has

shown to be concentration-dependent [220,221]. This directly translates into a concentration-

dependent sedimentation coefficient s(c), which is calculated according to [222]:

𝑠(𝑐)= 𝑠0

1+𝑘𝑠𝑐

(7)

The sedimentation coefficient at infinite dilution is s0. The Gralen coefficient ks is an

empirically introduced constant. Furthermore, the (protein) mass concentration is provided in

units of kg/m3. Apart from hydrodynamic effects, the thermodynamic contribution must be

considered. In particular, the virial expansion of the reduced osmotic pressure is provided by

[190]:

𝑅𝑇𝑐 =1

𝑀(1+𝐵22𝑀𝑐+𝑂(𝑐2))

(8)

M is the molar mass of the species with the osmotic pressure



. The universal gas constant is

R. The second virial coefficient is denoted as B22, which accounts for concentration non-

ideality. In the context of our results, we apply the second virial coefficient in order to account

for non-specific protein-protein interactions. It can be pointed out that the entire protein-protein

interactions in solution determine the value of the second virial coefficient B22, which has

positive values for globally repulsive protein-protein interactions and negative values in the

case of global attraction [221]. Higher-order terms are referred to as O(c2) and take into account

non-linear effects including second-order and higher terms. These effects are typically observed

at high molar concentrations [190]. At higher protein molar concentrations, higher-order terms

are required in order to describe non-linear effects such as particle agglomeration and cluster

sedimentation [223–225]. Moreover, the ideal contribution of the osmotic pressure of the

solution is proportional to the number of molecules in solution, which is linked to the

dimerization constant, which has been introduced in equation 3. The relationship between these

two phenomena describes a central aspect of this manuscript.

From equation 8, a concentration-dependent diffusion coefficient D(c) can be derived:

𝐷(𝑐)=𝐷01+2𝐵22𝑀𝑐−𝑣𝑐+𝑂(𝑐2)

1+𝑘𝑠𝑐

(9)

A detailed derivation of equation 9 from equation 8 is provided in literature [185]. The diffusion

coefficient at infinite dilution is D0. Furthermore, there are thermodynamic approaches to

account for the presence of protein oligomers during SV-AUC experiments for a defined

number of species (e.g. dimeric and trimeric oligomers of a protein) in solution [221,226].

Correia et al. showed the analysis of SV-AUC experiments with respect to concentration-

dependent sedimentation and diffusion coefficient and expressed the interactions constants as

matrices, with elements ks,ij and B22,ij [226]. The individual terms represent self-interactions

(diagonal matrix elements) and cross-correlations (non-diagonal matrix elements) between the

Manuscript II

individual defined species. In the case of two species in solution (i.e. monomers and dimers),

the concentration-dependent sedimentation coefficient s1(c) of the first species is written as

[226]

𝑠1(𝑐)= 𝑠1

1+𝑘𝑠,11𝑐1+𝑘𝑠,12𝑐2

(10)

The sedimentation coefficient at infinite dilution of the first species is s10. The mass

concentrations of the two individual species are denoted c1 and c2, respectively. Furthermore,

the respective concentration-dependent diffusion coefficient D1(c) is expressed as [226]:

𝐷1(𝑐)=𝐷1

0[1+2𝐵22,11𝑀𝑃,1𝑐1+2𝐵22,12𝑀𝑃,2𝑐2]

1+𝑘𝑠,11𝑐1+𝑘𝑠,12𝑐2

(11)

The diffusion coefficient at infinite dilution of the first species is D01. The molar masses of the

two individual species are denoted as MP,1 and MP,2, respectively.

II-3.4 Second virial coefficient from membrane osmometry measurements

The molar mass in equation 8 depends on the degree of dimerization in a monomer-dimer

equilibrium system like β-lg and can be represented by:

𝑀=𝑤𝑀

𝑀𝑀+𝑤𝐷

𝑀𝐷=1−𝑤𝐷

𝑀𝑀+𝑤𝐷

𝑀𝐷

(12)

Here, wM and wD are the weight fractions and MM and MD represent the molecular mass of the

monomer and the dimer, with MM = 0.5 MD and wM = 1 - wD. If the concentration is sufficiently

low and higher-order interactions can be neglected, the reduced osmotic pressure of a monomer-

dimer system is given by [163]:

𝑅𝑇𝑐𝑤=1

1+𝑤𝐷𝑀𝐷+𝐵22𝑐𝑤

(13)

The weight concentration of the protein is denoted cw. According to Schaink and Smit (2000),

the weight fraction wD for an ideal protein solution is given by [37,163]:

𝑤𝐷=1+𝑀𝐷𝐾𝐷

8𝑐 −√(𝑀𝐷𝐾𝐷

8𝑐 +1)2−1

(14)

By insertion of equation 14 into equation 13 and correcting for the reduced osmotic pressure

by subtracting the molecular weight dependent term in equation 13, B22 can be determined in

the case of known osmotic pressure and dissociation constant KD. When the molecular weight

corrected osmotic pressure is plotted against the protein concentration, a straight line is obtained

with a y-intercept at zero protein concentration. The slope gives B22.

As stated before, if there is more than a single species in the solution, the second virial

coefficient is associated with several contributions, namely self-interaction as well as cross-

correlations. This could already be seen in equation 11 and links this equation to equations 8,

12 and 13. In the case of membrane osmometry, a single value for the osmotic second virial

coefficient B22 from a concentration-dependent and molecular weight-corrected osmotic

Manuscript II

pressure is obtained from equation 13, which includes all contributions from monomer-

monomer interactions BMM and dimer-dimer interactions BDD as well as monomer-dimer

interactions BMD [3,187,190,226]. In the case of a monomer-dimer system, the second virial

coefficient consists of all contributions according to:

𝐵22 =𝐵𝑀𝑀

𝑀𝑀

2+2( 𝐵𝑀𝐷

𝑀𝑀𝑀𝐷−𝐵𝑀𝑀

𝑀𝑀

2)𝑤𝐷+(𝐵𝑀𝑀

𝑀𝑀

2−2 𝐵𝑀𝐷

𝑀𝑀𝑀𝐷+𝐵𝐷𝐷

𝑀𝐷

2)𝑤𝐷

(15)

Combining equations 13 and 15 leads to an expression for the reduced osmotic pressure in a

monomer-dimer system according to [227]:

𝑅𝑇𝑐𝑤=(1−𝑤𝐷

𝑀𝑀+𝑤𝐷

𝑀𝐷)+

+[𝐵𝑀𝑀

𝑀𝑀

2+2( 𝐵𝑀𝐷

𝑀𝑀𝑀𝐷−𝐵𝑀𝑀

𝑀𝑀

2)𝑤𝐷+(𝐵𝑀𝑀

𝑀𝑀

2−2 𝐵𝑀𝐷

𝑀𝑀𝑀𝐷+𝐵𝐷𝐷

𝑀𝐷

2)𝑤𝐷

2]𝑐𝑤

(16)

II-3.5 Interaction potential from xDLVO-CG calculations

In the present study, we use a recently reported extended DLVO approach, i.e. xDLVO-CG,

for the interaction potential W22(a) (equation 1) between β-lg monomers and dimers [203]. The

β-lg protein and protein oligomers are represented by the shape-based CG model, which is

visualized in Figure II-2. W22(a) is calculated as a sum of electrostatic, Wel(a), dispersion,

Wdisp(a), osmotic, Wosm(a) and ion-protein Wi-prot(a), interactions between the β-lg monomers

and dimers binary systems:

𝑊22(𝑎)=𝑊𝑒𝑙(𝑎)+𝑊𝑑𝑖𝑠𝑝(𝑎)+𝑊𝑜𝑠𝑚(𝑎)+𝑊𝑖−𝑝𝑟𝑜𝑡(𝑎)

(17)

Electrostatic interactions are calculated within DLVO theory using Debye-Hückel theory, to

account for interparticle interactions in the presence of electrolytes [205,228,229]:

𝑊𝑒𝑙(𝑎)= ∑ ∑ 𝑍𝑖𝑍𝑗𝑒2𝑒𝜅(𝑑𝑖𝑗−𝑎𝑖𝑗)

4𝜋𝜀0𝜀𝑟𝑎(1+𝜅𝑑𝑖𝑗

4)2

𝑁2

𝑗=1

𝑁1

𝑖=1 , 𝑎𝑖𝑗 >𝑑𝑖𝑗 +2𝜎

(18)

Here, a is the center-of-mass (COM) distance between two proteins, N1 and N2 are the total

numbers of CG beads of each protein, dij is the initial distance between beads i and j when

proteins are in starting position, aij is the current (variable) distance between beads during

pulling calculations, σ is the length of water layer around a protein (0.1 nm), εr is the relative

permittivity, Zi and Zj are the charges of each bead and κ is the inverse Debye length, which is

given by:

𝜅=√2𝑁𝐴𝑒2𝐼

𝜀0𝜀𝑟𝑘𝐵𝑇

(19)

I is the ionic strength. The dispersion potential Wdisp(a), which is used to describe the attraction

forces between macroscopic uncharged colloidal particles, is calculated as a result of the

summation of vdW interactions between CG beads representing β-lg proteins, as can be seen in

Manuscript II

Figure II-2 [230]. Here, these interactions are calculated using the Hamaker constant AH

estimated experimentally (see materials and methods):

𝑊𝑑𝑖𝑠𝑝(𝑎)=∑ ∑ 𝐴𝐻

12 1

𝑁1𝑁2[𝑑𝑖𝑗

𝑎𝑖𝑗

2−𝑑𝑖𝑗

2+𝑑𝑖𝑗

𝑎𝑖𝑗

2+2𝑙𝑛(1−𝑑𝑖𝑗

𝑎𝑖𝑗

2)]

𝑁2

𝑗=1

𝑁1

𝑖=1 , 𝑎𝑖𝑗 >𝑑𝑖𝑗 +2𝜎

(20)

In addition to the Hamaker-based approach, we calculated B22 using the dispersion interactions

based on the Lennard-Jones potential between β-lg molecules (Fig. S II-1). The osmotic

potential Wosm(r) between two proteins due to salt ions exclusion from the protein interspace at

short distances, which raises local osmotic pressure imbalance and causes additional attractive

interaction between proteins, was calculated according to equation 21 [231]:

𝑊𝑜𝑠𝑚(𝑎)= ∑ ∑ 1

𝑁1𝑁24𝜋𝑘𝐵

3𝑇𝐷𝑖𝑗

𝑁2

𝑗=1

𝑁1

𝑖=1 𝜌3(1−3𝑎𝑖𝑗

4𝐷𝑖𝑗 +𝑎𝑖𝑗

16𝐷𝑖𝑗

3), 𝑎𝑖𝑗 +2𝜎≤𝑎𝑖𝑗 ≤2𝐷𝑖𝑗

(21)

where Dij is defined by equation 22 with R3 as the mean hydrated radius of the salt (taken as a

sum of anion and cation radii) and ρ3 as the salt density:

𝐷𝑖𝑗 =𝑑𝑖𝑗 +𝑅3+𝜎

(22)

The last term in the PMF (equation 17), i.e. the ion-protein potential, describes the total

dispersion interaction between protein and all ions in its surrounding. In this model, the protein

is represented as an ideal sphere with the charge Z, while ions are placed non-uniformly around

the protein sphere according to the Gouy-Chapman model. The total potential is calculated by

integrating the contributions of each ion according to:

𝑊𝑖−𝑝𝑟𝑜𝑡 =−4𝜋𝐵𝑎𝑛𝑖𝑜𝑛∫𝑐𝑏𝑢𝑙𝑘𝑒−𝑧𝑎𝑛𝑖𝑜𝑛𝜙(𝑎)

𝑘𝐵𝑇

𝑎𝑑𝑎

𝑅𝑃+𝑑

𝑅𝑃+𝜎

−4𝜋𝐵𝑐𝑎𝑡𝑖𝑜𝑛∫𝑐𝑏𝑢𝑙𝑘𝑒−𝑧𝑎𝑛𝑖𝑜𝑛𝜙(𝑎)

𝑘𝐵𝑇

𝑎𝑑𝑎

𝑅𝑃+𝑑

𝑅𝑃+𝜎

(23)

where Banion and Bcation represent the ion-macroion dispersion coefficients taken from literature,

RP is the protein radius, d is the thickness of the spherical shell around a protein, in which ions

are placed, zcation/zanion are the charges of the cation/anion, cbulk is the salt concentration and φ(a)

is the electrostatic potential around a protein sphere with charge Z calculated from [232,233]:

𝜑(𝑎)=𝑍2𝑒2𝑒𝜅(2𝑅𝑃−𝑎)

4П𝜀0𝜀𝑟(1+𝜅𝑅𝑃

2)2 𝑎>2(𝑅𝑃+𝜎)

(24)

Notably, throughout our xDLVO calculations, salt-specific ion-macroion dispersion

coefficients are taken in order to calculate the ion-protein dispersion interaction of ions around

proteins as a function of protein COM distance. This is in accordance with approaches taken in

literature [232,234–238]. The second osmotic virial coefficient between the β-lg monomers and

Manuscript II

dimers was calculated for different sampled configurations by the numerical integration of the

average PMF according to equation 25:

𝐵𝐵22 =1

16𝜋𝜋2𝑁𝑁𝐴𝐴

𝑀𝑀2∫ ∫ ∫ ∫ ∫ ∫ (𝑒𝑒−𝑊𝑊

𝑘𝑘𝑘𝑘 −1)

∞

𝜋𝜋

2𝜋𝜋

𝜋𝜋

2𝜋𝜋

0𝑟𝑟12

2𝑑𝑑𝑟𝑟12𝑠𝑠𝑠𝑠𝑠𝑠(𝜃𝜃)𝑑𝑑𝜃𝜃𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

(25)

Here, Euler angles α, β and γ specify orientation and ϕ and θ angles specify the angular

orientation of the second protein with respect to the first protein, which is placed at the center

of the coordinate system. M denotes the molar mass of the protein, i.e. of two β-lg monomers,

of one monomer and one dimer, and of two dimers for BMM, BMD and BDD, respectively.

According to the reconstructed structure of the β-lg (3ph5 code), as described in the materials

and methods, a molar mass of β-lg monomer of 18.182 g/mol and 18.156 g/mol was used for

β-lg at pH 3.0 and pH 7, respectively.

II-4 Materials and Methods

II-4.1 Coarse-grained molecular calculations

The original DLVO model accounts for electrostatic and vdW interactions between two charged

spherical particles. To gain an impact of other non-specific PPIs and to account for the

differences in the charge distribution over the protein, we used a CG representation of

monomeric β-lg and its oligomers, which is visualized in Figure II-2.

The all-atom structure of β-lg was taken from the Protein Data Bank with the 3ph5 code [239].

The chosen structure contains two β-lg units placed in a crystallographic cell, which was taken

to represent the β-lg dimer. Both protein units have several missing residues (chain A: ILE 18,

VAL 19, TYR 115, LYS 117, chain B: VAL 19, THR 20, GLN 21, THR 22, ASP 49). They

were modeled by Swiss Model program [240]. The reconstructed structures were protonated at

pH = 3.0 and pH = 7.0 using the PROPKA method (version 3.3) and PDB2PQR online web

server [241,242]. This resulted in the charge of the β-lg monomer of +18e- and -8e- at pH 3.0

Figure II-2: Coarse-grained representation of β-lg monomer (A) and dimer (B) used to

calculate the second osmotic virial coefficient B22 by means of xDLVO

-CG.

Manuscript II

and pH 7, respectively (while experimentally determined charges are +20e- at pH 2.5 and -9e-

at pH 7.5) [243]. The reconstructed and protonated all-atom structures were used to map the β-

lg into the CG representation (Fig. II-2; variant β-lg -A). One CG bead equals to approximately

500 atoms of a protein (6 and 12 beads for the β-lg monomer and dimer, respectively) with the

center of the bead placed in the COM of atoms, which constitute each bead, estimated by the

neural the bead placed in the COM of atoms, which constitute each bead, estimated by the

neural network algorithm within the shape-based CG model, implemented in VMD program

(version 1.9.3) [244,245]. Each bead has a charge equal to the sum of atomic charges, therefore

depends on the specific protonation state of the β-lg residues represented by a bead. equations

20 to 25 were calculated by summing interactions between the corresponding bead pairs from

both CG-proteins. The PMF and the corresponding B22 were calculated by the in-house code.

Calculations were performed for β-lg monomers, dimers and mixtures at pH 3.0 and pH 7.0

with salt concentrations of 10 mM and 100 mM sodium chloride. A Hamaker constant of 5.1

kBT was taken from experimental data to calculate the dispersion potential [194].

B22 was calculated by numerical integration of the average PMF according to equation 25 and

the procedure described by Pusara et al [203]. Conformational sampling of starting protein-

protein configurations was done performing 16 different rotations at each of the 83 starting

radial positions, resulting in 1328 starting configurations. Each of them was used for a separate

PMF calculation based on pulling one β-lg protein along a vector connecting the COM of the

second β-lg protein. The PMF up to a COM distance of 30 nm was calculated. Finally, B22 was

calculated using an average of all PMFs, which corresponds to averaging along all different

configurations (equation 25).

II-4.2 Umbrella sampling simulations

Umbrella sampling simulations (US) between β-lg monomers at studied experimental

conditions were performed using the CHARMM36m force field and SPC water model as

implemented in the GROMACS package (version 2019.2) [246–248]. All calculations were

performed using periodic boundary conditions with a rectangular box of the size 18.0 × 9.5 ×

9.5 nm3, where the β-lg monomers were aligned to the x-axis with respect to their center-to-

center distance vector. Structures of the reconstructed and protonated β-lg proteins, as discussed

before, were charge neutralized and used in all further simulations. Hydrogen atoms at specific

pH were added according to PROPKA method49 (version 3.3) and PDB2PQR online web

server [225]. Protein protonation states at specific pH were assigned by PROPKA method49

(version 3.3) and PDB2PQR online web server. Na+ and Cl- ions were added to fulfill salt

concentrations of 10 mM and 100 mM, used in the experiments. All systems were initially

minimized by the steepest descent algorithm during 30.000 steps with position restraints applied

to proteins heavy atoms. Equilibration under canonical (NVT) and later under constant-pressure

(NPT) ensembles at 300 K and for 400 ps/each were performed using a Berendsen thermostat

[249]. The Berendsen weak coupling method was also used to isotropically maintain pressure

at 1.0 bar. All simulations were performed with the timestep of 2.0 fs. Short-range nonbonded

Manuscript II

interactions were cut off at 1.2 nm. The full electrostatic interactions beyond 1.2 nm were

evaluated by the particle mesh Ewald (PME algorithm) [250]. To optimize the US setup, pulling

simulations along the x-axis for 1.2 ns using the spring constant of 1000 kJ/(mol nm2) and a

pull rate of 0.005 nm/ps were performed. This setup was applied for all β-lg systems except for

a solution pH of 3.0 and a salt concentration of 100 mM sodium chloride. Here, the spring

constant was 1500 kJ/(mol nm2). Proteins were pulled from their starting position (COM

distance of 3.0 nm) up to a COM distance of 8.5 nm. The snapshots from the collected pulling

trajectories were used to generate starting configurations for the respective US windows. An

asymmetric distribution of sampling windows was used: the window spacing of 0.0625 nm (or

smaller) and 0.125 nm was used for COM distances shorter than 4.1 nm and longer than 4.2 nm,

respectively. In total, 61 US windows were generated. In each window, the system was

equilibrated using NPT ensemble at 300 K and 1.0 bar for 400 ps with the following 20 ns MD

run using NPT ensemble with Nosé-Hoover thermostat and Parrinello-Rahman barostat

[251,252]. Analysis of all US simulations was performed with the weighted histogram analysis

method (WHAM) [253].

II-4.3 β-lactoglobulin

β-lg AB was isolated from bovine whey protein isolate (Bipro, Agropur Diary Cooperative Inc.,

Minnesota, USA). The protein was isolated according to the method described by Keppler et

al. (2014) with slight modifications [254]. The ultrafiltration was replaced by dialysis against

distilled water for 3.0 days using BioDesingnDialysi TubingTM (Thermo Fischer Scientific,

Waltham Massachusetts, USA) with a molecular weight cut-off of 14 kDa. Prior to freeze-

drying, the solution was adjusted to a pH of 7.0 using 100 mM HCl and 100 mM NaOH (Carl

Roth GmbH, analytical grade, Karlsruhe, Germany). The resulting protein powder consisted of

97.6 % native β-lg, 2.0 % denatured β-lg and 0.4 % α-lactalbumin as measured by HPLC

according to Keppler et al. (2014) [254]. According to the reconstructed structure of the β-lg

(3ph5 code), the molar mass of β-lg monomer is 18182 g/mol and 18156 g/mol at pH 3.0 and

pH 7, respectively.

II-4.4 Protein sample preparation for analytical ultracentrifugation

For the determination of the dissociation constant KD, concentration series of β-lg were

measured by analytical ultracentrifugation. β-lg was investigated at a solution pH of 3.0 and 7.0

at salt concentrations of 10 mM and 100 mM sodium chloride (≥99.8%, Carl Roth GmbH,

Karlsruhe, Germany), respectively. Prior to dilution, a highly concentrated β-lg stock solution

with a protein concentration of 1000 µM was prepared at a fixed solution pH and salt

concentration and dialyzed against 600 mL of a solution with the same solution pH and salt

concentration to ensure constant ionic strength within each protein concentration series.

Following the protocol by Schuck et al. (2020), the dialysate was changed after 6.0 hours and

dialysis was continued overnight [255]. Afterward, the β-lg stock solution was filtered using

syringe filters with 0.2 µm pore size and a 1:20 dilution was prepared subsequently. The filtered

stock solution concentrations were determined via UV-Vis spectrometry using a specific

Manuscript II

extinction coefficient of 17679 cm/M, which was determined beforehand for a wavelength of

280 nm (Fig. S II-2). Protein concentrations between 0.25 µM and 500 µM were prepared via

dilution and measured again with UV-Vis spectrometry to confirm the protein concentration.

In order to ensure a constant ionic strength within the protein dilution series, all protein samples

were diluted with the respective dialysate. The pH was adjusted to the desired value by adding

HCl (0.1 M Honeywell™ Fluka™, Thermo Fisher Scientific Inc, Schwerte Germany) or NaOH

(0.1 M Merck KGaA, Darmstadt, Germany). All solutions were prepared in deionized Millipore

water with a resistivity of at least 17 MΩcm.

II-4.5 Analytical ultracentrifugation experiments

For all sedimentation velocity (SV) experiments, a commercial ultracentrifuge, type OptimaTM

AUC from Beckman Coulter (Krefeld, Germany), was used. The samples were measured at a

fixed rotor speed of 40,000 rpm or 50,000 rpm for 10 hours until complete sedimentation of all

species was observed. The temperature was kept constant at 20 °C. Depending on the sample

and preparation, the wavelength was adjusted in order to obtain the optimal signal during the

SV experiment. SV experiments were conducted using centerpieces with an optical path length

of 12 mm or 3.0 mm in order to adjust the optical signal. When converting intensity data to

absorbance data, the pseudo-absorption of each sample was calculated and analyzed as

described by Kar et al. (2000) [256]. Following the protocol by Schuck et al. (2016, 2020), SV

data were first analyzed with the continuous c(s) model which is implemented in the SEDFIT

software (Version 16-1c) [3,213,255]. The sedimentation coefficient distributions and the

weight-averaged sedimentation coefficients for varying protein concentrations were determined

using the partial specific volume of 0.751 mL/g for β-lg as calculated from Sednterp [257]. The

solvent density and viscosity were set to the values of the solution at the respective salt

concentrations at 20 °C. Determination of the dimer dissociation constant was subsequently

conducted via fitting the isotherms, i.e. weight-averaged sedimentation coefficient for varying

protein concentration at a fixed pH value and salt concentration, using the software SEDPHAT

and following the protocol of Zhao et al. (2020) [3,255].

II-4.6 Protein sample preparation for membrane osmometry experiments

For membrane osmometry measurements, β-lg stock solutions with a protein powder content

of 40 g/L were prepared in 10 mM and 100 mM sodium chloride solution at pH 3.0 and pH 7.0.

The stock solutions were stirred for 1.0 h and stored in a refrigerator overnight. The samples

were diafiltered (ÄKTACrossflowTM, GE Healthcare, Uppsala, Sweden) for precise

adjustment of the ionic strength and the pH value. The volume of the stock solution was

exchanged 10 times with the corresponding, pH-adjusted sodium chloride solution. The

diafiltration was performed according to Hundschell et al. (2020) [163]. To remove any

potential protein aggregates, the diafiltered samples were centrifuged for 30 min at 4.0 °C and

10,000 g. The residue was discarded and the protein concentration of the supernatant was

determined by measuring the absorbance at 278 nm with a Helios Omega UV-vis

Manuscript II

spectrophotometer (Thermo Fisher Scientific, Waltham Massachusetts, USA) using a specific

extinction coefficient of 0.96 L/(g cm).

II-4.7 Membrane osmometry experiments

Osmotic pressure measurements were performed at various protein concentrations as

previously described by Hundschell et al. (2020) [163]. The osmotic second virial coefficient

was determined using equations 12-14.

II-5 Results and Discussion

II-5.1 Coarse-grained molecular B22 calculations

PPIs between the β-lg (β-lg -A) monomers and dimers are highly modulated by the solution

pH, resulting in the total charge per monomer (PROPKA method) of +18e and -8e at pH 3.0

and pH 7, respectively. The dimer binding site of β-lg, stabilized by several H-bonds (often

five), is schematically depicted in Figure II-3 [198]. It is seen that this part of β-lg is highly

positively charged at pH 3, therefore, an assembly into dimers without any salt addition is not

possible. This is changed after an increase of the salt concentration, which is analyzed

subsequently. The interaction potential (equation 17), which we calculated to derive B22,

consists of several potentials. Figure II-4 depicts the contribution of the electrostatic and

dispersion interactions at different pH values and salt concentrations to the overall interaction

potential. We see the highest contribution of the electrostatic repulsion, which drops down

Figure II-3: Graphical representation of the charge state of the β-lg monomer and dimer as a

function of the solution pH. The dimer binding site is indicated. The electrostatic potential was

calculated using an Adaptive Poisson

Boltzmann Solver (APBS) with a default grid dimension,

as implemented in the APBS software

[1].

Manuscript II

significantly when increasing the salt concentration from 10 mM to 100 mM sodium chloride,

especially at pH 3.0. Strong reduction of the repulsion occurs at higher salt concentrations and

upon increasing the solution pH. At the same time, the strength of the dispersion interactions,

calculated using the Hamaker constant (equation 20) and the Lennard-Jones potential (Fig. S

II-1) is one order of magnitude lower, suggesting the dominant role of the non-specific

electrostatic interactions between the β-lg proteins. Similar trends were also observed in the

case of the monomer-dimer and dimer-dimer interactions. This observation with the reported

change of the PMF upon an increase of the salt concentration, which was shown by MD

simulations in combination with a three-dimensional Reference Interaction Site Model (3D-

RISM) solvent model [204].

The contribution of the ion-protein interactions and the osmotic pressure imbalance, i.e. osmotic

potential, to the PMF at low salt concentrations, as used in the present study, are negligible.

The strength of these potentials is in the range of ~10-23 J and 10-22 J at salt concentrations of

10 mM and 100 mM sodium chloride, respectively. The local density distribution and binding

of Cl- anions by charged residues, responsible for the charge screening of the positive charge

of β-lg at pH 3, was shown by Srivastava et al. (2020) [204]. Finally, upon an increase of the

solution pH and the ionic strength, the surface charge of the β-lg protein changes (Fig. II-3),

which causes different PPI patterns and the interplay between non-specific and specific

interactions. Moreover, there is a further change of the ratio between electrostatic repulsion and

attractive vdW forces. The theoretically calculated values for B22 can be seen in Figure II-5.

The dependence of B22 on the salt concentration within the β-lg system is slightly different for

monomer-monomer, monomer-dimer and dimer-dimer interaction (with a larger difference at

pH 3). However, all B22 values at salt concentrations of 10 mM and 100 mM sodium chloride

are rather similar, indicating an equilibrium state. Notably, both monomers and dimers tend to

bind Cl- ions by the charged residues with the same affinity, resulting in a similar mechanism

Figure II-4: Interaction potential W

(a) as a function of the protein-protein COM distance.

The electrostatic interaction potential (W

el) is shown for a salt concentration of 10

mM sodium

chloride (solid lines) and 100

mM sodium chloride (dashed lines) at pH 3.0

(in green) and pH

.0 (in blue) alongside the contribution from dispersion interactions (marked in red).

Manuscript II

of screening the electrostatic repulsion [204]. The values for B22 are listed in Table S II-5. In

Figure II-5A and II-5B, we observe the typical decrease of B22 upon an increase of the salt

concentration, as the electrostatic repulsion is screened and the attraction between β-lg

monomers drives the dimer formation. However, all B22 values at salt concentrations of 10 mM

and 100 mM sodium chloride are rather similar, indicating similar strength of non-specific

interactions between monomers and dimers. Moreover, the decrease of B22 as a function of the

ionic strength is significantly steeper at pH 7, promoting protein assembly. This is caused by

the differently charged states of β-lg with a lower contribution from repulsion. Due to the lower

β-lg charge at pH 7, hence reduced repulsion screening, we further observe B22 values ~ 0

mol/(mLg2) at higher sodium chloride concentrations at pH 7.0. This does not occur at pH 3.0

due to the lower β-lg charge at pH 7.0 and, hence reduced repulsion screening. Values of B22

for β-lg monomers, dimers and mixtures are rather similar at pH 7.0 and pH 3.

A traditional DLVO approach lacks the adequate charge distribution over a spherical particle

(one protein – one particle with a point charge). It should be noted that the traditional DLVO

approach overestimates the second virial coefficients of all species considered by a factor of ca.

1.5 - 2.5 at pH 3.0 and even by a factor of 3.0 at pH 7.0 (Fig. S II-2) due to the lack of adequate

charge distribution and anisotropy over a spherical particle (one protein – one particle with a

point charge) that is accounted for in xDLVO-CG calculations (Fig. S II-3). All-atom and

coarse-grained MD simulations overestimate protein-protein binding affinities [204]. Finally,

within this manuscript, we provide a detailed insight into the nature of PPI interactions and

develop a methodology to quantify non-specific interactions as well as their impact on the

specific PPIs. So far, the extent of non-specific interactions was theoretically quantified using

an xDLVO-CG approach. Our simulations revealed a strong dependence of the non-specific

interactions on the electrostatic properties, as has been demonstrated in Figure II-4 and Figure

II-5. Moreover, the chemical nature of the dimer binding site was demonstrated.

Figure II-5: Osmotic second virial coefficient B

as calculated using xDLVO-CG for β-lg

monomer

-monomer, monomer-dimer and dimer-dimer interactions as a function of the salt

concentration at pH 3

.0 (A) and at pH 7.0 (B).

Manuscript II

II-5.2 Dimer dissociation constant from analytical ultracentrifugation

For the determination of the dimer dissociation constant via AUC experiments, a β-lg

concentration series was prepared for each solution pH (pH 3.0 and pH 7) and salt concentration

(10 mM and 100 mM sodium chloride). For each combination of solution pH and buffer

concentration, the sedimentation and diffusion properties were determined from SV-AUC

experiments.

Sedimentation profiles for a solution pH of 7.0 and a salt concentration of 100 mM sodium

chloride with a β-lg concentration of 55 µmol/L are provided in Figure II-6A. Sedimentation

coefficient distributions for the β-lg system for a solution pH of 7.0 at different protein loading

concentrations are shown in Figure II-6B. The presence of sedimentation non-ideality is already

visible in the data and indicated by minor shifts in the sedimentation coefficient distribution at

different β-lg concentrations, as can be seen in Figure II-6B [221]. Moreover, a shift of the ratio

of β-lg monomers to dimers becomes obvious from the plot in Figure II-6B, depending on the

β-lg loading concentration. Notably, sedimentation coefficient distributions for the β-lg system

for a solution pH 3.0 and 7.0 at different salt concentrations are shown in the left panel of Figure

S II-6 in order to illustrate the pH and salt concentration dependence of the dimer dissociation.

Following the protocol by Schuck et al. (2020), all SV-AUC data sets were analyzed with

respect to the weight-averaged sedimentation coefficient [255]. For a fixed solution pH and salt

concentration, the weight-averaged sedimentation coefficient as a function of the β-lg loading

Figure II-6: (A) Exemplarily measured sedimentation profiles as obtained from AUC

experiments for a solution pH of 7

and a salt concentration of 100 mM sodium chloride and

a protein concentration of 18

µmol/L. Data acquisition was carried out at a wavelength of

280

nm. The color code indicates the course of the sedimentation profile over time [2]

(

B) Retrieved sedimentation coefficient distributions for β-lg in water at pH 7.0

and a salt

concentration of 100

mM sodium chloride at various protein loading concentrations. The

sedimentation data was analyzed using the c(s) model

[3]

. The plot was created using GUSSI

[2]

Manuscript II

concentration provides the monomer-dimer equilibrium. Each isotherm, i.e. weight averaged

sedimentation coefficient for various protein concentrations, contains information about the

dissociation of the dynamically interacting system [255]. Determination of the dimer

dissociation constant KD was subsequently conducted via fitting the isotherms using the

software SEDPHAT [3]. Notably, the dissociation constant is directly linked to the dissociation

energy, which will be discussed in a later section of this manuscript. Notably, during the data

analysis in SEDPHAT, we kept the value of ks constant at a value of 10 mL/g, which reflects

the excluded volume for globular proteins [255]. Moreover, in order to test the influence of

hydrodynamic interactions on the retrieval of the dimer dissociation constant KD, we treated the

Gralen coefficient ks as a floating parameter during the analysis in SEDPHAT. We found for

the concentration range within the isotherms no significant difference from the value reflecting

the excluded volume [255]. Almost identical values for the dissociation constant KD were

retrieved from the analysis with floating and constant ks. Therefore, we continued the

determination of the dissociation constant with a constant value for the Gralen coefficient.

Moreover, the influence of hydrodynamic non-ideality further explains the minor difference

between the fitted isotherm and the measured data at elevated protein concentrations, as the

influence of hydrodynamic non-ideality increases at higher protein concentrations. Finally, our

experimentally determined isotherms are graphically shown in Figure II-7 for a solution pH of

3.0 and 7.0 at a salt concentration of 100 mM sodium chloride and a solution pH of 7.0 at a salt

concentration of 10 mM sodium chloride. Notably, the measured isotherm at a solution pH of

3.0 and a salt concentration of 10 mM sodium chloride did not follow the expected trend (Fig.

Figure II-7: Weight-averaged sedimentation coefficients as measured by AUC experiments

versus β-lg loading concentration. The isotherms are determined for different solution

conditions: (A) pH 3.0 with a salt concentration of 100 mM, (B) pH 7.0 with a sodium chloride

concentration of 100 mM and (C) pH 7.0 at a salt concentration of 10 mM sodium chloride.

Each isotherm is fitted using the software SEDPHAT in order to determine the dimer

dissociation constant. Notably, beyond protein concentrations of 10-4 M, the influence of non-

ideality phenomena is strongly increased, thus extrapolation of the isotherms is not possible

and cannot be interpreted in a physical manner.

Manuscript II

S II-6B). Consequently, we were not able to analyze this isotherm with respect to KD. This

observation is attributed to a significant influence of the primary charge effect throughout the

AUC experiments, which can be explained as follows. The difference in sedimentation velocity

of charged particles and their respective counter ions is the origin of the primary charge effect.

This effect is more important for technical conditions at a low ionic strength, which is the case

for our system at a salt concentration of 10 mM sodium chloride [1,3]. In the context of our

results, the total number of charges in the system is determined by the β-lg loading

concentration as the charge screening is significantly reduced at the salt concentration of 10 mM

sodium chloride. Thus, the influence of the primary charge effect scales with the β-lg loading

concentration, which makes analysis of the weight-averaged sedimentation coefficient for

varying protein loading concentration with respect to dimer dissociation impossible at a

solution pH of 3.0 and a salt concentration of 10 mM sodium chloride, as can be seen in the

right panel of Figure S II-6.

The dimer dissociation constants for the three other solution conditions were analyzed and the

retrieved values are provided in Table II-1. Notably, the confidence intervals for the calculation

of the error bars were set to 68 %: The statistical errors were calculated using Monte Carlo

simulations based on the provided confidence interval. From the plot, it can be taken that the

dimer dissociation depends on the solution pH, which is directly in line with a previous AUC

study on genetically modified β-lg systems [197]. While dimers predominantly form at pH 7,

dimer dissociation is stronger at pH 3.0. This is further in agreement with the results from

Mercadante et al. (2012) [258]. In this work, it was shown how the β-lg dimerization is

significantly influenced by the buffer type and concentration over a broad range of solution pH

values. As already pointed out, the dimer dissociation is further influenced by the ionic strength,

which is caused by the strong modulation of PPIs, necessary for subsequent dimerization, and

by the charge state of the protein. This can further be related to the protein CG model in Figure

Table II-1: The dimer dissociation constant as obtained from fitting of the isotherms, which

are determined from AUC experiments. The dimer dissociation constants are provided as a

function of solution pH and salt concentration. At a solution pH of 3.0 and a salt concentration

of 10 mM sodium chloride, the AUC experiments are influenced by charge effects. The values

for the dimer dissociation constant based on a confidence interval of 68 % are provided.

pH 3

pH 7

NaCl

concentration

10 mM

100 mM

10 mM

100 mM

Dimer

dissociation

(µM)

Strong charge

effects

29.2

19.3

2.1

Confidence

intervals 68 %

(µM)

NA / NA

27.6 / 31.2

18.1 / 20.6

2.1 / 2.3

Manuscript II

II-3, which indicated a high charge density at the dimer binding site. In this context, Gottschalk

et al. (2003) studied the salt-dependent monomer-dimer equilibrium and revealed a significant

difference between no addition of salt and a 1.0 M sodium chloride solution [259]. The authors

show an essentially monomeric state in the absence of salt and a solution pH of 2.5 while

dimerization is observed at a salt concentration of 1.0 M sodium chloride [259]. Notably, it was

not possible for the investigated range of concentrations by AUC to retrieve the osmotic second

virial coefficient directly from experimental data, hence we restrict our AUC analysis of the β-

lg system to the retrieval of the dimer dissociation constant and exclude the determination of

the second osmotic virial coefficient with respective self and cross-term interactions (equations

10 and 11). This is attributed to the fact that we experimentally investigate a mixture of two β-

lg variants (A and B) since β-lg is considered a relevant protein in food technology as a milk

protein [197].

Therefore, while the number of self-interaction terms significantly increases (e.g. A-A, AA-

AA, B-B, AB-AB, etc.), the cross-term interactions in equations 10 and 11 would involve at

least eight terms (e.g. A-AA, A-AB, etc.). Therefore, it is not possible to analyze these

interactions from SV-AUC data when a high number of unknowns are included in additional

terms in equations 10 and 11. Moreover, we point out that the heterogeneity of the species

contributes to the broadening of the sedimentation boundary, which directly influences the

sedimentation analysis with respect to the second virial coefficient. Notably, the hydrodynamic

non-ideality constant ks remains an effective constant representing the hydrodynamic non-

ideality of both, the β-lg monomer and the dimer as well as their cross-terms. Furthermore, a

recent analysis of self-interaction and cross-term interactions for therapeutic antibodies in a

highly concentrated environment via SV-AUC experiments by Correia et al. (2020) has shown

that the absolute values of the retrieved individual cross-terms do not show significant

variations in direct comparison (variation by 5.0 %- 10 %) [189,226]. Such small differences

cannot be resolved from our SV-AUC data. In this context, it was further shown that an

extensive systematic study via SV-AUC over a broad range of protein loading concentrations

with different detection systems, such as the Aviv AU-FDS optical system, is required to study

the wide range of protein interactions, which eventually provides insight into self and cross-

term interactions [189]. We rely on the determination of the second osmotic virial coefficient

from membrane osmometry measurements, which relies on the determination of the dimer

dissociation constant from AUC. Our approach aims to establish an experimental protocol for

the determination of PPIs for dynamically interacting systems such as the complex system with

β-lg monomers and dimers. The measured dissociation constant KD by AUC thus represents the

equilibrium of β-lg monomers and dimers as defined in equation 3.

II-5.3 Determination of the osmotic second virial coefficients from membrane

osmometry experiments

Following the results from AUC experiments for each combination of solution pH and salt

concentration, the reduced osmotic pressure was determined from membrane osmometry

Manuscript II

measurements for various β-lg loading concentrations. Our results are presented in Figure

II-8A. Evidently, the extent of the concentration-dependency varies with the combination of

solution pH and salt concentration, thus the nature of the electrostatic properties. The extent of

the non-specific interactions was quantified by fitting equation 13 to the molecular weight

corrected reduced osmotic pressure for various β-lg loading concentrations, which is only

possible in case the dimer dissociation constant is known. For each solution pH and salt

concentration, the dimer dissociation constant was taken from Table II-1 as measured by AUC.

For a solution pH of 3.0 and a salt concentration of 10 mM sodium chloride, the dimer

dissociation constant was taken from literature [197]. Notably, the dimer dissociation constant

KD can be estimated to be in the order of 250 µM from our plot in Figure S II-6. Assuming

values for the dimer dissociation constant KD between 50 µM and 1000 µM has only little

impact on the evaluation of B22 from membrane osmometry data since the impact of B22 on the

reduced osmotic pressure is strong in comparison to the dimer dissociation constant KD in the

evaluated protein concentration range.

The influence of non-specific interactions and dimerization due to specific interactions on the

reduced osmotic pressure can be seen in Figure S II-7. Non-aggregating macromolecules with

absent or balanced repulsive and attractive interactions yield a straight line with a slope of zero.

In the case of pronounced attractive or repulsive intermolecular interactions, a negative or a

positive slope is observed, respectively. This is true if the protein concentration is sufficiently

Figure II-8: (A) Experimentally determined molecular weight-corrected osmotic pressure for

concentration

-dependent molecular weight for β-lg

in sodium chloride solutions as a function

of protein loading concentration. Results are shown for different pH values and salt

concentrations. (

B) The osmotic second virial coefficient B22

for different pH values and sodium

chloride concentrations. The coarse

-grained xDLVO calculations provide values for monomer

monomer (M

-M), monomer-dimer (M-D) and dimer-dimer interactions (D-

D). Experimental

values are retrieved from a combination of the results from AUC and membrane osmometry

(green bars). For a solution pH of 3

.0 and a salt concentration of 10

mM sodium chloride, the

dimer dissociation constant for the calculation of the osmotic second virial coefficient was

taken from literature

Manuscript II

low and higher-order interactions can be neglected. If additionally, protein oligomerization

occurs, the concentration dependence of the osmotic pressure can no longer be described as a

linear function, even at low protein concentrations. For the case of β-lg, the decrease of the

osmotic pressure due to the increase of the dimerization at higher protein loading concentration

is superimposed with the influence of binary intermolecular interactions. Since the number of

dimers asymptotically approaches a maximum (100 %), the number of particles changes less

with increasing concentration. Therefore, dimer dissociation directly affects the molecular

weight-corrected reduced osmotic pressure at low protein concentrations. This can be observed

especially in systems with less pronounced PPIs (Fig. II-8A for pH 3, 100 mM; pH 7, 10 mM

and 100 mM). Here, dimerization induces an initial decrease in the reduced osmotic pressure.

Since the monomer-dimer ratio is less dependent on the protein concentration at higher protein

concentrations, an approximately linear dependence of the reduced osmotic pressure is

observed, which is largely determined by the extent of non-specific PPIs. To account for the

influence of dimerization, the reduced osmotic pressure needs to be corrected in terms of the

concentration-dependent molecular weight. Since the osmotic pressure is corrected for specific

interactions, a linear fit is obtained as shown in Figure II-8A. Here, the slope corresponds to

B22. The measured B22 from membrane osmometry are presented in Figure II-8B. Moreover,

we see that the theoretically calculated values using xDLVO-CG and the experimentally

measured osmotic second virial coefficients correlate well. Evidently, B22 significantly depends

on the charge state of the system, hence higher B22 values are obtained at pH 3.0 than at pH 7.0.

As stated before, the charge screening reduces the extent of the non-specific interactions, which

is controlled through the salt concentration. These findings are directly in line with literature

[37,190].

In addition, the measured values for B22 from membrane osmometry reveal a strong contribution

from dimer-dimer interactions, when comparing with the theoretical predictions. This

observation is in line with the fact that the monomer-dimer equilibrium is predominantly shifted

towards dimers at protein concentrations above 2.5 g/L, which has been revealed by our AUC

measurements. This is further visualized in Figure S II-9, which shows the theoretical weight

fraction of β-lg monomers and dimers for an equilibrium constant of 39.7 µM. Therefore,

considering equation 15, the slope from molecular weight corrected osmotic pressure in Figure

II-8A is strongly influenced by dimer-dimer interactions, which is directly reflected by our

results.

We have further supported our argument by theoretical calculations of the osmotic second virial

coefficient for various protein concentrations based on equation 15, which is presented in the

left panel of Figure S II-8. For the calculations, the values for the self-interactions BMM, BDD as

well as the cross-term interactions BMD were taken from the xDLVO-CG calculations, which

are presented in Figure II-8A. The results from Figure S II-8 reveal a strong decrease of the

second virial coefficient at small protein loading concentrations (below 2.0 g/L) and a further

minor decrease of the second virial coefficient with increasing protein loading concentration.

Manuscript II

These observations support the argument that our reported experimentally determined second

virial coefficients are strongly influenced by dimer-dimer interactions.

Moreover, xDLVO-CG calculations reveal a similar extent of the intermolecular interactions

between β-lg monomers and dimers as well as their cross-correlation. Notably, this result is in

line with our argumentation of the similarity of the individual terms of cross-term interactions

and findings in literature from AUC experiments [226]. Furthermore, B22 for monomer-

monomer interactions is the highest for a solution pH of 3, which is attributed to the strongest

repulsion PPIs due to the charged state of the protein and less pronounced dimer formation via

the dimer binding site, as can be seen in Figure II-3. The similarity of the osmotic second virial

coefficients for β-lg may be attributed to the fact that interactions between monomer-monomer,

monomer-dimer and dimer-dimer are in the same order of magnitude, thus cross-correlations

influence the experimental methods only to a minor extent. Moreover, either β-lg monomers or

β-lg dimers are predominantly present, thus a small contribution from higher oligomers does

not influence the experiments.

Finally, we have calculated the molecular-weight reduced osmotic pressure for various protein

concentrations based on equation 16, which is presented in the right panel of Figure S II-8.

While minor experimental uncertainties prevent a direct comparison of the theoretical and

experimental data, the slopes of the theoretical curves are in line with our experimental results

from Figure II-8A. Notably, all protein concentrations in Figure II-8A are provided as weight

concentrations. This is due to the fact that the data must be in accordance with equation 13 for

the evaluation, which requires cw as protein weight concentration. Moreover, a direct

determination of self-interaction terms BMM and BDD and cross-term interactions BMD from the

experimental data was not possible as fitting of the data is associated with too many fitting

parameters and minor experimental uncertainties in the measured osmotic pressure.

Following our results from Table II-1 and Figure II-8, we believe to have provided a

comprehensive tool to determine the extent of PPIs for the dynamically interacting system β-lg

with a concentration-dependent monomer-dimer equilibrium by a combination of AUC and

membrane osmometry measurements. We show the determination of the osmotic second virial

coefficient based on a molecular weight-corrected reduced osmotic pressure as a function of

the protein loading concentration. In this context, our experimental protocol allows the

quantification of the effect of self-dissociation, charge interactions and vdW interactions at the

same time. Notably, the measured second virial coefficients show positive values, which

indicates global repulsive protein-protein interactions [221].

II-5.4 Relationship between the osmotic second virial coefficient and the dimer

dissociation energy

In the final part of this manuscript, we aim towards relating non-specific protein interactions

and dimer dissociation from an experimental as well as theoretical point of view. The extent of

specific interactions for the β-lg system was retrieved from free energy calculations using the

Manuscript II

US technique. The Gibbs free energy ΔG is directly related to the dimer dissociation constant

through the following relationship [260]:

∆𝐺𝐺 = 𝑅𝑅𝑅𝑅 𝑙𝑙𝑙𝑙 𝐾𝐾𝐷𝐷

(26)

From equation 26, it is evident that the dissociation energy directly scales with the thermal

energy kBT. The free energy of the β-lg monomers is significantly promoted at pH 7.0 and the

β-lg binding energy is -8.3 kcal/mol and -6.9 kcal/mol at salt concentrations of 10 mM and 100

mM sodium chloride, respectively, as can be seen in Figure II-9A. These values correlate well

with the available experimental data [145]. The binding free energy of the β-lg dimer at pH 3.0

is less favorable, approximately -4.2 kcal/mol at a salt concentration of 100 mM sodium

chloride and shows less pronounced dimerization. It is worth noting that at this buffer condition,

the binding of the β-lg still has an attractive character, therefore, both forms of β-lg are present.

Notably, this is in accordance with results from AUC experiments, as can be seen in Figure

II-6. Contrary to that, if the salt concentration is lower (green curve in Figure II-9A), i.e. 10 mM

sodium chloride, dimerization of the β-lg is suppressed and higher amounts of β-lg monomers

are present. The binding energy of the β-lg dimer in this case is positive (+1.2 kcal/mol),

therefore, the formation of the β-lg dimer is thermodynamically unstable. Finally, we

summarize our theoretical predictions from xDLVO-CG (B22 coefficients) and MD simulations

with US free energy calculations (ΔG) in Figure II-9B. Notably, all umbrella sampling

histograms and calculated PMF are provided in figures S II-10 and S II-11.

For a comparison of theoretical and experimental results, our measured dissociation constants

(Table II-1) were converted to Gibbs free energy using equation 26. To establish the

Figure II-9: (A) Free energy of β-lg dimerization at different studied solution conditions

obtained from umbrella sampling simulations at 300

K and atmospheric pressure. (B

) Second

virial coefficient from membrane osmometry as a function of the dissociation energy as

determined from SV

-AUC (red circles). The experimental results are compared with the

theoretical results from xDLVO

-CG (B22) for monomer-monomer interactions and MD/US

simulations for the Gibbs free energy (black circles).

Manuscript II

relationship between B22 and the dissociation constant of the β-lg system, we combined the

experimental data for the nonspecific interactions from membrane osmometry, which are

represented by the second virial coefficient and the measured dimer Gibbs free energy, which

is provided in Figure II-9 (B). Notably, we did not consider the data point for a solution pH of

3.0 and a salt concentration of 10 mM sodium chloride for two reasons. First, we could not

directly measure the dissociation constants by AUC due to a significant influence of charge

effects. Second, this data point is within the thermodynamically unstable region, as shown by

our free energy calculations. Finally, our results depicted in Figure II-9B can be interpreted as

follows. On the one hand, the osmotic second virial coefficient relates to the dissociation energy

and significantly decreases with an increase of dissociation energies (i.e. higher binding

energy). Conclusively, the osmotic second virial coefficient can be qualitatively used as a

predictor for protein dissociation. Notably, a similar relationship for the second osmotic virial

coefficient is established in the context of protein solubility. Moreover, as the supersaturation

is directly related to the crystallization, the second osmotic virial coefficient serves as a measure

for protein crystallization [202,261–263]. In our manuscript, we point towards establishing a

relationship to controlled protein oligomerization.

Furthermore, our experimentally determined values for the Gibbs free energy lie within the

thermodynamically stable region for the dimerization. However, the theoretically calculated

binding free energies quantitatively match our experimental results only at specific

experimental conditions, i.e. pH of 7.0 and 100 mM sodium chloride. Discrepancies between

other values of binding energy are attributed to the limited accuracy of density fluctuations of

salt ions around protein macromolecules during in-silico free energy calculation. Moreover,

while our experimental results are based on a mixture of two β-lg variants (A and B), our

simulation were conducted for a single variant A. Minor differences are further attributed to a

small difference in temperature during experiments, which directly affects the solution density,

hence the sedimentation properties through the product of the partial specific volume of the

proteins and the solution density (equation 4). Therefore, the final conclusions can only be

drawn in a qualitative manner.

II-6 Conclusions

In this manuscript, we studied the dynamic monomer-dimer equilibrium of β-lg with two

variants (A and B) with respect to PPIs based on a unique combination of AUC and membrane

osmometry measurements. While the dimer dissociation constant is provided from AUC

experiments, the molecular weight-corrected osmotic pressure from membrane osmometry

provides the second osmotic virial coefficient for the dynamically interacting system β-lg. With

this protocol at hand, both specific and non-specific PPIs between β-lg species were

investigated at a solution pH of 3.0 and 7.0 and two salt concentrations in order to mimic

technical conditions, namely 10 mM and 100 mM of sodium chloride. While specific

interactions were accounted for by the dissociation constant as measured by SV-AUC, we

determined the extent of non-specific interactions with the osmotic second virial coefficient by

Manuscript II

means of membrane osmometry. Data analysis revealed a strong dependence of the dimer

dissociation on the charge state of the protein, which is controlled by the solution pH. These

findings are in line with literature. Our measured values agree well with predictions from an

extended xDLVO-CG approach, which was applied to calculate PPIs between β-lg at different

solution conditions and charge states from B22 coefficients. With this unique combination of

the two techniques, we provide an experimental protocol to study specific interactions, i.e.

dimerization and non-specific interactions at the same time for a dynamically interacting system

such as β-lg. Finally, we evaluated our experimental approach by analyzing the relationship

between the osmotic second virial coefficients, which represents the extent of non-specific

intermolecular interactions, and to the β-lg dimer dissociation constant. In order to predict the

binding free energies of the β-lg oligomerization, umbrella sampling simulations were

performed. A thermodynamically stable and unstable region was revealed by the extent of the

binding energy. Finally, a comparison of the experimentally measured and theoretically

calculated Gibbs free energies was possible in a qualitative manner. As the contribution of the

osmotic pressure of the solution is proportional to the number of molecules in solution, this is

further directly related to the dimerization constant. Therefore, a relationship of the two

phenomena was addressed in our manuscript. Our experimental protocol aims towards enabling

the determination of the osmotic second virial coefficient, which will serve as a predictor for

the β-lg protein dissociation. This conclusion points towards establishing a structure-property

relationship for controlled prediction of protein oligomerization. Finally, the study of

genetically modified β-lg variants may serve as a promising model system for further studies

including the application of AUC to the determination of the second virial coefficient with a

specific focus on the determination of cross-term interactions.

Manuscript III

Osmometric and viscometric study of levan, β-lactoglobulin

and their mixtures

Food Hydrocolloids (2020), accepted manuscript

The publication is online available at https://doi.org/10.1016/j.foodhyd.2019.105580

Authors

Christoph S. Hundschell1; Sabrina Bäther1; Stephan Drusch2; Anja M. Wagemans1

1: Food Colloids, Technische Universität Berlin, Germany

2: Food Technology and Food Material Science, Technische Universität Berlin, Germany

Manuscript III

III-1 Abstract

The current study investigated the molecular interactions of the exopolysaccharide levan (low

and high molecular weight), β-lactoglobulin and their mixtures at different NaCl concentrations

(2.5 mM and 100 mM, pH 7) using viscometry and membrane osmometry. Both methods were

used to predict the phase behavior of the mixed polymer systems. A positive second cross-virial

coefficient indicates repulsive pair interactions between levan and β-lactoglobulin due to the

excluded volume effect at both salt concentrations. A higher molecular weight of levan seemed

to enhance the repulsive forces, while the NaCl concentration had only a minor influence. For

the phase behavior, the charge of the β-lactoglobulin and therefore the NaCl concentration plays

an important role. At low salt concentrations, the repulsive, electrostatic forces between the

individual β-lactoglobulin molecules counteract the concentration of the protein in one phase.

Therefore, both polymers seem to be co-soluble regardless of the molecular weight of levan. At

100 mM NaCl, the electrostatic repulsion between the β-lactoglobulin molecules is screened

and attractive protein-protein interactions predominated. This facilitates the formation of two

phases and segregative phase separation due to the excluded volume effect becomes more

likely.

Figure III-1: Graphical abstract of manuscript III.

Manuscript III

III-2 Introduction

To predict the structure and functionality of foods as complex multiphase systems, the

understanding of the molecular interactions between the two main types of food biopolymers –

polysaccharides and proteins – is essential. The molecular interactions of food biopolymers

determine the phase behavior of a food system and whether the biopolymers are miscible or

immiscible. Miscible systems are compatible due to the absence of strong forces of attraction

or repulsion between the polymers. Phase separation occurs due to repulsive interactions

(segregative phase separation) or attractive interactions (associative phase separation).

Associative phase separation also referred to as complexation of different biopolymers is

widely exploited, for instance, to stabilize emulsions or suspension as well as to form gels

[20,41,264,265]. In contrast, segregative phase separation is often undesired in food systems,

however, it can also be used to create new structures and textures such as micro-phase separated

gels [39].

In our study, the molecular interactions of the protein β-lactoglobulin (β-lg) and the

polysaccharide levan were investigated. The polysaccharide levan is of high interest as a food

ingredient, due to unique techno-functional properties such as thickening, gelling or clouding

properties that vary with the molecular weight [11,14,59,133,160,266]. The uncharged levan is

composed of β-2,6-linked fructose monomers and its molecular conformation is determined by

the molecular weight: low molecular weight levan has a random coil-like structure, while high

molecular weight levan has a very dense and spherical structure [53,160]. Detailed information

on the production, techno-functional properties and possible applications can be found in recent

reviews [110,129,132,161].

The whey protein β-lg is present in many foods and its properties have been investigated

extensively in numerous studies. Consequently, information on the molecular weight and size

is available, which is essential for understanding and discussing molecular interactions. In this

context, β-lg was found to polymerize into dimers or octamers depending on the pH and the

ionic strength, [32,33,35]. For the β-lg monomer, a molecular weight of 18.4 kDa and a

hydrodynamic radius of 2.0 to 3.0 nm was reported [60,144,267].

Phase behavior can be predicted by measuring molecular interactions in dilute polymer

solutions. Molecular interactions between two polymers of one species are described by the

second virial coefficient, while molecular interactions between two polymers of two species are

described by the second cross-virial coefficient. The second virial and second cross-virial

coefficient can be determined using light scattering techniques, sedimentation experiments or

membrane osmometry. Compared to the other methods, membrane osmometry has the

advantage that the osmotic pressure is directly measured and that the number average values

are determined, which makes this method insensitive to sample impurities such as dust and

aggregates. The second virial coefficient and second cross-virial coefficient of protein mixtures

[49,268–270] as well as protein-polysaccharide mixtures [63,271] have been determined using

membrane osmometry.

Manuscript III

Another approach to determine the molecular interactions of polymer mixtures and predict the

phase behavior at high polymer concentrations is the viscometric characterization of polymer

mixtures at low concentrations. For this purpose, the intrinsic viscosity, the Huggins coefficient

of the individual polymers and interaction coefficients of the polymer mixtures are determined.

Viscometric measurements provide a simple, fast and inexpensive way to study polymer

mixtures. The phase behavior of synthetic polymer [272,273] and biopolymer mixtures [274–

278] have been studied using viscometry.

As mentioned above, protein and carbohydrate interactions have been investigated using

osmometry and viscometry. However, no research has focused yet on interactions and phase

behavior of protein-levan mixtures. Therefore, we chose β-lg as a model protein and studied

the subject using osmometry and viscometry. Since the ionic strength has an impact on the

electrostatic interactions between β-lg molecules as well as their monomer-dimer-equilibrium,

the sodium chloride concentration was varied accordingly.

In detail we hypothesized the following:

➢ Molecular interactions between β-lg and levan are repulsive due to the excluded volume

effect. Since this effect depends on the volume of the molecules, it should be more

pronounced for mixtures containing the high molecular weight levan.

➢ An increase of the ionic strength shifts the monomer-dimer-equilibrium of β-lg towards

dimers and thus influences the molecular interactions between levan and β-lg, due to an

increased excluded volume of the double molecule.

➢ The phase behavior of levan-β-lg solutions depends primarily on the ionic strength. A

decrease of the ionic strength hinders the concentration of β-lg in one phase due to

electrostatic repulsion of the protein molecules and thus prevents phase separation of

mixed levan-β-lactoglobulin solutions.

To test these hypotheses, the molecular interactions in pure levan and β-lg systems as well as

levan-β-lg mixtures have been determined, while different sodium chloride concentrations were

considered. In order to analyze the influence of the levan size and structure on the protein-

polysaccharide interactions, two levans with different molecular weights were used: a low

molecular weight levan with a random coil-like structure (LevCoil) and a high molecular weight

levan with a compact spherical structure (LevSphere).

III-3 Theory

III-3.1 Osmometry

Osmometry measures the osmotic pressure of dilute polymer solutions. It can be used to

determine the number average molecular weight Mn (also osmotic average molecular weight)

and the second virial coefficient B' of polymers of one species as well as the second cross-virial

coefficient of polymers of two different species. The osmotic pressure Π is a colligative

property, meaning that it depends on the number of molecules in a volume and not on their

mass or their identity.

Manuscript III

For polymers systems containing one species, Π can be described as a function of the polymer

concentration cp using the virial equation [72]:

𝛱

𝑅𝑇𝑐𝑝=1

𝑀𝑛+𝐴′𝑐𝑝+𝐴′′𝑐𝑝

2+⋯

(1)

Where Π/RTcp is the reduced osmotic pressure, R is the gas constant and T is the absolute

temperature. The first term of equation 1 is related to the number average molecular weight and

refers to the ideal behavior of a polymer solution according to the Van ’t Hoff law (S. F. Sun,

2004). The interaction coefficients A', A'' and higher coefficients account for deviations from

the ideal behavior. Most dilute systems are described sufficiently by considering only the first

two terms of equation 1. The second virial coefficient B’ can be deduced from A' and Mn by the

following equation [63]:

𝐵′=𝐴′𝑀𝑛

(2)

The second virial coefficient depends on the solvent affinity of a polymer and reflects the

interactions between a pair of individual molecules in solution. Repulsive interactions are

indicated by B' > 0, whereas B' < 0 represents attractive interactions.

For polymer systems containing two species, Π can be calculated from the following equation

considering the first two terms of equation 1 [49]:

𝛱

𝑅𝑇𝑐𝑝=1

𝑀𝑛



+𝑐𝑝(𝐴′1,1𝑤1

2+𝐴′2,2𝑤2

2+2𝑤1𝑤2𝐴′1,2)

(3)

Here, A'1,1 and A'2,2 are the interaction coefficients of each single polymer species and w1 and

w2 are the corresponding weight fractions of each polymer. The number average molecular

weight of the polymer mixture Mn



introduced in equation 3 is defined as [49]:

𝑀𝑛



=𝑤1

𝑀𝑛,1 +𝑤2

𝑀𝑛,2

(4)

The interaction coefficient A'1,2 accounts for interactions between the different polymer species

and is related to the second cross-virial coefficient B'1,2 via [63]:

𝐵′1,2 =𝐴′1,2𝑀𝑛,1𝑀𝑛,2

(5)

With Mn,1 and Mn,2 as the number average molecular weight of polymer 1 and polymer 2. The

second cross-virial coefficient is a measure of the polymer-polymer interactions between two

polymer molecules of different species. As with the second virial coefficient, a negative value

of B'1,2 indicates attractive interactions and a positive value repulsive interactions.

In concentrated polymer mixtures with negligible attractive interactions between the individual

polymers, segregative phase separation is a common phenomenon. An estimation whether a

mixture tends to segregative phase separation or not is given by [42,43]:

Manuscript III

𝐴′1,1𝐴′1,2 <𝐴′1,2

(6)

If the interaction coefficients meet this criterion, it is likely that segregative phase separation

occurs at sufficient high polymer concentrations.

III-3.2 Viscometry

Viscometry can be used to determine the intrinsic viscosity [η], which is often used to describe

the hydrodynamic volume of macromolecules. The hydrodynamic volume depends on the size

and the conformation of the polymer. Similar to the reduced osmotic pressure, the reduced

viscosity ηred can be described as a virial equation depending on the polymer concentration

[164].

𝜂red =𝜂𝑠−𝜂0

𝜂0𝑐=𝐷1+𝐷2𝑐+𝐷3𝑐2+⋯

(7)

Here, ηs is the viscosity of the solution and η0 is the viscosity of the solvent. For dilute systems,

c2 and higher power terms can be neglected. Therefore, equation 7 can be reduced to the

Huggins equation [164]. Where D1 is equal to [η] and D2 is equal to kH[η]2.

𝜂𝑟𝑒𝑑 =𝜂𝑠−𝜂0

𝜂0𝑐=[𝜂]+𝑘𝐻[𝜂]2

(8)

The Huggins coefficient kH can be used to describe the polymer-polymer and polymer-solvent

affinity of polymer solutions. A more detailed overview of the Huggins coefficient is provided

by the work of Pamies et al. (2008) [182].

Based on the Huggins equation, Sun et al. (1992) postulated an equation describing the

interactions of a polymer mixture containing two different polymer species [273]. This equation

consists of three terms and considers thermodynamic as well as hydrodynamic interactions:

𝑘𝑚=𝑘ℎ𝑦𝑑𝑟𝑜 +𝑘𝑎𝑔𝑔𝑟𝑒 +𝛼

(9)

where km is the Huggins coefficient of the polymer mixture. The first term accounts for long-

range hydrodynamic interaction of pairs of single molecules.

𝑘ℎ𝑦𝑑𝑟𝑜 =𝑘1[𝜂]1

2𝑤1

2+𝑘2[𝜂]2

2𝑤2

2+2√𝑘1𝑘2[𝜂]1[𝜂]2𝑤1𝑤2

([𝜂]1𝑤1+[𝜂]2𝑤2)2

(10)

Here, k1, k2, [η]1 and [η]2 are the Huggins coefficients and the intrinsic viscosities of polymer 1

and polymer 2, respectively. The second term considers the formation of double molecules of

different species due to aggregation.

𝑘𝑎𝑔𝑔𝑟𝑒 =𝐾

[𝜂]2([𝜂]𝐴−[𝜂]𝐵)

(11)

where [η]A is the intrinsic viscosity of the double molecule, [η]B is the intrinsic viscosity of the

single molecule and K is a constant. In the absence of aggregation due to a lack of strong specific

attractive interactions between the different polymer species and at sufficiently low

Manuscript III

concentrations, this term can be neglected. The third term α takes intermolecular attraction or

repulsion into account. An α > 0 reflects attractive interactions and an α < 0 indicates repulsive

interactions. Assuming that equation 11 can be neglected, α can be determined by

𝛼=𝑘𝑚−𝑘ℎ𝑦𝑑𝑟𝑜 −𝑘𝑎𝑔𝑔𝑟𝑒 ≈𝑘𝑚−𝑘ℎ𝑦𝑑𝑟𝑜

(12)

According to Sun et al. (1992) α can also be used to predict the phase behavior of polymer

mixtures at higher polymer concentrations [273]. A negative α, and therefore repulsive

interactions, is an indicator for segregative phase separation while miscibility is predicted by a

positive α.

III-4 Material and Methods

III-4.1 β-lactoglobulin

Bovine β-lg powder with a dry matter content of > 99 % was provided by the Kulozik Food

Process Engineering and Dairy Technology research group (Technische Univeristät München,

Munich, Germany) [279].

β-lactoglobulin Sample Preparation. For the preparation of the β-lg stock solution, 40 g/l

protein powder was dissolved in distilled water, stirred at room temperature for 1.0 h and stored

overnight in a refrigerator. To adjust the sodium chloride concentration and the pH of β-lg

solutions, diafiltration (ÄKTACrossflowTM, Ge Healthcare, Uppsala Sweden) was used.

Therefore, the volume of the stock solution was exchanged 10 times with a sodium chloride

solution (2.5, 5.0, 10, 50 and 100 mM) adjusted to pH 7.0. For diafiltration, a hollow fiber

cartridge (UFP-10-C-3MA, Ge Healthcare, Uppsala Sweden) was used at a feed flow of

500 ml/min and a transmembrane pressure of 3.0 bar. After diafiltration, samples were

centrifuged at 4.0 °C and 10.000 g for 30 minutes. The residue was discarded and the protein

concentration in the supernatant was determined using the Dumas method (DUMATHERM®

CN, C. Gerhardt GmbH & Co KG, Deutschland). A factor of 6.25 was used to convert nitrogen

to protein content (g/1000g). In order to obtain the protein concentration in g/l, the density ρ of

the solution was measured with a bending vibrator (DMA 38, Anton Paar GmbH, Germany).

The protein content was converted using c (g/l) = ρ·c (g/1000g).

III-4.2 Levan

Cultivation and Levan Production. The acetic acid bacterium Gluconobacter (G.) albidus

TMW 2.1191, isolated from water kefir [136], was cultivated in sodium gluconate medium

(NaG) containing 20 g/L sodium gluconate, 3.0 g/L yeast extract, 2.0 g/L peptone from casein,

3.0 g/L glycerin, 10 g/L mannitol and 3.0 g/L glucose. For fermentative levan production,

mannitol and glucose were replaced by 80 g/L of sucrose. For agar plates, 20 g/L of agar was

added. To obtain a preculture, a single colony of G. albidus was transferred into a 500 mL

Erlenmeyer flask containing 50 mL of NaG medium and cultivated overnight at 30 °C and 200

rpm in a rotary shaker to an optical density (600 nm) of approximately 2.5.

Manuscript III

Fermentative Levan Production of LevCoil. After pre-cultivation, the microorganisms were

centrifuged for 5.0 min at 5000 g and re-suspended in 5.0 mL of fresh sucrose-containing NaG

medium. 1.0 mL of this suspension was used to inoculate 200 mL of sucrose-containing NaG

medium in 2.0 L Erlenmeyer flasks. After growth for 48 hours at 30 °C and 200 rpm, the cells

were removed by centrifugation (10.000 g, 15 min). The levan in the supernatant was

precipitated with twice the volume of ethanol and stored overnight at 4.0 °C. The subsequent

purification of the levan was performed according to Jakob et al. (2013) [53]. Levan that was

produced in a cell-containing medium is abbreviated with LevCoil in the following part of the

manuscript. Because LevCoil contained low molecular weight components that could permeate

through the semipermeable membrane of the osmometer, this sample was purified by

diafiltration (ÄKTACrossflowTM, Ge Healthcare, Uppsala Sweden). Therefore, 6.0 g of LevCoil

was dissolved in 270 mL of distilled water. Subsequently, the volume of the solution was

exchanged 10 times against distilled water using a hollow fiber cartridge with a cut-off of 30

kDa (UFP-30-E-3MA, Ge Healthcare, Uppsala Sweden). A feed flow of 500 mL/min and a

transmembrane pressure of 3.0 bar were set. After diafiltration, LevCoil was freeze-dried (Beta

1-8 LSCplus, Martin Christ Gefriertrocknungsanlagen GmbH, Deutschland).

Enzymatic Levan Production of LevSphere. The treatment of the preculture and inoculation of

the working culture was carried out using sucrose-free NaG medium, as described in 3.2.1.

After cultivation for 24 hours at 30 °C and 200 rpm, the cells were centrifuged for 10 minutes

and re-suspended in 200 mL of 0.1 M sodium acetate buffer (pH 4) containing 0.1 M sucrose

in 2.0 L Erlenmeyer flasks according to Jakob (2014) [160]. To isolate the enzyme, the cell-

containing buffer was incubated for 3.0 h at 30 °C and 200 rpm in a rotary shaker. Subsequently,

the cells were centrifuged and 200 mL of 0.1 M sodium acetate buffer with 0.7 M sucrose was

added to the enzyme-containing buffer. The subsequent levan production was performed at

30 °C for 24 h. The separation of the levan from the buffer and the purification were carried out

as described in 3.2.2. Levan produced using levansucrase-containing, cell-free supernatants is

abbreviated to LevSphere.

Levan Sample Preparation. Levan stock solutions were prepared by weighting the levan

(adjusted for dry weight) into the sodium chloride solution (pH 7, 2.5 and 100 mM).

Subsequently, the samples were stirred for at least one hour and kept overnight in a refrigerator.

The conversion of g/1000 g into g/L was carried out as for the β-lg solution. The ternary

solutions containing mixtures of levan and β-lg were made by adding levan to the β-lg solution.

Therefore, a mixing ratio of 50:50 was chosen.

III-4.3 Osmometry

The osmotic pressure was measured at 28 °C using a 090 membrane osmometer (Gonotec

GmbH, Berlin, Germany). The osmometer was equipped with a semipermeable cellulose

triacetate membrane, which was purchased from the osmometer manufacturer. A molecular

weight cut-off of 5.0 kDa was found to be impenetrable for levan and β-lg. Each time the solvent

was changed, a new membrane was used. The assembly and the calibration of the osmometer

Manuscript III

were carried out as described by the manufacturer. To fill the pressure measuring chamber of

the osmometer, the respective sodium chloride solution from diafiltration was used. This

solution was also used to dilute the stock solution. For each polymer and the polymer mixtures,

the osmotic pressure was measured at six concentrations. The β-lg samples and the polymer

mixtures were measured in the concentration range from 5.0 g/L to 17.5 g/L. The concentrations

for LevCoil and LevSphere ranged from 5.0 g/L to 12.5 g/L and from 10 g/L to 20 g/L, respectively.

After a stable baseline was set, each concentration was injected four times into the sample

chamber of the osmometer, starting with the lowest concentration. The values of the last two

measurements of each concentration were used for the calculations. To obtain the number

average molecular weight and the second virial coefficient, the osmotic pressure was fitted to

the first two terms of equation 1 using linear least square regression. The measurements were

performed in duplicate and the given errors account for the standard error of regression of each

measurement. The raw data from osmometry measurements are listed in table S III-1 in the

supporting information.

III-4.4 Viscometry

Viscometry measurements were performed at 28 °C utilizing a rolling ball viscometer (LOVIS

2000M, Anton Paar GmbH, Germany). A glass capillary with a radius of 1.59 mm and a steel

ball with a radius of 1.5 mm at an inclination angle of 50 ° were used. For each polymer and

the polymer mixtures, the viscosity was measured for least at six concentrations. The β-lg

samples were measured in the concentration range from 5.0 g/L to 35 g/L. The concentration

for LevCoil and LevSphere ranged from 2.0 g/L to 4.5 g/L and 2.0 g/L to 8.0 g/L respectively. The

polymer mixtures were measured between 4.0 g/L and 9.0 g/L. The reduced viscosity was fitted

to equation 8 using a linear least square regression to obtain the intrinsic viscosity and the

Huggins coefficient. Each measurement was performed in duplicate. The given errors from

viscometry results are expressed as uncertain in fitting parameters from regression. The raw

data from viscometry measurements are listed in table S III-2 in the supporting information.

III-4.5 Dynamic Light Scattering

The hydrodynamic radius RH of the levan fractions was measured with a ZetaSizer Nano ZS

(Malvern Instruments, UK) utilizing dynamic light scattering. Each levan was measured three

times with automatic measurement duration at an angle of 173°. The solvent refractive index

for both salt concentrations was calculated with the instrument software. Both levans were

measured using a concentration of 1.0 g/L. The intensity distribution and the mean Z-average

hydrodynamic Radius RH were determined. All data analysis was performed using the

instrument software.

Manuscript III

III-5 Results and Discussion

III-5.1 β-lactoglobulin

Figure III-2A and III-2B show the molecular weight and the second virial coefficient of β-lg at

different NaCl concentrations (2.5 mM, 5.0 mM, 10 mM, 50mM and 100 mM). With increasing

ionic strength, the molecular weight increased while the second virial coefficient decreased.

The change in molecular weight is due to the monomer-dimer-equilibrium of β-lg at pH 7.0 that

depends on the temperature and the salt concentration. The monomer content wM and the dimer

content wD can be estimated using the following correlation:

𝑤𝑤𝑀𝑀=𝑀𝑀𝐷𝐷−𝑀𝑀𝑛𝑛

𝑀𝑀𝑀𝑀

= 2 − 𝑀𝑀𝑛𝑛

𝑀𝑀𝑀𝑀

(22)

𝑤𝑤

𝑀𝑀

+ 𝑤𝑤

𝐷𝐷

= 1

(13)

The molecular weight of the β-lg monomer MM (18.4 kDa), calculated from the amino acid

composition, was taken from literature [60]. The polymer concentration also influences the

monomer-dimer-equilibrium which affects the osmotic pressure. This might lead to measured

values for the molecular weight and the second virial coefficient that differ from the actual

values. Because equation 12 does not address the concentration dependency of the monomer-

dimer equilibrium, it must be seen as an approximation.

At the lowest salt concentration of 2.5 mM NaCl, a molecular weight of 21.5 ± 0.3 kDa was

found, which corresponds to a monomer content of 83.3 percent. At this salt concentration, a

second virial coefficient of 0.70 m3/mol reflects repulsive interactions between the individual

β-lg molecules due to the negative net charge of the protein at pH 7.0. With increasing NaCl

concentration an increase in molecular weight and a decrease in the second virial coefficient

Figure III-2: (A) Molecular weight of β-lg in dependence of the sodium chloride concentration.

The dotted lines represent the molecular

weight of the β-lg monomer and the β-lg dimer. (B

)

Second virial coefficients of β

-lg in dependence of the sodium chloride concentration. Filled

and unfilled symbols represent one repetition each.

Manuscript III

were observed. The monomer content decreased from 64.9 percent at 5.0 mM NaCl to 1.0

percent at 50 mM NaCl. At 50 mM NaCl, a second virial coefficient close to zero indicates that

electrostatic repulsion and attractive interactions such as hydrogen bonding or hydrophobic

interactions are equal. At 100 mM NaCl, a molecular weight of 38.9 kDa was determined,

which is higher than the value for a β-lg dimer found in literature [60]. This may be explained

due to the presence of a small number of β-lg aggregates. At this salt concentration, a negative

second virial coefficient of -0.03 m3/mol indicated weak attractive forces between the β-lg

molecules, which may cause aggregation. Accordingly, the increasing molecular weight and

the decreasing second virial coefficient with increasing salt concentration were caused by

electrostatic screening of positive charged sodium ions.

With increasing salt concentration, the electrostatic screening of the negative protein charge

increases and therefore the repulsion between the individual protein molecules decreases. The

reduction of electrostatic repulsion allows smaller spatial distances between the β-lg monomers.

As a result, hydrogen bonds can form between the monomers which stabilize the β-lg dimer.

Ersch et al. (2016) observed similar trends for β-lg at a pH of 6.8, a temperature of 40 °C and a

NaCl concentration of 3.0 to 100 mM using membrane osmometry [271]. They found a

decreased second virial coefficient with increasing NaCl concentration. In contrast to our study,

the dimer content predominated even at low NaCl concentrations. This can be attributed to their

use of a 20 mM MOPS buffer as a solvent, while in our study no buffer system was used. The

ionic strength of a buffer adds to the total ionic strength and increases electrostatic screening of

the protein charge, which in turn led to dimerization and a negative second virial coefficient at

3.0 mM NaCl in their study. The decrease of the second virial coefficient with rising ion

concentration is a common observation for β-lg and other charged polymers [144,280–283]. At

the isoelectric point of β-lg, Schaink & Smit (2000) found negative second virial coefficients,

which increased with increasing salt concentration. From their results, they concluded that

mainly dipole-dipole interactions are responsible for this behavior [37].

The intrinsic viscosity of β-lg (Fig. III-3A) ranged from 4.5 mL/g to 5.7 mL/g. Previously

published values, measured at various pH and ionic strengths, ranged from 3.1 mL/g to

4.1 mL/g [284–287]. Despite increasing molecular mass due to dimer formation, a decrease in

intrinsic viscosity was observed with rising sodium chloride concentration. According to

Harding (1997), three effects contribute to the change of the intrinsic viscosity of globular

proteins with the ionic strength: The primary effect results from the hydrodynamic resistance

of the diffuse, electrostatic double layer surrounding the protein. The repulsion between the

double layers of different proteins causes the secondary effect. A tertiary effect, which is known

to be small for globular proteins, occurs due to a change in protein shape [288]. Due to the

screening of the protein charge, the primary and secondary effects lead to a decreased intrinsic

viscosity with increasing ionic strength. In our experiments, the tertiary effect is associated with

the dimerization of β-lg in the NaCl concentration range from 2.5 mM to 50 mM. Dimerization

increases the hydrodynamic volume of the protein and therefore the intrinsic viscosity should

also increase with ionic strength. Nevertheless, between 2.5 mM and 10 mM a substantial

Manuscript III

decrease in intrinsic viscosity was observed. At low ionic strength, the primary and secondary

effects are particularly pronounced and therefore outweigh the tertiary effect [288]. Similar

results were found for 11S and 7S subunits of soybean globulins [289]. Here, an increase of

ionic strength caused a decrease in intrinsic viscosity despite the dimerization of the proteins.

Figure III-3B shows the Huggins coefficient as a function of the sodium chloride concentration.

As the ionic strength increases, an initial increase followed by a decrease in the Huggins

coefficient was observed. This behavior correlates with the dimerization of β-lg. The smaller

the difference between monomer and dimer weight fraction, the higher the Huggins constant.

A possible explanation for this behavior is the sensitivity of the Huggins coefficient to polymer

aggregation and therefore also to dimerization. In addition, the Huggins coefficient may be

influenced by electrostatic interactions and by a change in the spatial protein structure [182].

Also, a change in the solvent affinity of the protein may affect the Huggins constant as the

sodium chloride concentration changes [182,183,290].

III-5.2 Levan

Table III-1 shows the molecular weight, osmotic second virial coefficient, intrinsic viscosity,

Huggins coefficients and the mean Z-average hydrodynamic Radius of LevCoil and LevSphere at

2.5 mM and 100 mM NaCl. The intensity-based distributions of the hydrodynamic radius of

LevCoil and LevSphere at both salt concentrations are shown in the supplementary data

(Fig. S III-3). As expected for an uncharged polysaccharide, NaCl concentration plays a minor

role for the levan properties mentioned above. Despite their different molecular weights, the

intrinsic viscosities of LevCoil and LevSphere differ only slightly at both salt concentrations, which

is due to the molecular weight dependent structure of levan. At low molecular weights, levan

has a compact random coil-like structure. With increasing molecular weight, levan transforms

into a spherical polymer whose density increases with increasing molecular weight. Therefore,

the intrinsic viscosity of levan changes only slightly with the molecular weight [53,54,134,160].

The similar values for the second virial coefficient and Huggins coefficient at 2.5 mM and 100

Figure III-3: (A) Intrinsic viscosity of β-lg in dependence of the sodium chloride concentration.

(

B) Huggins coefficients of β-

lg in dependence of the sodium chloride concentration. Filled and

unfilled symbols represent one repetition each.

Manuscript III

mM indicate no change of solvent quality thru the addition of NaCl. However, both coefficients

vary with the molecular weight. Compared to LevSphere, lower B' and kH indicate stronger

polymer-solvent interactions for the low molecular weight LevCoil.

Table III-1: Number average molecular weight, osmotic second virial coefficient, intrinsic

viscosity, Huggins coefficient and Z-average hydrodynamic Radius of LevCoil and LevSphere at

2.5 mM and 100mM.

LevCoil

LevSphere

NaCl (mM)

2.5

100

2.5

100

Mn (kDa)

150 ± 3

128 ± 9

563 ± 31

600 ± 29

B' (m3mol-1)

4.4 ± 0.3

4.3 ± 1.0

13.67 ± 1.3

15.7 ± 1.2

[η] (mL/g)

36.5 ± 0.1

37.0 ± 0.2

38.5 ± 0.1

39.5 ± 0.2

kH (-)

0.67 ± 0.02

0.68 ± 0.05

1.13 ± 0.02

0.98 ± 0.04

RH (nm)

35.5 ± 0.5

36.6 ± 0.6

100.1 ± 0,6

104.2 ± 1.6

III-5.3 β-lactoglobulin Levan Mixtures

Molecular weight: The number average molecular weight of the mixtures (Fig. III-4A) has

been determined following two different approaches. On the one hand, it can be obtained

experimentally from the intercept of equation 3. On the other hand, equation 5.0 may be used

to predict a theoretical molecular weight from the individual polymer measurements. At 2.5

mM, comparing the molecular weights using this theoretical approach with those determined

using equation 3, the latter were larger by 6.7 kDa and 6.3 kDa for the mixtures containing

LevCoil and LevSphere, respectively. Nichol, Ogston, & Wills, 1981 stated that protein self-

association of an inert polymer can be caused due to the excluded volume effect [291].

Figure III-4: (A) Average molecular weight of levan-β-lg mixtures at 2.5 and 100 mM NaCl.

Diamonds represent molecular weights calculated from the individual polymer measurements

according to equation 5. Triangles show the molecular weichts meausred in the polymer

mixtures.

(B) Cross-virial coefficient of levan-β-lg mixtures at 2.5 and 100 mM NaCl.

Filled

and unfilled symbols represent one repetition each.

Manuscript III

Therefore, the differences between the experimental and the theoretical approach to determine

the molecular weight of the polymer mixtures are probably caused by the dimerization of β-lg

in the presence of levan. The differences in molecular weight at 2.5 mM correspond to a

reduction of the monomer content to 58.9 and 64.8 percent in mixtures containing LevCoil and

LevSphere, respectively. A similar result was found by Schaink & Smit (2007) for mixtures of β-

lg and dextran at the isoelectric point of the protein [63]. They found a slight shift in the dimer-

octamer-equilibrium towards octamers. In our results, for β-lg-levan mixtures at 100 mM NaCl,

the theoretical and the experimental molecular weight of the mixtures differed only slightly,

since the entire protein is already present as a dimer at this salt concentration.

Cross-virial Coefficients: Figure III-4B shows the second cross-virial coefficient of β-lg and

levan at both NaCl concentrations. The positive values of the second cross-virial coefficient

indicate thermodynamically unfavorable and therefore repulsive interactions between both

polymers. This is a common observation in mixtures of uncharged polysaccharides and proteins

and is explained by the excluded volume effect [42,43]. The excluded volume is an area around

a polymer that cannot be occupied by the center of another polymer due to steric interactions.

If two molecules of the same species approach each other, their excluded volume overlaps. The

overlap volume is now accessible for the second species which increases the available free

volume of the system. Therefore, the overall entropy of the system is increased, which is the

driving force behind the excluded volume interaction [39]. One main factor influencing the

excluded volume interaction is the volume of the polymers. The larger a polymer, the greater

the gain in free volume and entropy, when the excluded volume of two polymers overlaps [40].

Therefore, the second cross-virial coefficient of β-lg and the larger LevSphere is higher than that

of β-lg and LevCoil. Since levan is an uncharged polysaccharide, the pair interactions between

levan and β-lg are only partially affected by NaCl. A possible influence of NaCl on the second

cross-virial coefficient could result from the difference in monomer-dimer ratio of β-lg.

However, this effect should be rather small, since the excluded volume of the monomer and the

dimer differs only slightly [144].

Phase behavior: When calculating the interaction coefficient α (equation 10), the formation of

double molecules of different species must be considered. Since the positive second cross-virial

coefficient indicates only repulsive interaction between levan and β-lg, kaggre (equation 10) was

neglected for the calculation of α. In contrast to the second cross-virial coefficient, which is a

measure of the interactions between two individual polymer molecules of different species, α

allows to draw conclusions about the phase behavior of the mixture [273]. In addition, the

comparison of the interaction coefficients A11, A22 and A12 from osmometry using equation 6

can provide information about the phase behavior of polymer mixtures [42,43].

In comparison to the second cross-virial coefficient, α of levan-β-lg mixtures was found to be

less dependent on the molecular weight. In contrast, the sodium chloride concentration affected

α. At 2.5 mM NaCl, an α > 0 and an A122 < A11A22 suggest miscibility of both polymers at low

ionic strength. As indicated by a positive second virial coefficient of β-lg, individual protein

Manuscript III

molecules repel each other due to electrostatic forces at this low salt concentration. These

repulsive interactions may counteract the accumulation of β-lg in one phase and therefore phase

separation could be prevented. When discussing α at low ionic strength, the dimerization of β-

lg due to the presence of levan must be taken into account. The shift of the monomer-dimer-

equilibrium towards dimers could alter the Huggins coefficient of β-lg. As discussed in 4.1, the

Huggins coefficient increases as the monomer fraction approaches 50 percent. Therefore, the α

of mixtures containing LevCoil and LevSphere at 2.5 mM may be overestimated and appears higher

(Fig. III-5) than the actual value. At 100 mM, the measured interaction coefficient for both

levans and β-lg are found to obey equation 6 and α is close to zero. As a consequence, it is

likely that phase separation occurs at a higher polymer concentration. A negative second virial

coefficient of β-lg at 100 mM NaCl indicates attractive forces between protein molecules. These

associative interactions could facilitate the accumulation of the protein in one phase and

therefore phase separation becomes more likely.

Although low ionic strength promotes the stability of protein and neutral polysaccharide

mixtures due to the hindrance of the protein self-association, co-solubility of the polymers is a

rare phenomenon [42]. The miscibility of β-lg-levan mixtures could be favored by the

macromolecular structure of the globular protein and the spherical levan molecule. Compared

to extended proteins such as gelatin, globular proteins have a low excluded volume and thus

contribute to a better miscibility [21]. Moreover, the molecular structure of levan is very

compact compared to other polysaccharides and should therefore have a low excluded volume.

The low excluded volume combined with the hindrance of protein association due to

electrostatic repulsion may explain the co-solubility of β-lg and levan at low ionic strength.

Figure III-5: Interaction coefficient α from viscometry of levan-β-lg mixtures at 2.5 and 100

mM NaCl. Filled and unfilled symbols represent on repetition each.

Manuscript III

III-6 Conclusion

The understanding of the behavior of the individual biopolymers as well as the protein-

polysaccharide mixtures in dilute solutions reveal the basic mechanistic principles and allow to

predict the performance of levan in protein-based systems. The second cross-virial coefficient

reveals repulsive pair interactions between levan and β-lg at pH 7.0 due to the excluded volume

effect. The repulsive forces between the two polymer species are independent of ionic strength

at the investigated NaCl concentrations and seem to be stronger for the high molecular weight

levan. The main factor influencing the phase behavior of the mixtures is the electrostatic

interaction between the β-lg molecules. At 2.5 mM NaCl β-lg molecules repel each other due

to their unscreened negative charge. These repulsive forces seem to counteract the accumulation

of β-lg in one phase, whereas attractive protein-protein interactions at 100 mM could cause the

opposite effect. Therefore, ionic strength could be used selectively to induce or prevent

segregative phase separation in levan-β-lg mixtures. In the future, these findings can enable

predicting and controlling the performance of levan in protein-based food systems. To support

this purpose, the rheological properties and the phase behavior of levan in protein-rich gelled

systems should be investigated.

Manuscript IV

Influence of Levan on the Thermally Induced Gel Formation

of β-Lactoglobulin

gels (2021), accepted manuscript

The publication is online available at https://doi.org/10.3390/gels8040228

This article is licensed under a Creative Commons license (CC-BY 4.0,

https://creativecommons.org/licenses/by/4.0/)

Authors

Christoph S. Hundschell1; Juliane Brühan1; Theresa Anzmann2; Reinhard Kohlus2; Anja M.

Wagemans1

1: Food Colloids, Technische Universität Berlin, Germany

2: Department of Process Engineering and Food Powders, University of Hohenheim,

Germany

Manuscript IV

IV-1 Abstract

In this study, the influence of levan on the phase behavior and the thermally induced gelation

of the mixed β-lactoglobulin—levan gels as a function of polymer content, molecular weight

and ionic strength was characterized. For this purpose, rheology was used to study the

mechanical properties of the gels and the water binding of the network structure was

investigated by time-domain nuclear magnetic resonance. Phase behavior and network type

were analyzed by optical observation and electron microscopy. Levan enhanced the aggregation

and gel formation of β-lg due to segregative forces between the polymer species. Segregation

was caused by the excluded volume effect and was more pronounced at lower ionic strength,

higher levan contents and higher levan molecular weights. The presence of levan increased the

water binding of the gel networks. However, this effect decreased with increasing levan content.

At high ionic strength and high levan content, phase-separated gels were formed. While

segregative forces enhanced network formation, and therefore, increased the gel strength of

mixed gels at low ionic strength, levan had also antagonistic effects on the network formation

at high ionic strength and high polymer contents.

Figure IV-1: Graphical abstract of manuscript V.

Manuscript IV

IV-2 Introduction

To predict the structure and functionality of foods as complex multiphase systems, the

understanding of the molecular interactions between the two main types of food biopolymers –

polysaccharides and proteins – is of central importance and therefore part of ongoing research

[96,163,292–294]. Systems consisting of two different polymer species, co-solubility,

complexation or thermodynamic incompatibility may occur depending on the molecular

interactions [43]. Co-solubility of two polymers is rare since most polymers interact attractively

or repulsively [21]. Attractive interactions cause the formation of soluble complexes or complex

coacervation. Segregative phase separation occurs in thermodynamic incompatible systems

when the phase separation threshold is exceeded [39]. This type of phase behavior occurs when

both polymers interact repulsive or both polymers differ in their affinity for the solvent [43].

In polymer mixtures in which one or both polymers can form a gel, the formation of different

networks is possible. An interpenetration network is rarely formed. Here, both polymers must

be able to form a gel with the resulting networks of both polymers being independent of each

other [19]. If dissimilar polymers bind to each other due to associative interactions, coupled

networks are formed [48]. In coupled networks, the intermolecular adhesion zones between

both kinds of polymers enable the gel formation for polymers that individually would not form

a gel [41]. The most common network types are phase-separated networks, which are formed

between dissimilar polymer species that repel each other [48]. In addition, phase-separated

networks are formed when the critical gelation concentration is greater than the phase-

separation threshold and therefore phase separation occurs before or during gelation [38].

Swollen networks are gels in which only one polymer is involved in the formation of the

network, while the other polymer is dissolved and/or homogeneously dispersed over the

network [46]. This type of gel can be formed in co-soluble systems or in thermodynamic

incompatible systems below the phase separation threshold. The excluded volume effect, which

leads to a local increase in concentration, can enhance the gelation of the network-forming

component in this kind of gel. This effect arises from a reduction of the excess entropy of

mixing since different polymer species do not have access to the volume occupied by the other

species. [48].

A well-known and established model protein is β-lactoglobulin (β-lg). It is a globular protein

and the main protein component of whey. It has a molecular weight of 18.4 kDa and a

hydrodynamic radius of about 2.0 nm [60,144]. The ability of whey proteins to form a gel is

exploited in many food products. The gelation of β-lg can be induced by heating, cold setting,

or high pressure [146–148]. Heat-induced gelation of β-lg occurs in two steps. Firstly, heating

causes denaturation and consequently refolding of the protein. Secondly, aggregation of the

proteins enables the network formation [60]. The structure of the formed network depends

largely on the electrostatic interactions between the protein molecules and therefore on the pH

value and ionic strength [68]. Far off the isoelectric point and at low ionic strength, when

electrostatic repulsion dominates, fibrillar gels are formed. Fibrillar gels have a transparent

Manuscript IV

appearance and the diameter of the gel strands is in the nm range [69]. At a high ionic strength

or near the isoelectric point, opaque particle gels with gel pores in the µm range are formed

[89]. The presence of polysaccharides in β-lg gels can modify the resulting network. The

addition of polysaccharides can antagonistically or synergistically modify the structure and

properties of β-lg gels depending on the chemical structure of the polysaccharide, the mixing

ratio, and the gelation mechanism [19,65,67].

Levan is a β-2,6 linked fructan which is produced by many food-grade starter cultures

[102,295–298]. It occurs naturally in fermented foods such as sourdough bread or kefir

[299,300]. It has prebiotic properties, it is a source of dietary fiber and it can improve the

structural properties of foods [13,16,53,137,301,302]. Its macromolecular and rheological

properties are strongly dependent on the molecular weight [132]. In aqueous solution, low

molecular weight levan has a random coil structure, a low viscosity and a Newton-like flow

behavior. High molecular weight levan has a compact spherical structure. It causes high

viscosity and shear thinning behavior, both being more pronounced with increasing molecular

weight. From a content of 5.0 wt%, the elastic properties of high molecular weight levan

predominate the viscous properties and the dispersion shows a gel-like behavior [15,163,303].

In a previous study, we reported repulsive pair interactions due to the excluded volume effect

in dilute mixtures of native β-lg and levan [163]. These interactions seem to be more

pronounced at a higher molecular weight of levan, while the ionic strength has only a minor

influence. In contrast to the pair interactions, the predicted phase behavior was mainly affected

by electrostatic interactions and therefore by ionic strength. At low ionic strength, the

electrostatic repulsion counteracts the accumulation of the β-lg in one phase and therefore phase

separation is less likely. The opposite happens at high ionic strength, where attractive

interactions between the protein molecules seem to facilitate phase separation.

Due to the unique physicochemical properties, levan is a promising polysaccharide to enhance

the nutritional and techno-functional quality of food systems. However, for its targeted use in

food systems, the interactions with other biopolymers, particular with proteins, must be

established. For this purpose, we investigated the influence of levan on the phase behavior and

the heat-induced gelation of the model protein β-lg. Two different ionic strengths were chosen

to obtain either a fibrillar or particle β-lg gel. To ensure gel formation – even at a low ionic

strength – protein contents of 10 wt% were chosen. In addition, the content and molecular

weight of levan were varied as it directly affects the phase behavior and network formation of

the mixed gels. Based on the interactions in dilute systems, we hypothesize the following:

➢ Heat-induced aggregation of β-lg enhances the segregative forces between β-lg and

levan, due to the excluded volume effect.

➢ A higher levan content and molecular weight promotes phase separation between β-lg

and levan and therefore the formation of phase-separated networks.

➢ A higher ionic strength promotes phase separation since the reduced electrostatic

repulsion between the β-lg molecules facilitates the accumulation of the protein.

Manuscript IV

IV-3 Materials and Methods

IV-3.1 β-lactoglobulin and levan production

Bovine β-lactoglobulin (β-lg) was isolated from whey protein isolate (Bipro, Agropur Diary

Cooperative Inc., Minnesota, USA). The isolation followed the procedure by Keppler et al.

2014 with slight modifications [254]. Ultrafiltration was replaced by dialysis against distilled

water for 3.0 days using BioDesingnDialysis TubingTM (Thermo Fischer Scientific, Waltham

Massachusetts, USA) with a molecular weight cut-off of 14 kDa. Prior to freeze-drying, the pH

of the β-lactoglobulin solution was adjusted to pH 7.0 using 10 % HCl (Carl Roth GmbH,

analytical grade, Karlsruhe, Germany).

The acetic acid bacteria G. albidus was used to produce three levan samples with different

molecular weights. A low molecular weight levan (LevF) was produced by fermentation of a

sucrose-containing sodium gluconate medium. Two high molecular weight levan samples

(Lev4, Lev5) were produced in a cell-free, enzyme-containing sodium acetate buffer at pH 4.0

and pH 5, respectively. Both levan production methods are described in [303]. The molecular

weight of LevF, Lev4 and Lev5 were 1.4·106 Da, 2.0·108 Da and 6.5·108 Da, respectively [303].

The dry mass of β-lactoglobulin and levan was determined with an infrared dryer (LP16,

Mettler-Toledo GmbH, Greifensee, Switzerland).

IV-3.2 Sample preparation

All analyzed samples were prepared in 10 mM and 100 mM NaCl solution and contained

10 wt% β-lg. To investigate the influence of the levan content on the gelation of β-lg, five

samples with Lev4 at contents ranging from 0 wt% (w/w) to 5.0 wt% (w/w) were prepared. The

influence of the molecular weight was analyzed using levan samples LevF, Lev4 and Lev5 at a

polysaccharide content of 3.0 wt% (w/w). To prepare the solutions, levan and β-lg were

weighed in a beaker, mixed with the respective NaCl solution and dissolved on a magnetic stir

plate at 300 rpm. Subsequently, the pH value of the solution was adjusted to 7.0 using 100 mM

HCl or 100 mM NaOH solution (Carl Roth GmbH, analytical grade, Karlsruhe, Germany). To

ensure complete hydration, all samples were stored for 14 hours in a refrigerator. Prior to the

measurements, the pH value was checked and adjusted if necessary.

IV-3.3 Rheological measurements

All rheological measurements were carried out in triplicate using the rheometer Physica MCR

102 or Physica MCR 301 from Anton Paar GmbH (Graz, Austria) equipped with a concentric

cylinder system CC27 (Anton Paar GmbH, Graz, Austria). The samples were covered with a

layer of paraffin oil and a protective hood was used to prevent evaporation. All experiments

were carried out at a frequency of 1.0 Hz and a strain of 1.0 % unless otherwise specified.

Before each measurement, the samples were equilibrated at 20 °C. The gels were formed by

submitting the samples to the following thermal cycle: heating from 20 °C to 90 °C at a constant

rate of 1.0 °C/min, holding at 90 °C for 20 min, cooling from 90 °C to 20 °C at a constant rate

of 1.0 °C/min, holding at 20 °C for 10 min. Afterward, a frequency sweep over the range of

Manuscript IV

0.01 Hz to 10 Hz was carried out at 20 °C. Finally, a strain sweep test was performed from 0.1

% to 100 % to confirm the experiment was conducted in the linear viscoelastic region. The

calculation of n and the gel point temperature was performed using the RheoCompas (Anton

Paar GmbH, Graz, Austria) software. The gel point temperature was chosen as the temperature

at which G' and G'' intersect during heating. For samples that gelled after reaching 90 °C, the

holding time to attain the intersection of G' and G'' was also reported.

IV-3.4 Scanning electron microscopy (SEM)

To produce gels for SEM imaging the solutions were prepared according to the procedure

described in 2.2. For gelation, the samples were heated in a water bath at 90 °C for 30 min.

After cooling, cubes with an edge length of 1.0 cm were cut from the gels. To observe the

optical effects of the thermally induced gel formation, photos were taken after gelation. For

freezing the samples were immersed in liquid nitrogen. The sample 100 mM, 5.0 wt%, Lev4

did not gel during the heat treatment. Therefore, it was placed in a container made of aluminum

foil and frozen therein. Immediately after freezing, the samples were dehydrated by freeze

drying (Beta 1–8 LSCplus, Martin Christ Gefriertrocknungsanlagen GmbH, Osterode,

Germany). Lyophilized samples were carefully broken into pieces and the breakage site was

gold sputtered in a sputter coater SCD 030 (Balzers, Wiesbaden-Nordenstadt, Germany). SEM

imaging was carried out at the Center for Electron Microscopy (ZELMI, Technische Universität

Berlin, Berlin, Germany) with a S-2700 scanning electron microscope (Hitachi, Tokyo, Japan).

Images were recorded at a magnification of 100x, 300x and 1000x. SEM was carried out at

least on time for each formulation.

IV-3.5 NMR

The water binding strength of the heat-induced β-lg gels was analyzed using NMR relaxation

measurements (time domain (TD)-NMR, Minispec 20 MHz, Bruker Biospin GmbH, Germany).

The spin-spin or “transverse” relaxation time T2, and the rate of decay of transverse

magnetization, depends on the interaction of the nuclear spins with their environment. Fast

molecular movements of the molecules carrying the nuclei result in short interaction times with

their neighbors and lead to a slower relaxation process. Transverse relaxation times T2 were

recorded using the software application “t2_cp_mb”, a Carr-Purcell-Meiboom-Gill (CPMG)

pulse sequence provided by Bruker. For each measurement, 4500 data points were collected.

Pulse separation between 90° and the 180° pulse was 1.0 ms and the recycle delay was set to

8.0 s. Data were accumulated with eight scans. Measurement temperature was 20 °C and

measurements were performed at least in triplicate.

To calculate the transversal relaxation time a mono-exponential function was fitted to the NMR

intensity (I) data with the fitting toolbox of MATLAB R2019a (The Mathworks Inc., USA):

𝑰=𝑨∙𝒆−𝒕

𝑻𝟐

(1)

Manuscript IV

Where I is the NMR intensity (%), t is the measurement time (ms), A is the amplitude at time

zero (%) and T2 is the transversal relaxation time of protons (ms).

Inverse Laplace transform was applied to NMR data to obtain the distribution of transverse

relaxation times T2 (MATLAB R2019a (The Mathworks Inc., USA)). For inverse Laplace

transform, the application (rilt) regularized inverse Laplace transform [g,yfit,cfg] = rilt

(t,y,s,g0,alpha) was used [304].

IV-4 Results and Discussion

IV-4.1 Heat-induced gelation

The temperature sweeps of β-lg gels and mixed gels with varying contents of the high molecular

weight levan Lev4 (2.0·108 Da) and salt concentration are shown in figure IV-2. The gelation

of β-lg varied considerably with the salt concentration. For the 10 mM β-lg gels, the onset of

gelation (initial increase of the storage modulus Gʹ) occurred later and more time was needed

Figure IV-2: Development of the storage modulus in the temperature sweeps of gels containing

different

contents of Lev4 (A and B), different molecular weights (C and D

) at 10 mM NaCl

(left panel) and 100 mM NaCl (right panel). The temperature ramp ranged from 20 °C to 90

°C. Shown is the range from 45 °C to 90 °C and the holding phase at 90 °C, where gelation

takes place.

Manuscript IV

to reach a constant value of Gʹ compared to the 100 mM β-lg gels. For the 100 mM, β-lg gels,

the gel point temperature (crossover of Gʹ and Gʹʹ) was reached at 76.7 ± 0.1 °C, whereas for

10 mM β-lg gels a holding time of 2.9 ± 0.9 min at 90 °C was necessary after the maximum

temperature of the heat ramp has been reached (Fig. IV-3). Electrostatic interactions play a

significant role in the gelation of whey proteins such as β-lg. By varying the pH value and ionic

strength, electrostatic forces and therefore the gelling mechanism and the resulting gel

properties can be influenced [68]. The 10 mM β-lg samples formed fibrillar networks and the

gelation occurred at higher temperatures [47,148]. At 100 mM a particle network was formed.

The difference in the gelation is caused by the electrostatic shielding of the salt ions. Without

heat denaturation, β-lg molecules in 10 mM repel each other due to predominant electrostatic

interactions, whereas in 100 mM an equilibrium between attractive and repulsive electrostatic

interactions is reached [163].

The heat treatment causes unfolding of the proteins. Therefore, the hydrophobic core is exposed

and thus enables protein aggregation [305]. At low ionic strengths, the repulsive electrostatic

interactions between the negatively charged β-lg molecules must be overcome and therefore

the proteins form an extended, fibrillar network and the aggregation occurs at higher

temperatures. At high ionic strengths due to charge shielding, the proteins first aggregate into

colloidal particles, which further aggregate into fractal gel networks [47,306,307]. Due to the

shielding of the negative charges of the protein, the network formation at 100 mM occurred

faster and at a lower temperature than the gelation of the 10 mM β-lg gels.

In the 10 mM mixtures, the onset of gelation (as indicated by the initial increase of Gʹ during

heating) and a constant Gʹ were reached earlier with increasing levan content. Moreover, the

gel point temperature of these mixtures decreased with increasing levan content from 90°C

(+2.9 ± 0.9 min) for 1.0 wt% Lev4 to 81.4 ± 0.5 °C for 3.0 wt% Lev4. A increase of levan

content to 5.0 wt% of Lev4, decreased the gel point temperature only slightly to 80.4 ± 0,1 °C.

Figure IV-3: Gel point temperature of samples containing different Lev4 contents (left side)

and different molecular weights of levan (right side). *Sample gelled after a holding time of 2.9

± 0.9 min at 90 °C.

Manuscript IV

In the 100 mM mixtures, the gel point temperature shifted to lower temperatures with increasing

Lev4 content. However, the differences were less pronounced and the gel point temperatures

were generally lower compared to the 10 mM mixtures. Furthermore, the increase of Gʹ after

the onset of gelation was steeper in 100 mM mixtures. The gel point temperature of these

mixtures decreased with increasing levan content from 76.7 ± 0.1 °C (0 wt% Lev4) to 75.2 ± 0.3

°C (3 wt% Lev4) and plateaued upon further increase of the levan content. In mixed gels, a

decrease of the gel point temperature with increasing content of one polymer is commonly

observed if segregative interactions between the polymer species dominate the system [308–

310]. This type of interaction is caused by thermodynamic incompatibility and is often seen in

mixtures of whey proteins and polysaccharides [65,311–314]. Segregative forces between levan

and native β-lg have already been demonstrated and ascribed to the excluded volume effect

[163]. Since the excluded volume effect between polymers is affected by the molecular weight,

heat-induced aggregation of proteins affects the segregative behavior [21]. As the molecular

weight of the protein aggregates increases, the molecular weight difference between the two

polymer species increases as well, resulting in more pronounced segregation. The increased

segregative forces result in a stronger local accumulation of one of the polymer species,

allowing the other species to aggregate and form networks more easily [19]. In our study, this

effect was much more pronounced at lower NaCl concentrations. This can be attributed to the

shielding of the electrostatic charges. After the heat-induced unfolding of the proteins,

aggregation and network formation of the β-lg occurred. At 100 mM, the negative charges of

the proteins were largely shielded and attractive molecular interactions allowed a rapid increase

of the molecular weight through aggregation and network formation, which could be

accelerated only slightly by segregative forces. By contrast, in 10 mM solution, the electrostatic

repulsion of the β-lg molecules had to be overcome after denaturation of the proteins to enable

network formation. In this context, the local accumulation of β-lg in the presence of levan,

facilitated the approximation of the repelling proteins, allowing the fibrillar protein network to

form more rapidly and at lower temperatures.

The molecular weight of levan affected the heat-induced gelation of the mixed gels in

dependence of the NaCl concentration. In 10 mM solutions, the onset of gelation occurred

sooner the higher the molecular weight. The storage modulus of the mixed gels containing the

high molecular weight levan Lev4 (2.0·108 Da) and Lev5 (6.5·108 Da) increased earlier

compared to the low molecular weight LevF (1.4·106 Da). In addition, a constant value of Gʹ

was reached earlier for the mixtures containing Lev4 and Lev5. The gel point as function of the

molecular weight is displayed in figure IV-3 (right panel). For the 10 mM mixtures, a decrease

of the gel point from 88.4 ± 0.5 °C (LevF) to 81.4 ± 0.5 °C (Lev4) and 82.0 ± 0.2 °C (Lev5)

was observed. By contrast, in the 100 mM mixtures, no effect of the molecular weight on heat-

induced gelation was observed. Regardless of the molecular weight, the onset of gelation started

slightly earlier if levan was added. The gel point of the 100 mM mixtures dropped by 1.5 to

2.5 °C in the presence of levan (LevF: 74.2 ± 0.0 °C, Lev4: 75.1 ± 0.3 °C, Lev5: 75.2 ± 0.1 °C).

The molecular weight dependency of the mixed gels is most likely caused due to the excluded

Manuscript IV

volume effect. At the beginning of the protein aggregation, the levan molecules were

significantly larger than the β-lg monomers or dimers. Since the excluded volume effect is more

pronounced the higher the molecular weight difference between two polymer species is, the

initial effects of segregation were more pronounced the higher the molecular weight of the

levan. Therefore, β-lg mixtures with high molecular weight levan formed gels more rapidly and

at lower contents compared to mixtures containing low molecular weight levan. This correlation

was also shown for other segregative interacting mixed gels [309,310].

IV-4.2 Water binding

Time-domain nuclear magnetic resonance (TD-NMR) is a fast and noninvasive tool to study

the distribution and mobility of water populations present in food samples [315,316]. The water

binding is an important parameter because it can be related to the gel strength of the heat-

induced β-lg gels. Besides the determined stress (rheology) and network type (SEM), the water

mobility (NMR) completes the characterization of networks [317].

The influence of the salt concentration and the addition of levan on the relaxation times T2 of

the heat-induced β-lg gels can be seen in figure IV-4. The relaxation time T2 is related to protons

(1H) with defined rotational mobilities, which can be referred to the water population within the

β-lg gels. An increase of the relaxation time T2 means a higher mobility of the water within the

gel structure and a less strong water binding. The T2 of the 10 mM β-lg gel and the 100 mM

β-lg gel indicated a stronger water binding at a higher salt concentration. This correlated with

the gel point temperature. The stronger the water binding in the gel was, the lower was the gel

point temperature during the heat treatment. Furthermore, propositions on the gel strength can

be made by determining the relaxation behavior of the samples, since network formation and

water binding are mutually dependent as shown in other studies [318–320].

The addition of Lev4 initially decreased the relaxation time T2 of the mixed gels at both salt

concentrations (Fig. F-4). The relaxation time of the 10 mM mixed gels decreased with

increasing Lev4 content until an addition of 2.0 wt%. This lower relaxation value was a result

of a stronger water binding within the heat-induced β-lg gel with increasing levan content. A

Figure IV-4: Relaxation times T

of gels containing different Lev4 contents (left side) and

different molecular weights of levan (right side).

Manuscript IV

further increase of the levan content to 3.0 wt% did not lead to a stronger water binding,

although the total polymer content was higher. The mixed 100 mM gels showed similar

behavior but less differences in T2 with increasing levan content. For the higher salt

concentration, the T2 value decreased only slightly and remained constant at high Lev4 contents.

Almost the same behavior was observed for the gel point temperature in dependency of Lev4

content and salt concentration. This corroborates the hypothesis that the water binding in the

mixed gel network corresponds to the network formation and therefore with the strength of the

segregative behavior of the mixed gels.

On the right-hand side of figure IV-4, T2 as a measure of water mobility in the gels is shown as

function of the molecular weight of levan. Regardless of the salt concentration, T2 of the mixed

gels containing 3.0 wt% high molecular weight levan (Lev4 or Lev5) was higher than T2 of the

gel containing 3.0 wt% low molecular weight levan (LevF). At molecular weight of levan, the

water molecules are more tightly bound to the gel network resulting in a lower mobility of the

water protons, which again correlates with the strength of the segregative behavior observed

during the heat-induced gelation.

IV-4.3 Phase behavior and network structure

Rheology: After the heating cycle, a frequency sweep was performed to characterize the gels.

To ensure that all measurements were performed within the linear viscoelastic range, an

amplitude sweep was performed afterwards. All rheological tests following the temperature

sweep were performed at 20 °C. Exemplarily, Gʹ and Gʹʹ of β-lg and β-lg + 3.0 wt% Lev4 at 10

and 100 mM are displayed in figure IV-5 A and IV-5 B. In addition, Gʹ, Gʹʹ and the loss tangent

tan(δ) of all gels at a frequency of 0.45 s-1 are listed in table IV-1. The loss tangent is defined

as the quotient of Gʹʹ to Gʹ. It can be considered as a measure of the ratio of energy lost to energy

stored in the cyclic deformation [321]. In addition, table IV-1 contains n, which corresponds to

the slope in a double logarithmic plot of Gʹ versus frequency in the frequency sweep and can

be considered as a measure of the frequency dependency of a gel [322]. For a perfectly cross-

Figure IV-5: Frequency sweep of the pure β-lg gel (lighter colors) and the β-lg gel containing

.0 wt% Lev4 (darker colors) at 10 mM (A) and 100 mM (B)

NaCl. Filled symbols indicate the

loss modulus (Gʹʹ) and open symbols indicate the storage modulus (Gʹ).

Manuscript IV

Table IV-1: Storage modulus (Gʹ), Loss modulus (Gʹʹ), tan(δ) and n of the heat-induced β-lg

with different levan contents or with different levan molecular weights during the frequency

sweeps.

Sample

Gʹω = 0.45

(10-3 Pa)

Gʹʹω = 0.45

(10-3 Pa)

tan(δ)ω = 0.45

(-)

β-lg 10 mM

1.6 ± 0.3

0.18 ± 0.01

0.11 ± 0.02

0.071 ± 0.009

+ 1 % Lev4

3.6 ± 0.7

0.30 ± 0.02

0.09 ± 0.02

0.054 ± 0.008

+ 2 % Lev4

5.1 ± 0.1

0.38 ± 0.01

0.07 ± 0.00

0.048 ± 0.000

+ 3 % Lev4

11.4 ± 1.2

0.83 ± 0.11

0.07 ± 0.00

0.047 ± 0.001

+ 5 % Lev4

6.8 ± 0.4

0.51 ± 0.03

0.08 ± 0.00

0.048 ± 0.000

+ 3 % LevF

2.9 ± 0.5

0.25 ± 0.03

0.09 ± 0.00

0.055 ± 0.004

+ 3 % Lev5

9.5 ± 1.0

0.64 ± 0.09

0.07 ± 0.00

0.041 ± 0.001

β-lg 100 mM

75.6 ± 15.4

8.06 ± 1.76

0.11 ± 0.00

0.071 ± 0.001

+ 1 % Lev4

115.5 ± 1.6

13.28 ± 0.15

0.12 ± 0.00

0.071 ± 0.001

+ 2 % Lev4

122.7 ± 1.4

14.13 ± 0.32

0.12 ± 0.00

0.070 ± 0.000

+ 3 % Lev4

40.0 ± 7.5

4.54 ± 0.83

0.11 ± 0.00

0.068 ± 0.000

+ 5 % Lev4

22.0 ± 0.9

2.40 ± 0.09

0.11 ± 0.00

0.068 ± 0.000

+ 3 % LevF

33.5 ± 1.4

3.59 ± 0.16

0.11 ± 0.00

0.068 ± 0.000

+ 3 % Lev5

82.5 ± 11.3

9.18 ± 1.35

0.11 ± 0.00

0.071 ± 0.000

linked covalent gel n has a value of 0 while a physical gel has a n > 0. Consequently, the slope

is a measure of the similarity of the gel to a covalent gel [148]. All frequency sweeps showed a

similar course with Gʹ > Gʹʹ and both modules were largely independent of frequency.

Irrespective of the levan addition, the 100 mM particle gels had a significantly higher Gʹ and

Gʹʹ than the 10 mM fibrillar gel networks. Both gels showed n values between 0.041 and 0.071

and a tan(δ) between 0.07 and 0.15, indicating strong cross-linked gels. Without levan, the 100

mM gel showed an almost 50-time higher Gʹ than the 10 mM gel. The Gʹ of the gels correlated

with the water binding observed in the NMR measurements. For the 100 mM β-lg particle gel,

a stronger water binding was found compared to the 10 mM fibrillar gel. The correlation

between the gel strength (rheology) and the water binding (NMR) was also shown in other

studies [318–320]. The gel strength of globular proteins is exponentially related to the protein

content and depends on pH and ionic strength [31]. For β-lg, this relationship has been

demonstrated at pH 7.0 and increasing NaCl concentration (0 to 100 mM) [323,324]. This is

consistent with the results of our study. We could show that particle gels are associated with a

stronger water binding than fibrillar gels. Despite the differences in water binding and network

type, both 10 mM and 100 mM gels showed a similar n (0.071) and tan(δ) (0.11). In other

studies, a lower n was found for fibrillar gels [148]. This can be explained by influencing factors

such as protein content, heating rate and heating time that may also alter the frequency

dependency of the gels.

Manuscript IV

The addition of Lev4 initially increased Gʹ of the mixed gels at both salt concentrations and

further decreased after a critical levan content was reached. In 10 mM gels, a maximum of Gʹ

was reached at 3.0 wt% Lev4. Upon further levan addition, Gʹ decreased but was still higher

compared to Gʹ of the pure ß-lg gel. Accordingly, tan(δ) and n of the 10 mM mixed gels

decreased with increasing Lev4 content and reached their minimum at 3.0 wt% levan. In 100

mM gels, the maximum of Gʹ was observed at 2.0 wt% Lev4. A further increase of the levan

content decreased Gʹ below the value of the pure ß-lg. This indicated a weakening effect of

levan in the 100 mM gels. In contrast to the 10 mM mixed gels, the mixed 100 mM gels showed

almost no difference in tan(δ). Moreover, n decreased hardly with increasing Lev4 content. The

initial increase in Gʹ with increasing Lev4 content was caused by the accumulation of β-lg in

the continuous phase, as there is an exponential relationship between the gel strength and

protein content [323,324]. The decrease in n and tan(δ) with increasing levan content also

indicated an increasing network stability. This behavior was caused by the accumulation of β-

lg due to the segregative behavior and resulted in an increased number of crosslinks. By forming

a two-phase system, the protein content in the β-lg-rich phase increased and therefore the

stability of the formed network increased. In the content range from 1.0 wt% to 3.0 wt%, also

T2 decreased indicating a stronger water binding of the mixed gel network. With further

increasing Lev4 content, the water binding remained constant or slightly decreased despite the

higher total polymer content. In this context, it should be mentioned that gelation and

segregative phase separation can occur simultaneously and influence each other as well as the

water binding within the network [19,311]. The formation of a three-dimensional gel network

with a high viscosity can lead to an arrested state and completely prevent the

thermodynamically favorable formation of a two-phase system [50]. In our study, this

phenomenon could be observed for the 10 mM, 5.0 wt% Lev4 mixed gel as discussed in the

next chapter.

Regarding the effect of the molecular weight of levan in the 10 mM gels, differences between

the low molecular weight (LevF) and the two high molecular weights (Lev4 and Lev5) could

be observed. The storage modulus of LevF mixed gel was more than three times lower than

Lev4 and Lev5 mixed gels. Accordingly, tan(δ) and n of the gel containing LevF showed higher

values indicating a less cross-linked gel structure for the low molecular weight levan. A weaker

water binding of the LevF gel was also found in the NMR experiments when compared to the

gels containing high molecular weight levan. Since the 10 mM mixed gel containing LevF still

showed a stronger water binding, a higher Gʹ and a lower tan(δ) and n compared to the pure

β-lg gel, levan had a synergistic effect on gel formation at 10 mM, which was more pronounced

at a higher molecular weight. The effect of molecular weight on gel strength could be explained

by increased aggregation due to segregation. Since the excluded volume effect is more

pronounced with increasing molecular weight, the segregative forces also increased [50].

However, since only the gel with Lev5 had a comparable Gʹ to the pure β-lg gel, the molecular

weight dependency of the gel strength could also be attributed to steric effects. The lower the

Manuscript IV

molecular weight, the more levan molecules can sterically hinder gel formation and reduce gel

strength.

Microstructure: To distinguish between phase-separated and swollen gels, water binding and

rheological measurements are usually not sufficient. To obtain further information, the

appearance of the gels can be evaluated and imaging techniques can be used. Therefore, we

used SEM imaging to reveal the network structure of mixed gels containing levan and β-lg.

The microstructure and the optical images of the β-lg gels and the mixed gels containing Lev4

are shown in figure IV-6. SEM images at 1000x magnification display the structure of the

continuous β-lg network. The optical appearance can be linked to the gel structure. The fibrillar

β-lg gel at 10 mM was transparent since the diameter of the gel strands was in the nm range

[69]. A particle network with an opaque appearance was formed at 100 mM because the

dimensions of the aggregates were within the µm range [324]. The SEM images of both β-lg

gels showed a porous structure which were similar in size but differed in the regularity of the

structural elements. It should be noted that the freeze and the freeze-drying process might have

affected the structure of the β-lg networks. Therefore, differences between the gels may not

only be attributed to the different formulations but also to the alteration of the network structure

during preparation.

The SEM images of all Lev4 mixed gels (Fig. IV-6), with exception of 5.0 wt% Lev4 mixed

gel at 10 mM, showed spherical, partial filled inclusions. These spherical inclusions, visible in

figure IV-6 (100x), differed in structure from the surrounding matrix, indicating. segregative

phase separation due to thermodynamic incompatibility. This is supported by the fact, that the

pore-like structure surrounding the spherical inclusions was comparable to the pure β-lg gels.

Therefore, it can be assumed that the filling of the spherical inclusions was a levan-rich phase

surrounded by a β-lg-rich continuous phase. Not all spherical structures were filled, which can

be explained by the loss of the filling material during the preparation process. A further

indication of phase separation in the 10 mM mixed gels, was the increasing turbidity with

increasing Lev4 content as the presence of two phases with different refractive indices leads to

light scattering. Although one could expect phase separation at a high levan content, the SEM

images of the 5.0 wt% Lev4 mixed gel at 10 mM showed no phase-separated inclusions. The

5.0 wt% Lev4 sample was also less turbid and had a lower Gʹ than the 3.0 wt% Lev4 gel. One

explanation could be that the viscosity increase caused by levan, may have prevented the

separation into two phases [15]. Without the formation of two phases, levan may have led to

steric hindrance of gel formation resulting in a decrease of gel strength. Since the 100 mM

mixed gels were opaque irrespective of the Lev4 content, the optical evaluation does not

provide any information.

Although the network formation of β-lg occurred earlier and faster at high salt concentration,

all SEM images of the 100 mM mixed gels showed inclusions and therefore indicate the

formation of phase-separated networks. This was even true for 5.0 wt% Lev4, which did not

phase-separate at 10 mM but showed phase-separated inclusions at 100 mM. The shape of those

Manuscript IV

Figure IV-6: SEM images and photographs of the mixed β-lg gels containing different Lev4

contents in 10 mM and 100 mM NaCl. SEM images at 100× magnification focus on phase-

separated regions, if present, and SEM images at

1000× magnification are focused on the

continuous phase.

Manuscript IV

inclusions differed from the spherical shape, presumably due to the high viscosity of the sample

prior to gelation. The fact that phase separation at 100 mM was not or only partially stopped by

gelation – regardless of the levan content – indicated that NaCl enhanced the segregative

behavior. In non-heated mixtures of β-lg and levan, it could be shown that phase separation is

more likely at a higher NaCl concentration [163]. By shielding the electrostatic charges, the

accumulation of β-lg in one phase may have been prevented and made phase separation more

likely. The same is true in heat-treated systems, in which phase separation is enhanced due to

the aggregation of the globular proteins [21]. In contrast to the 10 mM mixed gels (which had

a higher Gʹ than the β-lg gel regardless of the Lev4 content), the Gʹ of the 100 mM mixed gels

decreased below the β-lg gels with 3.0 wt% or more Lev4. Also, n and tan(δ) were merely

affected by the Lev4 content at 100 mM. Therefore, segregation supported the gelation of the

fibrillar gel (10 mM), while antagonistic effects occurred in the particle gels (100 mM). In 100

mM gels, the accumulation due to the segregation had less impact, since particle gels were

already dense due to electrostatic shielding. Especially at higher polymer contents, the system

might have been in an arrested state due to the higher viscosity prior to gelation and faster

network formation at 100 mM. This resulted in a more homogeneous distribution of levan

within the β-lg-rich phase. Consequently, the formation of a coherent network in the β-lg-rich

continuous phase was impaired causing Gʹ to decrease. The homogeneous distribution of Lev4

in the β-lg-rich phase can also explain the structural change of the continuous β-lg phase in the

SEM images of the 100 mM mixed gels containing ≥ 3.0 wt%Lev4.

The molecular weight of levan also influenced the phase behavior during gelation. The addition

of the low molecular weight LevF resulted in transparent gels without inclusions at 10 mM,

whereas the two high molecular weight levans formed opaque gels with phase-separated

spherical inclusions (Fig. IV-7). The absence of phase separation in the mixed gel of LevF and

β-lg could be due to the smaller size difference between the two polymers. Therefore, the

excluded volume effect causes less pronounced segregative forces, which are not sufficient to

separate the system into two phases [50]. That segregative forces still acted during gelation, can

be seen from the decrease of the gelation temperature and the increase of Gʹ compared to the

pure β-lg gel. However, in contrast to the two high molecular weight levans, the increase in Gʹ

was only marginal. At a salt concentration of 100 mM, Gʹ increased continuously with the

molecular weight of levan. The mixed gel containing Lev5 reached a slightly higher Gʹ than the

pure β-lg gel, while Gʹ of the LevF and Lev4 gels were at least two times lower. All three mixed

gels showed a tan(δ) of 0.11 and n differed only slightly between 0.068 (LevF, Lev4) and 0.071

(Lev5). The influence of the molecular weight on gel strength of these gels also corresponded

to the strength of the water binding. Despite of the higher total polymer content, the T2 of the

LevF mixed gels was only slightly lower than T2 of the 100 mM pure β-lg gel. The mixed gels

containing Lev4 and Lev5 exhibited stronger water binding than the pure β-lg gel. The 100 mM

mixed gels had an opaque appearance and the SEM images showed phase-separated inclusions

regardless of the molecular weight. The continuous phase of these gels differed from the pore-

Manuscript IV

100

like structure, which indicates that levan interfered with the formation of the β-lg particle

network at this NaCl concentration regardless of its molecular weight.

IV-5 Conclusion

The water binding, rheological and structural properties of heat-induced β-lg gels and mixed

gels containing various levan contents and molecular weights were studied at two different

NaCl concentrations. It was observed that levan enhances the aggregation and gel formation of

β-lg. Due to the presence of levan, the water binding of the gel network increased, the onset of

gelation occurred earlier and the gel point decreased. This was caused by segregative forces

due to the excluded volume effect, which was more pronounced at lower NaCl concentrations,

higher levan contents and higher levan molecular weights. Under numerous conditions, a phase-

separated gel was formed during the heat treatment. Only at a low NaCl concentration (10 mM),

mixed gels with no phase separation could be formed. Here, the repulsion due to unscreened

negative charges prevented the local accumulation of protein and the formation of a separated

phase. For low molecular weight levan, the segregative forces due to the excluded volume effect

were not sufficient to cause phase separation. Furthermore, the high viscosity caused by levan

Figure IV-7: SEM images and photographs of the mixed β-lg gels containing levan of different

molecular weight in 10 mM and 100 mM NaCl. SEM images at 100× magnification focus on

phase

-separated regions, if present, and SEM images at 1000× magnification are focused on

he continuous β-lg network.

Manuscript IV

101

could have prevented phase separation at the highest polysaccharide content due to an arrested

state. While segregative forces based on the presence of levan enhanced network formation and

therefore increased the gel strength of all 10 mM mixed gels, levan had also antagonistic effects

on the 100 mM mixed gels. As the polymer content increased, the gel strength decreased and

the mixed gels became weaker than the pure β-lg gel. However, these effects could be

compensated by increasing the molecular weight of levan.

This study showed that levan can be used to influence the gelation of β-lg and modify the

properties of the resulting mixed gels. Furthermore, NaCl concentration, polysaccharide content

and molecular weight can be used to control phase separation, gel strength, optical appearance

and water binding. Therefore, our results are a first step towards the understanding the behavior

of levan in complex food systems. In the future, these results can be transferred to complex

food matrixes containing the functional ingredient levan in order to tailor the structure, texture

and appearance of food systems.

General Discussion

102

4. General Discussion

The functional properties of various exopolysaccharides and exopolysaccharide-protein

mixtures have been the subject of recent research. These studies focused on the structure of the

polymers, their interactions and phase behavior since these determine the functional properties

such as gelation, stabilization or thickening [6,39,265]. However, there is only a limited amount

of information available focusing on levan [11,14,59,133,160,266]. Therefore, this thesis aimed

to investigate the structures and interactions of levan, β-lactoglobulin and their mixtures. For

this purpose, the polymers have been analyzed at three levels (dilute – binary, dilute – ternary,

concentrated – ternary) leading to four objectives. The first objective was to investigate the

molecular weight dependence of the macromolecular structure and molecular interactions of

levan in dilute binary systems (manuscript I). The second objective was the development of a

method to examine the non-specific and specific interactions in the dynamically interacting

monomer-dimer system of β-lactoglobulin (manuscript II). The third objective was the

characterization of the interaction and phase behavior of levan and β-lactoglobulin in dilute

ternary systems (manuscript III). And finally, the fourth objective was the analysis of the

network structure and phase behavior of heat-treated concentrated ternary levan-β-lactoglobulin

systems (manuscript IV).

4.1 Levan in dilute binary systems

To investigate the macromolecular conformation and molecular interactions of levan in

dependence on the molecular weight, three types of levan with different molecular weights were

produced (manuscript I). For a more defined molecular weight and a lower dispersity, samples

were fractionated using gradual ethanol precipitation. A total of three untreated and 16

fractioned levan samples with varying molecular weights from approximately 104 Da to 109 Da

could be obtained. When comparing the molecular weights of levan measured by multi-angel

laser light scattering (MALLS) (manuscript I) and membrane osmometry (manuscript III), the

molecular weight obtained by the latter is lower. This is due to the fact that the number average

molecular weight (osmometry) and the weight average molecular weight (MALLS) are

different measures calculated using different methods. In case of polydisperse samples, the

number average molecular weight is generally lower because it is less influenced by the size of

the individual molecules. Furthermore, the osmotic pressure measurements of high molecular

weight levan (LevSphere) were close to the resolution limit of membrane osmometry (manuscript

III) which could have led to measurement inaccuracies. Nevertheless, the intrinsic viscosity and

hydrodynamic radius of both levan samples coincided in manuscript I and manuscript III.

In general, the low molecular weight levan from G. albidus was found to have a compact

random coil structure for 104 Da to 106 Da and a spherical molecular structure for higher

molecular weights at around 106 Da, as commonly described in the literature [54,58]. Besides

these two regimes, for the first time a third regime above 108 Da was identified within this thesis

(Fig. 8). Here, not only the size but also the polymer density increased with increasing

General Discussion

103

molecular weight for the spherical molecules of the levan from G. albidus. This was shown by

decreasing intrinsic viscosity, and hydrodynamic coefficient (manuscript I) as well as

decreasing ratios of RG/RH or Rgeo/RH with increasing molecular weight. These results suggest

an increase in polymer-polymer interactions and a decrease in polymer-solvent interactions. A

change in the molecular interaction with increasing molecular weight was also indicated by a

shift of the Huggins coefficient. For low molecular weight levan, theta conditions were found

(polymer-polymer and polymer-solvent interactions are equal), whereas the Huggins

coefficient of high molecular weight levan indicated stronger attractive polymer-polymer

interactions (manuscript I & III). However, a positive second virial coefficient, which was more

pronounced for high molecular weight levan, indicated repulsive interactions between levan

molecules (manuscript III). This implies that stronger attractive polymer-polymer interactions

with increasing molecular weight are limited to intramolecular interactions whereas

intermolecular interactions remain repulsive. Within a molecule, the polymer segments are

sufficiently close to each other to interact and form attractive interactions. Whereas two distinct

molecules in a dilute system may never approach each other and therefore interact repulsively.

Combining these results from dilute binary systems with the studies of Hundschell et al. (2020),

conclusions can be drawn about the structure formation of concentrated binary levan

systems [15]. As stated in 2.5.1 low molecular weight levan acts like a Newtonian fluid with

low viscosity even at high polymer concentrations, whereas high molecular weight levan shows

a gel-like behavior above a certain concentration. In the study of Hundschell et al. (2020), the

gel-like behavior is explained either by the formation of a highly entangled network or by the

formation of a colloidal network of soft spheres [15]. Considering the positive second virial

coefficients (repulsive interactions) of levan (manuscript III) a colloidal glass must be

considered. Here, the repulsively interacting spherical levan molecules would immobilize each

other at high polymer volume fractions due to steric interactions [325]. As a result, a

dynamically arrested system is formed in which the motion of the individual molecules is

slowed or stopped, leading to the formation of gel-like properties. Nevertheless, an unfolding

of high molecular levan and the formation of an entangled network due to intermolecular

Figure 8: Schematic representation of the macromolecular conformation of levan from G.

albidus in dependence of the molecular weight.

General Discussion

104

interactions at high concentrations cannot be completely neglected. Therefore, further research

is required to understand the structure formation of concentrated binary levan systems at the

supramolecular level, which will be discussed further in chapter 5.

4.2 β-lactoglobulin in dilute binary systems

Based on the analysis of the monomer-dimer equilibrium of β-lactoglobulin, the molecular

interactions of the protein can be divided into specific and nonspecific protein-protein

interactions. Specific interactions occur between two β-lactoglobulin monomers in the form of

hydrogen bonds and contribute directly to the monomer-dimer equilibrium. Non-specific

interactions are mainly caused by electrostatic forces and van der Waal forces and act

ubiquitous [200]. Therefore, these interactions occur between monomers, dimers and between

monomers and dimers. Consequently, monomer-monomer interactions and the monomer-dimer

equilibrium are influenced by both, specific and non-specific interactions. Furthermore, the

monomer-dimer equilibrium is dependent on the protein concentration. Due to this delicate

interplay between specific and non-specific interactions and the polymer concentration, the

determination of the molecular interactions of β-lactoglobulin remains a challenge and was,

therefore, addressed in manuscript II. A new experimental protocol to analyze the specific and

nonspecific interactions of β-lactoglobulin was established using analytical ultracentrifugation

and membrane osmometry. Analytical ultracentrifugation was used to measure the dimer

dissociation constant, which quantifies the specific molecular interactions. Furthermore,

membrane osmometry was used to determine the non-specific interactions in terms of the

second osmotic virial coefficient. Since the osmotic pressure is a colligative quantity and

therefore depends on the number of particles, the concentration dependence of the monomer-

dimer equilibrium must be considered. This was achieved by correcting the reduced osmotic

pressure for the concentration-dependent molecular weight. For this purpose, the portion of

monomers and dimers was calculated using the dimer dissociation constant known from

analytical ultracentrifugation. This unique combination of methods allowed the quantification

of specific and non-specific interactions in a dynamically interacting monomer-dimer system.

To verify this experimental protocol, the molecular interactions of β-lactoglobulin were studied

at different pH (pH 3, pH 7) and at 10 mM or 100 mM NaCl and the results were compared to

xDLVO-CG calculations (manuscript II). Different pH and NaCl concentrations were chosen

to alter the electrostatic interactions, which are known to be crucial for changing the non-

specific interactions of proteins [191]. Analytical ultracentrifugation revealed that dimerization

and therefore specific protein-protein interactions due to hydrogen bonds were more

pronounced at pH 7.0 and higher NaCl concentrations. At pH 7, the xDLVO-CG model

(manuscript II, Fig. II-3) showed a lower charge density of the dimer binding site and thus a

stronger dimerization. Consistent with these results, the second virial coefficient indicated

stronger repulsive non-specific interactions (positive values of B22) at pH 3.0 compared to pH

7.0. These differences resulted from the different net charges, which were +18e- for pH 3.0 and

-8e- for pH 7.0 (manuscript II). For both pH values, the second virial coefficient decreased with

increasing NaCl concentration from 10 mM to 100 mM. An increase in NaCl concentration

General Discussion

105

caused a decrease in repulsive interactions due to the screening of electrostatic charges. At

pH 3.0 and 100 mM, a positive second virial coefficient indicated repulsive interactions. In

contrast, at pH 7.0 and 100 mM, a second virial coefficient close to 0 indicated almost no

interactions. This can be attributed to weaker electrostatic interactions due to the lower total

charge at pH 7.0. These experimental results demonstrated that in the presence of strong

electrostatic interactions, non-specific interactions can overpower specific interactions,

preventing the β-lactoglobulin molecules from coming into close proximity to form specific

interactions. Moreover, the results were in agreement with the second virial coefficients from

xDLVO-CG calculations and literature [37,190]. Comparable results were also obtained in

manuscript III. Here, β-lactoglobulin was measured as a function of NaCl concentration (2.5

mM, 5.0 mM, 10 mM, 50 mM, 100 mM) at pH 7.0 using membrane osmometry and viscometry.

However, in contrast to manuscript II, dimerization was not considered in the determination of

the second virial coefficient. Nevertheless, the results from both manuscripts were mostly

consistent. The second virial coefficients as a function of NaCl concentration obtained by

xDLVO-CG calculations (manuscript II, Fig. II-5B) and the experimentally determined values

(manuscript III, Fig. III-2B) showed the same trend. At pH 7.0 and 100 mM NaCl, the second

virial coefficients in manuscript II and manuscript III indicated weakly repulsive and weakly

attractive interactions, respectively. However, both second virial coefficients were close to zero,

suggesting almost no interactions between the β-lactoglobulin molecules. The similarity of

results in both manuscripts can be explained by the minor effect of dimerization. In manuscript

III, higher protein concentrations, namely 4.0 g/L - 17 g/L, were chosen compared to manuscript

II with 1.0 g/L - 15 g/L. At high protein concentrations, mainly dimers are present. As a result,

the osmotic pressure was less affected by the concentration-dependent monomer-dimer

equilibrium. This is especially true for higher NaCl concentrations, that favor dimerization.

Using the dimer dissociation constants from manuscript II, the concentration-dependent shift

in the dimer fraction can be calculated: In the concentration range used in manuscript III, the

dimer fraction increased faintly from 0.94 to 0.97 for 100 mM and from 0.82 to 0.90 for 10

mM. Therefore, it can be assumed that almost only dimer-dimer interactions were measured.

Furthermore, the xDLVO-CG calculations showed that monomer-monomer, dimer-dimer and

monomer-dimer interactions differed only slightly, especially at pH 7.0. Also, the particle

number and therefore the osmotic pressure is affected when a dimer dissociates in two

monomers. Since the change in dimer fraction was small this effect should be marginally. As a

consequence, the influence of the concentration-dependent dimerization on the osmotic

pressure and thus on the second virial coefficient should be negligible. However, it must be

noted that this effect leads to an underestimation of the second virial coefficient at lower NaCl

concentrations (2.5 mM and 5.0 mM manuscript III) or pH values that deviate more from the

IEP. Under those conditions, the electrostatic repulsion is stronger. Therefore, more monomers

are present even at high protein concentrations. As a result, the effect of concentration-

dependent dimerization could cause an underestimation of the second virial coefficients.

General Discussion

106

In addition to the second virial coefficient from membrane osmometry, the Huggins coefficient

from viscometry can be used to estimate molecular interactions [183]. Nevertheless, a direct

comparison of the Huggins coefficient (manuscript III) and the second virial coefficient

(manuscript II, manuscript III) is difficult. The second virial coefficient is influenced by

molecular interactions, whereas the Huggins coefficient is additionally influenced by

hydrodynamic interactions. Therefore, the Huggins coefficient as a function of the salt

concentration was influenced by conformational changes in addition to electrostatic

interactions. The conformational changes were caused by concentration-induced changes in the

macromolecular structure and the monomer-dimer equilibrium. Since all these effects are

superimposed, it is difficult to evaluate the Huggins coefficient of β-lactoglobulin. The increase

in the Huggins coefficient (Figure III-3) at NaCl concentrations between 2.5 mM and 10 mM

could have been attributed to concentration-dependent dimerization as the Huggins coefficient

is sensitive to oligomerization [182]. Above 10 mM the Huggins coefficient decreased. At these

salt concentrations, the shift in the dimer fraction for the measured protein concentrations was

small. (10 mM: 0.83 - 0.93; 100 mM: 0.94 - 0.98). Therefore, dimerization only slightly affected

the Huggins coefficient. Nevertheless, for an accurate evaluation of the Huggins coefficient of

β-lactoglobulin in dependence of the NaCl concentration, the concentration-dependent

dimerization must be considered. Similar to the approach in manuscript II, the dimer

dissociation constant would need to be determined at different salt concentrations in order to

be included in the calculation of the intrinsic viscosity and the Huggins coefficient.

4.3 Levan and β-lactoglobulin in dilute ternary systems

The molecular interactions between levan and β-lactoglobulin were measured at two different

NaCl concentrations and for two different levan molecular weights. The NaCl concentration

alters the electrostatic repulsion between the individual β-lactoglobulin molecules. Therefore,

the polymer mixtures were studied at 2.5 mM and 100 mM NaCl where the second virial

coefficients of β-lactoglobulin indicated strongly repulsive or almost no/weakly attractive

molecular interactions, respectively (manuscript II, manuscript III). A low molecular weight

levan with a random coil-like macromolecular structure and a high molecular weight levan with

a compact spherical macromolecular structure were analyzed (manuscript I). The interactions

were studied using membrane osmometry and viscometry determining the second cross-virial

coefficient and the interactions parameter α, respectively. The second (cross-)virial coefficient

reflects the pair interactions between two single molecules. In contrast, the interaction

parameter α is considered a measure of the compatibility of the system. The compatibility is

determined by cross interactions and additionally by the polymer-polymer and polymer-solvent

interactions of the individual polymers. According to Grindberg (1997), the phase behavior can

also be derived from the second virial coefficients of the mixture and the single polymers

(manuscript III, formula 6). The second cross-virial coefficient showed repulsive interactions

between levan and β-lactoglobulin for both NaCl concentrations and both levan molecular

weights due to the excluded volume effect. Since levan has no charged groups, the NaCl

concentration did not affect the pair interactions (second virial coefficients). However, an

General Discussion

107

increase in the levan molecular weight resulted in stronger repulsive interactions (higher second

cross-virial coefficients). This can be attributed, to the larger excluded volume of the high

molecular weight levan, which increased the extent of the excluded volume effect [40]. While

the ionic strength did not affect the pair interactions between two levan molecules, a significant

effect on the phase behavior of the mixtures was shown. Both the interaction coefficient α and

the second virial coefficients (equation 6, manuscript III) predicted miscibility at 2.5 mM NaCl

and phase separation at 100 mM, regardless of the molecular weight of levan. This can be

attributed to the pair interactions between β-lactoglobulin molecules. At 2.5 mM repulsive

interactions between the proteins counteracted the accumulation of β-lactoglobulin in one phase

and therefore phase separation was prevented. At 100 mM these repulsive interactions were

screened. Therefore, no repulsive forces counteracted the accumulation of β-lactoglobulin and

the excluded volume effect caused phase separation.

The macromolecular structure of levan should not have substantially affected the pair

interactions and the phase behavior. As stated in manuscript I, the volume of levan does not

increase linear with the molecular weight, since the macromolecular conformation becomes

more compact. If the macromolecular conformation of levan would not be affected by

molecular weight, the molecular volume would be larger. Therefore, the excluded volume effect

would be stronger. However, the observed trend, that phase separation is only enabled at high

ionic strength due to screened electrostatic repulsion of β-lactoglobulin, would most likely

remain the same.

As mentioned in chapter 4.2 the dimerization of β-lactoglobulin was not considered when

determining the second virial coefficients and the interaction parameter α in manuscript III,

since almost exclusively dimers were present at the concentration range used at pH 7.0 and 100

mM NaCl (manuscript II). This is true for 100 mM, however, at 2.5 mM NaCl, it is more likely

that the concentration-dependent dimerization affected the determination of the second cross-

virial coefficient and the interaction parameter α. Nevertheless, it should be noted that

concentration-dependent dimerization affected the measurement of individual polymers as well

as the measurement of polymer mixtures – both needed for the calculation of the cross-virial

coefficient. Therefore, the effects of dimerization should be balanced out when calculating the

molecular interactions. Furthermore, the xDLVO-CG calculations showed that the second virial

coefficients between monomers, dimers and monomers and dimers hardly differ. Therefore, the

influence of concentration-dependent dimerization on the cross-interaction term (see formula 3

manuscript III) of the second cross-virial coefficient was limited. Another effect influencing

the determination of both parameters could have been a shift in the monomer-dimer equilibrium

caused by levan. The presence of an inert polymer like levan can result in the self-association

(dimerization) of proteins due to the excluded volume effect [291]. This effect was evident at

2.5 mM NaCl when the measured molecular weights of the polymer mixtures were compared

with the values calculated from the individual molecular weights of the two polymers and their

weight fractions. Here, a difference of about 6.0 kDa indicated a shift in the monomer-dimer

equilibrium toward dimers. This shift in the molecular weight of β-lactoglobulin may have

General Discussion

108

affected the determination of the second cross-virial coefficient and α. However, the effect of

monomer-dimer equilibrium is particularly pronounced at low concentrations, which did not

apply to the measurements. Furthermore, the difference in the macromolecular volume between

β-lactoglobulin monomers (RH = 2.0 nm) and dimers (RH = 3.2 nm) was only small compared

to the size of levan (low molecular weight: RH ≈ 36 nm, high molecular weight: RH ≈ 100 nm).

Therefore, the excluded volume effect depends mainly on the molecular volume of levan and

the effect of volume increase of β-lactoglobulin due to dimerization should be almost negligible

[144].

These results obtained under specific conditions (pH 7, 2.5 mM and 100 mM) can be applied

to levan-β-lactoglobulin mixtures in general. Repulsive pair interactions between

β-lactoglobulin molecules decrease with decreasing charge (with increasing vicinity to the

isoelectric point) and increasing ionic strength due to reduced electrostatic interactions. Since

levan is an uncharged polysaccharide, the macromolecular structure and the interactions with

the solvent should not be substantially affected by pH and ionic strength. As a consequence, the

pair interactions between levan and β-lactoglobulin should also be largely independent of these

solvent parameters, since there are no electrostatic interactions between these two polymer

species. An exception could be the region of the isoelectric point since higher oligomers can be

present in addition to monomers and dimers. As they occupy a larger volume, the size difference

between the levan and β-lactoglobulin becomes smaller, which should weaken the excluded

volume effect and thus the repulsive pair interactions between both molecules. When

considering phase separation, cross-pair interactions as well as binary polymer-polymer and

polymer-solvent interactions must be considered. Therefore, the tendency for phase separation

should increase with decreasing charge (with increasing vicinity to the isoelectric point) and

increasing ionic strength as the repulsive electrostatic interactions between proteins decrease

and the accumulation of β-lactoglobulin in one phase is more likely. The direct vicinity of the

isoelectric point may again be an exception to the observations. On the one hand, the

electrostatic repulsion should be minimal and thus phase separation should be favored. On the

other hand, the formation of higher oligomers results in a weakening of the pair interactions,

which counteracts phase separation. Which of these effects predominates, is difficult to predict.

The transfer of these results to dilute mixtures of levan and other proteins is more complex. Due

to the structural similarities of β-lactoglobulin to globular plant proteins (spherical structure,

hydrophobic core, hydrophilic shell, charged), a similar relationship could be expected, at least

for soluble plant proteins. This would imply repulsive pair interactions due to the excluded

volume effect. In this case, the phase behavior of levan and plant proteins should not be

particularly different from that of levan and β-lactoglobulin. In general, less electrostatic

repulsion (higher ionic strength, pH close to IEP) between the proteins should favor segregative

phase separation as shown for β-lactoglobulin. Since many plant proteins have a low affinity

for aqueous solvents, protein-protein interactions should be more pronounced. As these

interactions favor the accumulation of protein in one phase, segregative phase separation is

more likely. Therefore, a mixture of plant proteins and levan could phase separate under

General Discussion

109

conditions where a mixture of β-lactoglobulin and levan is still co-soluble. However, it must be

noted that plant proteins exist as fractions of different protein types such as globulins and

albumins. These can interact with each other in complex manners. In the case of aggregate

formation between the different plant protein fractions, the phase behavior of levan-protein

mixtures would be significantly affected. The formation of soluble aggregates would reduce the

size difference between proteins and levan and therefore the excluded volume effect. If

aggregation results in the precipitation of a part of the proteins, the entropy gain due to the

excluded volume effect would also be reduced as the total concentration of soluble polymers is

decreased. In both cases, the co-solubility of the system becomes more likely. Another

alteration of pair interactions and phase behavior could be caused by specific attractive

interactions between levan and the protein. Differences in the secondary structure of the

proteins could theoretically allow the formation of hydrogen bonds between specific regions of

the protein and levan and therefore the formation of protein-polysaccharide complexes.

However, the formation of specific interactions would be untypical for polymers without

ordered secondary structures. Therefore, a detailed discussion of this eventuality is not relevant

for this thesis.

4.4 Levan and β-lactoglobulin in concentrated ternary systems

Finally, the influence of levan on the heat-induced gel formation of β-lactoglobulin was

investigated (manuscript IV). Rheology, time domain nuclear magnetic resonance and electron

microscopy were used to study the network structure, the phase behavior and the water binding

of mixed levan-β-lactoglobulin gels. The experiments were performed at two different NaCl

concentrations since electrostatic interactions and therefore ionic strength affect the structure

of heat-induced β-lactoglobulin gels (chapter 2.6). At pH 7.0 and 10 mM NaCl, β-lactoglobulin

formed a fibrillar gel whereas at 100 mM a particle gel was formed. The characterization of

dilute ternary levan-β-lactoglobulin mixtures predicted that NaCl concentration determines

whether a system is co-soluble or phase-separated (manuscript III). As phase separation

depends on the total polymer concentration and the mixing ratio, four levan concentrations

ranging from 1.0 wt% (w/w) to 5.0 wt% (w/w) were investigated at a constant β-lactoglobulin

concentration. Furthermore, three different levan molecular weights were studied, since the

molecular weight was a key parameter affecting the pair interactions between the polymers

(manuscript III). A low molecular weight levan with a random coil-like structure and two high

molecular weight samples with a compact spherical structure were investigated.

The heat-induced gel formation and the gel network structure of β-lactoglobulin were strongly

dependent on NaCl concentration (manuscript IV). The fibrillar gel (10 mM NaCl) was formed

at higher temperatures and had a lower gel strength than the particle gel (100 mM NaCl). This

can be attributed to the screening of electrostatic interactions at different salt concentrations.

The negative charge of β-lactoglobulin at pH 7.0 (-8e-) resulted in the repulsion of the native

proteins at 10 mM, as demonstrated by a positive second virial coefficient (manuscript II,

manuscript III). At 100 mM, a second virial coefficient of about 0 indicated that none or slightly

General Discussion

110

attractive interactions were present (manuscript II, manuscript III). Since the charge of the

proteins does not change due to heat denaturation, the electrostatic forces still affected the

gelation. In contrast to 100 mM NaCl, the electrostatic repulsion of the proteins at 10 mM NaCl

must be outweighed by other attractive molecular interactions. Therefore, network formation at

100 mM proceeded faster and at lower temperatures.

All mixed levan-β-lactoglobulin gels showed a decrease in gelation temperature and faster

gelation with increasing levan content (manuscript IV). This is a typical behavior of

thermodynamic incompatible systems and is often observed in mixtures of uncharged

polysaccharides and proteins [308–310]. The driving force for this behavior are repulsive

interactions due to the excluded volume effect. Repulsive interactions were also predicted by

osmometry and viscometry measurements in manuscript III as discussed above. In addition to

repulsive interactions, the results of manuscript III predicted segregative phase separation for

100 mM and co-solubility for 10 mM, regardless of the levan molecular weight. This prediction

was only partially confirmed in the concentrated systems. For 100 mM, phase separation and

thus, the formation of a phase-separated network could be observed independently of the levan

concentration and the molecular weight of levan. However, at 10 mM, the formation of phase-

separated networks was also observed. Only the gels containing the low molecular weight levan

or the highest content of high molecular weight levan showed no evidence of macroscopic phase

separation. This deviation from predictions can be explained by the change in molecular

interactions due to protein denaturation. The heat-induced transition of the tertiary structure

resulted in attractive hydrophobic interactions between the β-lactoglobulin molecules [305].

These attractive interactions competed with the electrostatic repulsion. Therefore, the repulsion

between the proteins was reduced or attractive interactions dominated. Since attractive/less

repulsive protein-protein interactions favor the accumulation of proteins, phase separation

becomes more likely. In the 10 mM mixed gel, containing the low molecular weight levan, the

enhancement of phase separation due to more attractive protein-protein interactions was

probably not sufficient to cause segregative phase separation. The repulsive pair interactions

between β-lactoglobulin and levan depend on the excluded volume effect and therefore on the

size difference between the polymers (manuscript III). Since the size difference between low

molecular weight levan and β-lactoglobulin was small, phase separation did not occur even if

the proteins are denatured. The absence of phase separation in the 10 mM mixed gel at the

highest levan content was most likely caused by an arrested state. The high viscosity caused by

levan may have prevented phase separation completely, even if it was thermodynamically

favorable. This phenomenon was at least partially present at 100 mM, as indicated by a change

in the continuous phase in the SEM images. Due to the incomplete phase separation, some levan

remained in the continuous phase. Therefore, levan sterically interfered with gel formation and

thus changed the gel structure. The change in the gel structure was also evident from the gel

strength. While the storage module initially increased with the levan content, it decreased when

a change in the continuous phase was shown by SEM. This phenomenon may be used to modify

gel strength, network structure and phase separation of levan-β-lactoglobulin gels. Protein

General Discussion

111

denaturation simultaneously induces network formation and phase separation which are two

competing processes. Therefore, the heating rate could have a significant influence on the

network structure of mixed gels. A higher heating rate results in faster network formation. The

levan has less time to accumulate in one phase and more levan remains in the continuous phase.

This should weaken the gel network structure and segregative phase separation becomes less

likely. Conversely, a lower heating rate should promote phase separation. Therefore, less levan

remains in the continuous phase which would result in higher gel strength.

Concluding Remarks and Outlook

112

5. Concluding Remarks and Outlook

The results from this thesis contributed to a better understanding of the exopolysaccharide

levan. New insights into the macromolecular structure and the molecular interactions in

dependence of the molecular weight were gained. In addition, the interactions with the model

protein β-lactoglobulin in binary and more food-relevant concentrated ternary systems were

elucidated. It has been shown that knowledge about structures and interactions in dilute binary

and ternary systems is essential to understanding and controlling the properties of food-relevant

concentrated systems. In detail, the structure and interactions of levan and levan-β-lactoglobulin

mixtures were analyzed at three levels (dilute – binary, dilute – ternary, concentrated – ternary).

In dilute binary systems, the molecular weight showed a major influence on the macromolecular

structure and the molecular interactions. With increasing molecular weight, the macromolecular

structure of levan shifted from a random coil-like molecule to a sphere. In addition, a third

regime in the Mark-Houwink-Sakurada plot could be identified for the first time, which

indicated a continuous increase in polymer density of the spherical levan for molecular weights

above 108 Da. The whey protein β-lactoglobulin was used as a model protein since it is well-

studied and commonly used as a component in the food industry. However, the determination

of specific and non-specific interactions of β-lactoglobulin in dilute binary systems remains a

challenge due to the monomer-dimer equilibrium. Therefore, a measurement protocol based on

analytical ultracentrifugation and membrane osmometry was established in this thesis. The

specific molecular interactions were determined in terms of the dimer dissociation constant and

the non-specific interactions in terms of the second virial coefficient. These measurements

confirmed the strong contribution of electrostatic interactions on both types of interaction. In

dilute ternary systems, levan and β-lactoglobulin showed repulsive pair interactions due to the

excluded volume effect. These were more pronounced for high molecular weight levan. In

addition, it was shown that electrostatic interactions between the β-lactoglobulin molecules did

not affect the pair interactions but were decisive for the phase behavior of the mixtures. These

results could be confirmed in concentrated ternary systems. On the one hand, unscreened

repulsive electrostatic interactions and a low levan molecular weight resulted in the formation

of swollen gels. On the other hand, high molecular weight levan and/or screening of the

electrostatic interactions led to the formation of phase-separated gels. In general, it could be

shown that the cross-pair interactions between levan and β-lactoglobulin in all systems were

dominated by repulsive interactions due to the excluded volume effect. These results

contributed to a better understanding of protein aggregation in the presence of an inert

polysaccharide and can be used to control the gel network structures of levan-β-lactoglobulin

mixed gels.

Although this thesis contributes to extending the knowledge about levan, it also raises new

questions for future research. In the following section, some important challenges are addressed

and possible solutions will be discussed.

Concluding Remarks and Outlook

113

In this thesis, the dependence of the macromolecular conformation and the molecular

interactions on the molecular weight was shown for the levan of G. albidus in aqueous

solutions. However, levan is produced by various microorganisms and the degree of β-

2,1 -linked branches can vary depending on the organism [129]. The degree of branching is

known to affect both, macromolecular conformation and molecular interactions. Therefore,

further studies of levan with different degrees of branching could contribute to a global

understanding of levan. The low degree of branching in G. albidus levan may be crucial to the

fact that molecular density increases with molecular weight [132]. A higher degree of branching

usually results in more compact molecules [326]. Therefore, levan may reach a maximum

density that does not change with molecular weight. To test this hypothesis, levans with

different degrees of branching must be obtained and subsequently analyzed according to

manuscript I. The most comparable results would be obtained when a highly branched levan is

gradually debranched enzymatically or chemically. However, these reactions could cause

uncontrolled hydrolysis of levan and therefore may not be a suitable option. In this case, levan

of different microbial origin must be compared, considering the effects of different molecular

weight and dispersity. In any case, a careful analysis of the degree of branching is required,

which can be performed by NMR [327].

Another open question concerns the transition from a random coil to a compact, spherical

macromolecular structure. In manuscript I, this transition was found to occur with increasing

molecular weight and was ascribed to stronger intramolecular polymer-polymer interactions.

Furthermore, high-molecular levan with a compact spherical structure causes high viscosities

and gel-like structures, while low-molecular levan with a random coil-like structure causes low

viscosities and behaves Newtonian [15]. Combining these two observations, a correlation

between the rheological properties and the macromolecular conformation of levan could be

suggested. Therefore, the question arises whether the macromolecular conformation and thus

the rheological properties of levan can be controlled. For several polymers, such a transition

can be induced by changes in solvent quality [328]. A reduction in solvent quality results in

weaker polymer-solvent and stronger polymer-polymer interactions and thus can induce the

collapse of a random coil into a spherical and compact molecule and vice versa. It is still

unknown whether this transition is possible for levan. One way to induce the transition of a low

molecular weight random coil into a compact spherical molecule could be the addition of an

organic solvent such as ethanol to aqueous solutions. As a non-solvent for polysaccharides,

ethanol reduces the solvent quality of aqueous solvents and may trigger the transition [329].

Another possibility would be to improve the solvent quality by an increase in temperature. Thus,

it might be possible to convert a compact spherical high molecular weight levan to a random

coil state. However, to observe these possible transitions, the change in the macromolecular

structure must be analyzed as a function of the solvent quality. For this purpose, the intrinsic

viscosity, the hydrodynamic radius or the gyration radius can be determined by viscometry,

dynamic light scattering or static light scattering, respectively. In addition, membrane

osmometry could be used to determine the second virial coefficient and the molecular weight.

Concluding Remarks and Outlook

114

The second virial coefficient reflects the solvent quality. An increase in the molecular weight

with a decrease in the solvent quality indicates aggregation. This would indicate that a change

in macromolecular conformation is not caused by a transition from a random coil to a sphere

but by aggregation.

Another issue directly related to the macromolecular structure is the formation of

supramolecular structures in concentrated binary levan systems. As discussed in chapters 2.5.1

and 4.1, compact spherical levan molecules could form a colloidal gel, a colloidal glass, or

levan molecules could unfold and form a highly entangled network. To distinguish between

these supermolecular structures is a difficult task since the properties of these viscoelastic solids

are quite similar. Nevertheless, rheological studies can provide indications of the

supermolecular structure. Typically, the storage modulus of a colloidal glass in a frequency

sweep is largely independent of the oscillation frequency and the loss modulus exhibits a

minimum [325,330,331]. In contrast, a colloidal gel shows an increase in both moduli with

increasing oscillation frequency [332]. In addition, a colloidal gel and a colloidal glass may

differ in the non-linear region of an amplitude sweep. On the one hand, the storage modulus of

a colloidal gel should decrease in two steps after crossing the limit of the linear viscoelastic

region. The first decrease can be attributed to the overcoming of the attractive interactions

between the colloids and the second decrease to the breakdown of the supramolecular network

structure. On the other hand, the colloids in a colloidal glass interact repulsively and no

attractive interactions must be overcome. Therefore, the decrease in the storage modulus is

directly linked to the breakdown of the supermolecular structure and occurs in a single step

[325,331,333]. To distinguish the formation of a highly entangled network from a colloidal

glass or colloidal gel, rheology may be insufficient. Another useful analysis/ technique to

further investigate the structural differences is small-angle-X-ray scattering. At high polymer

concentrations, the structure factor can be determined which reveals the arrangement of the

polymers in relation to each other. Furthermore, it allows the determination of macromolecular

structures and the formation of aggregates [334]. Thus, X-ray scattering can be used to

distinguish between an entanglement network and a system of colloidally dissolved

nanoparticles. Furthermore, the determination of the structure factor can be used to distinguish

between a colloidal gel and a colloidal glass [335].

In manuscript III, a shift in the monomer-dimer equilibrium of β-lactoglobulin towards the

dimer was observed due to the addition of levan at a NaCl concentration of 2.5 mM. This effect

results from the reduction of the excluded volume by the dimerization and was also shown for

mixtures of β-lactoglobulin and polyethylene glycol [336]. For proteins in general, the addition

of an inert polymer can result in increased aggregation [291]. Although the principle of

enhanced β-lactoglobulin dimerization is known, no studies could be found attempting to

quantify this effect. Unlike the aggregation of many other proteins, the dimerization of

β-lactoglobulin is an equilibrium reaction in which two monomers always bind in the same way

with the participation of certain functional groups. Therefore, specific interactions can be

quantified in terms of the dimer dissociation constant (manuscript II). However, in this

Concluding Remarks and Outlook

115

particular case analytical ultracentrifugation is not suitable as an analytical method to analyze

specific interactions. Here, a mixture of β-lactoglobulin and an inert polymer would be

separated according to size, shape and density. Even partial separation is expected to interfere

with molecular interactions. In addition, the presence of a second polymer species should cause

problems when evaluating the sedimentation profile to determine the dimerization constant.

Another method to determine the dimer dissociation constant of β-lactoglobulin is isothermal

titration calorimetry. Here, a stepwise injection of β-lactoglobulin into a calorimetric cell is

used to measure the exothermal heat flow of dimer formation as the protein concentration

progressively increases [337]. Unlike analytical ultracentrifugation, the presence of an inert

polymer should not interfere with isothermal titration calorimetry measurements since inert

polymers such as levan and β-lactoglobulin interact only via the excluded volume. The polymer

species do not bond and thus no exothermic nor endothermic process should interfere with the

exothermic dimer formation. By continuously injecting a β-lactoglobulin into an inert polymer,

it should be possible to observe the increased dimerization. To avoid a dilution of the inert

polymer, the solution in the measuring cell and the injected β-lactoglobulin solution must

contain the same concentration of inert polymer. Thus, the indirect influence of the excluded

volume effect on the specific interactions (dimer dissociation constant) of β-lactoglobulin could

be determined. In addition, this method can be used to determine the Gibbs free energy change

of dimerization (ΔG) as well as its enthalpic (ΔH) and entropic (ΔS) contributions [338].

Therefore, these studies could contribute to a better understanding of protein-protein

interactions in thermodynamically incompatible protein-polysaccharide mixtures. For example,

the influence of the type, concentration, and molecular weight of the inert polymer could be

studied. Furthermore, the determination of the cross-virial coefficient in β-lactoglobulin-levan

mixtures can be improved. For this purpose, the dimer dissociation constant should be measured

as a function of levan concentration. The dependence of the dimerization on the levan

concentration can subsequently be included in the calculation of the virial coefficient.

To date, the full extent of exopolysaccharide functionality in various food systems has not been

completely understood. Even though levan has been studied in food systems such as sourdough

bread, fermented fava bean dough, and fermented vegetables, the structure-function

relationship is not understood [9,13,339]. In these studies, quality-enhancing effects of levan

could be demonstrated, but the fundamental mechanisms resulting in the improvement could

not be elucidated. To gain a better understanding of these systems, this thesis contributed

through systematic investigation of levan, β-lactoglobulin and levan-β-lactoglobulin mixtures

in dilute and concentrated systems. Molecular polymer-polymer and polymer-solvent

interactions as well as the macromolecular structures of the polymers were analyzed in dilute

systems (manuscript I – III). The influence of the levan molecular weight as well as the impact

of electrostatic protein interactions in binary and ternary systems could be understood. On the

one hand, levan molecular weight was crucial for the magnitude of the excluded volume effect.

A higher molecular weight resulted in stronger repulsive cross-pair interactions between levan

and β-lactoglobulin. Therefore, segregative phase separation in concentrated ternary systems

Concluding Remarks and Outlook

116

becomes more likely with increasing molecular weight. On the other hand, unscreened

repulsive electrostatic interactions between proteins counteracted the accumulation of

β-lactoglobulin in a phase. Therefore, segregative phase separation becomes more likely with

increasing NaCl concentration. These predictions based on the molecular interactions

contributed significantly to the understanding of the structure formation in food-relevant levan-

β-lactoglobulin mixed gels (manuscript IV). As expected, the measurements showed the

formation of phase-separated gels for high molecular weights and high NaCl concentrations.

For a low levan molecular weight in combination with low NaCl concentration, the formation

of a swollen gel could also be proven. In addition, it was shown that the gel strength not only

depends on the type of gel but also on the competition between phase separation and gel

formation. The fundamental mechanisms should be transferable to mixtures of proteins and

levan in general, thus contributing to a better understanding of levan in food-related systems.

These observations should be particularly relevant for plant proteins since they have a globular

macromolecular structure and exhibit a similar salt- and pH-dependent gelation mechanism,

resulting in the formation of fibrillar gels or particle gels. [340,341]. Therefore, the addition of

levan could most likely be used to modify the gel strength and the gelation temperature in plant

protein gels. In addition, the gel structure could be manipulated selectively due to segregative

phase separation. As such, levan could potentially be used as a thickening and texturing agent

in protein-based food systems. This could be particularly interesting for fermented products

such as yogurt, where levan could be produced in situ by suitable microorganisms. However,

most foods are complex systems and cannot be completely represented by a ternary model

system. Other food ingredients such as polysaccharides, sugars or fats may interfere with

structure formation. Therefore, the influence of these substances on the structure of levan and

the structure formation in levan-containing systems should be investigated in the future.

Another aspect that should be studied is the in situ formation of levan in fermented foods. For

products such as bread or yogurt, differences between the in situ production of

exopolysaccharides and the addition as an additive could be demonstrated [299,342]. On the

one hand, the presence of other food ingredients could alter the exopolysaccharide itself. In the

case of levan, a change in molecular weight could occur. As shown in this thesis, this can have

substantial effects on the macromolecular structure and interaction with proteins, and thus on

the phase behavior and stability of the system. However, this could also be exploited to produce

an exopolysaccharide with the desired properties by adjusting the fermentation conditions. On

the other hand, cross-linking of exopolysaccharides through anchoring or interactions with the

synthesizing microorganisms could contribute to structure formation [106]. Therefore,

microbiological polysaccharide production, structures and interactions at the molecular level

and the macroscopic structure of the food must be considered holistically to achieve the targeted

use of exopolysaccharides.

References

117

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Analysis of Levan Produced by Lactic Acid Bacteria in Fermented Doughs.

Carbohydr. Polym. 2019, 208, 285–293, doi:10.1016/j.carbpol.2018.12.044.

340. Nicolai, T.; Chassenieux, C. Heat-Induced Gelation of Plant Globulins. Curr. Opin.

Food Sci. 2019, 27, 18–22, doi:10.1016/j.cofs.2019.04.005.

341. Munialo, C.D.; Euston, S.R.; de Jongh, H.H.J. Protein Gels. In Proteins in Food

Processing: Second Edition; 2018; pp. 501–521 ISBN 9780081007297.

342. Mende, S.; Rohm, H.; Jaros, D. Influence of Exopolysaccharides on the Structure,

Texture, Stability and Sensory Properties of Yoghurt and Related Products. Int. Dairy

J. 2016, 52, 57–71, doi:10.1016/j.idairyj.2015.08.002.

Annex

141

Annex

List of Conference Contributions

Bäther, S., Seibt, J. H., Hundschell, C. S., Wagemans, A. M.; Towards understanding the

structure formation of alginate-gelatin based scaffolds in 3D-bioprinting (2022) 2nd Edible Soft

Matter conference, Wageningen, Netherland

Hundschell, C. S., Bäther, S., Wagemans, A. M.; Structure-functionality of the

exopolysaccharide levan in food systems (2022), 2nd Edible Soft Matter conference,

Wageningen, Netherland

Bäther, S., Hundschell, C. S., Wagemans, A. M.; Impact of solvent properties on molecular

interactions and phase behaviour in alginate-gelatin systems (2022), 18th Food Colloids

Conference, Lund, Schweden, online

Hundschell, C. S., Drusch, S., Oechsle, A. M.; Structural characterization and molecular

interactions of β-lactoglobulin, levan and their mixtures (2019), 20th Gums & Stabilisers for

the Food Industry Conference, San Sebastian, Spain

Hundschell, C. S., Jakob, F., Vogel, R. F., Drusch, S., Oechsle, A. M.; Molecular structure and

polymer density of exopolysaccharide levan as function of molecular weight (2018), Structure

and Functionality Forum Symposium, Montreal, Canada

Annex

142

List of Additional Publications

Hundschell, C. S., Wagemans, A. M.; Rheology of common uncharged exopolysaccharides

for food applications, Current Opinion in Food Science (2019), 27, 1 – 7,

https://doi.org/10.1016/j.cofs.2019.02.011

Hundschell, C. S., Braun, A., Wefers, D., Vogel, R. F., Jakob, F.; Size-Dependent Variability

in Flow and Viscoelastic Behavior of Levan Produced by Gluconobacter albidus. Foods (2020),

9, 192, https://doi.org/10.3390/foods9020192

Bäther, S., Hundschell, C. S., Kieserling, H., Wagemans, A. M.; Impact of the solvent

properties on molecular interactions and phase behaviour of alginate-gelatin systems, Colloids

and Surfaces A: Physicochemical and Engineering Aspects (2022), 130455,

https://doi.org/10.1016/j.colsurfa.2022.130455

Annex

143

Supplementary Data Manuscript I

Supplementary data S I-1: Molecular Sizes of levan and its fractions.

Fraction

(Da)

geo

(nm)

PDI

(-)

H,DLS

(nm)

H,visc

(nm)

[η]

mL/g

LevF

1.4·106

21.9

19.9

8.1·106

8.1

5.4·105

2.9

1.0·105

2.2

3.9·104

2.1

2.1·104

Lev4

2.0·108

120

108

1,5

112

109

3.3·108

139

118

1.3

128

130

2.8·108

133

115

1.2

124

128

2.6·108

131

111

1.2

122

2.2·108

124

109

1.2

119

115

1.4·108

110

1.4

105

100

8.4·107

2.3

1.0·107

31.1

Lev5

6.5·108

168

131

1.7

161

154

1.2·109

193

139

1.2

202

190

8.2·108

179

136

1.4

188

164

4.6·108

153

128

1.5

142

140

4.5·108

154

129

1.5

138

141

Supplementary data S I-2: Dependence of the specific extinction coefficient on the geometric

radius of levan.

Annex

144

Supplementary data S I-3: Polymer concentration as a function of the retention time during

the aF4-MALLS measurement. Solid line RI detection, dashed line UV detection, dotted line

corrected UV detection. Lev4 F6 (A), Lev4 F5 (B).

Supplementary data S I-4: Cumulative molecular weight distribution as a function of the

molecular weight. Solid line RI detection, dashed line UV detection, dotted line corrected UV

detection. Lev4 F6 (A), Lev4 F5 (B).

Annex

145

Supplementary Data Manuscript II

Supplementary data S II-1: Dispersion potential derived from the Hamaker constant and the

Lennard-Jones potential between the β-lg monomers (A) and BLG dimers (B). Potential was

calculated using xDLVO-CG method, described in literature.

Supplementary data S II-2: The osmotic second virial coefficient B22 for different pH values

and sodium chloride concentrations as calculated from xDLVO-calculations and the 2-sphere

DLVO approach. Values are provided for monomer-monomer (M-M), monomer-dimer (M-D)

and dimer-dimer interactions (D-D).

Annex

146

Supplementary data S II-3: Anisotropy of the total charge of β-lg proteins in xDLVO-CG

model.

Supplementary data S II-2: Measured extinction at a wavelength of 280 nm for various

protein concentrations in water at pH 7.0 and salt concentration of 10 mM sodium chloride.

The linear slope provides the extinction coefficient.

Annex

147

Supplementary data S II-3: Osmotic second virial coefficients (in 10-3 mol/ (mL g2))

calculated using the dispersion potential based on the Hamaker constant and Lennard-Jones

potential (see equations 13-21).

Potential for the

calculation of

B22

pH 3

10 mM sodium chloride

100 mM sodium chloride

M-M

M-D

D-D

M-M

M-D

D-D

Hamaker

3.90

3.25

2.29

0.36

0.32

0.23

Lennard-Jones

4.45

3.24

2.29

0.37

0.26

0.17

pH 7

Hamaker

1.50

1.34

0.99

0.13

0.10

0.09

Lennard-Jones

1.04

1.31

0.97

-0.33

-0.97

Supplementary data S II-4: (A): Sedimentation coefficient distribution as retrieved from data

analysis in SEDFIT for a protein mass loading concentration of 1.0 g/L. The solution pH and

the salt concentration are indicated in the legend. (B) Weight averaged sedimentation

coefficient for varying protein concentration at a solution pH of 3.0 and a salt concentration of

10 mM sodium chloride.

Annex

148

Supplementary data S II-5: Reduced osmotic pressure for β-lg in sodium chloride solutions

as a function of protein loading concentration. Results are shown for different pH values and

salt concentrations.

Supplementary data S II-6: Second virial coefficient as calculated from equation 15 for

different protein loading concentrations. (Right): Theoretical calculated molecular weight-

corrected osmotic pressure from equation Fehler! Verweisquelle konnte nicht gefunden

werden. for concentration-dependent molecular weight for β-lg in sodium chloride solutions as

a function of protein loading concentration.

Annex

149

Supplementary data S II-7: Theoretical weight fraction of monomers and dimers for an

equilibrium constant of 39.7 µM. This corresponds to a solution pH of 3.0 and a salt

concentration of 10 mM NaCl.

Supplementary data S II-8: Umbrella sampling histograms obtained from molecular

dynamics simulations of 61 US windows of β-lg dimer at pH 3.0 and 7.0 with the salt

concentration of 10 mM and 100 mM sodium chloride.

Annex

150

Supplementary data S II-9: Potential of mean force showing the free energy of β-lg

dimerization at different solution conditions.

Annex

151

Supplementary Data Manuscript IV

Supplementary data S III-1: Raw data osmometry.

Polymer

NaCl

(mM)

Polymer

concentration

(kg/m3)

Reduced

osmotic

pressure

(mol/kg)

Polymer

concentration

(kg/m3)

Reduced

osmotic

pressure

(mol/kg)

Measurement 1

Measurement 2

Levcoil

2.5

5.29

0.00761

5.30

0.00784

6.88

0.00796

6.89

0.00809

8.47

0.00821

8.48

0.00835

10.06

0.00851

10.06

0.00858

11.65

0.00875

11.65

0.00896

13.07

0.00924

13.23

0.00939

Levcoil

100

5.00

0.00976

5.00

0.00844

6.49

0.00994

6.59

0.00898

7.99

0.01043

9.80

0.00984

9.49

0.01083

11.40

0.01032

10.99

0.01121

13.72

0.01108

13.21

0.01182

LevSphere

2.5

11.43

0.00235

10.95

0.00235

16.00

0.00247

14.93

0.00237

20.57

0.00260

18.92

0.00253

25.14

0.00287

23.90

0.00266

29.71

0.00315

28.87

0.00289

33.31

0.00342

34.35

0.00321

LevSphere

100

9.99

0.00206

9.99

0.00227

18.98

0.00239

14.99

0.00235

23.98

0.00263

19.98

0.00253

28.97

0.00287

24.98

0.00267

34.39

0.00326

29.97

0.00299

34.49

0.00325

β-lg

2.5

4.63

0.05223

4.55

0.05485

6.95

0.05761

6.83

0.05754

9.27

0.05970

9.11

0.05980

11.59

0.06363

11.39

0.06381

13.90

0.06736

13.66

0.06807

16.22

0.07072

15.94

0.07137

β-lg

4.64

0.04352

4.57

0.04440

6.96

0.04352

6.85

0.04508

Annex

152

9.28

0.04704

9.14

0.04551

11.60

0.04763

11.42

0.04855

13.92

0.04955

13.71

0.04922

16.24

0.05161

15.99

0.05134

β-lg

4.37

0.03814

4.60

0.03612

6.55

0.03674

6.90

0.03650

8.74

0.03832

9.21

0.03753

10.92

0.03687

11.51

0.03747

13.11

0.03885

13.81

0.03846

16.39

0.04043

16.11

0.03932

β-lg

5.01

0.02564

4.45

0.02859

7.51

0.02545

6.67

0.02753

10.02

0.02650

8.90

0.02833

12.52

0.02574

11.12

0.02824

15.03

0.02585

13.35

0.02852

17.53

0.02593

15.57

0.02839

β-lg

100

4.70

0.02513

4.67

0.02639

7.13

0.02483

7.06

0.02588

9.44

0.02488

9.36

0.02588

11.90

0.02486

11.73

0.02594

14.21

0.02470

14.16

0.02586

16.55

0.02486

16.56

0.02599

Levcoil –

β-lg (1:1)

2.5

4.83

0.02719

4.88

0.02474

7.24

0.02760

7.31

0.02578

9.66

0.02914

9.75

0.02768

12.07

0.03098

12.19

0.02895

14.49

0.03258

14.63

0.03045

16.90

0.03441

17.07

0.03212

Levcoil –

β-lg (1:1)

100

4.99

0.01754

4.71

0.01887

7.48

0.01782

7.06

0.01905

9.97

0.01808

9.41

0.01945

12.46

0.01855

11.76

0.01982

14.95

0.01894

14.12

0.02017

17.44

0.01941

16.47

0.02054

LevSphere –

β-lg (1:1)

2.5

4.83

0.02481

5.00

0.02202

7.25

0.02553

7.50

0.02318

9.66

0.02694

10.00

0.02381

12.07

0.02819

12.49

0.02532

14.49

0.02927

14.99

0.02675

16.90

0.03112

17.49

0.02760

LevSphere –

100

5.02

0.01355

5.02

0.01361

Annex

153

β-lg (1:1)

7.53

0.01364

7.53

0.01380

10.03

0.01395

10.04

0.01388

12.54

0.01400

12.54

0.01397

15.05

0.01423

15.06

0.01430

17.56

0.01444

17.56

0.01436

Supplementary data S III-2: Raw data viscometry.

Polymer

NaCl

(mM)

Polymer

concentration

(g/mL)

Reduced

viscosity

(mL/g)

Polymer

concentration

(kg/m3)

Reduced

viscosity

(mL/g)

Measurement 1

Measurement 2

Levcoil

2.5

20.6

38.44

20.5

38.32

25.7

38.85

25.7

38.72

30.9

39.19

30.8

39.34

36.0

39.70

36.0

39.89

41.2

40.23

41.1

40.16

46.2

40.75

46.2

40.57

Levcoil

100

20.6

38.68

20.6

38.90

25.8

39.48

25.8

39.20

31.0

40.04

31.0

40.11

36.1

40.41

36.1

40.30

41.3

40.89

41.3

40.53

46.4

41.38

46.4

41.16

LevSphere

2.5

20.0

41.57

20.0

41.43

25.0

42.96

25.0

42.98

30.0

43.69

30.0

43.70

35.0

44.52

35.0

44.41

40.0

45.10

40.0

45.21

45.0

46.16

45.0

46.09

50.0

46.69

50.0

46.82

55.0

47.55

55.0

47.47

60.0

48.49

60.0

48.41

70.0

50.12

70.0

50.12

80.0

52.08

80.0

52.13

LevSphere

100

20.0

42.55

20.0

42.87

25.0

43.61

25.0

43.88

30.0

44.14

30.0

44.20

35.0

44.52

35.0

44.79

40.0

45.16

40.0

45.58

Annex

154

45.0

45.62

45.0

46.35

50.0

46.62

50.0

47.24

55.0

47.55

55.0

48.15

60.0

48.35

60.0

48.49

70.0

50.02

70.0

50.15

80.0

52.26

80.0

52.34

β-lg

2.5

97.2

6.34

98.5

6.14

145.7

6.43

147.8

6.31

194.3

6.69

197.1

6.60

242.9

6.89

246.4

6.85

291.5

7.16

295.6

7.18

340.1

7.37

344.9

7.41

β-lg

94.7

5.49

94.6

5.71

142.1

5.70

141.9

5.80

189.4

5.92

189.1

6.05

236.8

6.19

236.4

6.34

284.1

6.36

283.7

6.54

338.8

6.69

340.4

6.87

β-lg

98.2

5.17

96.4

5.29

147.3

5.43

144.6

5.44

196.4

5.72

192.7

5.74

245.5

6.01

240.9

5.97

294.6

6.27

289.1

6.20

351.8

6.67

337.3

6.46

β-lg

95.9

4.81

96.8

4.91

143.9

5.19

145.3

5.12

191.8

5.26

193.7

5.27

239.7

5.44

242.2

5.43

287.7

5.64

290.6

5.61

339.5

5.82

339.0

5.77

β-lg

100

99.9

4.59

96.0

4.74

149.8

4.71

144.0

4.88

199.8

4.84

192.0

5.01

249.7

4.91

239.9

5.14

299.6

5.03

287.9

5.25

349.6

5.15

335.9

5.39

Levcoil –

β-lg (1:1)

2.5

39.5

21.30

39.8

20.77

49.4

22.11

49.7

21.39

59.3

22.63

59.7

22.00

69.2

22.86

69.6

22.48

79.1

23.36

79.5

22.92

Annex

155

89.0

23.60

89.5

23.07

Lev

coil

–

β-lg (1:1)

100

40.0

21.46

40.0

21.15

50.0

21.95

50.0

21.59

60.0

22.28

60.0

22.11

69.9

22.45

70.0

22.26

79.9

22.77

80.0

22.66

89.9

22.91

89.9

22.78

Lev

Sphere

–

β-lg (1:1)

2.5

39.5

24.32

39.7

24.77

49.3

25.52

49.7

25.89

59.2

26.56

59.6

26.20

69.1

26.83

69.5

27.12

79.0

27.34

79.5

27.64

88.8

28.05

89.4

28.34

Lev

Sphere

–

β-lg (1:1)

100

40.0

23.76

40.0

23.79

50.0

24.59

50.0

24.54

60.0

25.13

60.0

25.15

69.9

25.29

70.0

25.47

79.9

25.89

80.0

26.13

89.9

26.30

90.0

26.51

Supplementary data S III-3: Cumulative distribution of the Z-average hydrodynamic radius

of Lev

Coil (black lines) and LevSphere (grey lines) at 2.5 mM (solid lines) and 100 mM (dashed

lines) NaCl.