In teraction of Pr oteins w ith Mu ltivalen t Polyelectro lytes vorgelegt von M.S c. J acek Wal kow iak an der Fakult ät II – Math em atik und Nat urwi ssen s chaften der Technischen Universität Ber lin zu r Erlangun g d es akad e mi schen G rad es Doktor der Naturwissenschaften - Dr. rer. nat. - g e nehmigte Dis serta tion Promotionsausschuss: Vorsitzender: Prof. Dr. Arne Thomas Gutach ter: P rof. Dr. Matt h ias Bal lauf f Gutachter: Prof. Dr. Michael Gradzi elsk i Gutachter: Prof. Dr. Alexander Böke r Tag der w iss ens chaftl ich en A ussp rach e: 09.09.20 20 Ber lin 2020 ABSTRACT In the present work the the rmodynamics of prote in adsorption to charg ed pol y electrol y tes is explored. Unravelling intera ctions of proteins with highl y ch arged polyelectrol y tes as e.g. DNA is a ce ntral topic in biophysic s since many y ears. 1,2 I t is now well - est a blished that ionic interactions play a major role for the strength of binding as ex pressed through the thermodynamic binding constant K b . Moreove r, counterion release has been identified as the driving force f or binding: Patches of positivel y charged amino acid residues located on the surface of the protein act as multivalent counterions that compensate the charge of the pol yelect rol y t e. 1–3 I n this way a concomitant number of counte rions condensed to the polyelectroly t e ar e rel eas ed. 3 The fi rst p ar t of this thesis contributes to the under standing of counterion condensation that determ ines the ef fecti v e char ge of a p ol yelec t rol yte. The in ter actio n between dend rit ic polygl y cerol sulfate (dP GS) and divalent ions (Mg 2+ and Ca 2+ ) were ana l y z ed b y com bin a tion of exper iment (isother mal titration ca lorimetry ( I TC)) and th eory (non - linear p enetr abl e Poisson- Boltzmann (PPB) model). The discussed lack o f ion - specific effects upon adsorption of divalent ions to dP GS and a clear comp etition between mono - and diva lent ions a llows a better under standing of the fundamentals of pol y e lectrolyte - protein (PE - P) interac tion that a r e presented in the f ollowin g c hapters. In the second part, a comprehensive ther mod ynamic study o f the PE - P interaction is prese nted. Starting form a linear (h eparin) and low mol ecular weight (β c yclodextrin sulfate (β - CD - S)) polyelectroly t es up to a pol y electrol y t e brushes - a detailed picture of the binding driving forces is given. A qua ntitative anal y sis of the thermodynamic proce sses involved in t he interac t ion of the model glyc osaminogl ycan (G AG) - heparin and l y soz y m e is presented. The binding constant K b was determined b y ITC as the function of temperature and io nic strength adjusted through the concentration c s of added salt. The dependenc e on s alt co n cent rati on c s was used to determine the ne t number of released counterions. Moreover, the bind in g con stan t at a refe ren ce salt concentra tion of 1M K b (1M ) w as determined by ex trapolation. The depe ndence on temp eratur e of K b was used to dissect the bi nding free energ y ∆ G b into the respective enthalpies ∆ H b and entropies ∆ S b togeth er with the s pecifi c heat cap aci t y chan ge ∆ C p . A strong e nthalp y - entro py cancellation (EEC) wa s found similar to th e re sults for many ot her sy stems. 4–9 T h e binding free energy ΔG b could furthermore be split up into a part ΔG ci due to counterion release and a res idual part ΔG res . The latter qua nt ity reflects specific c ontributions as e.g. sa lt bridge s, van der Waals interactions or h y dro gen bonds. The entire anal y sis shows that heparin - ly so z y me int eractio ns are m ainl y caused b y counterion release, that is, ca. t hree co un terio ns are b ein g released upon binding of one lysoz y m e molecule. The presented approach was then applied in studies of β - CD - S - l y soz y m e binding. In that case also, three counterions relea sed durin g the adsorptio n are the main driving force of the analy zed process. The reported approach of quantifying interactions between GAGs and CDs with proteins is in general applicable and suitable to provide new insights in the physical modulation of biomolecular sig nals. Sub sequently, the a nal ysis of the P E - P intera ct ion is extend in order to obtain the f ull thermodynamic information on the binding of protein to pol y electrol y te brushes. Thus, a thermodynamic stud y o f the adsorption of hu man serum albumin (HS A) onto spherical polyelectroly t e brushes ( SPB) is presented. The SPBs are composed of a soli d poly st y r ene core bearin g lon g chai ns of pol y(acr ylic acid) (PA A). ITC measu remen ts do ne at d ifferent tempe ratures and ionic str engths le ad to a full se t of thermod yna m ic binding constants to gether with the enthalpies and entr opies of binding. The adsorption of HSA onto SPBs is desc ribed with a tw o - step model w ith a bindin g constant K b on the order of 10 5 and 10 4 M -1 for t he fi rst and second binding step, respectivel y . The free en erg y of bindin g ∆ G b depends onl y w eakl y on temperature bec ause of a marked compensation of enthalpy b y entrop y . S tudies of the adsorbed HSA by Fourier transform infrared spectroscopy (FT - I R) demonstra tes no sign ifica nt disturbance in the secondar y structur e of the protein. The quantitative anal y sis demonst rates that counterion release is the major drivin g force for adsorption. A comparison with t he analysis of previously discussed s y s tems demonstrat es that EEC is a ge n eral phenomenon dominated by released counter ion that alwa ys a ccompanies the binding of proteins to polyelectrol y tes. The la st part of this thesis pr esents a qua rtz cry st al micr obalance with dissipation ( QCM - D) study of HSA adsorption onto a planar polye lectrol yte br ush (PP B). This allows a quantitative compa rison w ith calorimetric studies of HSA - SPB interac tion. For this, the preparation of a PAA brush, poly m erized by atom transfer ra di cal pol y merization (ATRP) of ter t - bu t y l acr y l at e ( t BA) and subs equent acid h y drol y sis, on the flat gold surfaces of QCM c rystals is presented. The P AA b rush was ch aract eriz ed b y FT - IR spe ctr os cop y , elli pso metr y an d wat er co ntact an gle anal y sis. The interaction of the brush with HSA w as studi ed for a r an ge of ioni c stren gths an d pH conditions. The quant itative analysis showed a strong adsorption of prot ein molecules onto the brush. By incr easing the ionic strength a fraction of the initi ally adsorbed HSA was relea sed. A comp arison with re cent calorime tric stu dies r elated to the bind ing of HSA to poly electrol y t es allo wed to an al y ze the Q C M dat a bas ed on the res ul ts o f the t hermo d ynami c an al ysis o f the P E - P binding process. 10 – 13 KEYWORDS : Pol y electrolyte , pol y el ectrolyte brush, protein, I TC, QCM - D, thermody n amic, counterion re lease, entha lpy- entro p y cancell atio n. ZUSAMME NFASSUN G In der vorliegenden Arbeit wird die Thermodynamik der Proteinadsorption an geladenen Pol y elektrol yten unte rsuc ht. Die Untersuchung von Wechselwirkungen von Proteinen mit hoch gelad enen P ol yelektr ol yten , wie z . D NA ist sei t vi elen J ahr en ein z ent rales T hema i n der Bioph y sik. 1,2 Es ist mittle rwe ile bek annt, d ass ionisc he Wechselw irkungen eine w ichtig e Rolle für die B indungsstärke spielen, die durch die ther modynamische Bindungskonstante K b ausgedrüc kt wird. D arüber hinaus wurde die Freisetzung von Gegenionen als treibende Kraft fü r di e Bindun g id enti fiz iert : Po sit iv gelad ene Ami nosäu reres te auf d er O ber fl äche d es P rotei ns wirken als multivalente Ge genionen, die die La dung des Pol y el ektrol y t en kompensiere n. 1–3 Au f dies e Wei se wir d ei ne An zah l vo n am Polyelektrolyten kondensierten Gege nionen freigesetzt. 3 Der er ste Teil dieser Arbeit trägt zum Verständnis der Gege nionenkondensation bei, die die effe ktive Ladung eines Pol y elektrol y ten besti mmt. Die Wechselwirkung zwischen dendritischem Polyglycerinsulfat (dPGS) und z weiwertigen Ionen (Mg 2+ und Ca 2+ ) wurde durch Kombination von Experiment (isother me Titrationskalorimetrie (I TC)) und Theorie (nonlinear pe netrable P oisson - Boltzmann (PPB) - Mod ell ) anal y s ier t. Das Fehlen ionenspezifischer Effekte a uf die Adsorption zwe iwertiger Ionen an dPGS und eine klare Konkurrenz zwischen ein - und zweiwertigen I onen ermöglichen ein besseres Ver ständnis der Grundlagen der Wechselwirkung zwischen Pol yelektroly t und Protein ( PE - P), die in den folge nden Kapit eln vorgestellt werden. I m zweiten Teil w ird eine umfassende ther modynamische Untersuchung der PE -P- Wechselwirkung vorgestellt. Ausge hend von linearen (Heparin) und niedermolekularen (β - Cyc lodextrinsulfat (β - CD - S)) Pol y el ektrol y t en bis hin z u Pol y elektrolytbürsten wird ein deta illierte s Bild der Bindungsantriebskräfte gegeben. Eine qu antitative Anal y se d er thermodynamischen Prozesse, die an der Wec hselwirkun g des Mode lls Gl y cos aminoglycan (GAG) - Hep arin und Ly s oz y m beteili gt sind, wird vorge s tellt. Die Bindung s konstante K b wurde d ur ch ITC al s Fu n ktion der Temperatur und der Ionenstärke bestimmt, die durch die Konzentration c s des zuge setz ten Salzes eingestellt wurden. Die A bhängigkeit von der Salzkonz entration c s wurde ve r wendet, um die Nettozahl der freigesetzten Gegenionen zu bestimmen. Darüber hina us wurde die Bindungskonstante bei einer Referen zsalzkonzentration von 1 M K b (1 M ) durch E xtrapolation bestimmt. Die Abhängigkeit von K b von der Temperatur wurde verwendet, um die freie Bindungsenergie ΔG b in die jewe ili gen Enthalpie n ΔH b und Entropien ΔS b zu samm en mi t der s pez ifis chen W ä rm ekapaz it ätsän derun g ΔC p zu zerlege n. Eine starke Enthalpie -Entropie- Auf hebun g (E EC) wur de ähnlich wie bei vielen anderen Systemen gefunden. 4–9 Die freie Bin dungsen er gie ΔG b konnte aufgrund der Freisetz ung von Gegenionen und ein es Restte ils ΔG res in einen Te il ΔG ci auf get eil t werden . Die let zt ere Größe s pi egelt spez ifi sche B ei träg e wie z . S alz brücken , Van - d er - Waal s - Wechselwirkungen oder Was serst offbrü ck en wid er. Die g esamt e A nal yse zei gt, das s Heparin - L ys o z ym - Wechselwirkungen ha upts ächlich durc h di e Freisetzung von Gegenionen verursacht werden. Bei der Bindung eines Lysoz y mmole kül s w erden d rei Ge gen ionen frei ges et z t. D er vor gest ell te Ansatz wurde d ann in S tudien zur Bindun g von β - CD - S - Ly soz y m angewendet. Auch in diesem Fall sind drei während der Adsorption freigesetzte Gegenionen die Hauptantriebskraft des anal ysiert en P roz ess es. Der beschrieb ene Ansa tz z ur Quantifizierung von Wechselwirkungen zwischen GA Gs und CDs mit Proteinen ist allge mein anwendbar und geeignet, um neue Erkenntnisse über die phy sikalische Modulation biomolekularer Sig nale zu gewinnen. Anschließend wird die Anal yse der P E -P- Wechs elwirkung e rweitert, um die vollständige n thermodynamischen Informationen über die Bind ung von Protein an Pol yelektroly tbü rsten zu erhalten. Da h er wird eine thermodyna mis che Unter suchung der Adsorption von Humanserumalbumin (HSA) an kugelför mi ge n P olyele ktrol y tbürsten (SPB) vorgestellt. Die SP Bs best ehen aus ei ne m fes ten P ol yst yrolk ern, der lan g e Kett en au s P ol y(acr ylsäu re) (PA A) träg t. I TC -Messungen, die bei unterschiedlich en Temperaturen und Ione nstärken durch geführt werden, führen zu einem volls tändige n Satz thermod y namis cher Bindungskonstanten, zusammen mit den Enthal pien und Entropien der Bindung. Die Adsorption von HSA an SPBs wird mit e inem zweistu f ige n Modell mit einer Bindung skonstante K b in der Größenordnung von 10 5 und 10 4 M -1 für den ersten bzw. z weiten Bindungsschr i tt beschrieben. Die freie Bindungsenergie ∆ G b hä ngt aufgrund einer deutlichen Kompensation der E nthalpie durch Entropie nur schwach von der Temperatur ab . Untersuchunge n der ads orbierten HSA durch Fourier- Transfo rmatio ns - I nfrarotspektroskopie (F T - I R ) zeigen keine signifikante Störung der Sekundärstruktur des Proteins. Die quantitative Analy s e zeigt, dass die Freisetzung von Gegenionen die Hauptantriebskraf t für die Adsorption ist . Ein Vergleich mit der Analyse zuv or diskutierter Systeme zeigt, dass die EEC ein all gemeines Phänomen ist, das von der Freisetzung von Gegenionen dominiert wir d und immer mit de r Bindung von Proteinen an Poly elektrol yte einh ergeht. Der letzte Teil die ser Arbeit präse ntiert eine Quarzkrist all - Mikrowa a ge mit Dissipation (QCM - D) zur H SA - Adsorption auf einer pla naren Pol y e lektrol y tbürste (PPB). Dies ermöglicht einen quantita tiven Verg leich mit kalorime trisch en Studie n der HSA - SPB - Wechselwirkung . Hierzu wird die Her stellung einer PAA - B ürste vor g estellt, die dur ch Atomtrans fer - Radikalpolymer isation (ATRP ) von tert - Bu ty la cry la t ( t BA) und anschließende Säurehydr ol yse auf den flachen Goldob erflächen von QCM - Kristallen poly merisiert w i rd. Die PAA - Bü rst e wurde durch FT - IR - S pektroskopie, Ellipsometrie und Wasserkontaktwinkelanal y se charakt eri siert . Di e Wechs elwi rkun g der Bü rst e mit HSA wurde fü r eine R eihe v on Ionenstärke n und pH - Be dingungen unte rsucht. Die quantitative Anal y se zeigte eine starke Adsorption von Proteinmolekülen an der Bürste. D urch Erhöhen der Ione nstärke wurde ein T eil des anfä nglich adsorbierten HSA freigesetzt. Ein Verg leich mit kürz lich durc h geführten kalorimetrischen Studien zur Bindung von HSA an Pol ye l ektrol y te ermö glichte die Anal y se der QC M - Daten auf der Grundlage der Er gebnisse der thermod y namischen Anal yse des PE -P- Bindungsprozesses. 10 – 13 SCHL AGWÖRTER : Pol y elektrol yt, Polye lektrol y tbürste, Protein, I TC, QCM - D, thermodynamisch, Gegenionenfreisetzung, Enthalpie-Entropie-Aufhebung. Table of Co ntents 1. Intr oduction .................................................................................................................. 1 1.1. Pol y electrol y tes in Inhibit ion and / or Enhance m ent of Protein Adsorption ................ 1 2. Ob jective o f th e Th esis ................................................................................................. 4 3. F undame ntals and The ory ........................................................................................... 5 3.1. Pol yelectrol ytes ............................................................................................................. 5 3.1.1. Linear and Low M olecul ar Pol yelect rol y tes ...................................................... 5 3.1.1.1. Heparin (H ep) ............................................................................................. 5 3.1.1.2. β - Cyc lodextrin S ulfated (β - CD - S) .................................................................. 6 3.1.2. Hyperb ran ched P ol yelect rol ytes Pol yelectrol ytes .............................................. 7 3.1.2.1. Dendritic Polyglycerol Sulfate ( dPGS) ...................................................... 7 3.1.3. Pol yelectrol yte Brush es ...................................................................................... 8 3.1.3.1. Pl anar Po l y ele ctrol yte Bru shes (PP Bs) ...................................................... 9 3.1.3.2. Sph erical P ol yelect rol y t e Bru sh es (S PBs) ............................................... 10 3.2. Proteins ........................................................................................................................ 11 3.2.1. L ys o z ym e ( L ys ) ................................................................................................ 11 3.2.2. Human Serum Albumin (HSA) ........................................................................ 11 3.3. Prot eins and P ol yelectr ol ytes ...................................................................................... 13 3.3.1. Protein Structure upon Binding ........................................................................ 13 3.3.2. Thermod y namic Anal y sis of Protein I nt eraction with P oly el ectrol y tes b y I sothermal T itration Calorime tr y (ITC) ............................................................ 14 3.3.2.1. Therm od ynamic An al ysi s ................................................................................ 14 3.3.2.1.1. Counterion Condensation........................................................... 14 3.3.2.1.2. Counterion Release .................................................................... 15 3.3.2.1.3. Effec t of the Ionic Stre ngth on t he Binding Free Energ y .......... 16 3.3.2.1.4. Donnan Effect ............................................................................ 18 3.3.2.1.5. Counterion Release in PE Br ushes ............................................ 19 3.3.2.1.6. Effec t of Temperature on the Binding ....................................... 20 3.3.2.1.7. Enthalpy – E ntropy Ca n cellation ............................................... 22 3.3.2.2. I sothermal T itration Calorime tr y .............................................................. 23 3.3.2.3. Evaluation of ITC Data ............................................................................ 25 3.3.2.3.1. Single Set of Ide ntical Bi nding Sites (SSIS) Model .................. 25 3.3.2.3.2. Two Sets of Indepe ndent Binding Sites (TSIS) Model ............. 26 3.3.2.3.3. Two Component L igand Binding (TCLB) Model ..................... 27 3.3.3. Analy sis of Pol yelectrolyte Brush upon Interaction with Proteins b y Quartz Cr ystal Mi crob alanc e (Q CM ) ........................................................................... 28 3.3.3.1. Quar tz Cry stal Micr ob alance with Dissipa tion Monitoring (QCM - D) ... 28 3.3.3.2. Evaluation and Inter pret ation of QCM- D Data ....................................... 30 4. Results and Discussion ............................................................................................... 33 4.1.Adsorption of Mono- and Divalent Ions to dPGS ........................................................ 33 4.1.1. Binding Isotherms ............................................................................................ 34 4.1.2. Analy sis of th e Interaction Between dPGS and Divalent Cations ................... 35 4.1.2.1. Ion Specificit y .......................................................................................... 35 4.1.2.2. Ion - Speci fic P en etrabl e P oi sson -Boltzmann (PPB) Model ....................... 36 4.1.2.3. Comparison of ITC Data with PPB Model ................................................... 37 4.1.2.4. Conclusion ........................................................................................................ 39 4.2.Protein Adsorption to Heparin ..................................................................................... 39 4.2.1. Binding Isotherms ............................................................................................ 40 4.2.2. Thermod y namic Anal y sis of Ly soz y m e Binding to Heparin ........................... 42 4.2.2.1. Depende nce of the Bindi ng Constant K b on I onic Strength ..................... 42 4.2.2.2. Depend ence o f th e Bind i ng Fre e Ener g y ΔG b on T emperature ............... 46 4.2.2.3. Enthalpy- Entrop y Cancellation ................................................................ 47 4.2.2.4. Conclusion ................................................................................................ 49 4.3.Protein Adsorption to β - CD -S ...................................................................................... 49 4.3.1. Binding I sotherms ............................................................................................ 50 4.3.2. Thermod y namic Anal y sis of Ly soz y m e Binding to β - CD -S ........................... 51 4.3.2.1. Depende nce of the Bindi ng Constant K b on I onic Strength ..................... 51 4.3.2.2. Conclusion ................................................................................................ 54 4.4.Protein Adsorption onto SPBs...................................................................................... 54 4.4.1. Analy sis of th e Secondary St ructure of Adsorbed Protein b y FT- IR Spect rosco p y ..................................................................................................... 55 4.4.2. Binding I sotherms ............................................................................................ 55 4.4.3. Thermod y namic Anal y sis of HSA Interaction with SPBs ............................... 56 4.4.3.1. Depende nce of the Bindi ng Constant K b on I onic Strength ..................... 57 4.4.3.2. Temper atur e Dep enden c e of t he Bindi ng Fre e En er gy ΔG b .................... 58 4.4.3.3. Contribution of Counterion Release Entrop y t o the Bindin g of HSA ...... 60 4.4.3.4. Conclusion ................................................................................................ 61 4.5.Protein Adsorption onto PPBs...................................................................................... 62 4.5.1. Course of Experiment ....................................................................................... 62 4.5.1.1. Protein Adsorption onto PPBs .................................................................. 62 4.5.1.2. Response of Protein-Free Br ush to pH ..................................................... 63 4.5.2. Effec t of Ionic Strength and pH on Protein Adsorption ................................... 63 4.5.3. Influence of pH on the Swelling of the PAA B rush ......................................... 65 4.5.4. The Amount of Adsorbed Protein Deter mined b y the I oni c Strength .............. 66 4.5.4.1.Number of HSA Molecules per PAA Cha in ............................................. 68 4.5.5. Conclusion ........................................................................................................ 69 5. Summary and Outlook ............................................................................................... 70 6. Materia ls a nd Method s .............................................................................................. 72 6.1. Materi als ....................................................................................................................... 72 6.2.Proteins and Buffers ..................................................................................................... 72 6.3.S y nthesis and Characterisation of SP Bs ....................................................................... 73 6.3.1. S y nthesis o f Pol yst yrene (P S) C ore Latex ........................................................ 73 6.3.2. S y nthesis of Core- Brus h P articl es .................................................................... 74 6.3.3. Purific ation of S PB Par ticles ............................................................................ 74 6.3.4. Dy namic L i ght Scatter in g (DL S ) ..................................................................... 75 6.3.5. Conductometric and Potentiometric Titration .................................................. 77 6.3.6. Determ inat ion of the M o lecul ar Wei ght of th e Tet hered P ol yelectro l y t e C hai ns .......................................................................................................................... 78 6.3.7. Cryoge nic Transmission Electron Microscop y (Cryo- TEM) ........................... 79 6.4.S y nthesis and Characteriz ation of PPBs ...................................................................... 80 6.4.1. I mmobili zation of DTBU I nitiator on the Surface of QCM Cry stals ............... 80 6.4.2. ARGET ATRP Pol y meri zation of pol y ( t ert - bu t yl acr y l ate ) (P t BA) ................ 80 6.4.3. Conversion of poly( t ert - but y l acr y late) brush into pol y( acr y lic acid) brush ... 80 6.4.4. St atic W ater C ont act Angle ( SW CA) ............................................................... 81 6.4.5. Ellipsome try ..................................................................................................... 81 6.4.6. Dete rmina tion of the G rafting Densit y ............................................................. 83 6.5. Fourier T ransfo rm Infrar ed (FT - IR) S pect ro scop y ...................................................... 83 6.5.1. FT -IR of HSA Adsorbed onto S PBs ................................................................ 84 6.5.2. FT - IR o f PPBs .................................................................................................. 84 6.6. ITC Me asurem en ts ....................................................................................................... 85 6.7. QCM - D Meas ur ement s ................................................................................................ 87 6.7.1. Determination of the N umber of HSA Molecules per PAA Chain .................. 87 7. Supple me nt ................................................................................................................. 88 7.1.Calculation of the Bulk Concentration c i 0 f or the Ion- Speci fic P PB Mo d el ................ 88 7.2. Materi als an d ITC Is o t h e rm s for d PGS - Divalent Ion I nteraction Descr ibed in Sections 4.1.2.1. and 4.1.2.2. ...................................................................................................... 88 7.2.1. Materi als ........................................................................................................... 88 7.2.2. ITC Isotherms ................................................................................................... 89 7.3. Detai ls on Hep - L ys Int eract ion Desc ribed in C hap ter 4.2. .......................................... 94 7.3.1. ITC D at a ........................................................................................................... 94 7.3.2. Effec t of Different Concentrations of Ly s and He p on the Binding Constant K b ........................................................................................................................ 106 7.3.3. Fract ional Ch arge o f Hep arin ......................................................................... 108 7.3.4. Ionization of He parin ...................................................................................... 109 7.4. Deta ils on SPB - HSA Interact io n D escrib ed in C h apter 4.4. ...................................... 111 7.4.1. ITC D at a ......................................................................................................... 111 7.4.2. Therm od ynamic D ata ..................................................................................... 115 7.5. Deta ils on PPB - HSA Interact io n D escrib ed in C h apter 4.5. ...................................... 119 7.5.1. QCM - D Dat a fo r I - and pH Cyc le upon HSA Ads orption ............................. 119 7.5.2. QCM - D Data for pH In duced Swe lling /Deswelling of a Prote in - Free PAA Brus h ............................................................................................................... 121 BIBLIOG RAP HY ................................................................................................................ 123 List of Abbreviations ............................................................................................................ 144 Lis t of Figu res ....................................................................................................................... 146 List of Table s ......................................................................................................................... 151 List of P ublications ............................................................................................................... 153 Presen tatio ns at Con fer en ces an d Meeti ngs ...................................................................... 154 Ac knowledgm ent s ................................................................................................................. 155 1 1. Introduc tion 1.1 . P oly elect rolyt e s in Inh ibiti on and / o r Enhan ce men t of Prote in Ad sorp tion T he interaction of proteins wit h s y nthetic pol y electrolytes (PEs) in aqueous sol ution has been a long - standing subj ect in colloid and poly mer science and the number of papers on this subj ect is hard to overlook. 3,14 – 17 Thus, polye lectrol y t es may f o rm complex coacervates with proteins of opposite charge and the formation of these complex es is strongly depending on the ionic stren gth in the syste m. 17,18 I t is now we ll - established tha t ionic inte ractions play a major role for the strength of binding as expressed through the thermod y namic bindin g constant K b . Of te n comple x formation is followed by precipita tion and phase sepa ration 14, 17 – 19 and possible non- equilibr ium states may ren der the thermo dy namic analy sis a difficult ta sk . At the same time , the interaction of highly charged biopol y mers as e.g. DNA or RNA with specific protein s h as been under intense scrutin y be cause of its obvious biological rele vance. 2,7,28 ,20 – 27 Work along these lines has revealed that binding is often brought about b y count erion release : 1– 3,29 – 31 A patch of positively char ged groups on the surface of the protein interacts with the highl y ch arged biopol y mer. Thus, this patch now balan ces the char ge of t he pol y e lec tro l y te so that the count erion s con den sed t o it m ay be rel eas ed. T he gain of entro p y gain ed b y rel eas e o f the condensed c ounterions presents a strong dr iving force for binding that is even oper ative under phy siologic al co nditions. The incr ease of entropy thus effected scales with the number of released counterions and the lo ga rithm of the bi nding consta nt, l og K b i s pred icted to be proportional to the logarit hm of the salt concentrati on, log c s in the s y st em. Counterion re le as e has been identifie d as major driving force for the binding of many n atural 2 ,30 and sy nthetic pol yelect rol y t es 3 to proteins. 3,3 2,33 The releas e or u pt ake of wat er m ust be r ega rded as a s econd entro pic fac tor tha t ma y come in to play as w ell. Figure 1. Hydration shell o f (a) prote in, (b) DNA an d (c) phosph olipid bi lay er (s napsh ots from s i mulation described in ref. 34–36 ). Water molecules may be bound to t he surfac e o f proteins and released upon complex ation. 37 – 40 Osmotic stress experiments have bee n used to probe this effect and there is quite a number of papers that re po rt on such experiments showing that the rele ase of water can be an important factor. 37,40 – 45 Many years ago, Tanford pointed out t hat the activit y o f water is inevitably bound to the activit y of the added salt ions b y virtue of the Gibbs- Duh em rel at ion . 46 Hence, ch an gin g the act ivi t y o f s alt i ons neces sa r y to p robe t he d ep en dence of the bindin g of counterion release 2 will cha nge the water a ct ivity as well a nd shift possible c ontributions to K b that are due to the releas e of wat er. R e cord et al . 2 include d this effect in their general a nalysis while Ha et al . 47 and Mascotti and L ohma n 48 per formed the first e xperiments showing that c ount erion relea se ma y be acco mpan ied b y water rel eas e. Evi dent l y, the chan ge of wat er act ivi t y sh oul d becom e more decisive at higher salt concentration. Thus, in a series of experiments, Bergqvist, Ladbur y, an d their associates dem onstrated that protein bin ding to DNA in halophil ic bacteria can onl y be treate d quantitativel y when invoking this effect. 44, 49 – 51 I n particular, plot s of log K b vs . log c s are found to be highly non - linear and the weakening of c om plex formation between DNA and the protein may be even reversed at high salt concentra tions (see the discussion of this point in ref. 49 ). However, as al ready pointed out by Tanford , 46 the ch ange o f w ater a cti vit y ma y be v e r y s mall for sa lt concentratio n c s over the order of 0.001 to 0.01 M used nor mally in ex perim ents related t o co unt erion rel ease. Hen ce, th e effe ct o f w ate r rel eas e m a y go un not iced in such a n experiment. Osmotic stre ss experime nts may be a way to circu mvent th is problem. 37, 40 However, the polymer or the solute added to the sy st em in order to dec re ase the activity of w ater ma y not be inert and diff erent agents have been shown to lead to considera bl y different result s. In a num ber o f r ecent s tu di es it has been shown that the count erion rele ase effe ct can b e an al y z e in deta il by a combina t ion of ca lorimetric inv estig ations with mole cular d y namics (MD) simulations : 3, 12,13 ,31,52 ,53 First, the complex forma tion of human serum album in (HSA) with sin gle chai ns o f pol y(ac ryli c aci d) (P AA) w as in vest igated: 52 I n this study , isotherma l titration calorimetry (I TC) was used to stud y the complex formation in aqueous solution, vary ing b oth temperature and ionic stre ngth. 52 T he ex perim ental st udies were co mbined with MD simulation with expl icit co unter ions . Both experime ntal data as well as simu lations led to th e con clusion that counterion release is full y domi nating the formation of the 1:1 complex of PAA and HSA. Moreo ver, the ex p erimen t al K b coincides wi th the calcula ted one w ithin the limits of e rror. The free energ y of binding, ∆ G b was found to depe nd ha rdly on tempe rature whereas the dire ctly measu red ent halp y, ∆ H ITC varied strong l y with T . Thus, bi nding of H SA t o PAA - chains is accomp ani ed b y a marked cance l lation of enthalpy and entropy that is a c ommon feature f or prote ins inter actin g w ith natur al polye lectrolyte s. 28,54 – 56 Secondly , the interaction of dendrit ic polygl y cerolsulfate (dP GS) with various proteins was investig ated in aqueous solution b y ITC , 12,13, 31 wit h ioni c stren gth and t emperat ur e as tw o deci sive v ariabl es . 1 3,53 The binding constant K b was then compared to the results of MD - simulation s on a qu antitative le vel. In th is case, good agreement of theory and experiment w as also found. 31 While con siderin g the inte raction betwe en prote ins and natura l / s y nthetic polyme rs, str uctures such as pol y mer brushes must be discussed . Th e se s ystem s can be d escr i bed in general as polymer c h ains densel y grafted b y one end to an i nt erface. 17 I nteractions of proteins with suc h structures have been, for many years now, a subject of sig nifican t inte rest and in vestig ation in colloid and polymer scie nce. 14 – 17,19,57 ,58 In man y c ases poly mer brushes are studi ed to control the protein adsorption onto surf aces 59, 60 . This bec omes more complex when the brush is composed of cha rged pol y mer chains, i .e. , polyelectrol y tes. 15,6 1 – 65 Surfa ces modified with pol yelect rol y t e brus hes have b een f req uentl y invest igated as t he y are re lat ed t o “smar t” o r stimuli re sponsive surfa ce coa tings 66 and bios ensors. 67 Furthermore, poly e l ectrolyte brushe s can be a pplied to prevent biofouling. 62 It is known that proteins adsor bed and immobilized onto polyelectroly t e brushes r etain their conformation 68 as well a s their (enzymatic) a ctivity . 69,70 3 Understanding protein adsorption to pol y electrolyte brushes is therefore obviousl y ne eded for nanotoxicology and nanomedicine. 71 Figure 2. Multiple interaction of proteins w i th mater ials for whic h prevention or enha nce ment of intera ction with polyel ectrolyte brushes are applicable. (a) bi ofou ling (b) protein corona on the surf ace o f a nanoparticle and (c) dr ug e nca psu la tio n. 72 P ictures repr int ed fro m : https:// www. slides hare.net/ ANJUNI TH IKURUP /pro tein - coron a - associated - wit h - nanoparticles and https:// www. sintef.no /en/oc ean/initiati ves/bio foulin g/#/ . Prot eins can b e tak en up or r eleas ed fro m p ol yelectro l y t e brus hes dependin g on salt concent rat io n . 3, 73 As discussed a bove this is rela ted to the c ounterion relea s e mechanism. 2 Thus the effective deg ree of ioniz ation and the char ge distribution in the pol y electrolyte br ush - w hich strongly depends on the salt concentration and pH of the solution 74 - is c rucia l fo r pro tein adsorption. The charact eriz atio n of po l y el ectro l y t e brushes and their stimulus response to changes in salt concentration and pH has been th e focal point of a large num ber of articles. The effect of gra fting density on brush conformation, 7 5,76 the hy ste retic memory of brushes, 74 the ion specific effects on brush conformation 77 and the interactions with proteins 62,7 5,78 h ave been studied in detail. Delcro ix et al . studied the pH - and salt - de pendent poly mer conformation and protein adsorption on sever al pol y m er brushes. 79 I n particular, they defined a protocol for sys tematic evaluation of the change of pol y mer conformational upon pr otein adsorption b y quar tz crysta l micro balance with dissipation monit oring (QCM - D). Recent work of Henzler et al . showed that thermody n amics and driving forces of the β - Lactoglobulin (BLG) adsorption on spherical polyele ctrolyte brushes (SPBs) with long chains of poly (st y rene sulfonate) can be well stud ied by ITC. 3,80 The resulting complexes of the S PB and the pro tein sta y stable in solution and can be studied b y a wide variety of methods including s m all an gle X - r a y s c atter in g (SAXS ). 73,8 1 Recently , a first theore tical stud y on the interac tion of prote ins with SPBs has b een given. 82 4 2. Objective of th e Thesis The st ud y d escrib ed in t his thesis is dedi cated t o the investigation of the mechanism and the anal y sis of the driving forces upon poly electrol y t e- protein ( PE -P ) inte raction. The main inte rest of this stud y is to gain detailed thermod ynamic information of protein bi nding. Well -defined polyelectroly t es (PEs) wi th differe nt morpholo gies e.g. linear P Es and pol yelec t rol y t e brushes were used to i nves tigat e thes e compl ex i nterac tions. The formation of PE -P compl ex es was speci ficall y altered b y chang es in the ph ysicoch em ical propert ies of th e s urrounding solution such as , sal t con centrat io n, pH an d temperature. The studies of PE -P inter actio ns presented in this work include: A) The anal y si s of the counterion condensation to pol y electrol y tes. Here the ion- speci fic eff ects and the competition between monovalent and divalent cations upon binding to dendritic polygl y c e rol su lfate (dP GS ) were an al y ze d . C alorime tric studies in this reg ard , ba sed on the two compone nt ligand binding (TC LB) model were direct l y compared with theoret ical appro ach based on t he non- line ar p enetrab le Poisson- Boltzmann (PPB) model . The l ack o f i on - sp ecific eff ects an d a cle ar compe tition betw een mo no - and divalent ions upon binding to dPGS contribute to a better understanding of the fundamentals o f pol y el ectrol y t e - protei n (PE - P ) intera ction . B) In anot her set o f ex perim ents t he interaction of proteins with linear and low- mol ecular wei ght p ol yelect rol ytes is presented. He re a comp rehens iv e inv es tigati on of the bindin g o f l y soz yme (Lys) to heparin (Hep) and sulfated β - C y c lodextrin (β - CD - S) is discussed . This investig ation is based on the analysis of the binding constant K b as t he function of salt conc entration c s and temperature. The dependence on c s can be u sed to anal yze t he rel ease o f counterions and water mol ecules upon binding. The dependence of K b on T , on the oth er hand, leads to the ent halpy of binding ∆ H b . T he present analysis is based on the inter relation of K b with tw o variables a nd not on the dependence on c s onl y . T he comprehensive analysis of K b thu s affe cted allows to discuss the marked enthalp y - e ntrop y c ancellation (EEC) that is found for the present s y s tem. V arious c ontribut ions to the enthalpy and entropy of binding are d is cus sed . The related EEC i n clud es not onl y th e contribution of count erion rel ease bu t als o of th e rele ase of wat er. C) F inally , the stud y of PE - P in teract ions was ex tended to include bindi ng of proteins with pol y electrol y te b rushes of planar and spherical geometr y . A f ull thermodynamic ana l ysis of the interaction of human serum a lbumin (HSA) with a spherical poly e lectrol y t e brush (SPB) bearing c hains of pol y (acr ylic ac id) (PAA) is disc ussed . I sothermal titra tion ca lorimetr y ( IT C ) was used t o determine the binding constants at different ionic strength and te mperature. In or der to ensure that t he heat signal is not due to a pa rtial unfolding upon binding, additional Fourier transform infrared sp ectro s cop y (FT - IR ) - stu dies of th e com plex es were p erf ormed . Addition all y a quar tz cry stal microba lan ce w ith dissipation moni toring ( QCM -D) study o f HSA adsorption onto a planar PAA brush is descri bed . This allows a quantita tive compar ison with calor imetric studie s of the same p roble m . I n t hat w a y precise structural information can be combined with thermodynamic information. 5 3 . Fundamenta ls a nd Theory 3.1 . Polyel ectroly tes Pol yelectrol ytes (P Es) are l inea r or b ranch ed p ol ymers con tai nin g charged groups with dissociable counterions withi n their monomer units. Based on t he structural properties of th e se units, PEs va r y in terms of their f lexibilit y in solution. Classific ation of PEs exclude s proteins due to their high struc t ural organization, with emphasis on their tertiary st ructure that lea ds to unique solution behavior. Neve rtheless other biom olecul es, e.g. DNA and in general short ionic pol ypeptid es that can be chara cter iz ed b y w ell - define d sec ondary structu res along with limited flexibilit y are often included in the overall broad group of polyelectrolytes. PEs are intensively studied for their inte raction w ith charged s urfac es. The n umb er of ex peri ment al and theor etical work describing polyelectrolyte adsorption to such surfaces as well as the resulti ng bound state is hard to overlook. 83 PEs due to their conf ormatio n flexibil it y can intera ct with fla t surfa ces as well a s with c olloidal pa r ticles. Over p ast years in ter acti on s bet ween PEs and pro tei ns w ere ex t ensiv el y stud ied b y combi ned ex periment and theory in order to elucida te ph y si cochemical fundamentals of this process. 3 A speci al ex peri ment al effo rt wi th co rres pond in g t heoret ical anal yses has b een p aid t o th e interaction of PEs with variet y of opposit el y char ged particles such as micelles, lipos omes, and inorga nic colloids. 84,85 Moreover, bi ndi n g takes p lace even wh en PE an d p rotei n ar e a lik e - charge d. This i s a conse qu ence of protein charg e anisotr op y , resulting from the a s y mmetric distribution of charged amino acid residues often clustered on th e protein exterior forming so calle d charged pr otein patc h. This a llows PEs t o interac t electrostatic ally with regio ns of oppo sit e char ge on th e pr ot ein s urfac e. A particular subgroup of PEs is constituted b y gl ycosaminog l y c ans (GAGs). These l inear an d flexible bio - poly sa ccharides occur on the surface of ce l ls, in connective tissues, and in th e extrac ellula r matr ix. From a struc tural point of view GAGs can be describe d as highl y heterogeneous due to the disaccharide building blocks, type of sulfation, pattern of sulfation and the overall chain le ngth. Such structural div ersity is a consequ ence of the non - template driven biosynthe sis of th ese mo lecu les which allows s tructu ral mod ifications of GAGs in resp onse to var iable phy s iologica l stimuli . 86 One of the con sequen ces o f su ch st ructu ral diver sity, despite of clear influen ce on phy sicoc hemical cha racter istics of GAG s is their ability to inter act w it h numerous proteins. 87,88 Their in ter actio ns with proteins are widel y s tudied and in d etail descri bed in s ev eral r evi ews 87,89 – 91 y et recogn iti on of GAGs as p ol y electrol y tes still has not a high profile. 3.1. 1 . Linear a nd Low Mole cular Po lyel ectrol yte s 3.1.1.1. Hep arin Heparin is c ommonl y u sed as blood anticoagulant 92 and play s a fundamental r ole in cell sign aling a s it occurs on the surf ace of most ce lls b y b eing proteogl y c an sidechains. 93 H eparin is rel ated t o pr ocess es s uch as angio gen esi s 94 and can cer . 95 It has been iden t ified as a sel ecti ve re gu l a tor o f l i gand - re cept or i ntera cti on s. 96 Spe cial atten tion is paid to heparin i n surger y and in 6 trea tment of long- ter m di s eases . H ere, it is essential to modula te the a m oun t of heparin avai labl e in the blood plasma to prevent fr om bleeding and overdose. 97 Fro m a structur al point of view he parin is a lin ear GAG that cons ist s of repeat in g, v ariab l y sulfated disaccharide units of uronic acid and glucosamine (see Fig ure 3 ). Var iabl e substitutions with N- and O- sulfo and N- acet yl gro ups, as wel l as t he epi meriz a tion of the uronic acid are t he cause of var iation in the structure of the ma in disaccharide unit of a native hepa rin. 88 Pharm aceuti c al hep arin , com mon l y u s ed as mac ro mo lecul ar d ru g 98 is a highly sulfated t ype of nati ve hepari n (s ee Fi gu r e 3 ) found in mast c ell granulates. 88 A great deal o f curr ent int erest is paid to study the heparin - protein binding i n which highl y sulfated t y pe (Hep) play s a dominant role. 87, 99, 100 Although PE -P complex ation is not exclusively ionic in nature, Hep is a v ery useful model f or study in g th is process in deta iled. 99 Figure 3 . C h emical structure of h i ghly sulf a ted m aj or repe ating unit of heparin : 2 -O - sul fa t ed iduronic acid and 6 - O- sulfated, N - sulfated glu cosamine, I doA (2S) - GlcN S(6 S) . 87 3.1.1.2. Sulfat ed β - Cyclo dextri n Rapid progr ess in development of therapeutic poly mers is confronted b y t he chal len ges of t he effective drug de liver y . Major obstacles for polymers as drug candidates are solubilit y , stabilit y a nd membrane permeabilit y . 101 M any attempts of improving bioavailability of poorl y -solubl e drugs, was based on th e complex ation with solubiliz i ng a ge nt s . 102 I n this r egard c y clod extrins (CDs) are able to eliminate so me of th e limitations o f pol y m er d ru g cand i dates and improv e their deliver y. 103 Figure 4 . Chem ical structure and schematic representation of a spatial str ucture o f β - CD - S. 7 CDs are c y cl ic oli gos acchar ides sh aped of a tru ncat ed cone o r t orus . 104 Their structure (see Figure 4 ) i s characteriz ed by hydr ophobic cavit y a ccessible for variet y o f compounds. H y d r o x yl groups l oc ated on t he f ace of the s tru ct ure ensure water s olubility . 105 Complexatio n of hydr ophobic drugs with CDs was applied in s eparation methods 106 – 108 an d pharm aceu tical che mistry . 109 The re ar e more than 30 a vailable drugs with improved stability and solubili ty du e to CDs complexation. 109, 110 S pec ial atte ntion was paid to sulfa ted cy clodextrins (S - CDs). There were st udied as an alt ern at ive fo r hep arin in repairing process and used in di rect m easur emen t of lipoprotein cholesterol in serum. 111 β - CD - S which is composed of seven α - 1,4- linked gluc ose units presented a lack of hemolytic a ctivit y in early studies on binding to ery t hrocytes 112 w hi c h resu lted in inc reasing intere st of this partic ula r CD. 3. 1.2. Hyperbranche d P oly ele ctrol ytes Hyperb ran ched mac romo lecul es c an b e in gen eral d escrib ed as composed of randoml y branched s truct ur es that consist of one focal point and at least two br anching points. 113 Thi s class of pol y me rs has become intensivel y investigated due to its bi omedical applications. One of the medically mos t promising class of hy p erbranched macromolecules is represented by dendritic polyglycerol sulfate (dPGS). 3.1.2.1. Dend riti c Poly gly cerol S ul fa te (dPGS ) This compound was inve stiga ted ori gina ll y as potentia l alternativ e for h eparin , e xhibi ting intere sting properties such as ant i - inflammato ry a ctivity sui tabl e for v ariet y of applications. 114 Figure 5 shows the struct ure of a n idealiz ed dPGS molecule. Dernedd e e t al . showed a high anti - inf l ammatory effec t o f dPGS in vi vo . 115 By vary ing the size of dPGS as well as the degr ee of its sulfation they obt ained a detailed relationship of dPGS structure and activity. T he y evidenced a strong binding of dPGS to P - and L - s electi n wi th cl ear correl ati on b etween b i ndi ng affinity, increasing size and deg ree of sulfation. O O O O +Na-O 3 SO +Na-O 3 SO O O O O +Na-O 3 SO +Na-O 3 SO +Na-O 3 SO O +Na-O 3 SO +Na-O 3 SO +Na-O 3 SO +Na-O 3 SO O O +Na-O 3 SO O +Na-O 3 SO +Na-O 3 SO O +Na-O 3 SO O +Na-O 3 SO +Na-O 3 SO O +Na-O 3 SO O O +Na-O 3 SO +Na-O 3 SO +Na-O 3 SO O O OH O O +Na-O 3 SO O +Na-O 3 SO +Na-O 3 SO +Na-O 3 SO +Na-O 3 SO Figure 5 . Idealized stru cture of dPGS. 8 Finally , it was found that dPGS b y bindin g to, and inhibiti on of P - and L - sel ectin s th at caus e the leukocy t e extravasation di minishes the inflammatory r esponse. Over the re cent years the eff ect of dPG S was studie d against multiple diseases a ssociated w ith inflammatory events suc h as oste oar thritis, 116 – 120 rheu matoid a rthritis 116 and neurological disorder. 121, 122 I n al l th ese studies dPGS appeared as a promising candidate for medical treatment. 3.1 .3 . P olye l ectro l yt e Brushes P o l ye l ectrol yte (P E) brus h es aris e wh en lo n g linea r pol y el ect rol y t e chains are d en sel y grafted to a solid surfa ce . 123 Dependin g if t he PE chai ns a re at ta ched to a p lana r 123 – 125 or curve d as e.g . spher ical s urf ace , 126 – 132 a plan ar - o r sph eri cal po l y e lect rol yte b rush will be generated. The brush struc ture result s from a sufficientl y dense grafting of the chains which means that the len gth of the PE chain i s m uch lar ger t han t he av er age di stan ce bet ween t wo n ei ghb orin g chai ns graft ed on t he surf ace. In a mo re t an gible wa y it can b e form ulat ed that the av erage dis tance ( D ) between neighboring grafted chains should be sm aller than two times of the gyration radius ( R g ) of a fr ee PE chai n (see Fi gure 6 ). 133 Depending on the re s idual groups of grafted P E chains, two ty pes of brushes can be distinguished. The Quen ched brush is a resu lt o f attachmen t of a s tron g pol y el ect rol y t e as e.g. poly(styrene sulfonic acid). In t his case th e ch ar ges alon g the ch ai n are inde pendent of th e pH in the sy stem . 134 Upon graftin g a weak p ol yelect r ol yte as e.g. pol y (a crylic acid), an anne aled brush will result. H ere the de gree of ionization of the chains de pends on the pH within the brush lay er . 74 At hig h pH the acid groups of monomeric units are dissociated leading to a highly charge d s y stem. Conseq uently, at low pH the acid groups are full y protonated and the s ystem beha ve s similar to a ne utral b rush . An increasing intere st in PE brushes is due t o the fac t, that th e stro ng elect rost ati c in teract ion s bet ween cha rged and d ensel y gr afted c hai ns all ow a wi de use of the se s y s tem s, espe cial l y when comp ared to brushes of grafted, uncharged pol y mers . 15,1 35 Figur e 6 . Schemat ic representation of t he structure of th e P lanar - and Spherical Polyelectrolyte Brush wit h grafted anioni c PE chains on their surface. R – radius of spherical substrate surface, L – t he co nto u r le ngt h o f the a tta ched chains, ci – cou nteri ons. 9 It has been shown that the confinement of a large number of c ounterions compensating the charge of pol y ele ctrol y t e chains within the brush l a y e r constitute an essential proper t y of the se sys tems . 136, 137 As a consequence of tha t, the PE cha ins will be stretched by t he high osmotic pressure of the counterions retained within the br ush layer. The resulting osmotic brush ex ists in a s alt -free solution (s ee Fi g u r e 7 ). Figure 7 . Sch ematic representation of the transi tion between osmotic - and sl ated br ush on th e exampl e of anioni c spherical polyel ectrol yt e brus h. PE c hai ns o f t he o smoti c brush are stret che d b y the hi gh o smot ic p re ss ure ; suc h br ush ex ist s in a sal t - free s ol uti on. In a salt ed brus h the st rong electro static inte r action between PE chain s are screened as cons eq uence of increased ionic strength. However, if the ionic strength of the solution i s increased by addition of s alt , t he strong electro stat ic i nte racti on b etw een PE chai ns w ill be screen ed and t he bru sh w ill becom e a salted brush . Withi n this regime PE brush behaves simil ar to unchar ge d monola yer of grafted pol ymer chains. Therefore b y regul ation of the ionic s treng th PE brushes can switch betwe en different states . This tra nsition between osmotic brush and salted brush regime was demon strate d through X- ray reflecto metry by monitorin g the height of the brush la y er. 138, 139 T he swel lin g beh avior of the PE brush cannot be understood only on the basis of electrostatic intera ctions alone . On t he example of planar pol y ( N - meth y l - p yridinium) brush it was demonstrated that ion - speci fic e ffe cts can l ead to bru sh shrinking in t he swollen state . 140 I n this part icular case the increase of iodine counterions conce ntration resulted in the dra matic collapse of the brush. Further inc rease of the iodine ions concentration however resulted in brush re- swell ing. T her efor e “salt i ng - out” and “salting - in” driven by ion -spe cific e ffects at hi gh i onic stren gth can ove rrul e the elect rost ati c int eract ion s. 3.1.3.1. Plana r Poly ele ctro lyte B rus hes ( PPBs ) M uch attention has bee n given to PPBs in order to immobilize proteins or e nz y mes. From the fac t that protein molec ules immobilized b y PE brus hes keep their confor mati o n and ( enz y m ati c) activ ity , 62 PP Bs appears as pro mi sing s y s tem s to use as biosensor . 67 P PBs can b y char acte riz ed b y as e.g. wat er cont a ct angle anal ysis, el lip so met ry , 141 atomi c forc e m icros cop y (A FM ) , 74 Fourier transfo rm infra red (F T - IR) sp ect roscop y, near - edge X - ra y absorption fine structu re 10 (NEXA FS) s pectro scop y 76 and qu artz crystal m icro balance w ith dis si p ation moni toring (Q CM- D) . 142 PPBs ba sed on poly(a cr ylic acid) ch ains supported on silicon wafer were us ed to stud y the adsorption of bovine serum albumin ( B SA ) by f ixe d - ang le optical reflecto metr y . 62 It w a s found that approxim ately 30% of the brush volume is occupied b y protein molecules and that protein conce ntration in sol ution play s almost no e ffec t on the amount of ads orbed proteins. 3.1.3.2. Sp heri cal Poly el ectroly te B rus hes ( S PBs) SPBs can be char act eri zed by numero us ex peri ment al t echni ques s uch as dy namic light scatt erin g (D LS) , 1 4 3,144 smal l angl e X - r a y a n d neutron scattering (SAXS, SANS) , 145, 146 cryog enic tran smission electron micro scop y (cr y o - TEM) , 147 chain cleav age and condu ctometr ic titration . 133 SPBs are a class of functional colloida l particles with a wid e application potential. Ca tionic SPBs composed of poly st y r ene ( PS ) c ore and poly - (2 - amin oeth ylmeth acr y l ate ) ( PAEM H) ch ains wer e us ed as c arri ers for catal ytical l y acti ve met al nanop articl es such as A u and Pd. 1 48 I t was shown that the res ulting composite pa rticles exhibit excelle nt colloid al stab ility and their cataly ti c activity was monitore d b y a model rea ction of the reduction of 4 - nitrophenol b y s odium borohydride (B H 4 - ). SPBs including quench ed and annealed brushes we re u sed for immobilization of la rge number of proteins thus opening the possibilit y of substantial biomedical applications. It was shown that BS A and β - La ctoglobulin (BLG) can b e sep arated b y cationic and anionic SPB s ba s ed on protein charge anisotropy. 149 11 3.2 . Protei ns 3.2. 1 . Lys ozy me (Lys) Lysoz yme ( Lys) i s an ant i mi crobi al enz yme that re present s t he cl ass o f gl y c os ide h ydrolas es. 150 It cataly z e the h ydrolysis of the ( 1→4) - β - gl y c os idi c lin kages b etwe en N - a cet ylmur amic a cid and N - acet yl -D- glucosamine in the peptidog l y c a ns o f bacteri al cell walls . 1 51 I ts antibacte rial properties and conformational stabilit y are the reasons of s uch interest an d wide use o f this protein. Over the ye a r s L ys has be en used in biotechnological and therapeutic applications. 152 ,15 3 Ly s is a globul ar and r el ative ly sma ll protein . 150 As for one of the first proteins wit h revea l ed three - dimensional s tructure 154 it is w idel y used in ex per imental and theoretical s tudies . 150 L ys is an e llipsoidal, sing le - chain polype ptide with m olecular weight of 14,3 kDa that consist of 129 residues orga nized i n six α - helices an d th ree β - sh eets co nn ected b y flex ibl e loo ps and gro p ed into two domains, α and β (se e Figu re 8 ). 155 Figure 8 . (a) Crysta l st r uctur e o f hen eg g white l yso z yme ( HE WL) . ( b) Electr ostatic s urface view of t he HEWL. (PDB : 1DPX) α - helice s contribute to about 30 - 40% to the secondary stru cture of this protein and the β - sheet content is less than 10%. Due to the presenc e of four disulfide brid ges and approximate dimensions of 30 x 30 x 45 Å it i s considered a s a rig id molecule. Ly s cont ain 14 acidic and 18 basi c resid ues and it i s chara ct eriz ed b y isoel ect ric po int of pI = 11 . The ac tive site of this prote in is loca ted within negativ el y char ged cr evi ce betw een d om ain s. Th e n egati ve ch ar ge is attribu ted to the presence of g lutamic acid - and as part ate r esid ues. 3.2. 2 . Human Serum Albumin (HSA) Human Serum Albumin ( HSA) represents a wide family of proteins that includes vitamin D- binding protein, human - specific c omponent (Gc) a nd α - fetoprotein (AFP) . 156 Unlike Gc and AFP , albumins are non - gl ycos y l ated an d t h e y are also non - act iv e in t erms o f immunosuppression. Those multi - domain an d relative l y l arge pro teins play s multiple physiological functions due to the fact that the y are the major soluble protein component o f the bloodstream. Therefore albumins are one of the main contributors to colloi d osmotic pressure of the blood. Moreover , t he extravascular protein stands for 60% of the total albumin . 156 H SA is best known for its si gnificant role in supporting the transport, di stribution and metabolism of numer ous endo - and exogenous ligands . 156 The se l igands c onstitute a chemically diverse group which includes amino acids, fatt y acids, steroids, metals (notabl y calcium, copper and zinc) and man y pharmac eut ical s. Due to its c ommonness - with blood concentration of about 7 x 10 -4 M a) b) 12 and its extraordinary bin ding ca pacit y , HS A af fect s th e drug effici en c y and rate o f deli ver y , thus being an importa nt factor with regard to devel opment of drug s and their availa bilit y . 157 HSA is a protein with molec ular weight of a bout 66 kDa that consist of 585 amino ac ids grouped into three homologous domains (I, II and III ). Each of those is composed b y t wo halical subdomains (A and B) th at are con nect ed b y rand o m coi l . 1 57 Therminal regions of s tru ctural l domains participa te in the formatio n of interd omain helice s t hat a re linking domain IB to IIA and IIB to IIIA, resp ecti v el y . The structural or ganisation of HSA is presented in Figure 9 . Figure 9 . (a) C rystal structure of HSA. Sudlo w site I (in subd omain IIA) is indicated b y red circle; Sud lo w site I I (in subdom ain IIIA) is indicated by blu e circle. ( b) Electr ost atic s urface view of the HSA. (PDB: 1AO6) From pre vious binding studies it became evide nt that HSA can reversibly bind a mult itude of diff erent li gands . 158,1 59 T he principal binding sites on HSA are loca ted in subdomains IIA and III A , and n amed as Sudlow I and Sudlow II, resp ective ly . 16 0,161 I n bot h these re gions a part of the h y drophobic core is surrounded by positivel y c harged residues to for m a pocket . 161 The pocket of subdomain IIA is formed b y h y drophob ic side chains and it is pr edominantly non- polar. The e ntrance of it, is surrounded by positi v el y ch arg ed ami n o acid resid ues . 161 Subdomain I II A, which i s almost the same size as subdomain IIA is c haracterized b y th e pocket with lar ge solve nt accessibility and a sin gle hy drox y l patch loc ated at the mouth of the pocked. 162 Due to the se s tru ctural feat ur es S udlo w sit e I acco mmo dat es m os t pr eferab l y bulk y hetero c yclic an ions , whe reas a rom ati c carb ox y lat es bind to Sudlow sit e II . 1 57 a) b) 13 3.3 . P ro tein s and Polye lec tro lyte s Pol yelectrol ytes ( P Es) and proteins in aqueous solution interact with ea ch o ther as well as with their surroundings resulti ng in formation of p olyelectroly t e - prot ei n co mpl ex es (P E - P). 11 – 13, 52,80 ,87, 163 Du e to its relation to the inte rac tion o f DNA with repair proteins it bec omes an important problem in moder n biophysics. 164, 165 By considering the adsor pti on of proteins onto surface, two funda mental approaches, regarding this process can be di stinguished. In the f irst approac h, in order to avoid biofouling the protein adsorption must be prevent. 166 Th e fact th at biomedic al devices suc h as implan ts or nanopa rticles will be imme diately covered b y a dense layer of adsorbed proteins upon implantation int o human bod y is the rea son of such intense res earch in this field. The re sulting prote in “corona” will c omplete l y isolate the device from its targe t and further more will ca u s e the i mm une resp ons e to t hese m aterial s . 1 67 – 170 In the second approach pro t ein immo biliz ation is desirab le. This is due to man y applicatio ns in whic h enz ymes ar e used as catal ysts . In most cases in both approac h es, PE brushes are used to contr ol the protein adsorption. Thus s urfac es co at ed wit h PE b rushes are f requ entl y st udi ed as th e y are related to “smart” and stimuli responsive materials often used as biosensors. 1 71 PE brushes are an ex cell ent s yste m to stud y protein adsorption, since protein immobiliz ed onto them retains their c onformation and (enzy matic) activity . 69,70 It ha s been shown that several proteins including human serum al bumin (HSA) can adsorb onto a - like ch arg e spherical polyelectrol y te brushes ( SPB s ). 32 I t w as revealed that the secondary struc ture of adsorbed proteins is undisturbed. 68 I t was also demonstrated that adsorbed pr oteins are distributed eve nl y within the brush la y er. 73,172 Moreover sev eral st udi es report ed a stro n g influ ence o f i onic strength on the amount of adsorbed pr oteins . 173 – 175 I n pa rti cular, t he upt ake decre ases with increas in g ion ic stren gth in dica ting the strong influe nc e of e lectrostatics in prote in inter action with PE brushes. T he formation of PE - P complex es is broug ht about b y a combination of electrostatic interactions and e ntropy gain. 52 ,82, 84 ,85,99, 176 The complexation is theref ore influenced by density, distribution and extent of ionization of the di ssociable groups on the prote in surface as well as on t he P E chain s. 3.3. 1. Pr ote in Stru ctu re upon B ind in g Protein conformation upon binding to PE s is one of the most important aspec ts of this process. The anal y sis of the prot ein structure can focus on demonstrating if the protein structure is preserved or on find an evidence of changes in protein conformation. 1 77 Thi s depends if the stud ied pro cess is rela ted to pr otein immobiliz ation or alloste ric intera ctions resu lting in enhancement or inhibition of the prot ein activi ty . Experimental techniques such as fluo rescen ce, cir cular di chroi sm (CD) and Fou rier tr ansfo rm in fra red ( FT - IR ) s pectro sc op y have b een us ed to est abl is h th at the stru cture of adsorbed proteins is l argel y preserved and stabilized by PEs . 13,1 78 I n contrast, the conformational change upon bindin g to heparin appears for several proteins in e.g. antithrombin. 179 FT - IR sp ectros co p y was us ed to anal y z e th e secondary st ructure of native and adsorbed prot eins. This technique, unlike the cir cular dichr oism is not li mited to tra nslucent solutio ns. 180 I t c an be successfully applied to turbid samp les s uch as l atex par ti cles . 181 Thus, it is s uitable f or anal y sis o f the secondar y stru cture of prot eins adsorbed onto P Es brushes. Proteins in I R spectra show characteristic absorption bands (amid e I and II) betw een 1500 and 1700 cm -1 . 182 – 1 84 T he ami de I b and ari s e in approximatel y 80% from stretching vibration of the C=O bond, whereas the amide II b and can be mainl y 14 asso ciated wi th C - N stret ching vibra t ions and bending of N - H bond. 185 The shape , positi on a nd intensity of t he ami de b ands depend strongl y on the secondary structure of the protein. I R signals ar isin g fr om the structural compone nts of the protein that are present in the amide I band are enli sted in T ab le 1 . 1 85 Table 1 . E le m e nts of t he prote in - secondary structure presen t in the amide I band. Wave n umber (c m -1 ) Stru cture el e ment 1620 – 1640 β – sheet 1640 – 1650 Random coil 1650 – 1658 α – helix 1660 – 1690 loops 1670 – 1680 β – sheet The standard de vi ation upon determination of elements of the sec ondary structure of the protein b y FT - IR spectroscop y does not ex ceed 5% . 186 Ov er the rec ent years th is t echni que was succes sful l y applied i n sev eral st udi es re gard ing protein immob ilization on PE brushes. 81, 163,1 81,1 87,18 8 3 .3. 2. The rm odyn am ic An alysis of Pr ote in I nt era cti on with Polyel ectr olyt es by Iso ther mal T itra tion C alorim etr y (IT C) 3.3.2.1. Therm odyna mic Analysis 3.3.2.1.1. Count erion C ondens atio n A hi ghl y char ged pol ye le ctrolyte in solution attr acts its surrounding counterions so that a cer t ain frac tion of them is condensed to the macr oion . 189 This condensation of c ount erions on a pol yelect rol y t e ( PE ) chai n can be anal y s ed bas ed on the O ns a ger -Manning- Oosawa t h eor y. 190 – 193 In tha t wa y , the charge of PE chain is balanced by condensed c ounterions and b y a fr acti on o f counterions that interact with PE chain via scr eened Deb ye - Hückel inte raction. 3 Condensation occurs wh en the char ge - densit y para meter, 𝜉𝜉 = 𝑙𝑙 𝐵𝐵 𝑙𝑙 (for the case of monovalent charge groups and counterions) is g r eater than unity. He re, 𝜆𝜆 = 𝑒𝑒 𝑙𝑙 is t he charg e densi t y of the p ol ymer chai n and 𝑙𝑙 𝐵𝐵 = 𝑒𝑒 2 4𝜋𝜋 𝜀𝜀 0 𝜀𝜀 𝑟𝑟 𝑘𝑘 𝐵𝐵 𝑇𝑇 is the B jerrum l ength, where e stands for the electron c harge, ε 0 for vacuum permittiv ity , ε r for dielectric constant and k B T for the t hermal ene rg y. 15 Figure 10 . Schem atic representation of the i on condens ation. A rod - like p o l ymer with hi g h cha rge ( l B > l ) attr acts a num ber of opposi tely c harged co unte ri ons. As show n by Mannin g, i n dilut e solutions for macroion s charact eriz ed b y ξ > 1 a fracti on o f 1- 1/ ξ of the counterions will condense on them i n order to low er ξ to uni t y . 189 Th e screening effect of the ions ar ound the PE chai n is equiva lent to a second fr action (2 ξ ) -1 of bound counterion s. Thus , a fract io n of 1- 1/(2 ξ ) i s relev ant for co unt erion r eleas e fro m t he macro ion . 165 3.3.2.1.2 . Cou nteri on Releas e Recent studies on PE-P b inding demonstrated an attractive intera ction of the proteins above its isoele ctric point ( pI ) wit h highly charged PEs at low salt concentration. 52, 194,1 95 Isotherm al titration calo rimetry ( ITC) r eveal ed th at the entr opy is one of the main dri ving forces for such intera ction . 52,19 6 The observe d entropic attraction i s d ue to coun teri on releas e. P rotei ns carr y patches of positive and ne gative char ge on their surface due to the a symmetric distribution of char ged resi dues . 197 This charge anisotropy a llo ws PE - P interaction. Upon such interaction prot eins can a ct as multivalent counterions in r egard to cha rged PE chains thus rele asin g a number of its condensed monovalent counterions. 198 Theoretic al predic tions estimate s that z [1- 1/(2 ξ )] is the number of r eleas ed counter ions upon binding, where z represents the number of char ged sit es of t he PE . As a consequence the c ons iderable ove r all gain in entropy can promote the adsorption of proteins, as mentioned before, even on the “wro ng sid e” o f isoele ctric point. T he attractive contribution t o the Gibbs free energy of bindi ng due to count eri on r eleas e, ΔG cr can be esti mat ed th rou gh: 16,1 96 ∆𝐺𝐺 𝑐𝑐𝑟𝑟 𝑘𝑘 𝐵𝐵 𝑇𝑇 = ∆𝑁𝑁 − ln � 𝑐𝑐 𝑠𝑠 𝑐𝑐 𝑝𝑝𝑝𝑝𝑝𝑝𝑐𝑐 ℎ � + ∆ 𝑁𝑁 + ln � 𝑐𝑐 𝑠𝑠 𝑐𝑐 𝑃𝑃𝑃𝑃 � (1) H ere ΔN _ is t he number of negative counterions re leased form the positive patch on the prote in surfac e. ΔN + is the numb er of positive counterions released from the PE chain . c s repres ents th e concentration of s alt in sol ution; c pat ch is the conce ntration of negative counterions that are 16 accumulate d on the positive patc h on the protein sur face and c PE st ands for t he concentration of counterions condensed on the PE chain. As discus sed in previous section c PE can be est imat ed b y On s a ger -Mannin g- Oosawa t heor y . 190 – 193 3.3.2.1.3 . Eff ect of th e Ion ic st rength on the B indi ng Free Energy The non - monotonic salt d ependence wa s observed for interac t ions of β -Lactoglobulin ( BLG ), 80 r ibon ucleas e ( RN ase ), 175 l ys o z ym e ( L ys ) 13 and hu m an serum albumin ( HSA) 52 w ith s y nthet ic strong polyanion a nd pol ycations as we ll as for heparin and anthitrombin. 86 This pa rticular behavior, namely the highest PE - P bindin g affinit y oc cur when the Deb y e length is of th e comp arable si ze as th e pr otei n radi us and is r efe rred as a non - speci fi c PE -P binding. A highl y influential study wa s rep orted by Record et al . 199 in wh ich a g ener al th erm od ynamic an al ysis on the effect of ionic strength on ligand - nucl eic a ci d interaction wa s develo ped. In the proposed approac h due to the counterion release as a main dr iving force for PE - P com plex formation (see Figure 11 ), the condens ed counterions must be included in the stoichiomet ry of the binding. 53 Also the role of water rel ease and h y d ration upon such process c annot be overlooked what has been considered by Ta nf ord. 46 Figure 1 1 . Schem atic ill ustratio n of the counterion release upon interaction between highly charged PE and pro tein. I n that way, for as soci ati on between ch ar ged p ol ymer PE and protein P an d formation of their non- covalen t com plex PEP, in sol ution containi ng an excess of the ele ctrolyte M p+ X p - the followin g c h emical e quil ibria can be form ulat ed: P + PE 𝐾𝐾 𝑏𝑏 � � 𝑃𝑃𝑃𝑃𝑃𝑃 + ( ∆𝑛𝑛 𝑀𝑀 ) 𝑀𝑀 + ( ∆𝑛𝑛 𝑋𝑋 ) 𝑋𝑋 + ( ∆ 𝑛𝑛 𝑊𝑊 ) 𝑊𝑊 (2 ) where 17 K b = [ 𝑃𝑃𝑃𝑃𝑃𝑃 ] 𝑎𝑎 𝑀𝑀 ∆𝑛𝑛 𝑀𝑀 𝑎𝑎 𝑋𝑋 ∆𝑛𝑛 𝑋𝑋 𝑎𝑎 𝑊𝑊 ∆𝑛𝑛 𝑊𝑊 [ 𝑃𝑃 ] [ 𝑃𝑃𝑃𝑃 ] (3 ) and K T = [ 𝑃𝑃𝑃𝑃𝑃𝑃 ] 𝛾𝛾 𝑃𝑃𝑃𝑃𝑃𝑃 𝑎𝑎 𝑀𝑀 ∆𝑛𝑛 𝑀𝑀 𝑎𝑎 𝑋𝑋 ∆𝑛𝑛 𝑋𝑋 𝑎𝑎 𝑊𝑊 ∆𝑛𝑛 𝑊𝑊 [ 𝑃𝑃 ][ 𝑃𝑃𝑃𝑃 ] 𝛾𝛾 𝑃𝑃 𝛾𝛾 𝑃𝑃𝑃𝑃 (4 ) and K b = 𝐾𝐾 𝑇𝑇 𝛾𝛾 𝑃𝑃 𝛾𝛾 𝑃𝑃𝑃𝑃 𝛾𝛾 𝑃𝑃𝑃𝑃𝑃𝑃 (5 ) However 𝑎𝑎 𝑀𝑀 , 𝑎𝑎 𝑋𝑋 and 𝑎𝑎 𝑊𝑊 are not independent var iabl es . Follow ing Tanford the activities of solute and solvent species can be related by the Gibbs-Duhem equation: 46 𝑑𝑑𝑙𝑙𝑛𝑛 𝑎𝑎 𝑊𝑊 = − 𝑛𝑛 𝑋𝑋 𝑛𝑛 𝑊𝑊 𝑑𝑑𝑙𝑙𝑛𝑛 𝑎𝑎 𝑋𝑋 − 𝑛𝑛 𝑀𝑀 𝑛𝑛 𝑊𝑊 𝑑𝑑𝑙𝑙𝑛𝑛𝑎𝑎 𝑀𝑀 (6 ) Here w e assum e th at the con centr ati on o f the p ol yelect rol y te is smal l [ PE P] ≈ 0. Equation (6) ca n be further ge neralized as proposed b y Tan ford. 46 𝑑𝑑𝑙𝑙𝑛𝑛 𝑎𝑎 𝑊𝑊 = − 𝑐𝑐 𝑠𝑠 𝑝𝑝 55 . 6 𝑑𝑑𝑙𝑙𝑛𝑛 𝑎𝑎 ± (7 ) where c s is the molal c oncentration of electrol y te, 55.6 is the molality o f wat er and 𝑎𝑎 ± = 𝑎𝑎 𝑀𝑀𝑋𝑋 1 𝑝𝑝 = �𝑎𝑎 𝑀𝑀 𝑝𝑝 + 𝑎𝑎 𝑋𝑋 𝑝𝑝 − � 1 𝑝𝑝 Here 𝑝𝑝 = 𝑝𝑝 + + 𝑝𝑝 − and f or a monovalent salt, 𝑝𝑝 = 𝑝𝑝 + = 𝑝𝑝− = 1 , thus 𝑝𝑝 = 2 Furthermo re, 𝑛𝑛 𝑀𝑀 𝑑𝑑𝑙𝑙𝑛𝑛 𝑎𝑎 𝑀𝑀 + 𝑛𝑛 𝑋𝑋 𝑑𝑑𝑙𝑙𝑛𝑛 𝑎𝑎 𝑋𝑋 = ( 𝑛𝑛 𝑀𝑀 + 𝑛𝑛 𝑋𝑋 ) 𝑑𝑑𝑙𝑙 𝑛𝑛𝑐𝑐 𝑠𝑠 + 𝑛𝑛 𝑀𝑀 𝑑𝑑𝑙𝑙𝑛𝑛 𝛾𝛾 𝑀𝑀 + 𝑛𝑛 𝑋𝑋 𝑑𝑑𝑙𝑙 𝑛𝑛 𝛾𝛾 𝑋𝑋 = ( 𝑛𝑛 𝑀𝑀 + 𝑛𝑛 𝑋𝑋 ) 𝑑𝑑𝑙𝑙𝑛𝑛𝑎𝑎 ± + 1 𝑝𝑝 ( 𝑝𝑝 − 𝑛𝑛 𝑀𝑀 − 𝑝𝑝 + 𝑛𝑛 𝑋𝑋 ) 𝑑𝑑𝑙𝑙𝑛𝑛 � 𝛾𝛾 𝑀𝑀 𝛾𝛾 𝑋𝑋 � ≈ ( 𝑛𝑛 𝑀𝑀 + 𝑛𝑛 𝑋𝑋 ) 𝑑𝑑𝑙𝑙 𝑛𝑛𝑎𝑎 ± (8 ) By combini ng e quations (3) – (8 ) the followin g relation is o btain 𝑑𝑑𝑙𝑙𝑛𝑛 𝐾𝐾 𝑏𝑏 = −∆ �𝑛𝑛 𝑀𝑀 + 𝑛𝑛 𝑋𝑋 − 𝑐𝑐 𝑠𝑠 𝑝𝑝 55 . 6 𝑛𝑛 𝑊𝑊 � 𝑑𝑑𝑙𝑙𝑛𝑛 𝑎𝑎 ± + 𝑑𝑑𝑙𝑙𝑛𝑛 � 𝛾𝛾 𝑃𝑃 𝛾𝛾 𝑃𝑃𝑃𝑃 𝛾𝛾 𝑃𝑃𝑃𝑃𝑃𝑃 � (9 ) The eff ect of ele ctrol y t e (M p+ X p- ) on K b can be anal y z ed more closely with consideration of binding between linear negativel y - ch arged polymer and a protein bearing patches of positive char ges on it s su rfac e (se e Fi gure 11 ). 𝑑𝑑𝑙𝑙𝑛𝑛 𝐾𝐾 𝑏𝑏 𝑑𝑑𝑙𝑙𝑛𝑛 𝑎𝑎 ± = −∆ �𝑛𝑛 𝑀𝑀 + 𝑛𝑛 𝑋𝑋 − 𝑐𝑐 𝑠𝑠 𝑝𝑝 55 . 6 𝑛𝑛 𝑊𝑊 � + 𝑑𝑑𝑙𝑙𝑛𝑛 � 𝛾𝛾 𝑃𝑃 𝛾𝛾 𝑃𝑃𝑃𝑃 𝛾𝛾 𝑃𝑃𝑃𝑃𝑃𝑃 � 𝑑𝑑𝑙𝑙𝑛𝑛 𝑎𝑎 ± (10 ) Due to the rele ase of cations condensed on the charged polymer it can be assumed that K b is dependent only on the co ncentration of cations [M + ] and independent on the concentration of 18 anions [X - ]. If considered interaction re sults in up t ake or rel eas e of wate r mol ecules as wel l as cations, the dependence of K b on monovalent electrolyte M p+ X p- can be fo rm ulat ed as 𝑑𝑑𝑙𝑙𝑛𝑛 𝐾𝐾 𝑏𝑏 𝑑𝑑𝑙𝑙𝑛𝑛 𝑐𝑐 𝑠𝑠 = − ∆𝑛𝑛 𝑐𝑐𝑐𝑐 + 2𝑐𝑐 𝑠𝑠 ∆𝑤𝑤 55 . 6 (11 ) where ∆𝑛𝑛 𝑋𝑋 = 0; ∆𝑛𝑛 𝑀𝑀 = ∆𝑛𝑛 𝑐𝑐𝑐𝑐 and the ac tivity coefficie nt is disregarde d: 𝑎𝑎 ± → 𝑐𝑐 𝑠𝑠 . ∆𝑛𝑛 𝑐𝑐𝑐𝑐 repres ent s th e mol es of released ( ∆ 𝑛𝑛 𝑐𝑐𝑐𝑐 > 0 ) counterions (in this particular case, c ations) and ∆𝑤𝑤 s tands for t he mol es of w ater mo lecul es rele ased ( ∆𝑤𝑤 > 0) upon bi nding. Integrating t he equation (11) in the boundaries for the concentrati on of electrolyte M p+ X p- , c s and 1M: ∫ 𝑑𝑑𝑙𝑙𝑛𝑛 𝐾𝐾 𝑏𝑏 = −∆𝑛𝑛 𝑐𝑐𝑐𝑐 ∫ 𝑑𝑑𝑙𝑙 𝑛𝑛𝑐𝑐 𝑠𝑠 + 0 . 036 ∆ 𝑤𝑤 ∫ 𝑐𝑐 𝑠𝑠 𝑑𝑑𝑙𝑙𝑛𝑛𝑐𝑐 𝑠𝑠 𝑐𝑐 𝑠𝑠 1𝑀𝑀 𝑐𝑐 𝑠𝑠 1𝑀𝑀 𝑐𝑐 𝑠𝑠 1𝑀𝑀 (12 ) resu lts in 𝑙𝑙𝑛𝑛 𝐾𝐾 𝑏𝑏 − 𝑙𝑙𝑛𝑛 𝐾𝐾 𝑏𝑏 ( 1 𝑀𝑀 ) = −∆𝑛𝑛 𝑐𝑐𝑐𝑐 𝑙𝑙𝑛𝑛 𝑐𝑐 𝑠𝑠 + 0. 036 ∙ ∆𝑤𝑤 ∙ ( 𝑐𝑐 𝑠𝑠 − 1 ) (13 ) Speci al attention must be paid to the integration c onstant 0.036 ∙ ∆ w which en sures the cor rect limit for c s = 1 M. 200, 201 Equa tion (13) shows that ∆ w must be of the order of 10 2 to produce a not iceabl e eff ect o n K b , t hat is, a noticeable curva ture in plots of ln K b vs. l n c s . Thi s h as b een shown clearly in the work of Bergq vist and Ladbur y. 202 Mor eover, if the second term in equ ation (13) can b e dismissed, these plots can b e used to ex trapolate the binding constant to high ionic strength whe re counterion release should no longer inf luence K b (see the discussion of this po int in ref. 53 ). Moreover , equation (13) shows that ∆ w must be of the order of 10 2 to produce a noticeable effect on K b , that is, a notice able curvature in plots of l n K b vs. ln c s . If th e second term in equation ( 13) can be dismissed, the se plots should be l inear and can be used to obtain the binding constant K b (1 M ). I n this the follow in g relatio n can be used for data evaluation: 𝑙𝑙𝑛𝑛 𝐾𝐾 𝑏𝑏 = 𝑙𝑙𝑛𝑛 𝐾𝐾 𝑏𝑏 ( 1 𝑀𝑀 ) − ∆𝑛𝑛 𝑐𝑐𝑐𝑐 𝑙𝑙𝑛𝑛 𝑐𝑐 𝑠𝑠 (13 a) 3.3.2.1.4. Donna n Ef f ec t The confine ment of coun terions compensating the charge of PE chains within the PE brush is an essential propert y of P E brushes. The phase boundar y betw een the bulk solution and charged PE brush and b y thi s an unequal ion distribution originates the electri c p ot enti al acros s th e boundary. Assuming the electrone utralit y of this sy s tem the concentration of counterions within the brush can be given, due to Donnan equilibrium b y : 68 𝑐𝑐 𝑏𝑏𝑟𝑟𝑏𝑏𝑠𝑠 ℎ 𝑐𝑐 𝑠𝑠𝑝𝑝𝑠𝑠 𝑝𝑝 = � 𝛼𝛼 𝑐𝑐 𝑝𝑝 2𝑐𝑐 𝑠𝑠𝑝𝑝𝑠𝑠 𝑝𝑝 � + � 1 + ( 𝛼𝛼 𝑐𝑐 𝑝𝑝 2𝑐𝑐 𝑠𝑠𝑝𝑝𝑠𝑠 𝑝𝑝 ) 2 (14 ) with the Donnan-potential expressed as follows ∆𝜑𝜑 = 𝑒𝑒 −1 𝑘𝑘 𝐵𝐵 𝑇𝑇𝑙𝑙𝑛𝑛 [ � 𝛼𝛼𝑐𝑐 𝑝𝑝 2𝑐𝑐 𝑠𝑠𝑝𝑝𝑠𝑠𝑝𝑝 � + � 1 + ( 𝛼𝛼 𝑐𝑐 𝑝𝑝 2𝑐𝑐 𝑠𝑠𝑝𝑝𝑠𝑠𝑝𝑝 ) 2 (15) where c p denotes the concentration of monomer units within the brush and α corresponds to t he frac tion of charged mono mer units. 19 Figure 12 . The phas e boun dary betw een PE brush a nd bulk s olu tion. (a) φ (z) rep re sent s t he Do nna n – po tential for anio nic P E br ush of 1 0 0 nm t hic kne ss a s a f unct io n o f dis tanc e z measu red from the solid su r face. (b) Schematic illustration o f a su r face functionali zed w ith PE brush. The brush charge i s compensated by co unterions co nfi ned within its la yer. In case of a negatively charged PE cha i ns the concentration of protons within the brush, ac ting as counterions, ca n be greate r than in the solution. As a c onsequence , p H w ithin the brush lay er can be l ow er than t h e p I of interac tin g pr otein . Th is effect can even l ead to a cha rge r evers al o f a g iven protein promoting the protein adsorption onto PE brushes . 3,203 Clearly du e to the role of charge - charge interac ti on the protein adsorption hi ghly depends on the overall ionic str ength , which fac t was prov en for planar and spherical PE brushes. 173 – 175, 204 – 206 3.3.2.1.5. Cou nterio n Rel ease in PE Br ushes It was found that positivel y and n egativel y ch arged patches on the pr otein surface interact with PE brush with a significant asy mmetr y . In pa rtic ular, positivel y char ged patches a re attracted where as ne gativ el y char ged p atches are repel led. Th is p attern ma nifested for PE brushes on any morphology. The observed protein binding to a like - charged PE brush at l ow ioni c streng th as well as the brush resistance for such pro cess at conditi ons of high ionic stren gth can be ex plai ned b y a po ssi ble char ge r evers al of the ad sorbed protein . 134, 207 I n a phenomenological approac h proposed b y Yigit et al . the total free ene rgy of binding ( w tot ) betw een protein and PE brush can be described as a sum of three major contribut ions: the van der Waals and ex clud ed - volume interaction ( w exl+vd W ), the ele ctrostatic inter action ( w ele ), a nd the counterion release contribution ( w cr ): 82 𝑤𝑤 𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑤𝑤 𝑒𝑒𝑒𝑒𝑐𝑐𝑙𝑙 + 𝑣𝑣𝑑𝑑𝑊𝑊 + 𝑤𝑤 𝑒𝑒𝑙𝑙𝑒𝑒 + 𝑤𝑤 𝑐𝑐𝑐𝑐 (16 ) These contributions can be in general divided into repulsive and attractive ones. Protein and PE brush should repel each other due to t he electrostatic and electrosteric repulsion. P rotein penetrating a PE brush causes unf avorable steric interaction with PE cha ins. I t also ra ises the osmotic pressure of c onfined counterions. Thus binding ca n occur onl y if an attractive force is capabl e to ov erco me thes e repulsive c ontributions. In a p p roach pr es ented i n equation (16 ) the 20 most prominent repulsive contribution is r efle cted b y the ex cl uded v olu me part whi ch is completely domi nated by osmotic contribution of the counterions. The electrostatic part takes into account the monopolar r epulsion and dipolar and Born attraction. Only the latter t erm is strong l y a ttractive . 208 Therefo re d ecr ease o f the s t ren gth of t he bi ndi ng bet ween prot ei n and PE brush at higher salt concentra tion can be related to a strongl y diminished counterion release effect . 3.3.2.1.6 . Eff ect of T emperatu re on the B in di ng With m odern cal orim ete rs, preci se values of the binding constant, K b an d th e free ener g y of binding, ∆ G b can be m easu red across a wid e r ange of temp erat ures ( e rrors f or ∆ G b ar e approximately 0.4 kJ/mol for recent anal ysis on various prot ein- liga nd s y stems). 209, 210 The enthalpic and e ntropic c ontributions to the binding c an be extracted from t he van’t Hof f anal y sis . 𝑑𝑑𝑙𝑙𝑛𝑛 𝐾𝐾 𝑏𝑏 𝑑𝑑 ( 1 𝑇𝑇 ) = − ∆𝐻𝐻 𝑏𝑏 𝑅𝑅 (17 ) This linear relation between the logarithm of the binding constant, ln K b and t he tem per ature T assu mes that t he heat capacit y chan ge ∆ C p of the a nalyzed binding process is zero . 211 Thus, t h e binding enthalpy ∆ H b and the binding entropy ∆ S b are temperat u re - independent. This assumption was often found to be too g eneral. 212, 213 S everal studies on prot ein - mac romolecule binding showed that temperature variation of ∆ H b can be q uit e la rge . 13,52 The resulting non - zero ∆ C p , can be t aken wi thin t he ex peri ment al error as a cons tant , resulting in the following rela tions: 2 11 ∆𝐻𝐻 𝑏𝑏 = ∆ 𝐻𝐻 𝑏𝑏 , 𝑐𝑐𝑒𝑒𝑟𝑟 + ∆ 𝐶𝐶 𝑝𝑝 ( 𝑇𝑇 − 𝑇𝑇 𝑐𝑐 𝑒𝑒𝑟𝑟 ) (18 ) ∆𝑆𝑆 𝑏𝑏 = ∆ 𝑆𝑆 𝑏𝑏 , 𝑐𝑐𝑒𝑒𝑟𝑟 + ∆𝐶𝐶 𝑝𝑝 ln ( 𝑇𝑇 𝑇𝑇 𝑟𝑟𝑟𝑟𝑟𝑟 ) (19 ) ∆𝐺𝐺 𝑏𝑏 = ∆𝐻𝐻 𝑏𝑏 , 𝑐𝑐𝑒𝑒𝑟𝑟 − 𝑇𝑇 ∆𝑆𝑆 𝑏𝑏 , 𝑐𝑐𝑒𝑒𝑟𝑟 + ∆ 𝐶𝐶 𝑝𝑝 [ 𝑇𝑇 − 𝑇𝑇 𝑐𝑐𝑒𝑒𝑟𝑟 − 𝑇𝑇𝑙𝑙𝑛𝑛 � 𝑇𝑇 𝑇𝑇 𝑟𝑟𝑟𝑟𝑟𝑟 � ] (20 ) Equation (20) is known as the nonlinear va n’t Hoff equation, where T ref denot es a refe ren ce temp eratur e that can be chos en and ∆ H b,ref and ∆ S b , ref represe nts th e enthalp y and ent rop y of bin ding at t hat t emper at ure, res pect ivel y. ∆ H b , ∆ S b and ∆ G b as a funct ion of tem perat ure ar e presen ted in Figu re 13 . T S is d efined as a charac teri sti c temp eratur e at w hich ∆ S b = 0. The second cha ract erist ic t em peratu re i s T H at wh ich ∆ H b = 0. 21 Figure 13 . T her modynamic p rofiles der ived fro m studie s of the site spec ific bi ndin g of B a mHI end o nuc le a se to DNA . Values for ΔG b are fitted with the inte grated for m of the nonlinear v a n’t Ho ff equa t i on ( eq uat io n ( 20 ) ). ΔH b and ΔS b co ntributions to ΔG b are pres ented by sol id red l ines. E xpe ri me ntal val ues (●) o f ΔH ITC w ere ob tained f rom direct calorim etric measurements. Plot is rep rinted for m ref . 7 A long discussion was de voted to the questioning of the application of equation (20 ) to experimental data due to the observed discrepancies between bindin g enthalpy , ΔH b and calo rimetr ic en thalpy, ΔH ITC . 214, 215 C oncerns were raised wh ether t h is d iscrep ancies are originating from the measurement errors and methods of th e anal y sis . 8, 54, 209,2 16 It mu st be stressed at this point , that ∆ H ITC so t he di rectl y measu red heat effect upon protein- macrom olecu le interac tion is often mistaken for th e enthalpy of binding (∆H b ). In realit y ∆ H ITC contains severa l contributions of the associated effects. F ollowin g the a s sumpti on of Kozlov and L ohman, the directl y measure d calorim etric e nthalpy can be split into: 217 ∆𝐻𝐻 𝐼𝐼𝑇𝑇𝐼𝐼 = ∆ 𝐻𝐻 𝑏𝑏 + ∆𝐻𝐻 𝑝𝑝𝑐𝑐 𝑡𝑡𝑡𝑡 + ∆𝐻𝐻 𝑐𝑐𝑡𝑡𝑛𝑛 (21 ) Here ∆ H pr ot represents the enthalp y associat ed with the protonation of f ree or bound prote in/mac romole cule and ∆ H ion is the enthalpy of ioni zation of the buffer. In fact, eq uati on (21 ) could be even expanded w ith ∆ H w in order t o incl ude t he heat eff ect ass ociat ed wi th t he hydration of protein, mac romolecule, prote in - ma cro molecu le complex and ions. As shown by Ran et al . 13 binding experiments done in two different buffer solutions allowed determination of the contribution of buffer ionization to the overa l l measured e nthalp y . Moreover they showed that ∆ H b can be ev en o f a d iffe rent s ign than ∆ H ITC . Nevertheless, as thorough l y discussed b y Xu et a l . t he measured binding constant K b in a properly conducted ITC experiment is a true equilibrium constant. 53 Thus, if ΔC p can b e assum e d to be a constant, the equation (20 ) is ex act. Therefo re t he non - linear van’t Hoff analysis g ives precise thermodynamic information of a given binding process. 22 3.3.2.1.7 . Entha lpy -E n tropy Cancellation F or a s ystem ch ara cteri ze d b y a non - zero h eat c apaci t y chan ge, ∆ C p that i s much l arger t han the binding entropy, ∆ S b , │ ∆ C p │ ≫ │ ∆ S b │ we get the following r elations : 218 ∆𝐻𝐻 𝑏𝑏 ≈ ∆𝐶𝐶 𝑝𝑝 ( 𝑇𝑇 − 𝑇𝑇 𝐻𝐻 ) (22 ) 𝑇𝑇 ∆𝑆𝑆 𝑏𝑏 ≈ ∆ 𝐶𝐶 𝑝𝑝 ( 𝑇𝑇 − 𝑇𝑇 𝑆𝑆 ) (23 ) ∆𝐺𝐺 𝑏𝑏 ≈ ∆ 𝐶𝐶 𝑝𝑝 ( 𝑇𝑇 𝑆𝑆 − 𝑇𝑇 𝐻𝐻 ) (24 ) These r elat io ns cle arl y s how t hat t he free energ y of bindi ng, ∆ G b is app rox i mat el y a co nst an t in a ran ge of t empe ratu res where bo th the binding enthalp y , ∆ H b and the binding entropy, ∆ S b are var y in g lin early with T and ch an ge th eir sign . This is the orig in of the entha lp y - entrop y canc ellat ion (EEC) meaning that enth alpic and entropic contributions to the bindin g compensate one another. 5 4,56 ,219, 220 Most importa ntl y , the EE C can be re lated to counterion condensation. As indicated b y Dragan et al . 28 the binding free ener gy ca n b e split int o: ∆𝐺𝐺 𝑏𝑏 = ∆ 𝐺𝐺 𝑐𝑐𝑒𝑒𝑠𝑠 + ∆𝐺𝐺 𝑐𝑐𝑐𝑐 (25 ) where ∆ G res i s the residual of the Gibbs free energ y of bindin g deriving from K b (1 M ) ( se e secti on 3.3.2.1.3. ) and ∆ G ci denotes the part related to counterion r elease. Since counterion releas e is an ent irel y ent r opic ef fect it can be assu med that : ∆𝐺𝐺 𝑐𝑐𝑐𝑐 ≈ −𝑇𝑇 ∆𝑆𝑆 𝑐𝑐𝑐𝑐 = −∆𝑛𝑛 𝑐𝑐𝑐𝑐 ∙ 𝑅𝑅𝑇𝑇 ∙ ln ( 𝑐𝑐 𝑐𝑐𝑐𝑐 𝑐𝑐 𝑠𝑠 ) (26 ) Here ∆ S ci repre sents the change of entropy of the counterions, c ci is the concentration of the condensed c ounterions 1,31, 221 and c s is the concentrations of counte rions in the bulk. 53 T h us equation (26 ) d emon strat es the gain of ent rop y relat ed to the rel ease of ∆𝑛𝑛 𝑐𝑐𝑐𝑐 co unterions from a phase w ith conc entrat i on c ci to the bulk phase wit h concentr ation c s . If the total binding entropy ∆ S b (T ) is known for different temperatures, its residual p art ∆ S res (T ) can b e obtai n ed through: 222 ∆𝑆𝑆 𝑐𝑐𝑒𝑒𝑠𝑠 ( 𝑇𝑇 ) = ∆𝑆𝑆 𝑏𝑏 ( 𝑇𝑇 ) − ∆𝑆𝑆 𝑐𝑐𝑐𝑐 ( 𝑇𝑇 ) (27 ) Over th e years a vas t num ber of w ell - con trol led and precis e ex perim ents gav e clea r evi denc e that EEC is a general fea ture upon protein interact ion with pol y electrol y te s. Li et al . with an extensive set of ITC measurements of a various ligand - recept or s y s te ms show that EEC i s a real physical phenomenon. 1 10 Fox et al . studied the possible molecular basis of EEC upon protein- ligand complex for mation by carefull y chosen model sy stems. 9 They show ed that between similar binding processes, not intermolecular contacts but ra ther molecular motion and the wat er n etwo rk r earra ngem ent ar e sou rces o f h i gh diff eren ces i n enthalp y and entrop y thus leading to their compensation. Followin g this unexpected result Xu at al . 53 re - anal y z ed a lar ge number of studies regarding pol y electrol y te interaction with various protei ns including early work of Recor d and Lohman 2, 164,1 99,20 1,223 – 226 on DN A up to most recent re ports of Ran et al . 12 ,13 on charge dendrimers. The y d emonstrated that the observed stron g E EC for formation of multiple PE -P complexes c an be attributed to wa ter release / uptake. As they shown the binding 23 or rele ase o f w ater mol ec ule at 293 K gives ch ang e in ∆ G b close t o z ero an d i s accom pan ied b y entropic contribution of appr oximatel y 6.5 kJ /mol. Thus the ∆ S b t erm m ust be co mpen sated b y concomitant ∆ H b . 3.3.2.2. Isothermal Titration Calorimetry I sothermal T itration Ca lorimetry ( I TC) is a n experime ntal techniq ue wide l y used in thermo dy namic studie s of mol ec ul ar interaction in solution. 227 A s it offer s fast and pr ecis e measu rement s of th e he at effect as soci at ed wit h bio mol ecular binding, ITC is an important technique in colloid and mater ial scienc e , drug design and bioc hemistr y. 228 – 230 Due to its sensitivit y ITC was used to analy z e the interaction of proteins with variety of species among which s y nth eti c and n atu ral p ol yelectro l ytes can be distinguish. 11 – 13,25 ,52, 80,17 5,231 The ITC instru ment is equipped w ith a high precis ion stirr ing sy rin ge (filled with o ne react ant in e.g. protein solution) a nd consist of two ide ntical cells composed of a highly efficient thermal conductive material which in additi on is inert to a l arge variet y of sol vents. Both cells a re enclo sed wi thi n an adi ab atic j acket. The des cribed s etup is schem atical l y presen ted i n Fi gu r e 14 . One of prev iou sl y m enti oned cells cont ains wat er and acts as a r efer ence c ell , whi le t he oth er contai ns t he seco nd react ant (i n e.g. polye l ectrol y t e solution) . During the measurement, before e ach titration the microc alorimeter equilibrate these two c ells at e x actly the sa me tempe rature. Howeve r while injecting reacta nt on e to the sample cell filled w ith reac tant two (when b indi ng o ccurs) t h e temp eratur e di ffer ence bet ween t he samp le - and th e refe rence cel l wil l appear. Thi s tem p eratur e chan ge i s ob se rved as t im e - dependent input that gives increm ental he at chan ge dQ/dt (Q’) in µ cal/ sec. Th e h eat sen sin g devi ces det ect that temp eratur e differen ce an d give diffe renti al power (DP ) fe edb ack to the heat ers , which compensate this differen ce and equil ibrat e the cell s t o the s ame t em peratu re. Figure 14 . Schemat ic representation o f an isothermal titration calorim eter (IT C). 24 During the course of experiment t he rea ctan t one p laced i nsi de of t he s yringe is succ essi vel y titrate d b y several injec tions into the sample cell. Th e time - dependent evolution of heat Q upon tit rati on com pared t o a refer enc e c ell i s a co re o f the ex p erimen t. Figu re 15 pre s ents t y pical I TC results of binding betwe en protein ( in this case l ys o z ym e ( L ys ) ) and polyelectrol yte ( in this case h ep ari n (Hep ) ). Integrated , with respe ct to the time, hea ts of each injection are divided b y the numbe r of moles of injectant a llows to calcula te th e increm ental heat , ∆ Q as a function of molar r atio bet ween protein and polyelectrolyte . In order to e valuate the binding data th e heat of dilution of the protein has to be subt ra cted. T h erefo re a s epar at e exp erim ent is requi red. A fter such correction the bindi ng sig n al can be fitted with an appr opriate model revealing the binding constant K b , the number of binding si tes N and th e cal orim etri c ent halp y ∆ H ITC . 02468 10 12 14 - 10 -5 0 5 0 100 200 300 400 - 1, 5 - 1, 0 - 0, 5 0, 0 0, 5 T i me ( mi n ) µcal / sec I = 25 m M T = 37 o C Lys + Hepari n Lys Di l ut i on n Lys /n Hepari n kcal / m ol e of Lys Figure 15 . I T C data for t he bi nding of Lys to Hep at pH 7.4 and tem peratur e of 37°C in phos phat e bu ffe r solu tion of 10 m M ioni c strength . NaCl was adde d in ord er to adjust the total ioni c str ength of the solu tion to 25 mM. T he upp er p anel sho ws t he ra w data o f the bi ndi ng ( bl ac k sp i kes ) and the d il uti on o f L ys b y buff er (red spikes). The integrated heat s of each injection are sh o wn i n the lower panel. The quality o f an I TC m easurement depends on severa l different conditions. All of them ca n influenced the sha pe and therefor e the quality of the I TC isot herm. The c oncentration of the macrom olecu le [ M] t and protein [ P] t are one of the most important issues to obtain a proper ITC measu rem ent. Ex act val ues o f the se con centrations depends on the binding mechanism and on the binding constant K b . Figure 16 presents a set of s imulated IT C i s oth erms i n th e cas e when PE binds to protein with 1:1 stoic hiometry . 232 25 Figure 16 . S i mulate d IT C t itr ati on c ur ves fo r va r yin g va l ue s o f c - para meter and with N set to 1. P lot is rep rinted for m ref. 232 T he valu e of W isem an c - par ameter wh ich r epr e sent the shape of the binding isotherm is determined by binding c onstant K b due to the following equ ation: 233, 234 𝑐𝑐 = 𝑁𝑁 ∙ 𝐾𝐾 𝑏𝑏 ∙ [ 𝑀𝑀 ] 𝑡𝑡 ( 2 8 ) Wh ere N refe rs to t he number of binding sites of macrom olecul e . This simulatio n lea ds to t he following conclusions: L arge valu es of c - par amet er lead s to an accur ate v alue o f the b ind in g enth alp y ∆ H ITC , but the accurate fitting of the bindi ng c onstant K b can be achiev ed on l y when c < 500. In the regime o f v e r y h igh c- v alues (c > 500) the shape of ITC isothe rm is nea rl y invar iant with K b . On the other hand, at small c val ues ( c < 10) the infl ection point becomes poorly defined a nd the binding stoichiometr y w ill be determined with a certain error. 3.3.2.3. Evaluation of ITC D ata 3.3.2.3.1. Single Set o f Identic al Binding Site s (SSIS) Mo del The single set of independent binding site (SSI S) model is based on the L angmuir equation. 235 I t assumes equili brium between the unoccupied bi nding sites within the macromolecule, the number of protein molecules in solution and the macr omolecule occupied binding sites. In principal it relates the f raction of adsorption sites in macromolecule containing bound protein mol ecules θ to the binding constant K b : 𝜃𝜃 = 𝐾𝐾 𝑏𝑏 [ 𝑃𝑃 ] 1+𝐾𝐾 𝑏𝑏 [ 𝑃𝑃 ] (29 ) where [P ] is the co ncentr atio n of free prot ein molecule s in solution. Since the total concentration of [P ] t in the solution is known, [P ] is c onnected to the [P ] t as follows: [ 𝑃𝑃 ] 𝑡𝑡 = [ 𝑃𝑃 ] + 𝑁𝑁𝜃𝜃 [ 𝑀𝑀 ] (30 ) 26 For macromolecule containing N adsorption sites, θ is N b /N wh ere N b represents the number of protein molec ul es bound per macromolecule and [ M] i s th e tot al macro molecul e con cent rat ion in solution. Subtracting equation (29) into equation (30) gi v es [ 𝑃𝑃 ] 𝑡𝑡 = [ 𝑃𝑃 ] + 𝑁𝑁∙ 𝐾𝐾 𝑏𝑏 [ 𝑃𝑃 ] ∙ [ 𝑀𝑀 ] 1+𝐾𝐾 𝑏𝑏 [ 𝑃𝑃 ] (31 ) Solving of equation (29) for [P ] leads to a quadratic equation 𝜃𝜃 2 − 𝜃𝜃 � 1 + [ 𝑃𝑃 ] 𝑝𝑝 𝑁𝑁 [ 𝑀𝑀 ] + 1 𝑁𝑁 𝐾𝐾 𝑏𝑏 [ 𝑀𝑀 ] � = 0 (32 ) The heat Q after each inj ectio n i is equal to 𝑄𝑄 = [ 𝑀𝑀 ] 𝑉𝑉 0 𝑁𝑁𝜃𝜃 ∆𝐻𝐻 𝐼𝐼𝑇𝑇𝐼𝐼 (33 ) Solving the equation (32 ) for θ and then sub stituting this into eq uation ( 33 ) giv es 𝑄𝑄 = 𝑁𝑁 [ 𝑀𝑀 ] ∆𝐻𝐻 𝐼𝐼𝑇𝑇𝐼𝐼 𝑉𝑉 0 2 � 1 + [ 𝑃𝑃 ] 𝑝𝑝 𝑁𝑁 [ 𝑀𝑀 ] + 1 𝑁𝑁𝐾𝐾 𝑏𝑏 [ 𝑀𝑀 ] − � � 1 + [ 𝑃𝑃 ] 𝑝𝑝 𝑁𝑁 [ 𝑀𝑀 ] + 1 𝑁𝑁𝐾𝐾 𝑏𝑏 [ 𝑀𝑀 ] � 2 − 4 [ 𝑃𝑃 ] 𝑝𝑝 𝑁𝑁 [ 𝑀𝑀 ] � (34 ) The analysis includes the effect of the increase o f the volume du ring titration. The experimental data are fitted by ca lculating the heat change of th e solution ∆ Q i releas ed wit h each inj ecti on i and correcte d for displaced volume ∆ V i ∆𝑄𝑄 𝑐𝑐 = 𝑄𝑄 𝑐𝑐 + 𝑑𝑑 𝑉𝑉 𝑐𝑐 𝑉𝑉 0 � 𝑄𝑄 𝑐𝑐 +𝑄𝑄 𝑐𝑐−1 2 � − 𝑄𝑄 𝑐𝑐 −1 (35 ) The pr ocess of f itting experime ntal data invo lves in itial gue sses for N , K b and ∆ H ITC ; calculatio n of ∆ Q i for each injection and comparison of these values with the measured heat for the corr esponding exper ime ntal inje ctions; impr ovement in the initial value s on the basis of the Marquardt methods. The iteration of the above procedure pro ceeds until the satisfac tor y fit is achiev ed. 236 3.3.2.3.2. Two Set s of Inde pendent Binding Site s (TSIS) Mod el This model represe nts th e binding process in which the ma cromolecule has two non - identica l binding sites. Each set o f binding sites is charact erized b y a binding con stants K b1 and K b2 describing the binding af finit y of a ligand to the corresponding site. There are six free parameters involved in this model: The binding constants K b1 and K b2 , the molar heat of binding ∆ H 1 ITC and ∆ H 2 ITC , and respective numbe r of binding sites N 1 and N 2 . Each t y p e o f sit e is therefo re ch ara cteri zed b y i ts ow n fr actio nal s atur ati on θ 1 and θ 2 . Hence, 𝐾𝐾 𝑏𝑏 1 = 𝜃𝜃 1 ( 1−𝜃𝜃 1 ) [ 𝑃𝑃 ] 𝐾𝐾 𝑏𝑏 2 = 𝜃𝜃 2 ( 1−𝜃𝜃 2 ) [ 𝑃𝑃 ] (36 ) Knowing the total concentrations of protein [P ] t and t he macro mol ecu le [M ] t in the s olution, the unknown free protein concentration [P ] can be related b y the following eq uation: 27 [ 𝑃𝑃 ] 𝑡𝑡 = [ 𝑃𝑃 ] + [ 𝑀𝑀 ] 𝑡𝑡 ( 𝑁𝑁 1 𝜃𝜃 1 + 𝑁𝑁 2 𝜃𝜃 2 ) (37 ) Solving equation (36) for θ 1 and θ 2 and substituting into equation (37) gives: [ 𝑃𝑃 ] 𝑡𝑡 = [ 𝑃𝑃 ] + 𝑁𝑁 1 [ 𝑀𝑀 ] 𝑝𝑝 [ 𝑃𝑃 ] 𝐾𝐾 𝑏𝑏1 1+ [ 𝑃𝑃 ] 𝐾𝐾 𝑏𝑏1 + 𝑁𝑁 2 [ 𝑀𝑀 ] 𝑝𝑝 [ 𝑃𝑃 ] 𝐾𝐾 𝑏𝑏2 1+ [ 𝑃𝑃 ] 𝐾𝐾 𝑏𝑏2 (38 ) Solving the equation (38) for [P ] results in a cubic e quation of the form: [ 𝑃𝑃 ] 3 + 𝑝𝑝 [ 𝑃𝑃 ] 2 + 𝑞𝑞 [ 𝑃𝑃 ] + 𝑟𝑟 = 0 (39 ) where: 𝑝𝑝 = 1 𝐾𝐾 𝑏𝑏 1 + 1 𝐾𝐾 𝑏𝑏 2 + ( 𝑁𝑁 1 + 𝑁𝑁 2 )[ 𝑀𝑀 ] 𝑡𝑡 − [ 𝑃𝑃 ] 𝑡𝑡 𝑞𝑞 = � 𝑁𝑁 1 𝐾𝐾 𝑏𝑏2 + 𝑁𝑁 2 𝐾𝐾 𝑏𝑏1 � [ 𝑀𝑀 ] 𝑡𝑡 − � 1 𝐾𝐾 𝑏𝑏1 + 1 𝐾𝐾 𝑏𝑏2 � [ 𝑃𝑃 ] 𝑡𝑡 + 1 𝐾𝐾 𝑏𝑏1 𝐾𝐾 𝑏𝑏2 (40 ) 𝑟𝑟 = − [ 𝑃𝑃 ] 𝑡𝑡 𝐾𝐾 𝑏𝑏 1 𝐾𝐾 𝑏𝑏2 Equations ( 39) and (40 ) are so lved num ericall y for [P ] in the c alorimetric software u s i n g Newton ’ s m ethod once t he f itt ing par amet ers N 1 , N 2 , K b1 , K b2 and the bulk c oncentr ations are assi gned. T he valu es for θ 1 and θ 2 are then given b y substi tution of [P ] into equation (36) . After ea ch inj ecti on, t h e h eat Q of th e solution withi n the volume V 0 of th e calorime tric cell is equal to : 2 36 𝑄𝑄 = [ 𝑀𝑀 ] 𝑡𝑡 𝑉𝑉 0 ( 𝑁𝑁 1 𝜃𝜃 1 ∆ 𝐻𝐻 1 𝐼𝐼 𝑇𝑇𝐼𝐼 + 𝑁𝑁 2 𝜃𝜃 2 ∆ 𝐻𝐻 2 𝐼𝐼 𝑇𝑇𝐼𝐼 ) (41 ) The ex peri ment al d ata ar e fit ted b y c alcul ati ng t he heat ch an ge of t he s olu tio n ∆ Q i rel eased wit h each in je ctio n i and corrected for the displaced volume ∆ V i as described in previous section. 3.3.2.3.3. Two Component Ligand Binding (TC LB) Model The adsorption of prote in t o polyele ctrol y te can be generalized to the binding of an y li gand to a given macromolecule. TC LB mode l dis cussed here is an ex tension of one component l igand binding model introduced previously b y Dzubiell a et al . 3 1 ,237, 238 Upon adsorption of N b li gand mol ecu les t o a m acromo lecul e, the t otal h eat ex chan ged p er macrom olecu le H (N b ) is rela ted to the he at Q measu red in the ITC ex peri ment as: 𝑄𝑄 ( 𝑥𝑥 ) = 𝑐𝑐 𝑑𝑑 𝑉𝑉 ∫ 𝑑𝑑𝑥𝑥′ 𝜕𝜕𝐻𝐻 ( 𝑁𝑁 𝑏𝑏 � 𝑒𝑒 ′ � ) 𝜕𝜕𝑒𝑒 ′ 𝑒𝑒 0 (42) where c 0 is the total ligand concentration, c d is the total concentration of the macromolecule, 𝑥𝑥 = 𝑐𝑐 0 / 𝑐𝑐 𝑑𝑑 is the molar ra tio, V is the titration volume and N b (x) rep resents the bindin g isotherm. The di ffer enti al heat 𝑄𝑄 ′ ( 𝑥𝑥 ) = 𝑑𝑑𝑄𝑄 / 𝑑𝑑𝑥𝑥 m easured in t he ITC ex peri men t is given as : 1 𝑐𝑐 𝑑𝑑 𝑉𝑉 𝑄𝑄 ′ ( 𝑥𝑥 ) = 𝜕𝜕𝐻𝐻 ( 𝑁𝑁 𝑏𝑏 ( 𝑒𝑒 ) ) 𝜕𝜕 𝑁𝑁 𝑏𝑏 𝜕𝜕 𝑁𝑁 𝑏𝑏 ( 𝑒𝑒 ) 𝜕𝜕𝑒𝑒 ( 4 3 ) Due to the complex intera ctions governing t he binding of a ligand to a mac romolecule, a linear proportion betwee n H (N b ) and N b is assume d: 28 𝐻𝐻 ( 𝑁𝑁 𝑏𝑏 ) = ∆𝐻𝐻 𝑁𝑁 𝑏𝑏 ( 4 4 ) where ΔH repr esent s th e h eat ex chan ged p er bou n d li gand. Thus, equation (43) c an be rewrite to connect the differe ntial heat exchange measured in the IT C experiment to the bi nding model N b (x) : 1 𝑐𝑐 𝑑𝑑 𝑉𝑉 𝑄𝑄 ′ ( 𝑥𝑥 ) = 𝛥𝛥𝐻𝐻 𝜕𝜕𝑁𝑁 𝑏𝑏 ( 𝑒𝑒 ) 𝜕𝜕𝑒𝑒 ( 4 5 ) For the case o f t wo l igan ds A and B , respectivel y, when ligand A is titra te d to the solution of ligand B a nd the macromolecule, equation (45) changes as: 1 𝑐𝑐 𝑑𝑑 𝑉𝑉 𝑄𝑄 ′ ( 𝑥𝑥 ) = ∆𝐻𝐻 𝐴𝐴 𝜕𝜕 𝑁𝑁 𝐴𝐴 𝑏𝑏 ( 𝑒𝑒 ) 𝜕𝜕𝑒𝑒 + ∆𝐻𝐻 𝐵𝐵 𝜕𝜕 𝑁𝑁 𝐵𝐵 𝑏𝑏 ( 𝑒𝑒 ) 𝜕𝜕𝑒𝑒 = ( ∆𝐻𝐻 𝐴𝐴 + 𝜆𝜆∆ 𝐻𝐻 𝐵𝐵 ) 𝜕𝜕 𝑁𝑁 𝐴𝐴 𝑏𝑏 𝜕𝜕𝑒𝑒 (46) where 𝑥𝑥 = 𝑐𝑐 𝐴𝐴 / 𝑐𝑐 𝑑𝑑 is the mola r ration of lig and A to that of the mac romolecule and λ = 𝜕𝜕 𝑁𝑁 𝐵𝐵 𝑏𝑏 ( 𝑒𝑒 ) 𝜕𝜕 𝑁𝑁 𝐴𝐴 𝑏𝑏 ( 𝑒𝑒 ) is an ex chan ge rat io - assu med to be constant thorough the titration. Equation (46) ca n be further rewrite as: 1 𝜂𝜂 ∆𝑄𝑄 ∆𝑒𝑒 = ∆𝑁𝑁 𝐴𝐴 𝑏𝑏 ( 𝑒𝑒 ) ∆𝑒𝑒 ( 4 7 ) where 𝜂𝜂 = 𝑐𝑐 𝑑𝑑 𝑉𝑉 ( ∆ 𝐻𝐻 𝐴𝐴 + 𝜆𝜆 ∆𝐻𝐻 𝐵𝐵 ) is a constant. Hence, the he at ex chan ge as soci ated wi th t he i th injec tion ( i = 1, 2, 3, .. n ) ΔQ i is proportional to the number of bound mol ecules of ligand A ΔN b A (x i ) . The amount of the lig and A molecules adsorbed to the mac romolecule during the i and the following injections ca n be obtained tho rough: ∆𝑁𝑁 𝐴𝐴 𝑏𝑏 ( 𝑥𝑥 𝑐𝑐+1 ) = ∆𝑄𝑄 𝑐𝑐+1 ∆𝑄𝑄 𝑐𝑐 ∆ 𝑁𝑁 𝐴𝐴 𝑏𝑏 ( 𝑥𝑥 𝑐𝑐 ) ( 4 8 ) The further key a ssumption made here are that the amount of the ligand A in the fir st injection ( i = 1 ) i s ent irel y b oun d t o th e macrom olecu le and t hat t he di rectl y m eas ured cal ori met ric enth alp y ΔH I TC equals to that of the binding enthalp y ΔH b . 3. 3.3 . Analysi s o f Pol yelec tr olyte Brush upon I nt erac tion with Prote ins by Quartz Crys tal Microbala nc e (QCM) . 3.3.3.1. Quartz Crystal Microbalance with Dissipation Moni toring (QC M- D) Quartz C rystal M icrob al ance is an anal y tical tech ni que t hat has becom e widel y u sed t o stu d y so ft and solv ated i nterf aces . 2 39 – 244 I t works in liquids and provide s in - situ, rea l - time inf ormatio n on changes of the mat eri al o rgani zat ion at in ter face 245 It also provides information about the couple d solvent inside of the interf acial film. 246 – 248 A number of informa tion can be obtained fro m QCM da ta, in term s of the cha racter istics of the mater ial distribution at an inter fac e, its connection with the s urface , and the role of the liquid in whic h the interf a cial f ilm i s immerse d . 2 49 – 25 1 29 Figure 17 . Schemat ic representation o f the QCM instrumentation. QCM is bas ed on t he i nve rse p iez oele ctri c ef fect in which for cr y s tal lin e mat erial s ch ar acteri zed by a partic ular sy mmetry propertie s a mechanical de forma tion is driven by applic ation of voltage . 252 A ty pical QC M sensor is composed of a thin quar tz disc placed be t ween two metal electro de s. By var y in g of applied voltage acro ss the electrodes a c y clical def ormation is induced, which results in an oscillator y motion of ex cited crystal. A standing wave aris e inside the c r y stal if the fre qu ency of the applie d voltage matche s or multiples the r eson anc e freq uen c y of th e cr ystal. Th e kind of oscillation arising in the excited cr y stal dep ends on the cut of the crys tal in re gard to its cry sta llo graph ic ax es . 2 53 Sensors most commonl y used in th e QCM technique which are A T - cut qu artz cr y s t als v ibrat e in t he so - called thi ckn ess - shear mode. In this t y pe of vibration the two surfaces move relative to each other in an anti - paral lel m anne r. Wh en cr ystal i s in res on ance, t h e vibrat in g sur fa ces a re loc a ted at the antinodes of a standing wave wi th t he wavel eng th 2d/ n , where d is t he thic kness of the cry stal and n repr esents the overtone number. This leads to th e resonance frequenc y f n = n c/2d , wh e re c is the speed of sound in quartz. Shear - waves de ca y rap idl y in gases and liquids, thus m aking Q CM an int erface - s peci fic an al y ti cal techn iqu e. 244 30 Figure 18 . Schematics of QCM - D operat ion. (A) 5 MHz q uartz crystal (Q - Sense). The yellow color depicts the gold electrode. (B) Side view o f the cr ystal . B y varying of applied voltage across the electrod es a cycli cal deformation is induced, wh ich r esul ts in an osci llator y motion of excited crys tal. The third overtone (blu e wave in the midd le) is i llustrated . (C) Upon QCM - D e xpe ri ment t he dr ivin g vol tage i s t urne d o ff an d on, and t he o sci lla ti on decay is m o nitored. Upon QCM - D experiment an external voltag e is turned off and on, so the oscillations are left to d eca y freel y . 254 Due t o th e piez oelect ri c pr opert ies of qu art z, t hes e fr eel y deca y i n g mechan ic al os cill atio ns g enerat e a vol ta ge. T his s ignal i s r ecord ed an d yiel ds tw o param et ers per overtone, the resonance frequ ency f n and the dissipation D n . The common usage of quartz crys tals as oscilla tors results from their low energy dissipation and e x ceptional sta bility . The descri bed b asi cs of t he Q CM measu rement requi re an el ectrod e co at ing o f the cr y stal . The most important property of QCM te chnique in the context of the present work is its sensitivit y in regard to the org anizatio n of the materia l at a given in te rface. As ex amp le distinction between a la yer of adsorbed liposomes b y opt ical mass - sensitive techniques su ch as surf ac e plas mon reson an ce ( SPR ) or e llipsometr y rende rs a dif ficult ta sk. 244 Such distinction is fac ile with QCM technique. QCM is able to distinguish between layers of monom eric prote ins and protein aggregates, 251 mo nom eric and cl ust er ed m embr ane - bound p roteins, 249 su rface - graf ted DNA molecu les with diff ere nt organizatio n patte rn 255 etc . 3.3.3.2. Evaluation and Int erpreta tio n of Q CM - D Data The common us e of quart z cr ystals as micro bala nces is d ue the l inear relati ons hip between chan ges i n t he m ass per unit area of th e r eson ator , ∆ m f and the re sonance frequency at the n th harmonic, as defined b y S a u e r b r e y: 256 ∆𝑓𝑓 𝑛𝑛 = − 𝑛𝑛 𝐼𝐼 ∆𝑚𝑚 𝑟𝑟 (49 ) 31 The proportionalit y constant, C depends onl y on the fundamental resonanc e frequenc y and the mater ial properties o f th e qua rtz c r y stal ( - 17,7 n g∙Hz -1 cm -2 for 5 M Hz cr yst al) . 245 Kanaz awa and Gordon 257 proposed how to include the role pla yed by the liquid in which cr y st al is imm ersed. Thus, in l iquids the re sonance f requenc y of a cr y st al can be related with the viscosity η l and density ρ l of a given liquid medium: ∆𝑓𝑓 𝑛𝑛 = − 𝑟𝑟 𝑛𝑛 2 ∆𝐷𝐷 𝑛𝑛 = − 1 𝐼𝐼 � 𝑛𝑛 𝜌𝜌 𝑠𝑠 𝜂𝜂 𝑠𝑠 2𝜔𝜔 𝐹𝐹 (50 ) Here 𝜔𝜔 𝐹𝐹 = 2 𝜋𝜋 𝑓𝑓 𝐹𝐹 repr esent s th e an gular fun d ament al r eson ance fr equen c y. Equation (50 ) presen ts a pr oport ion al r elat ion b etween t he decr ease i n th e frequen c y and the i ncrease i n th e diss ipation to the square root of l iquid viscosit y and densit y . Due to the sens itivit y of the QC M technique to the properties of the bulk liquid, it is imperative to perfor m a reference measu rement in t he sam e medi um . I n that way it is possible to separate contribution of the bulk liquid fr om the f ilm prope rties. In order to interpret the QCM d ata for a th in fi l m i n a quan tit ativ e w a y a seve ral app ro aches have bee n developed over the years. 258 A common approa ch assumes a c onti nuum model with sample properties parametrized by one or more elements of a certain intrinsic properties such as th icknes s, d ensi t y and vi scoel asti cit y as e.g. V o igt - Voinov a model (see Fi g u re 19 ). 259 I n thi s mod el th e film is charact eri zed by four pa ramet er s: thi cknes s, t f , density , ρ f , shear viscosit y , η f and shear modulus, µ f . The bulk liquid a bove the film is a semi- infinite lay e r ( η l , ρ l ). H owever, a proper det ermi nati on o r even es tim ati on of p aram eters charact erizi ng the Vogit elem ent can rend er a diffic ult experimenta l task. Moreover this approach is not appli cable for films composed of discre te parti cles adsorbe d on t he surface of the cr ysta l, where the thickness of the film is of th e co mpara ble size as the diameter of adsorbed p artic les. 244 Figure 19 . Schem at ic representation of the la yered st ructure of V oigt - Voinov a model. The QC M sensor is covered by a f ilm modeled as a sing le Voigt elem ent (grey lay er) . Layer above the f il m is a semi - infinite Ne wtonian liq uid. Thus, if a late rall y homo ge nous film ca n be a pprox imated a s rigid th e Sauerb re y equati on can be used. 258 F or a rig id film the cha ng e s of the normalized frequency ∆ f n /n ex hibit no significa nt dependence on the harmoni c number or more quan titativel y the ratio of ∆ D n /( − ∆𝑟𝑟 𝑛𝑛 𝑛𝑛 ) ≪ 4 x 10 - 32 7 Hz -1 fo r a 5 MHz cr ystal . 2 44 I f these conditions are fulfill ed the Sauer brey e quation can be use d for deter mination of the ar eal mass densi t y, ∆ m f of the film. I t must be kept in m ind that if the film is solvated, the obt ained ∆ m f will include the mass of the adsorbate a nd of the solvent which requi res a wel l - considered experimental approac h i n order to obtain th e reliable data, e.g. referen ce m easu remen ts. 33 4. Results and Dis cussion 4.1. Ad sorp tion of Mon o - and D ivale nt Ion s to dP GS Condensed counterions are the ke y feature that determines the properties o f PEs in solut ion as pointed out in section 3. 3.2.1.1. Thus, understand ing the counterion condensation is crucial in order t o an al yse the co m pli cate in terac tions of PEs in biol ogica lly - re le vant sy stems. As a consequence of c ounterion condensation, the struc t ural charge Z of PE is effect ivel y neut ralis ed. 2 60, 261 E ffecti ve char ge Z eff of the PE is by this significantl y lo wer in comparison to the b are stru ctural ch arge Z . The d ifference b etw een Z and Z eff of PE therefo re acc ounts for the amount of counterions that ar e condensed to it. This phenomena influences the interaction of PE with othe r entities, 262,263 ,272 – 274, 264 – 2 71 among whic h the formation of PE - P co mplexes is the focal point in colloidal science. 16,1 7,19, 57,5 8,27 5,2 76 In recent studies on dPGS - Ly s interaction by Xu et al. 222,277 and Ran et a l . 13 it was established tha t the strong binding of Ly s to dPGS and formation of a pr otein co rona around dPGS is driven by counterion release. 31 Since dP GS i s a PE with pr omising biom edic al app licatio ns 11 5,278 ,279 (see s ectio n 3.1.2.1. ), it is importa nt to study how multivalent cations that are pre sent in the blood serum, such as Mg 2+ and Ca 2 + can influence the inter action of this molec ule with pro teins. This just ifies the s uitability of studies on the competitive ion partitioning between mono and divalent counterions as it will change the Z eff of dPGS influenc ing its interaction with proteins and other relevant components of the blood serum. Figure 20 . Schem atic ill ustratio n of the competitive bindi ng be tween divalen t and monovale nt cations to dP GS in water medium. R ed and blue color indicates th e negative and positive ch ar ge, respectively. The theory discussed here was developed b y Rohi t Nikam in his thesis ( Berlin 2020). He presented a theoretical analysis of the competition betwee n mono - and di valent counterions upon binding to dPGS - like PEs. The author compa red mean f iled continuum and discrete binding models along with corse - graine d computer simulations of dPGS. The presented models are f airly tr ansf erable to experimenta l studies thus h elping in s y stematic ana l ys is of the key electro stat ic f eatu res of d PGS -like PEs. 34 In pres ent chapt er o ne o f thes e model s, n amel y the mean - field Pois son–Boltzm ann (PB) mode l (see se cti on 4.1.2.2. ) as it is w idel y used in co llo idal scien ce and el ectro chem ist r y , 280 – 284 is direc tl y compared w ith calorime tric measureme nt s. I n order to con tribute to clarifica tion of the counterion condensation to PEs and available met hods of stud ying this phenomena, here a 1:1 comparison of theor etical approach with experiment is presented. F irstly , the ion - specif ic effects upon binding to dendr itic PE are ana lyzed b y comparison of the I TC isotherms repres ent ing th e Mg 2+ and Ca 2+ interaction with dPGS. Secondly , the competitive binding of mono- and divalent counterions to dPGS is analyzed addressing the challenges in the fitting of the binding model to the experimental data. 4.1.1. Binding Isotherms ITC ex per imen ts were conducted on a Microc al VP - ITC instrument (Microcal, Northampton, MA). All samples used in the measurements were prepared in a buffer solution of 10 mM MOPS and such NaCl concentration to adjust a certain ionic strength after the final injection of the tit rant (Mg 2+ , Ca 2+ ). The pH of each solution was fixed to 7.2. A total of 280 µL of Mg 2+ , Ca 2+ buff er solution was tit rated with 35 su ccessive injections of 8 μL each into the c ell containing 1.43 mL of dPGS sol ution. The stirring rate of 307 rpm was set wit h a time in terval of 300 s betwee n each injection. The concentrations of divalent ions in the injectant and the concentrations of dPG S are enli sted in t he section 6.6. Th e measu rem ent s w ere p erfo rmed at 30°C . Before each ex peri m ent al l s ampl es were degass ed and th ermos tatt ed for sever al m inut es at 1 d egree b elow the ex perim ental tem per ature. 0 10 20 30 40 50 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 0 50 100 150 200 0. 0 0. 5 1. 0 1. 5 T i me ( mi n ) µcal / sec T=30 o C dPGS + Mg 2+ Mg 2+ di l ut i on n ( Mg 2+ )/n (d P G S ) kcal / m ol e of Mg 2+ Figure 21 . ITC dat a f or th e binding of Mg 2+ io ns to dPGS at pH 7.2 an d tempe rature of 30° C in 10 m M MOPS buf fer . T he upp er p anel s ho ws t he ra w d ata o f t he b ind i ng ( bla ck sp i kes) a nd t he d il utio n of M g 2+ b y buffer (red spikes ). T he in te grated heats of each injection are s hown in the low er p anel. The evalua tion of ITC data is demonstrated in Fig ure 21 which shows the ra w - I TC signal of the binding (blac k cu rves and circles) and dilution of divalent - ion soluti on (red cur v es and 35 squares). For f urther anal y s is the he at of dilution of divalent-ions was subtr acted fro m th e heat of adsorption. 4.1.2. Analysis of the In teraction Between dPG S and Divalent Cations 4.1.2.1. Ion Specificity After evaluation of ITC data described in section 4 .1.1. due to anal y z e the ion specificit y upon adsorption of Mg 2+ and Ca 2+ to d PGS, the inte gr ated isother ms were fitted with SSI S mod el (see se cti on 3.3.2.3.1. ) as p resent ed in s emi - logar it hmic plot in F igu re 22 . The thermod yna m ic parameters for the binding are listed in Tab le 2 . All signals of the binding of divalent -ions to dPGS were endothermic in the entire ran ge indica ting that the driving force of this process is of the entropic origin. 196 Obt ained t herm od ynami c par amet ers (see T abl e 2 ) show , that in t he limit of error, there is no di fference in binding of Mg 2+ a nd Ca 2+ to dPGS. Thus, Z ef f of dPGS should depend only on th e valency of the condensed counterions and influe nce of their size (in regard to M g 2+ and Ca 2+ ) can be n eglect ed . Based o n that , th e fu rther an al ysis wil l be fo cus ed only on the one species of divalent-ions, namel y the Mg 2+ ions. 0 10 20 30 40 10 100 1000 Q in cal/mol of injectant n(ion)/n(d PGS) dPGS + Ca 2+ dPGS + Mg 2+ Figure 22 . Bi ndi ng iso ther ms fo r Ca 2+ and Mg 2+ i nterac ting with d PGS. So lid lines repre sent the SSIS fit. Ther m od ynamic d ata result ing fro m the fitting ar e listed i n Table 2 . Tab le 2. Ther mod yna mic p ar amet er s fo r t he b ind i ng o f Ca 2+ and Mg 2+ to dP GS as re sulting fro m th e SSI S fit. Ion I (mM) N b ∆ H ITC (kJ∙mo l -1 ) K b x 10 -3 (mol -1 ) ∆ G b (kJ∙mol -1 ) Ca 2+ 16,5 7,9 ± 0,2 6,8 ± 0,2 6,3 ± 0,5 - 22,0 ± 0,2 Mg 2+ 16,5 7,5 ± 0,2 8,1 ± 0,4 5,1 ± 0,4 - 21,5 ± 0,2 total concentrat ion of M g 2+ ions [ Mg 2+ ] tot and C a 2+ ions [Ca 2+ ] tot is 0, 8 mM. 36 4.1.2.2. Ion- Sp ecif ic Penetra bl e Pois son - Boltz man n (PPB) Mod el A non- linear cano nical P ois son -Boltzmann penetrable sphere model is implemented to make a quantitative comparison between the number of M g 2+ ions bound to dPGS. In presented approac h, based on re cent studies, 22 1,285 and developed b y R. Nikam dPGS is modelled as a spher e of b are r adius r d in aqueous bath of radius R and volume V . Figure 23 . Schemat ic representation of dP GS in the PPB model. The blue area represen ts the comput ational cell domain an d is assumed to be spherical with and w it h a un i form dielectric con stant of w a ter ε w = 78. The vol um e V is th e same as th e titration volume in ITC experim ent. Orange s phere at the center of th e computational do m ain represents the dPGS molecule with a charge valency Z . r eff i s the distance that separates the electric double layer r e g i me ( r > r eff ) fro m t he no n- linear counterion condensation regime ( r < r e ff ). P lot is repr inted wit h pe r missi o n fr o m R . N i k a m . The divalent and monovale nt cations as well as the monovale nt anions that are present in the dPGS solution are referred to with subscripts ++, + and - , re spectivel y. The tot al number of ions i ( i = ++, +, - ) in volume V is de noted as n i , while the c orrespondin g total and the bulk concentrations are denoted as c i tot = n i /V and c i 0 , respect ivel y. c i 0 is cal culat ed us in g the conserva tion o f mass prin ciple as sh own in the supplementa r y material. In order to mainta in the total e lectr oneutra lity in the domain th e tota l charge of anion s is exactly balance d b y the total charge of the cations. All ions and the dPGS molecule are assumed to be i n an aqueous ba th ha ving a uniform dielectric constant ε w = 78 at a tem perat ure T = 2 98 K. The Bj errum len gth (see se cti on 3.3.2.1.1. ) l B is 0.7 nm. The c harge profiles are resolved in the radial distance from the m acromo le cular cent er, r . Due to the structural properties of dPGS a penetrable model is chosen instead of a s tandard PB model t y pi call y us ed in studies of colloidal charge reno rmalizatio n. 286 – 288 dPGS is assum ed t o be a per fect p en etrabl e sph ere wi t h a char ge v alen c y Z = z s N s = - 34e and radius r eff . Thus, the c harged monomers of dPGS have a unifor m number distribution c s = N s /v eff within the volume v eff . c s is applicable only within the dPGS dom ain, i.e., c s (r ) = c s (1 - H (r - r eff )) , whe r e H (r ) is the heaviside - step func tion. As an improvement to the standard PB model, here a contribution of the intrinsic ion - specific inter action Δμ int, i between the ion and th e dPGS is considered. 28 9, 290 Δμ int, i represents the additional non - electro stat ic e ffe cts t hat can driv e ads orpt ion , e.g., dispersion, h y dration and hydrophobic forces and can b e int erpr eted as the i on - specific b inding chemical potential of the condensed ion. The inclusion of Δμ in t,i has been considered in previous works, for example, as a term ref lecting the steric io n - ion packing effects in a Donnan model for ion binding b y pol yelect rol y t es or char ged h ydro gels . 291 – 293 As sumin g the el ectro stat ic po t enti al far awa y from 37 dP GS, Φ (r → R ) = 0 , the chemical potential is bala nced for each ion, b etween the bulk r egime far fr om dP GS and th e regim e at the f ini te di stan ce r from the cente r of d PGS : 𝑙𝑙𝑛𝑛 𝑐𝑐 𝑐𝑐 0 = 𝑧𝑧 𝑐𝑐 𝛷𝛷 ( 𝑟𝑟 ) + 𝑙𝑙𝑛𝑛 𝑐𝑐 𝑐𝑐 ( 𝑟𝑟 ) + 𝛽𝛽𝛥𝛥 𝜇𝜇 𝑐𝑐𝑛𝑛𝑡𝑡 , 𝑖𝑖 ( 𝑟𝑟 ) (51 ) where β -1 = k B T is the t hermal ener g y and Δμ int, i is considered on a loc al level, i.e. , Δμ in t,i (r ) = Δμ in t,i (1 - H(r - r eff )) . The Boltzmann ansatz then becomes: 𝑐𝑐 𝑐𝑐 0 ( 𝑟𝑟 ) = 𝑐𝑐 𝑐𝑐 0 𝑒𝑒 𝑧𝑧 𝑐𝑐 𝛷𝛷 ( 𝑐𝑐 ) − 𝛽𝛽𝛽𝛽 𝜇𝜇 𝑐𝑐𝑛𝑛𝑝𝑝 , 𝑐𝑐 ( 𝑐𝑐 ) (52 ) The di stan ce - resol ved ele ctro stat ic po tent ial can b e cal culat ed from eq uati on (52 ) together with the Poisson equation as: ∇ 2 𝛷𝛷 ( 𝑟𝑟 ) = − 4 𝜋𝜋𝑙𝑙 𝐵𝐵 ( ∑ 𝑧𝑧 𝑐𝑐 𝑐𝑐 𝑐𝑐 ( 𝑟𝑟 ) + 𝑧𝑧 𝑠𝑠 𝑐𝑐 𝑠𝑠 ( 𝑟𝑟 )) ∀ 𝑖𝑖 = ++, +, − 𝑐𝑐 (53 ) which establishes the PPB model including ion - specific binding effects. The boundar y conditions used are (dΦ = d r ) (r → 0 ) = 0 and Φ (r → R ) = 0 . The number of bound ions of speci es i within the dPGS radius r eff , is then given by: 𝑁𝑁 𝑐𝑐 𝑏𝑏 = ∫ 𝑐𝑐 𝑐𝑐 ( 𝑟𝑟 ) 4 𝜋𝜋𝑟𝑟 2 𝑑𝑑𝑟𝑟 ∀ 𝑖𝑖 = +, + + 𝑐𝑐 𝑟𝑟𝑟𝑟𝑟𝑟 0 (54 ) 4.1.2.2. Comparison of ITC Data with PP B Mo del Ex perim ental data ev alu ated acco rdin g to t he tw o component ligand binding (T C LB) model described in section 3.3.2.3.3. are plotted in Figu re 24 and Figure 25 . In both, the number of adsorbed Mg 2+ ions per dPGS molecule is presente d as a func tion of total moles of Mg 2+ normalized per total moles of dPGS, n ++ /n dPGS . As shown in Fi gure 24, PPB model with the ion- spec ific in trinsic b inding chemical poten tial Δμ in t,i set to z ero, predicts that from 8 to 10 Mg 2+ ions are bound per dP GS molecule. Figure 24 . Num ber of bound cou nterions N i b ( i = Mg 2+ , Na + ) as a functio n of to tal a mount o f Mg 2+ ions nor mali zed per to tal moles of dP GS, n ++ /n dPGS . The io n - speci fic intrins ic binding che mical po tential Δμ int, i is set to zer o. 38 Figu re 25. Fitted n um ber of boun d counter ion s N i b ( i = Mg 2+ , Na + ) f ro m PPB m odel to that fro m TCLB model, as a f unct ion of tota l am ount of Mg 2+ i ons normali zed per t otal m oles of dPGS, n ++ /n dPGS . T he io n - specif ic intri nsic binding che mical po tentials for both monovalent a nd divale nt co unterions ar e calcula ted as Δμ int,+ = 1.63 k B T a nd Δμ int,++ = 1.18 k B T. When Δμ int, i for both, monovalent a nd divalent counterions is calc ulated as Δμ int ,+ + = 1.28 k B T and Δμ int,+ = 1.85 k B T as presente d in Fi gure 25, the obtained number o f bound Mg 2+ io ns becomes slig htl y n arrowed (from 8 to 9). On bo th fi gures a clea r and s ystem ati c correl ati on between i ncre asin g con c entrat ion of Mg 2+ ions and the number of bound Mg 2+ ions per dPGS molecule is evident. The ou tcom e of th eoreti cal predi ctio ns can be d irect l y co mp ared wi th e x peri ment al res ults display in g a similar trend and w ith the lim it of error , t he same number of bound divalent -ions. Regard less of Δμ in t, i , I TC results in Figure 24 and 25 show that approximately 9 to 10 Mg 2+ io ns are bound per dPGS molecule. This number stands in a very good ag reement with t heoretica l predictions. How ever, ex per imen tal res ult s do not s how a cl ear cor relati on b et ween th e numb er of bound Mg 2+ and its concentra tion. This is caused b y the limitations of the VP - ITC calorimeter on the one h and, and the assumptions involved in the TC LB mo del (s ee se ctio n 3.3.2.3.3. ) on the other. It must be kept in mind that the interaction discussed here is an example of low b inding a ffinity . Thus, the ac curacy o f calorimetric measu rements in th is case is limited to the number of bound Mg 2+ ions. The disti nction between the solution of higher M g 2+ concentration in a rang e between 0.8 a nd 2.5 m M is, unfortunately , too subtle for the VP - IT C calo rimete r. Most imp ortan tly, th e TCLB mod el assumes th at the c alorimetric enthalpy ΔH ITC is equal to the binding en thalpy ΔH b . A s pointed o ut in section 3.3.2.1.6. calorimetr ic enth alpy contains, in addition to ΔH b , severa l contributions of the associated effects. Howe ver, the obser ved a greem ent bet ween ex per imen tal an d t heoret ical res ult s ju sti fy th e assu mption made here and su g gest that the heat e ffe cts asso ci ated t o t he heat o f ad sorp tio n in t h e an al y zed s ystem are m argin al. Neve rth el ess, as di scuss ed in s ect i on 3.3.2.1.6. and as will be shown in the following sections, ΔH ITC can signifi cant l y differ fr o m ΔH b . Thus, special att ention must always be paid upon assumption that ΔH ITC equal s ΔH b . 39 4.1.2.3. Conclusion This chapt er pr esent a d irect co mpari son bet wee n calo rimet ric m eas urem ent s and co mpu ter simulations on the interaction of dPGS wit h divalent and monovalent ions in aqueous solution. The calo rim etric m eas ur ement s sh ow th at th e ion - specifi c ef fect s ar e mar ginal w ith regar d to Mg 2+ and Ca 2+ ions upon binding to dPGS. The overall number of Mg 2+ ions a dsorbed per dPGS mol ecule o btai ned b y ITC ex peri ment stands i n a ver y god a greement with theoretical predi ctio ns of the P PB model . Si nce P PB mo del gives a relat ivel y accu rate p ict ure of t he dP GS - counterion elec t rostatic binding affinit y , the reported approach is envisioned to become applied in the future anal y sis of counterion condensation and interactions between various different PEs and proteins. 4.2. Pro tein A d sor pt ion to He par in Heparin is a gl y cosamino gl y c an (GAG) consisting of disacc haride units with different sulfation patterns, as discussed in sec t ion 3.1.1.1. I t oft en s erves as a mod el for t he hep aran sul fat e polysaccharide components of proteog l y cans. 37 In general, GA G - bas ed mater ials receiv e increasing a ttention for their therapeutic application in sequestering or de fined delivery of cy tokines and growth fac tors. 294 A quantitative unde rstanding of the interaction of GAGs with prote ins is a c ritica l condition for tailo ring the functionality of the rela ted sy s tems. While the binding of proteins to heparin is often considered non - specific , the term “inte rm ediate speci ficit y” wa s suggested to account for the corre lation of sulfation patterns to protein binding. 295 M oreover , GAG chain conformations have been discussed to result in the disposi tion of charged moieties and a “hidden specificity” . The cu rren t vi ew i s th at whi le cert ain sets of GAG sulfate groups are identified to be particularl y im portant in protein binding, the definition of minimal binding epitopes is often lac king. 295 However, i t is ge nerall y agreed that well - defined pen tasa cch a ride s truct ures 296,297 ( m imicked in sy nthetic oligosaccharides such as in Fondapar inux 9 8,298 – 300 ) ar e necessary for a spec i fic binding of the blood coagulation enzy m e antithrombin and thus for hepar in’s anticoagulant activit y. For the pr esent discussion, it s uffices to ke ep in mind that one heparin re pe ating unit bear s, o n average, thre e sulfate groups and one ca rbox y l group. Hence, heparin is among the most highly charge d biopol ymers. Therefore, a large fraction of counterions should be condensed on the chain which is found indeed. 301, 302 In a numb er of r ecent s tud ies t he effect o f co unt erion rel eas e was stu died in de tail by a combina tion of calor imetric inve stiga tions with molecul ar d ynamics (MD) simulations . 12, 13, 31, 52,53, 303 The ionic str en gth in solution and temperature are the t wo decis ive var iabl es . 13,5 3 The binding c ons tants K b obtained by is other mal titration c alorimetry ( ITC ) 26,55 ,30 4,30 5 w ere compar ed to t he resu lt s of MD - simulations on a quantitative leve l . Good agree ment of theor y and experiment was found. 31 Plots of log K b vs. log c s where found to be strictly linear f or s y nthetic pol yelect rol ytes ( PEs) 3 1,53 as has bee n found in earlier studies on biolog ical s y stems. 2, 23,30 ,306, 307 Thus, these data could be extrapolated to a s alt concentration c s of 1 M wher e ele ctros tati c ef fect s sh ould pla y n o r ole an y mo re. 28,3 0,5 3 In this w a y the measu red binding constant K b and in turn the free energ y of binding ∆ G b can be decomposed into a part due to counterion release and a residual part still o perative at high s alt concentrations. 28,5 3 Here the binding of ly soz yme to heparin in aqueous solution is analy zed with re gard to varying ionic streng th and temp erat ure . The motivation of the p resent stud y ori ginates from rec ent work on 40 hydrogels that are capabl e of sequestering proteins and in p artic ular cytok ines that may prevent wound healing. 308 – 3 10 Since the early work of Olson et al. 311 and of Mascotti and L ohm an 306 it is we ll - establish tha t electro stat ic i ntera cti on and count erio n releas e pla ys a centr al rol e for th e b i nding of proteins to heparin. 17,1 95, 312 – 317 The p reval enc e of elect rost at ic in tera ctio n for t he int eracti on pro t eins with heparin has been corroborated by a considerable number of subsequent i nvestigations. 86 A number of studies suggests that counterion release should be operative since plots of log K b vs. lo g c s were found to be linear, at least at higher ionic strength. 86 , 195,30 6,311 However , this conclusion has bee n criticiz ed by Dubin and coworkers 17,8 6,3 18 an d th ere see ms t o be no general consensus on the main driving forces of protein binding to heparin. To contribute to a clarification of this point, this chapter present s a comp reh ensi ve st ud y o f the binding of l ysozy me ( Lys) to h epar in (Hep ) . The choi ce o f L y s deri v es f ro m t he f act th at thi s protein is stable in solut ion and has been used as model compound in earli er investigations. 13, 31 In particular, it turned out that Ly s can be used to a certain ext end as model for cytokines like the s electi ns (see th e di scus si on in ref. 31 ). Hen c e, t he resul ts o f th e pr e sent s tud ies can b e compared to the binding constant of Ly s to othe r P Es and may serve for a better understanding of the interaction of proteins with GAGs in general. The following stud y i s based on the anal ysis of the binding constant K b measu red b y ITC as a function of salt concentration c s and temper atu re T . Firstly, the binding constant K b is an al y zed sol el y in term s o f coun t eri on rel eas e, as dev ised r ecen tl y. 53 A pos sib le r eleas e or upt ake of water molecules upon binding will be considered as a second entropic factor. 37 – 4 0,319, 320 The comprehensive anal y sis of K b as the function of temperature and salt concentration thus allows to discuss the marked enthalp y - ent rop y canc ell atio n (EEC ; ref. 4–9 ) that is found for the present s ys t e m . 4. 2. 1. Bind ing I sothe rm s ITC ex perim ents were c on duct ed on a M icroc al i TC 20 0 instrument (Microcal, Northampton, MA). All samples used in the measur ements were prepared in a phosphate buffer . For that, 3.8 mM of Na 2 HP O 4 and 1.2 mM of NaH 2 PO 4 were dissolved in Milli - Q wat er. The p H o f the solution was adjusted, at r oom temperature (20 o C), to 7.4 by addition of NaOH. In order to prepare buffers with different ionic stren gths, NaCl was added into the buffer individuall y. A total of 39 µ L of Lys - buffer soluti on wa s titrate d into the sample cell with 39 suc cessive injections. The stirring r ate was set at 750 rpm wit h a time interval of 120 and 180 s between each injec tion. The sample cell contained 200 µL of Hep solution in a matching buffer. I n order to obtain a fu ll matr ix of ionic stren gth - and tem per atur e depen den ce the meas urem ents w ere performe d at ionic stren gth of: 25, 35, 50, 75 and 100 mM and temperature of: 15, 20, 25, 30, 35 and 37°C. Bef ore each experiment all samples we re dega ssed and thermostatted for several min utes at 1 d egree b el ow t he ex perim ental tem per atur e. The good rep roducibilit y of data was ensur ed fo r seve ral f act or s such as th e t ype of t he calor imet er, sti rrin g rat e, t ime i nterv al between eac h injection a nd the concentrations of the re actant s (see secti on 7.3.2. ). 41 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 Q in kJ/mol of Lys n Lys /n Hep a) µ cal/sec Time (min) 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 Q in kJ/mol of Lys n Lys /n Hep b) µ cal/sec Time (min) Figu re 26. I T C dat a of th e ads orption of Lys to Hep (a) and co r re spo nd ing da ta of t he L ys hea t o f dil ut io n (b) . Measurements were performed at pH 7.4, I = 25 mM an d T = 37 o C, [H ep] = 2 x 1 0 -4 m M. T he upper panel sho ws th e raw data of t he a dsorpt ion and th e diluti on of Lys b y buf fer sol ution . The evaluation of ITC data is demonstrated in Figu re 26 a) which sho ws the raw ITC signal of binding (top panel) and Figure 26 b) presenting the dilution of protein (top panel). For fu rther anal y sis the heat of dilution of the protein wa s subtrac t ed from the he at of adsorption. The accur ac y of the data w a s j udged b y the Wis eman p aramet er, 233, 234 as dis cuss ed in secti on 3.3.2.2. For the measurement displaye d in Figure 26 (a t I = 25 m M and T = 37 o C) the Wi seman paramet er c is 166. 0 2 4 6 8 10 12 14 -60 -40 -20 0 Q in kJ/mol of Lys n Lys /n Heparin 15 o C 25 o C 37 o C Figu re 27. Ef fect of tem perature on bin ding. Integrated heats o f adsorp tion of Lys to Hep a t constant io nic strength o f 25 mM are displa yed. Solid lines pr esents the sin gle set of ide ntical sites (SSI S) fit. 42 The single set of independent binding site (SSIS) model was c hosen to fit all data . 2 35 Figu re 27 displays t y pical fits obtained for 3 diff erent temperature. Additional measurements conducted at different Ly s and Hep concentrations were used t o ensure that the measured binding constants are independent of the co ncentrations of the reac tants (see supplement mater ial). All measurements we re conducted at low Hep concentrations to avoid the formation of complex coac ervates . 321 Aqueous solutions of Hep of higher concentration ([Hep] = 0.01 g/L) with Ly s turned turbid after 12 hours. This observation points to the onset of aggregation effected perhaps through crosslinking of complexes by Ly s . The time needed for this process, however, is much larger t han t h e tim e need ed for the ITC -runs described here. 4.2. 2. The rm odyn am ic An alysis o f Lys oz ym e Bindin g to He parin 4.2.2 .1. D ependenc e of the B inding Constant K b on Ionic Stre ngth All experiments were per formed with a sing l e batch of Hep purif ied by extensive dial y sis prior to use. The molecular weight ca . 15.000 g/mol which amounts to ca. 24 repeating units per chain (ave r age molecular weig ht of 580 g/mol of the he parin disacc haride unit taking into account the deg ree of sulfation; cf. re f 322 ). The exper iments were performe d in a buffer solution at fixed pH of 7.4. Und er these c onditions both the Ly s as well as the Hep carries opposite effect ive ch ar ges. Figu re 28. T otal ionizati on degree resu lting fro m the ionization of the sulfate and carbox yl gro ups of hep ar in a s a functio n of the solutio n pH for d ifferent salt conce ntratio ns of the electro lyte. T he ionization curves w ere calc ulated according to ref. 323 (for details see s upple mentary i nfor m atio n) for a tem perature of 37°C taking into account ch ai n end effects o n the fractional charge. 302,324 According to theor y fo r counterion condensatio n at linear polyelectroly t es d eveloped b y Manning 302, 324 , the frac t ion of charge d groups (not compensated by condensed ions) of the Hep used in this stud y is approxi mately 29 % to 35% (depending on the ionic strength and temperature; see the supple ment) of the total nu mber of ionizable g roups. The corr esponding sul fate an d carbox y l groups of Hep ar e com plet el y i onized at pH 7.4 (see Fi gu r e 28 ) providing the ba sis for electro static inter actio ns with pos itively charged patche s of Lys . 43 After the evaluation of the ITC data described in section 4.2.1. the integrate d isotherms were fitted w ith the SSI S model (se e section 3.3.2.3.1. ). F igure 27 shows the IT C - di agrams for t hre e differen t tem per atur es, t he d iagram s for t he re mai ning tem perat ur es a re gather ed i n the supplement. Table S2 g athers the matrix of data obtained as the function of both T and c s . The dep enden ce on temp eratur e for a giv en s alt concent rati on is relat ivel y sm all w hereas t here is a strong de pendence on ionic strength. These features have been observed for a wide variety of s ystems wh ere a h i ghl y cha r ged pol y ele ctrol yte as e.g. DNA is i ntera ction with proteins. 7,2 8,3 0,21 8 The same behaviour was found for Lys and human serum albumin (HSA) intera cting with a hig hly charge d dendritic poly el ectr ol y te. 12,13, 53 As di scussed in previous secti on , this finding points to a strong EEC which phenomena will be explored further below. 53 Tabl e S 2 shows that in a verage 6 Ly s m olecules are bound to one Hep molecule. T his number is relativel y constant and hardl y changes with temperature or salt concentration. Thus, th e complexes formed by Lys and Hep turn out to be c omparable over a r elativel y wi d e ran ge of temperature and ionic strength. Thus, Ly s forms well - defined complexes wi th Hep which is the prere quisite for the following anal ysis. However, at this st age there is no further information whether the binding is taking place at random in a non - specific m ann er or whet her ther e is a spec ific bin ding to well - defined p ent asa ccha ride st ructu res 296,2 97 (cf. also the discussion in ref. 86 ,297 ). Fig ure 27 shows that for I = 25 mM t he calorimetr ic enthalpy ∆ H ITC is pr act ical l y i nd epen den t of temperature. There is a decrease of its ma gnitude only at the highest salt c oncentration under consideration here. As discussed in se ction 3.3.2.1.6. , 1 3,53 ∆ H ITC can contain other contributions related to linked equilibria. Evidently, the assumption made for the two component ligand binding ( TC LB ) mo del (see s ect ion 3.3.2.3.3. ) appli ed in previous chapt er fo r dP GS - Mg 2+ int eractio n, i s in the pr es ent case i nv ali d. T he d iscrep an c y between ∆ H ITC and the binding constant ∆ H b that is observed here, shows the importance of a s y s tematic thermod y namic anal y sis . The n earl y van i shi ng dep enden ce o f ∆ H ITC on T and on c s demonstrates in a ddition that this qu anti t y is not direc tl y r elate d to the str ength of bindin g b ut to a loc al interac tion between the surface of the Ly s molecules and of the Hep. Several I T C - di agrams obtained a t diffe rent ionic str en gth are display ed in Figu re 29 . Up to a salt concentration c s of 75 mM, very precis e d ata c an be ob t ained whe reas th e hi ghes t sal t con centr ati on l ead s to a Wi seman paramet er o f 52 (s ee s ect i on 3.3.2.2. ). Hence, a salt concentration of c s = 100 mM t urned out to be the highest salt concentration where data with sufficient precision can be obtained. 44 0 5 10 15 -60 -40 -20 0 Q in kJ/mol of Lys n Lys /n Heparin 25 mM 35 mM 50 mM 75 mM 100 mM Figu re 29. Effect o f the io nic st re ngt h o n bi nd in g. T he inte gr at ed hea t s of a dso r pt ion a t c o nsta nt te mper at ur e o f 37 o C and four differe nt ionic s trengths are d ispla yed. So lid lines pr esents t he SSIS fit. The analysis of the experimental binding constan ts K b in terms of equation (13a) is shown in Figure 30 . Her e the dat a obtained at 25°C are shown; pl ots showing t he data for other tempe ratures are given in the s uppleme ntar y material. For all temperatur es plots with ve r y good linearity a r e obtained and fits with equation (13a ) turne d out to be fully suffi cient. Atte mpts to fit t hese d ata w ith equation (13) indicate tha t these data are c ompatible with a number of releas ed wat er mol ecule s ∆ w of the order of ≤ 200. Evidently, a possible rele ase of wate r molecules can ha v e onl y a minor contribution to the binding fr ee energy as it is obvious fr om equat ion (1 3). Hen ce, th e pres ent d at a can b e eval uated b y use o f eq u atio n (13a) as ou tli ned rec entl y f o r the inte raction o f Ly s with dendritic pol y gl y cerol sulfate (dPGS ). 53 -4 -3 14 16 18 20 ln K b ln c s Figu re 30. Depend enc e o f the lo gar ith m o f the b ind i ng c ons ta nt, ln K b on the logarit hm o f the salt concentratio n, ln c s at temperature of 25 o C. The solid blue li ne rep resents th e fit to equatio n (13a) . Data der ivin g f rom this analysis in terms of e quation (13a) are gathered in Table 3 . Approximatel y 3 ions are released per bound Lys. 45 Tab le 3. Therm od ynamic parameters result ing from the fit of experimental data to equation (13a). Tempe rature ( o C) ∆ n ci ln K b (1M) (M -1 ) ∆ G res (kJ/mol) 15 2.9 ± 0.2 9.2 ± 0.4 -22.1 ± 1.1 20 2.8 ± 0.2 9.1 ± 0.4 -22.2 ± 1.1 25 3.0 ± 0.1 8.1 ± 0.3 -20.1 ± 0.8 30 2.7 ± 0.2 8.7 ± 0.5 -22.0 ± 1.3 37 3.0 ± 0.3 7.7 ± 0.8 -19.9 ± 2.0 ∆ n ci : net num ber o f release count erions deriving from fits of equation (13a) to the ex perimental binding constants K b ; K b (1M) : Bindin g consta nt obta ined b y extrapo lation of the exper imental bi ndin g co nstants K b to a salt concentrati on c s of 1 M; ∆ G res : residual f r ee energy as def ined throug h equ ation (25), ∆ G res = - kT ln (K b (1 M )). 53 As indicat ed above, ∆ n ci is the ne t release of i ons and ma y include also the u ptake of ions upon binding. As found in many previous investigations 1 3,30 ,53,3 03 rel ated t o cou nterion release, ∆ n ci does not depend on temper ature with the present limits of error. T his observation is due to the fact th at th e releas e of co u nteri ons as well as t he releas e of w ater mo lecul es is a p urel y ent ropi c phenomenon (cf. the discussion in ref. 320 ). The ex cell ent l in earit y of plots according to equation (13a) can now be used for the extrapolation of the binding constant to the reference concentration of 1 M in order to obtain K b (1M ) . Tabl e S2 gather s t he respect ive resu lt s. ∆ G b (1M ) is around - 20 kJ/mol and depends hardly on temperature. A comparison with the data gathered in Tab le 3 shows that ∆ G b (1M ) makes up approximately 50% of the free energ y of binding. Compared to the vast l iterature on the interaction of DNA with proteins (see e .g. ref. 2,7 ,28, 30,21 8 and further citations given there), the number of studies considering explicitl y the s alt dependence of the binding of heparin to various p roteins is much smaller. Ol son and coworkers investigated the binding of heparin to thrombin. 3 11 Her e straig ht lines in plots of log K b versus lo g c s were found and the number of released ions was found to be approxim ately 5. A comprehensive investigation of the i nteraction of heparin with oli gopeptides b y Mascotti and Lohman containing basic amino acid s aga in demonstrated th at log K b de pe nds linearl y on log c s for t he ent ir e ran ge o f salt concent r atio ns. 3 06 Two i ons w ere r eleas ed fr om hepari n f or each bound tripeptide. These authors also anal ysed the older literature and found that up to 6 ions are r eleased per bound protein. I n recent study of Ly s binding to dPGS it was found that 3 counetrions are re leased per bound Ly s 13,31 whi ch compares well with the range of 2.7 – 3.0 found here . Data on the bindi ng o f fibroblast - gro w t h - fact or - 2 (FGF - 2 ) to hepar in reported by Thompson e t al. 325 s imilarly point at the imp ortan ce of e lectrosta tic interactions. FGF - 2 is a 16 kDa sized growth factor that controls cell survival, migration and differentiation and displa y s an overa ll basic net charge with strongl y positivel y charged patches. Thompson e t al. 32 5 found that three FG F - 2 molecules bind per 5 kDa hepari n which would relate to nine FGF - 2 bound per one 15 kDa heparin. The total binding energ y of -36. 4 kJ/mol per bound F GF - 2 of which 30% ( ΔG ci = -10. 9 kJ/ mol) can b e attri but ed to electro stat ic eff ects due t o the r eleas e of t wo to three counterions. The authors further more used systematic point mutations of FGF - 2 whic h provided evidence of lysine 125 a nd arg i nine 120 contributing more than 31% of the total binding ene rg y . Mol ecul ar modelling pointed to a distance of less than 0.3 nm of the two 46 charge d moieties to the sulfate groups of he parin which wa s interpreted a s a formation of two salt bridge s. Thus, bindin g of one FGF-2 require s five to six monosaccharide units with two to three counte rions released, contribute approximately - 11 kJ /mol to the tot al binding ene r g y . Here, th e co mpar abl y s ized and charged lysozy me requires eight to nine monosaccharide units for binding corresponding to the r elease of three counterions contributin g with -20 kJ /mol to the binding energy. Thus, for both proteins the entropy ga in due to counterion release effec ts ca n be concluded to con tribute 30 – 50% to the tot al binding energy. Moreover, salt - bri d ge formation resulting from t he release of counterions contributes to ∆ G res . In consequence, elec trostatic inte raction see ms to domina te pro tein binding to heparin in both cases. 4.2.2.2. Dependence of the Binding Free Energy Δ G b on T emperatu re 285 290 295 300 305 310 -48 -46 -44 -42 -40 -38 25 mM 35 mM 50 mM 75 mM 100 mM ∆ G b in kJ/mol of Lys Temperature (K) Figu re 31. Dependen ce o f th e free Gibbs en ergy of binding ∆ G b on tem pera ture for all io nic stren gths. Solid lines represents th e fits obtained from the nonl ine ar va n ’t Ho ff r el at io n eq uati on ( 2 0) . As discussed in section 3 .3.2.1.6. the dep en den ce o f Δ G b on temperature T can b e mo deled b y the nonlinear van’t Ho ff equation (20). 23, 326, 327 Figure 31 displays the f its fo r all salt concentrations under consideration here. The respective enthalpies Δ H b and entropies ∆ S b w ith the s pecifi c heats ∆ C p are gather ed in Table S 1. T hese fits are relat ivel y rob ust and t he resu lti ng paramet ers are h ardl y ch an ged b y small er ro rs of K b . Figure 3 2 display s th e comparison for all thermo dy namic data obtained for a ll salt co ncentrations. 47 285 290 295 300 305 310 -80 -60 -40 -20 0 20 40 ∆ H b T ∆ S b ∆ G b Contribution to ∆ G b (kJ/mol) Temparature (K) 25 mM 285 290 295 300 305 310 -60 -40 -20 0 20 40 ∆ H b T ∆ S b ∆ G b Contribution to ∆ G b (kJ/mol) Temperature (K) 35 mM 285 290 295 300 305 310 -80 -60 -40 -20 0 20 40 60 ∆ H b T ∆ S b ∆ G b Contribution to ∆ G b (kJ/mol) Temperature (K) 50 mM 285 290 295 300 305 310 -80 -60 -40 -20 0 20 40 ∆ H b T ∆ S b ∆ G b Contribution to ∆ G b (kJ/mol) Temperature (K) 75 mM 285 290 295 300 305 310 -80 -60 -40 -20 0 20 40 60 ∆ H b T ∆ S b ∆ G b Contribution to ∆ G b (kJ/mol) Temperature (K) 100 mM Figu re 32. T he thermodynamic parameters (∆G b , ∆H b and T∆S b ) ob tained for a ll salt co ncentra tions as a functio n of temperature . All t hermod yna mic data deriving fro m th e se fits are gathered in Table S2 . The dep end ence o f ∆ G b on T is h ard to see whe r eas resp ect ive en th alp ies ∆ H b and entropies ∆ S b vary s trongl y with temperature as predicted b y equations (22) – (24). Figure 32 also demo nstr ates t hat th e te mperat ures whe re ∆ H b and ∆ S b vanish, vary with salt concentration. Si mil ar featur es hav e b een fou nd fo r m an y oth er s ystems in w hich P Es i nteract with proteins. 28, 53, 303 4.2.2.3. Enthalp y-Entr opy Cancellation The prese nt data will be anal y zed as lined out in section 3.3.2.1.7. The plot of ∆ H b agains t T Δ S b for all ionic strengths under consideration here is displayed in Figure 33 a) . There is a mark ed cancellation of enthalpy and e nt ropy w hich becomes much clearer when Δ H b to TΔ S res are compared: Application of equa tions (25) and (26) leads to T Δ S ci which may be subtracted from TΔ S b in turn to obtain T Δ S res acc ording to equati on (27). 28,5 3 Figure 33 b) shows the resulti ng plot and demonstr ates that a ll data lie on a common ma ster curv e. The r esulting be st fit to the data presented in Figure 33 b) is given by: ∆𝐻𝐻 𝑏𝑏 = − 20 .9 𝑘𝑘𝑘𝑘 / 𝑚𝑚 𝑚𝑚𝑙𝑙 + 1. 02 ∙ 𝑇𝑇 ∆𝑆𝑆 𝑐𝑐𝑒𝑒𝑠𝑠 (55 ) The in ter cept o f -20. 9 kJ /mol represents the avera ge value of Δ G res for a ll temp eratur es an d reflects the fact that this part of the free energ y of binding is independent of temperature within the p res ent limits of e rror (se e Table 3 ) . The slope is 1.02 which is unity within t he limits o f error indicates a f ull compensation of enthalp y a n d entropy. 48 -40 -20 0 20 -80 -60 -40 -20 a) 25 mM 35 mM 50 mM 75 mM 100 mM ∆ H b (kJ/mol) T ∆ S b (kJ/mol) -60 -40 -20 0 20 40 -80 -60 -40 -20 0 20 b) 25 mM 35 mM 50 mM 75 mM 100 mM ∆ H b (kJ/mol) T ∆ S res (kJ/mol) Figu re 33. Enthalp y - ent rop y cancell ation for the binding betw ee n Hep and Lys. (a) Entha l py, Δ H b i s plo tted against TΔ S b for all ionic stren gths. (b) Ent ha lp y, Δ H b is plo tte d against TΔ S res for all ionic stren gths . T he solid red line r epre sents the fit by eq uation (55 ). The same be havior w as found for Ly s int eracting with dPGS recently 53 and for DN A interacting with various proteins. 28 Evidently, the EEC found here presents a far more ge neral phenomenon, most probably related to changes in the water struc ture upon comple x formation. 28 Moreover, the dissection of ΔG b into ΔG ci and ΔG res is applicab le to quite a numbe r of sy stems. As discussed in section 3.3.2.1.7. , ΔG res presents the part of the binding free energy ΔG b rel at ed to factors not re lated to c ounterion relea se. Thus, ΔG res com pris e factors such as h y d ro gen bond ing and sal t bri d ges and r efl ects i n man y r esp ect s th e sp ecif i c part o f ΔG b . ΔG res obtained for the binding of Lys to dPGS was analy z ed b y MD - simulatio n in deta il. For this sy stem ΔG res could be rationalized ma inl y in terms of ion - b ri dgi n g. 53 For heparin this poi nt is in need of further studies, preferably b y MD- s imulations. The foreg oing discussion has pointed to the intim ate rela tion between counterion release and the en thal py - entropy cance llation. This connection now lead to an im portant co nclusion regar ding the driving forces of binding: F igure 32 conveys the ide a that complexation between lysozyme a nd hep arin at 25 mM and low tempe ratur e is mainly enthalpy - driven. However, data taken at hig her salt concentration demonstrate that the e ntrop ic term becom es larger an d lar ger. Thus, at T = T H (which is around 57°C for c s = 25 mM) the binding enthalpy is zero and complexation is entirely driven by entrop y. For hig her c s thi s tem peratu re is ev en lo wer. Henc e, the data compa red in Figure 32 present only another way of showing the EEC. The thermodynamic data obtained by equation (20) should therefore be interpreted with caution. 326 The finding s p resent ed in this sec tion can now be compared to structural data of heparin discussed in section 4.2.2.1. : I t was found that all charged groups are ionized and that between 29 and 35% of the ch arges are not balanced. Minsk y et al. 302 fo und for a d e gree o f polymerization of 24 an e ffec tive char ge of 37% of the structural char ge (see Table 2 of ref. 302 ) which fully agrees with obtained value . With 1 nm being the length of the disaccharide unit (see Fi gure 3 ) and fo u r stru ctural ch arges, b = 0.25 nm and the charge parameter ξ = 2.84 (see secti on 3.3.2.1.1. ). The est im ate 1 -1/ ξ would lead to 65% of the c ounterion s being c ondensed. Hence, ca. 2.7 of 4 counterions are condensed to the main chain and are expected to be released upon binding of l ysozyme. Here, an ion release ∆ n ci of 2.7 to 3 was found which is in fully agree ment given the various approx imations. 49 Moreover, equation (1) allows to e stim ate th e surfac e con cent rati on c ci of the condensed counterions which a mount s to 0.91 – 0.92 M. This concentra tion compares well with t he on e found recentl y for dPGS which are of the order of 1 M or of double - str and ed DNA 1 which is similar ma gnitude. I t reflects the fac t that Hep is a mong the biop olyme rs with the high est ch arge density. It is evident that He p i nteracts with proteins much in the way DNA is binding p roteins . As pres ented i n chapt er 4.1. of dP GS interaction with mono - and divalent ions, the effective char ge, Z eff of h eparin s hould depend only on the valency o f counterions and should not be influenced by the ion - spe cific effects. Evidently, the investigation of interactions between less char ged, stru ct urall y dif fering GAGs with proteins 295, 328 will cer tainl y expa nd the scope and the power o f en gine ered G AG - based m ateri al s an d s ystems, incl udi n g G AG - based ant ivi ral therap euti cs. 329 4.2.2.4. Conclusion Upon I TC measurements of Hep - Lys inter acti on two decis ive v ariabl es have b een ch an ged s y s tem atic all y: The dep e nd ence on s alt co nc entrat i on c s th at lead s to the net nu mber o f releas ed counterions ∆ n ci and K b (1 M ), th e bin din g cons tant at a refer enc e sal t con cen t ratio n of 1 M (se e the discussion of eq.(13a) in section 3.3.2.1.3. ). Th e depend en ce on temp erat ure th at al lows to dissect the binding fr ee ener g y ∆ G b by use of eq.(20) into the respective enthalpies ∆ H b and entropies ∆ S b togeth er wi th t he sp ecific h eat ∆ C p . A strong enthalp y - ent rop y cancel lat ion was found s imilar to th e re sults for man y other syste m s. 28, 53 The binding f ree energy ΔG b could be dis sected int o a part ΔG ci due to counterion release and a re s idual part ΔG res . The la tter quantity ref lects spec ific contr ibutions as e.g. salt bridg es or h y dro gen bonds. 28, 53 Thus, the binding of l y soz yme t o hep ari n ma y directl y be comp ared t o t he wel l - studied bi nding o f proteins to DNA. The reported approach is envisioned to become applied in the future analysis of interactions between va rious different GAGs and signa ling proteins (cy tokines, chemokines, growth factors) , pavin g the wa y for the fabrication of GAG - based pol ymer hydroge l networks with rationally desig ned protei n binding charac t eristics. 4.3. Pr ot ein A dso rpt ion t o β - CD -S As solubiliz ing age nt s, c y c lodextrins ( CDs ) are us ed in pharmaceutical industr y to proc ess liquid dru gs in to micro crys talline o r amorphous powder, to reduc e gastrointestinal drug irritation and to prevent from drug–drug and drug – e xcipient inte rac tions. 1 02,1 03,33 0,331 Th e nati ve CDs in aqueous solution undergo self - asso ci atio n 332, 333 with the lowest solu bility fo r β - CDs. Szejtli 334 have attributed this phenome na to the formation of the intra molecular hy dro gen bonds of the β - CD rim. I t w as found that partial substituti on of the hy drox yl gr oups (even b y hydrophobic moieties such as methoxy - functional groups) , resulted in significant incre ase in the aqueous s olubilit y of β - CDs. 3 31 Enhanced solubili ty thus became the main reason for further chemical modifica tions o f β - CDs. 3 35 In recent studies, isothe rmal titr ation c alorimetry ( IT C ) was used to investig ate the complexation of β - CDs wi th s ever al dru gs s uch as: p aen ol, 3 36 acetov anil lon e, 336 sertaco n azol e 337 and ozinid e an itimalar ials. 338 I n al l cases the high binding constant ( K b ≥ 10 6 M -1 ) indicate a formation of strong complex es, proving hi gh solubil izing activit y o f β - CDs. This studies focused on l ow - molecular drugs for which inclusion in t he internal cavit y of CDs is possible. I nt eraction of CDs with bigger entit y was reported b y Merkus et al . 339 The authors showed, that dimeth y l -be ta- cyclode xtrin (DM - β - C D) can inhibit or reduce the efflux function 50 of P - gl y c oprotein (P - gp ) – an e f flux transp orter pr esen t in the a pic al region o f epith elial cells in the brain, liver, kidney and g astroin testina l trac t. 339 Ho wever, inves tigation on β - CDs enhancing bioavailability and stabilit y of hi gh - mol ecular d ru gs as w el l as t h e detai led s tud y on interaction between CDs and proteins have still a l ow rec o gnition. Here in orde r to contribute to the analy s is of the int erac tions between β - CDs with proteins the binding of lysoz y m e (Lys) to hi ghly sulfated β - CD (β - CD - S) in aqueous s olution is anal ys e d with re spect to varying ionic s treng th. β - CD - S i s a sul fated, c y clic ol igosa cch aride s hap ed of a truncated cone or torus ( see section 3.1.1.2. ) and the choi ce o f Lys as a mod el protein was discussed in chapter 4.2. The following stud y i s based on the anal ysis of the binding constant K b measu red b y IT C a s a function of salt concentration c s . The binding const ant K b is anal yzed so lel y in terms o f count erion rel ease, i n th e s ame wa y as discussed with regard to heparin in section 4.2.2.1 . 53 4.3. 1. Bind ing I sothe rm s IT C experiments were conducted on a Microcal VP - IT C instrument (Microcal, Northampton, MA). All samples used in the measur ements were prepared in a phosphate buffer . For that, 3.8 mM of Na 2 HP O 4 and 1.2 mM of NaH 2 PO 4 were dissolved in Mil li - Q w ater. Th e pH o f th e solution was adjusted, at r oom temperature (20 o C), to 7.4 by addition of NaOH. In order to prepare buffers with diffe rent ionic strengths, additional NaCl was added into the buff er individuall y . A total of 280 µ L of Ly s - buf fer sol ution was titr ated into the sa mple cell with 7 0 succ essive inje ctions of 4 µL each. T he stirring rate was se t at 307 rpm with a time inte rv al of 300 and 360 s between e ach injection. The cell was containing 1.43 m L of β - CD - S solution in a match in g buf fer. The meas uremen ts w er e per fo rmed at 37° C. Befo re each ex peri men t all samp les were d eg assed and therm ost att ed for several mi nut es at 1 d egree bel ow th e ex perim ental temp eratur e. The evalua tion of ITC data is demonstrated in Fig ure 34 which shows the ra w - I TC signal of binding (black curves and squares) and dilution of protein (red curves and s quares). For further anal y sis the heat of dilution of the protein was subtracted from the heat of adsorption. 51 024 -8 -4 0 4 0 100 200 300 400 -2 -1 0 1 T i me ( mi n ) µcal / s ec a) I =20m M T=37 o C Lys + β - CD- S Lys Di l ut i on n Ly s /n β - CD- S kcal / m ol e of Lys 024 -8 -4 0 4 0 100 200 300 -2 -1 0 1 T i me ( mi n ) µcal / s ec b) I =30m M T=37 o C Lys + β - CD- S Lys Di l ut i on n Ly s /n β - CD- S kcal / m ol e of Lys 024 -6 -3 0 3 6 9 0 100 200 300 -2 -1 0 1 2 3 Ti me ( mi n ) µcal / s ec c) I =40m M T=37 o C Lys + β - CD- S Lys Di l ut i on n Lys /n β - CD- S kcal / m ol e of Lys 0 2 4 -4 0 4 8 0 100 200 300 400 - 2, 0 0, 0 2, 0 T i me ( mi n ) µcal / sec d) n L ys /n ( β - CD- S ) kcal m ol -1 of Lys Figu re 34. I T C data for the ad sorption of Lys to β - CD - S at pH 7.4, (a ) I = 20 m M, (b) I = 30 mM, (c) I = 40 m M and (d) I = 60 m M at T = 37 o C. T he upp er p anel s ho ws t he ra w dat a o f t he ad so rp ti on ( bl a ck c ur ves) a nd dil ut io n of Lys by buffer (red curves). T he in tegrated heats of each injection are sh o wn in the lower panel. 4.3. 2. Th erm odyn am ic A nalysis of Ly soz yme Bindin g to β - CD -S 4.3.2.1. Dependence of the Binding Constant K b on Io nic St rengt h A series of ITC experiments was performed at fou r different ionic strengths : 20, 30, 40 and 60 mM. The experiments were perfor med in a buffer solution at constant tempera t ure of 37 o C and fix e d pH of 7.4. Under these conditions Ly s and β - CD - S carries op pos it e eff ectiv e ch arges (positive for Ly s and ne gative for β - CD - S) . The integ rated isother ms were fitted with the single set of identical binding si tes (SSIS) model. Figure 35 d emonstr ates the SSIS da ta fit. 52 0 1 2 3 4 -12 -10 -8 -6 -4 -2 0 a) Q in kcal/mol of Lys n Lys /n β -CD-S 0 1 2 3 4 -12 -10 -8 -6 -4 -2 0 2 b) Q in kcal/mol of Lys n Lys /n β -CD-S 0 1 2 3 4 -12 -10 -8 -6 -4 -2 0 C) Q in kcal/mol of Lys n Lys /n β -CD-S 0 1 2 3 4 -10 -8 -6 -4 -2 0 d) Q in kcal/mol of Lys n Lys /n β -CD-S Figu re 35. Int egrated heats of each injection af ter subtraction (corrected for pro tein h eat of dilution), (a) I = 20 mM, (b) I = 3 0 m M, (c) I = 40 mM a nd (d) I = 60 mM at T = 37 o C. Red line pre sents the single set of identica l sites (SSI S) fit. As shown in Fig ure 35 at low salt conc entrations (20 – 40 mM), the measur ed heat ef fect (∆H IT C ) did not change significantly. The free energ y of binding, Δ G b in this c ase pre sents onl y small dependence on the ionic strength ( see Table 4 ). Tab le 4. Therm od ynamic parameters result ing from the SSIS model. I ( mM) N K b x 10 -6 (M -1 ) ∆ H ITC (kJ/mol) ∆ G b (kJ/mol) 20 1.6 19.2 ± 10 -49.8 ± 0.5 -43.2 ± 1.9 30 1.9 6.6 ± 2.9 -49.3 ± 0.5 -40.5 ± 1.5 40 1.5 3.6 ± 1.7 -50.2 ± 0.7 -38.9 ± 1.8 60 1.8 0.81 ± 0.09 -40.5 ± 1.2 -35.1 ± 0.3 However, at high ionic str eng th of 100 mM the measured heat effect chan ges dramaticall y . Two adsorption si tes are present upon binding betwe en Lys and β - CD - S at hi gh salt concentration, thus the binding mecha nism changes with incr easi ng ionic stre ngth (see Fig u re 36 ). 53 0 2 4 0 2 4 6 8 0 100 200 300 400 -1 0 1 2 3 T i me ( mi n ) µcal / sec a) n Lys /n β - CD- S kcal m ol -1 of Lys 0 1 2 3 4 -8 -6 -4 -2 0 b) Q in kcal/mol of Lys n Lys /n β -CD-S TSIS model Figu re 36. (a) IT C da t a fo r th e ad so r p t io n o f L ys t o β - CD - S a t pH 7.4 , I = 10 0 mM a nd T = 37 o C. The upper panel shows the raw data of the adsorption (black cu rves) an d dilution of Lys b y buff er (red curves). The integ r ated heats of each in j ection are sh own in the low er p anel. (b) Integrated heats of each injection af ter subtraction (correcte d for p rotein heat o f dilution). Red line presents t he two set s of indep endent bindi ng site s (T SIS) fit. Tab le 5. Therm od ynamic parameters result ing from the TSIS model. I ( mM) N 1 K b1 x 10 -4 (M -1 ) ∆ H 1 ITC (kJ/mol) ∆ G b1 (kJ/mol) 100 0.5 ± 0.2 5.6 ± 1.4 -7.8 ± 3.5 -28.2 ± 0.6 N 2 K b2 x 10 -4 (M -1 ) ∆ H 2 ITC (kJ/mol) ∆ G b2 (kJ/mol) 0.8 ± 0.4 5.9 ± 1.1 6.2 ± 3.2 -28.3 ± 0.5 Following the anal y sis presented in s ection 4.2.2.1. , t he li near rel atio n bet ween ln K b and ln c s (see Fig ure 37 ) y ields ∆ n ion ≈ 3,0 ± 0,2 which means t hat approx imately 3 i ons are released upon binding of two Ly s molecules to a β - CD -S. -4 -3 14 16 18 ln K b ln c s Figu re 37. Depend enc e o f the lo gar ith m o f the b ind i ng c ons ta nt, ln K b on the logarit hm o f the salt concentratio n, ln c s at temperature of 37 o C. Solid black line rep resents the fit to equation (1 3a) . 54 4.3.2.2. Conclusion In this cha pter the depe ndence on salt conce ntration c s on β - CD - S inte rac tion with Ly s lead t o the net number of r eleased counterions ∆ n ci and K b (1 M ), (see the discussi on of eq.(13a ) in secti on 3.3.2.1.3. ). However, the investigation on β - CD - S interac tion with Ly s should be ex tended in o rder to verify th e depen den ce on t emperat ur e in t he sam e manner as d iscu ssed for Hep - Ly s in s ections 4.2.2.2. and 4.2.2.3. S uch expande d analysis may lead to direct comparison to well - studied binding of proteins to DNA . The repor ted approach may b ecome applied in the future ana l y sis of interacti ons between CDs a nd various different proteins, thus enabling the fabrication of pol y mer drugs with enhanced solubilit y a nd rationall y designed protein binding chara cteris ti cs. 4.4. Pro tein A d sor pt ion ont o SPBs Here, th e an al ysis o f the po l yelectrol yte - protein ( PE -P) inter actio n presented in previous chapt ers is extend in or der to obtain the full t hermod y n amic information on the binding of protein to sphe rical pol yelectro l yte b rushes ( SPBs ) . The S PB, shown schematicall y in Fi gu r e 38 , consist of a solid core pa rticle of approximatel y 115 nm diameter to which long PE chains are dens el y graft ed. 16,340 ,341 I sothermal titration calor imetr y ( IT C ) w as used to determine the binding constants at diff erent ionic strengths and for a range of temperatures. To ensure that the heat signal is not due to a partial unf oldin g upon binding, the complex was studied by Fouri er transfo rm infra red ( FT - IR ) spectrosc op y , where changes in protein secondary st ructure upon adsorption to the brush lay er would show up in the spectra immediatel y . 1 81, 342 T he anal ysis of all d ata ob tain ed here al l ow to present a com preh ensi ve discussion of the driving force s for adsorption, including the role of wa ter in the proces s. Figu re 38. Sche matic illustr atio n of a spherical p ol yelectrol y te brus h in the pro cess of pro tein adsor ption. T he poly elect rol yt e bru sh cons ist of a s olid poly styren e core (grey sph ere) with r adiu s R h,core = 57 nm an d surf ace graft ed pol y (acr y lic acid) chains. Red spheres on the PAA chains represen t t he negative charge of t he acidic residues, whil e blue spheres represent th e p ositive counterions; note the presence of con densed and free counterions wi thin the brush layer. The HSA molecules are represented by green sphe re s. T he r ad ius o f the br us h R = 288 nm decreased after protein adsorption to 196 nm . 55 4.4. 1. An aly sis of th e Seco ndary S truct ure of Ads orbed P rote ins by F T - IR Spe ctr oscop y The sp ectra o f human serum albumin (HSA) before and after adsorption onto SPBs are plotted in Figure 39 . Following the analy si s discussed in section 3.3.1. (ref. 81 ,181 ) it is poss ible to identify charac te ristic amide I ( mainly the C=O str etch) and amid e II (a C - N stretching coupled with N -H bending) band maxima at 1652 and 1546 cm -1 , resp ectiv el y 1800 1700 1600 1500 1400 1300 0,000 0,001 0,002 0,003 0,004 Intensity [a.u .] Wavenumber [cm -1 ] I=20mM, T=25 o C HSA HSA + SPB Figu re 39. FT - IR spectra o f free HS A (solid b lack line) a nd HSA i mmobilized o n SPB p articles (solid red line). After a dsorption onto SPBs, the peak position, pea k shape and the intensity of the bands remain unchanged w ithin the limits of error. This ana lysis showed no significa nt disturbance in the secondary structure of the protein adsorbed ont o these particles. Thus the ITC - signal arises e xclusivel y from the adsorption process and is not due to par tial unfolding of the pr otein (see the discussion of this point in references 13,6 8 ). 4.4. 2. Bind ing I sothe rm s ITC ex per imen ts we re cond ucted us in g a Mi crocal VP - I TC instrument ( Microca l, Northampton, MA). All samples used in the mea surements were prepared in a buffer solution of 10 mM MOPS and 10 m M NaCl to adjust the ioni c strength. The pH of each solution was fixed to 7.2. A total of 280 µL of HSA - buffer solu tion was titrate d into the ce ll containing 1.4 mL of SPB solution in 94 suc cessive injections of 3 µL e ach. The stirring rate of 307 rpm was set wi th a t im e int erv al o f 360 s bet ween ea ch i nject ion . The concen t rati o ns of H SA w ere as follows: 24.0 g/ L ; 35.0 g/L; 45.0 g/ L and t he co n centrat ion s o f SPB v aried from 1.38 to 1.84 g/ L. These c on centrations were chosen to obtain m ore data points at lowe r molar ra tios while increasing the te mperature. The mea surements were performed a t 25, 27, 29, 31, 33, 35, 36 and 37°C and at an ionic s treng t h of 20 mM and 50 mM. All samples were degassed and therm ost ated fo r sever al m inu tes at 1 degree bel ow the ex peri men tal t emperatur e befo re the ITC - m eas ur ement s. The evaluation of ITC data is demonstrated for the adsorption of HSA onto S PBs at T = 27°C. Special emphasis was g i ven to the subtraction of the hea t of dilution. Figure 40 a) shows the raw - IT C signal o f adsorption (black curves and cir cles) and dilution of HS A (green curves and points). The heat of dilution of HSA was subtracted from the hea t of adsorpt ion. For some cases the subtraction of the heat of dilution of HSA was insufficient. 56 0 10000 20000 0 2 4 6 8 10 0 100 200 300 400 500 600 0, 0 0, 1 0, 2 0, 3 Ti me ( mi n ) µcal / sec a) I =20m M T=27 o C HSA + SPB H S A D ilu tio n n( HSA) / n ( SPB) kcal / mol e of HS A 0 10000 20000 0 2 4 6 8 b) I=20mM T=27 o C HSA + SPB after first subtractio n SPB Dilution Q in kcal/mol of HSA n(HSA)/n(SPB) Figure 40 . (a ) ITC da ta for t he ads orption of HSA on to SPBs at pH 7.2, I = 20 mM , T = 27°C. The u pper panel sh o ws the raw dat a o f th e adsorpti on of HSA on to SPBs (black c urv es) and the dilution of H SA by buff er (gre en curves). The integrated heats of each injection are s ho wn i n t he l o wer pa nel. ( b) Integrated heats of each injection after first subtr action (co rrec ted for pro tein heat of dilution) ( black circ les) and the dilution o f SPBs by buffer (r ed points). At low protein conce ntration ( 24 g/ L ) a con sid erab le heat effect cau sed b y t he heat of di lut ion of SPB was observed. Therefore a double subt raction for measurements performed at low protein conce ntration was perfor med. Hence, after subt racting t he heat of diluti on of HSA from the heat of adsorption (see Fi gure 40 b), black circles) the heat of dilution of SP B was subsequently subtracted (see Figure 40 b), red points). I n thi s wa y I TC - m easurem en ts can b e performe d also under conditi ons in which the signal fr om the binding proce s s has become r ather weak. 4.4. 3. The rmod yn am ic An alysis o f HSA Inter action with S PBs The following stud y i s based on the anal ysis of the binding constant K b measu red b y ITC as a function of salt concentration c s and temper atu re T . Firstly, the binding constant K b is an al y zed solely in ter ms of counterion rele ase, in t he sam e w a y as d iscu ssed fo r hep ari n (secti on 4.2.2.1. ) and β - CD - S (s ectio n 4.3. 2.1. ). Under the conditions of performed I TC ex periments (see section 4.4.2. ) b ot h the H SA as wel l as th e SP B ca rr y a n et ne gativ e ef fe ctiv e ch arge. A fter th e ev al uati on of ITC d ata d escri bed in secti on 4.4.2. , the integ rated isother ms wer e fitted with the two set of inde pende nt sites (TSI S ) model and the results were c ompared to fit resu lts from th e sing le set of identic al sites (SSI S ) model. A semi- logarithmic plot was used to determine the be st fit . 11 Figu re 41 shows that the presen t dat a a re b ett er d escrib ed b y th e TS IS model , whi ch ass umes t he pres en ce of two differe nt bindin g sites of the SPB for HSA. 57 Figu re 41. Bindin g isotherm after double subtraction (corrected for HSA - , an d SPB heat of dilution ) for th e adsorpt ion of HSA onto S P B at pH 7. 2 (I = 2 0 mM, T = 27 °C ). T he f it qu ali ty for: (a) SSIS model a nd (b) T S IS m o del are demonstrated in a se m i - logarit hmic plo t (top p anels). Lower panels depicts the res idual errors for respec tive fits. This finding, observed previousl y in t he case o f SPB interacting with proteins, 196 m a y b e explained as follows: From the spherical geometry of the SPB particles two regions in the polyelectroly t e brush can be distinguished. The i nner reg ion with the higher c hain densit y in which proteins ca n interact with more than one ch ain, and the outer reg ion with the lower chain density in which proteins can interac t with only o ne pol y ele ctrol y te chain. In the pr esent case the fir st b inding s ite can be consid ered as the adsorption of HSA to uno ccupied p o l y( a c r yl i c acid) ( P AA ) chains of th e brush. The second binding site ma y represent the second adsorption step when HSA binds to a PAA chain alre ad y occupied b y a previously adsorbed prot ein. Evidently, the first binding step can be investigated with higher accurac y than the second one and the following discussion will be focused on t hese data. A ll data obtained with the TSI S model are given in Table S3 of the supplement. 4.4.3.1. Dependence of the Binding Constant K b on Io nic St rengt h To elucidate the effect of ionic stren gth on binding, I TC measurement at 3 7°C and I = 50 mM was performed. As shown in Figu re 42 , t he me asu red he at ef fect d ecr ease d dr amati call y with increas i n g salt concentration. Therefore, the binding constant K b at I = 50 mM could not be determ ined wit h suffi ci e nt accur ac y. 0 10000 20000 -0.4 -0.2 0.0 0.2 0 10000 20000 0.01 0.1 1 10 Residual in kcal/mol n(HSA)/n(SPB) Q in kcal/mol of HSA One Site Fit a) 0 10000 20000 -0.4 -0.2 0.0 0.2 0 10000 20000 0.01 0.1 1 10 Residual in kcal/mol n(HSA)/n(SPB) Q in kcal/mol of HSA Two Site Fit b) 58 0 10000 20000 30000 40000 50000 0 2 4 6 8 10 12 Q in kcal/mol of HSA n(HSA)/n(SPB) T = 37 o C 20mM 50mM Figu re 42. Effe ct of ioni c stren gth on binding . The in tegrate d heats Q of a dsorption of HSA onto S P B at cons tant tem peratu re of 37°C for I = 20 and 50 m M are dis pla y ed. Such results was not obse rved in presented studies of hep arin and β - CD - S but a simila r, strong d ecrease of bindin g wa s reported for short linear PAA binding to HSA. 52 For hig her ionic streng ths, the repulsive forces between the S PB and the protein prevail and no adsorption takes place. This can be ex p lain ed b y the th eo retic al co n sid eratio n pres en ted i n s ecti on 3.3.2.1.5 . 82 Si nce appro x imat el y the sam e free energ y o f bindi ng Δ G b a s derived previousl y 52 fo r the interaction of fr ee PAA with HSA was found, it c an be conc lude that the terms related to the brush lay er cancel each other out to a g ood approx imation. This c om parison sug gests that the first step of HSA bindin g onto SPB reflects most likely th e intera ction of PAA chains with the Sudlow I I site of a given protein, as previousl y found in the anal ysis of H S A binding to single PAA - chain s. 52 The effect of pH on binding has been studied b y Wittemann et al . 343 in detail. The pH was found to be an important but not dec isive parameter for the protein adsorption onto SPBs. The decisive parameter is the ionic s treng th whereas the pH only modifies the strength of adsorption. For single polyelectrol y te chains, this problem has been studied b y Dubin e t al . 176, 194 who cam e to comparable results. Therefore all experiments reported here were done at the optimal pH of 7.2. 4.4. 3.2. Tempe ratu re D epen den ce of th e Bin din g Free E ne rgy Δ G b Analy sis p resented in section 4.2.2.2. as well as the previous studies clearl y sho wed that t he temperature dependence of polyelectrol y te binding to protein yields the full thermod y n amic information on the binding process. 3,1 2,13 ,31 Figu re 43 di splays 3 IT C- isotherms, the remaining data fo r oth er t emper atu res a re shown in Figure S15. 59 0 10000 20000 30000 40000 50000 0 2 4 6 8 10 12 Q in kcal/mol o f HSA n(HSA)/n(SPB) 25 o C 31 o C 37 o C Figure 43 . Effect of te mperature on binding . The integrated heats, Q , of adsorption of HSA onto SPB at temperatures between 25°C and 37°C at I = 20 m M a nd the respective fits are shown. To improve clarity, data f o r only 3 tem p eratures are displayed. Fig u re 43 sh ows tha t the ove rall calor imetric enthalpy becomes str onger with in cre asin g temp eratur e. T he h eat ∆ H i ITC meas ured d ir ectl y by ITC i ncr eases app rox im atel y line arl y with increas in g temp erat ure ( Figur e S17 ) and reve als a s ignifi cant posi ti ve heat cap aci t y ch ange ∆ C p1IT C = 13.7 ± 1.6 kJ·mol -1 ·K -1 for the first step of binding and ∆ C p2ITC = 6.9 ± 1.7 kJ·mol -1 ·K - 1 for the sec ond step of binding . The results of the fits are listed in the Table S4 . Figure 44 a) displa y s th e m easured binding free ener gy Δ G b fo r the first and the second (Figure S18) adsorption step, an d clear l y shows the nonlinear temperature depe ndence of Δ G b . The solid lines represents the best fits to equation (20). The thermod y namic p arameters involved in HSA binding onto SPB were derived b y anal ysis with the nonlinear van’t Hof f equation (equation (20)) and the resulting values of Δ S b , Δ H b and Δ C pvH are lis ted in Tab le S 3. Th ese data i ndi cate a l arge posi ti ve heat cap acit y ch an ge Δ C p1 vH = 12.1 ± 2.7 kJ·m ol -1 ·K -1 fo r the firs t step of bind in g whil e a m uch lower Δ C p2v H = 1.7 ± 1.1 kJ·mol -1 ·K -1 is found for the second step of binding. From the we ll - studied phenomenon of protein binding to nucle ic acids it is known that even nonspec ific protein - ligand binding can lead to a positive heat capacit y ch ange du e to proton uptake or dissociation and conformational change of the p rotein. 24 For t he p resent system, however, a signif icant change of the secondar y structure of an adsor bed prot ein can be ruled out as shown in section 4.4.1 . Figure 4 4 a) p resen ts al s o th e temp erature d epe nd ence of Δ G b for the binding of HSA to dendritic pol y gl ycerol sulfate (dPGS) studied b y Ran et al. 12 and to short PA A chains as studied b y Y u et al . 52 In all cases, a s mall depen den ce of Δ G b is evident and arises from strong enthalp y - entro py cancel lat ion ( EE C ) , as will be further discussed . The same observation has be en made in cas e of h epa rin and β - CD - S as well as fo r a la r ge numb er of o th er bi oc hemi cal s y st ems . 23 – 25, 28,30 7 Studies on the inte raction of charged dendrimers with proteins are also consistent in this regard. 12,13 F ig ure 44 b ) display s all thermody na mic pa rameter s obtained for the first step of binding of HSA to the S PBs. The characteristic temperatures found for this s ystem are, T 1S ~ 304 K and T 1H ~ 306 K. 60 280 290 300 310 -32 -30 -28 -26 a) HSA + SPB HSA + dPGS HSA + PAA ∆ G b (kJ/mol) Temperature (K) 300 305 310 -150 -100 -50 0 50 100 b) ∆ G b T ∆ S b ∆ H b Contribution to ∆ G b (kJ/mol) Temperature (K) T 1H = 306 ± 1 K T 1S = 304 ± 1 K Figu re 44. ( a) Temperature dependen ce of the ΔG b f or the fi rst step of binding of HSA onto SPB (bla ck dots ). Red points an d blue trian gles represents the temperature dependence of the ΔG b fo r t he b ind ing o f H S A to char ged dendrim ers (dPGS) 12 and sho rt P AA cha ins 52 , respectivel y . So lid lines rep resent the fitting obtained fro m the in tegra ted f or m of the n o nli near v an’t Hof f e quat io n (e quat ion (20)). (b) Change s i n the the r mod yna mic pa ra me ter s ( Δ G b , Δ H b , T Δ S b ) t hat accom p any the f irs t step of binding of HSA ont o SPB as a fun ction of temperatu r e. Black squares s how the binding f ree energy. The solid black line shows t he th eoretical fit of Δ G b (equat ion (2 0)); T Δ S b is s ho wn as t he or an ge l ine a n d Δ H b is sho wn a s the bl ue line. The di screp anci es b etwe en Δ H ITC and Δ H b (see Tab le S 4 ) are significant for both steps and the calori metr ic v alues Δ H ITC are gr e ater than value s resulting f rom the van’t Hoff analy sis. Similar findings we re observed in the case of prote in intera cting with heparin (see sec tion 4.2.2.1. ), microgels, 163 short pol ye l ectrolytes 52 and c harged dendrimers. 13 I t was shown that the van’t Hoff entha lp y Δ H b ca n significa ntly deviate from the calo rimetr ic entha lp y Δ H ITC and ma y even chan ge si gn. 13 This discrepancy can be traced back to linked equilibria as discussed in sec tion 3.3.2.1.6 . Expanding the analy zed s y stem, form PEs interacting with multiva lent ions (dPGS - Mg 2+ i n chapt er 4.1. ), through PEs interacting w ith r elatively small proteins (he parin -l ys o z ym e in ch apter 4.2. ) to PE brushes interac ting with bulky proteins as discussed in t he presen t chap ter , the d iscrep anc y betwe e n Δ H ITC and Δ H b fro m margin al becom es dr am at ic. Ev iden tl y, the additional contribution to Δ H b that is related to t he linked e quilibria as d iscussed in s ection 3.3.2.1.6. cannot be overlooked while c onsidering the binding between proteins and PEs. 4.4.3.3. Contribution of Counter ion- Rele ase Entro py to the Binding of HSA In th e same w a y as fo r the binding between h ep arin and l ys o z ym e , the p rese nt data will be anal y zed as lined out in s ection 3.3.2.1.7. The enth alpy and the entrop y obta ined are displa y ed in Figure 45 a) . The linearity of the data in Figure 43 a) indicates a strong EEC. The resulting fit is given by the following equations: ∆H b1 = -30.4 kJ/mol + 1.0∙T∆S b1 (56 ) and ∆H b2 = -18.3 kJ/mol + 0. 9∙T∆S b2 (57 ) for the first and the second step (see Figure S20) of binding, respectivel y. The va lue of the int ercept at zero T Δ S bi repres ents the av era ge bi nd ing fr ee en erg y. The slope close to unit y indi cates that th e entr op y factor com pens at es th e e nth alp y nearl y ful l y over a range of ~ 170 kJ / mol in the first step of bi nding and over a range o f ~ 20 kJ/ mol in the second step of binding . Figure 45 a) also shows the compa rison with the binding of HSA to 61 dPG S and short PAA chains, and shows that the EEC found in these s yste ms is directl y compa rab le to tha t in the pres ent study of HSA in tera cting w ith SPBs. In summ ar y , it w as con clud e that the s mall d ependen ce o f Δ G b on temp eratur e and th e concomitant EEC is indeed a ge neral phenomenon that occurs also in more compli cated sy stems such as the HSA binding to SPBs, as shown here. All data evaluated so far point to the fact that the binding of a protein t o a PE is alwa y s ac com pani ed b y EEC. -100 0 100 -100 0 100 a) HSA + SPB HSA + dPGS HSA + PAA ∆ H b (kJ/mol) T ∆ S b (kJ/mol) -150 -100 -50 0 50 100 -100 0 100 b) HSA + SPB HSA + dPGS HSA + PAA ∆ H b (kJ/mol) T ∆ S res (kJ/mol) Figu re 45. (a ) E ner geti cs o f HS A b ind ing to SP B . D ep ende nce o f t he e nt ha lp y, Δ H b , on the entrop y factor, T Δ S b , in the first step of bi nding pr esented as black do ts. T he solid blac k line sho ws the li near fit r esulting fro m equatio n 50. Red points an d b lue trian gles rep resent t he energ etic s of in teraction of HSA with dPGS an d short PAA ch ains, respectively . ( b) Ent h a l p y – ent ro p y canc ell ati o n. T he b indi ng e ntha lp y, Δ H b , is plotted against T Δ S res according to equ ation (27). Thus, the full set of thermodyna m ic data can be analy z ed in an entirely qu antitative manner as presented in section 4.2.2.4. As discussed above, the first step of bindin g observed here is related to the adsorption of one HSA m olecu le per P AA chai n. Th erefo re, in further anal y sis t he value of Δ n ci = 3.0 ± 0.5, previously f urnished b y Yu et al . 52 wa s us ed. The c oncentration of condensed counterions on a lin ear PAA - ch ain m a y b e esti mated at a mbient tempe ratur e (see section 3.3.2.1.1. ) accord in g to Manning by: 1 𝑐𝑐 𝑠𝑠𝑐𝑐 = 24 .3 ∙ ( 𝜉𝜉 ∙ 𝑏𝑏 3 ) − 1 , (58 ) For a PAA chain b = 0.2 5 nm. For water at 25°C, ξ = (7.1· b -1 ). 1 For PAA chains under these conditions the c si ∼ 0.55 m ol/ L . Note, this concentration is independent of c s . 1 Fig ure 45 b) plots Δ H b as a func tion of T Δ S res obt ained from equation (27) (see Table S5). The plo t lead s to comparab le data fo r thes e s y st em s. T he in tercept loc ated near z ero repr esen ts t he avera ge valu e of Δ G res . Its small value demonstrates that the c ount erion rele ase is the onl y decisive contribution that leads to the bindin g of HSA to short pol ye l ectrol yte chains, charged dendrimers and SPBs. 4.4.3.4. Conclusion Presented experiments show that HSA adsorption onto SPBs is a two - step process. Moreover, the thermod y namic analy sis bas ed on the v ariation of c s and T revealed that the counterion release entropy is t he main contribution to the binding free energy ( Δ G b ). ITC meas uremen ts, performe d ove r a ran ge of temperatures between 25 and 37°C show a strong temperature depend en ce of the calori metri c enth alp y ( Δ H ITC ) a long with a nearl y te mper ature -invariant Δ G b . 62 A nonlinear van’ t Hoff anal y si s (according to eq. (20)) demonstrate d that thi s sy stem ex hibits a marked enthal p y - entro p y can cellat ion . The p erfo rmed an al ysis t hus al low s a s y st em ati c comp aris on of th e present res ults with h ep arin - ly s o z ym e in tera ct ion dis cussed above (see chapt er 4.2. ) as well a s with a larg e set of data fr om other s y stems. 7, 12,13 ,22 ,28,52 ,30 3 S u ch comp ariso n demo nst rat es that a str on g EEC is a general feat ur e o ccur ring in s ystems i n which the binding is dominated by c ounterion release. 4.5. Pro tein A d sor pt ion ont o PPB s I n this section a quartz cry stal microbala nce with dissipatio n monitorin g (QCM - D) s t u d y o f human serum albumin (HSA) a dsorption onto a planar pol y (acr y l ic a cid) ( PAA ) brush is pres ented . This stud y allows a quantitative comparison with ca lorimetr ic studies of the same pro blem, presented in ch apter 4.4. In that wa y precise structural information can b e combined with thermodynamic information. The brush lay er was s ynthesized through atom transfer radic al pol y merization (ATRP). 344 – 346 B y a n a l ys is of Q CM - D dat a bas ed on t hermo d y nam ic study o f a well - controlled model s y stem 52 a comprehensive stud y on b rush s y nt hesis and its interaction with proteins is discussed. A combin ation of established protocols 79, 347 based on vary i ng ionic stren gth and changing pH wa s used to probe the brush response. Figu re 46. Schematic illustratio n of the gold Q CM sen so r functionalized with P AA chain s. Green spheres represent th e human serum a lbumin (HSA). The re d arrow corre sponds t o the HSA desorption determ ined by increasing io nic strength (see section 4. 5.2. ). 4.5. 1. Cou r se of E xper imen t 4.5.1.1. Protein Adsorption to PPBs The QC M cr ystals wer e calib rated at const ant pH o f 7.2 in t he buffer solution containing 10 mM MOPS buffer and 10 mM NaCl. Fr om this point forward suc h buffer solutions chara cteriz ed b y pH = 7 .2 and I = 20 m M wil l be cal led t he st ar tin g buffer . Th e c alib rated crystals were then subjected to a 5 g/L HSA suspen sion in the matching buffer solution (10 mM 63 MOPS and 10 mM NaCl ) at controlled temperature of 25 o C and a flow rate of 50 µ L/min. Conditions of temperature and f low rate are unified for a ll solution used in this study . Afterw ards QCM cr ystal s were rins ed wi th t he s ta rting buffer. The in fluen ce of th e salt co ncent rat ion was st udi ed b y a step - wise in crease of ionic strength to I = 50, 75, 100 and 120 mM adjusted by NaCl added to the buff er. Afterwards QCM cr y s tals were r insed with the starting buffer. After the step - wise i ncreas e of t he io nic st rength t he QC M crystals were immersed in the buffer solution of t he same pH a nd ionic strength conditions as at the beginning of the experiment. In the studies regarding the influence of pH the QCM cr y stals we re then rinsed b y buf fer solution of constant ionic streng th (20 mM) but different pH (pH = 6.5 and 7.6, respec tivel y). In th e fi nal s tep t h e QC M cr ystal s w ere ri nsed wit h th e start in g buf fer. After p H ch an ge, the QCM cr y stals w ere immersed in the buffer solution of the same pH and ionic strength conditions (pH 7.2 and I = 20 mM) as at the beg inni ng of the ex periment. 4.5.1.2. Response of Protein- Free B rus h to p H The QCM cry st als were at first calibrated in buffer solution with ionic stren gth of 120 mM and pH of 7.2. After calibration, cry st als were rinsed with buffer solution of I = 20 mM and pH of 7.2. In the following steps QCM cry stals were rinsed with buffer solutions with pH of 6.5 and 7.6 at constant ionic strength (I = 20 mM). In the final step cr ystals were rinsed with buffer solution of I = 20 mM and pH 7.2. 4.5. 2. Eff ect of Ion ic St ren gth and pH on P rotein Adso rpti on The conformational response of a PAA brush with a p re - adsorbed HSA lay er w as studied as a function of incre asing salt concentra t ion and changing pH. The course of experiment is described in section 4.5.1.1. Protein adsorbed strong l y onto a - like char ged PA A brush as indicated by t he large Δf shif t in step I (see Figure 47 ). Correspondin gly, ΔD increased sharpl y at first but then, a fter reaching a maximum, d issipation star ted to de crease. Th is likely su gge sts that HSA at f irst accumu lated on the top of the brush and then started to “migra te “ toward the inside of the brush, making the brush more packed and sti ffer. 172 This was con clud e from a s lowl y decreasi n g ΔD which suggests the f ormation of an incre asingl y orga nized structure of the P AA brush as it is complexed by HSA. Accor ding to B ittrich et al . the observed long equilibration tim e in this step arises form constant incorporation of protein into the brush - protein lay er. 347 The rinse of HSA suspension with starting buffer in st ep II resul ted in a Δf increase (d ecreas ing mas s) and a ΔD decre ase. This suggests the removal of the bulk y HSA molecules tha t have accu mul ated on the surface of the PAA b rush. As a result the brush shoul d become more dis sipative. However, the loss of the viscous l a yer of proteins seems to be decisive in the overall ΔD dec reas e. In step s III to V I, the ionic strength wa s i ncrea sed from 20 to 50, 75, 100 a nd 120 mM in a st ep - wise fashion, at constant pH. The observed sy stem atic Δf increas e was at trib uted t o pro tein desorption and commensurate brush collapse. Furthermore, the small Δ D i ncreas e a ris es f rom the additional loss of HSA from the brush due to the increase of the ion concentration in the bulk solution. 74,3 47 Com pr ession of the brush, driven by increasin g ionic strength, ca n help to expel any w eakl y bound HSA, as shown b y Wong et a l . 348 As a result the PAA br ush becomes more dissipative. Rinsing of the brush with starti ng buffer in step V II decreased the ionic streng th from 120 to 20 mM . The resulting Δf d ecreas e an d conco mit ant i n creas e in Δ D can be 64 attributed to brush swelling due to the lower ion concentration in the bulk solution. 74 ,347 Thes e results are in good agree ment with similar studies of brush conformation in aqueous solution. 78 ,79,3 49 A predominant role of counter ions i n protein adsorption onto PAA brush upon increas in g salt concent rat ion was dis cuss ed in secti on 4.4.3.1. I mportantl y , the difference in Δf valu es betw een st eps II and V II cle arl y su ggest s t hat even after i n creasin g the N aCl concentration to the highest value anal yzed here, there i s still a si gnificant amount of HSA bound within the PAA brush. Figure 47 . Ion ic stre ngt h and pH in duced res ponse of a PAA bru sh with pre - ads orbed HSA l a y er m onitore d by QCM - D. Top pan el: QCM - D nor m alized frequency shift. Lo wer panel: QCM - D dis sipati on shi ft. S welling and deswelling ev e nts are in dicated b y Ro man n u merals. C orresp onding pH and ionic s trengths ar e indicated by red and bl ue color, respe ctively a s the foll owing: (I) 7.2; 20 m M with 5 g/L HSA sus pension (II) 7.2; 20 m M (III) 7.2; 50 m M (IV) 7.2; 75 m M (V) 7.2; 10 0 mM (V I) 7.2; 120 mM (V II) 7.2; 20 m M (VIII) 6.5; 20 mM (I X) 7.6; 2 0 mM ( X) 7.2; 20 m M. St eps I to VII: cons tant pH = 7.2. Step s: VIII t o X: con stan t I = 20 m M. The 5 th over to ne is displ a y ed. At step VIII e xperiments with changing pH star t. Upon changing the pH from 7.2. to 6.5 at constant NaCl concentration, Δf increas es and Δ D decre ases. Th ese ch an ges were at tri buted to brush collapse due to the less pronounced protonation of the carbox y l groups which allows them to f orm mor e O - H bonds. 350 As shown by W elsch, 351 t he pK a of the ca rbox y l groups of acrylic acid poly mers within the brush can increase by two units compared to the one in solution (pK a = 4.2 5). 3 52 This phenomenon, known as the pol y electrol y t e effect, ar ises from the mutual interactions of the ne ighboring charge d residues within the pol y electrolyte brush. 353 Therefore, even a small decrease in pH can result in marked protonation of the brush functional groups. Δf and ΔD shi fts upon subsequent increase of pH in step IX (from 6.5 to 7.6) indicate the exact opposite effec t to the one descr ibed above. Finall y , upon rinsing the QCM cry s tals with starting buffer in step X no Δf ch ange and on l y a small ΔD increas e was obs erved wh i ch in dicat es bru sh swel l ing. Importa ntl y, ther e is no significa nt difference in the Δf v alue b etween t he in iti al and final s tates o f the pH - af fected experiments (steps VII and X, respectivel y ) . It suggests that upon changing the pH the br ush swelling/deswelling wa s observed, rather than protein desorption. 02468 -5 0 5 ∆ D 5 (10 -6 ) Time (hrs) I II III IV V VI VII VIII IX X 02468 -80 -40 0 ∆ f 5 /5 (Hz) I II III IV V VI VII VIII IX X 65 4.5. 3. Inf luenc e of p H on t he S well ing of the PA A Brush To verify whether the br ush response during the pH - change arises from t he additional HSA desorption or mainly f rom the brush swelling / deswelling , the response of a prote in - free P AA brush as a func tion of pH was examined. The outcome of this experiment is pre sented in Figu re 48 . The t ime co urse o f th e ex peri ment is d escrib ed in sect io n 4.5.1. , and was desig ned to en able direct comparison with steps: VII, VIII , IX and X of the protein-a dsorption ex periment. Step A shows the response of th e PAA brush to de crea sing ionic st rength (from 120 to 20 mM) at constant pH of 7.2. The observed Δf decrea se and corresp ondi n g increas e in ΔD were attributed to brush swelling due to a decrea s ed ion concentration in the bulk solution. 74 ,347 Upon changing the pH from 7.2 to 6.5 at constant ionic s trength of 20 mM in step B, the expected collapse of the br ush due to the more pronounced protonation of the carbox y l groups was observed. 350 Decreasin g Δf and i ncreasi n g ΔD in st ep C (upon pH cha nge from 6.5 to 7.6) indicate brush swelling. The carbox y l groups in this s tep are balanced b y counterions to a greater extent than at pH 7.2 due to their increased dissociation driven b y sli ghtly alkaline conditions. As a conse quence the brush is not fully stretched which was conclude by comparison to the Δf and ΔD shifts in steps A a nd C . Preset results com pare w ell with those reported by Liu et al . 349 Figure 48 . pH indu ced resp onse of a protei n - fre e PAA bru sh m onitore d by QCM - D. T op pa nel: Q CM - D normalized frequency shift. Lo w er p anel: QCM - D dissipatio n shift. The QCM crystals were calibrated in buffer solutio n with ionic strengt h of 120 mM and pH of 7.2. Swelling and d eswelling eve nts are ind icated b y capital letters. pH and ion ic strengths cor responding to each step are hi g hlighted by red and blue color, respectively . (A) 7.2; 20 m M (B) 6.5; 20 m M (C) 7.6; 20 m M (D) 7.2; 20 m M. Ste p A: cons tant pH = 7. 2. St eps B, C and D: const a nt I = 20 mM. The 5 th overt one is dis play ed. In ste p D (upon chan ging the pH from 7.6 to 7.2) a strong Δf dec reas e al on g wit h in creasi ng ΔD was observed indicating brush swelling. Such behavior was not observed between steps IX a nd X of the protein - adsorption experiment due to the presence o f bound protein molecules within the PAA brush. The int ernal friction of a sw ellable pol y m er brush can b e co ns ider abl y incr eas ed by protein incorporation as shown b y Bittrich et a l . 347 The following analysis confirms that in the case of the pH changes in the studi es of protein adsorption (see se ction 4.5.2. ) the swelling of protein-complexed PAA brush wa s mainl y observed, r ather than the protein desorption. 0 1 2 3 4 0 5 ∆ D 5 (10 -6 ) Time (hrs) A B C D 0 1 2 3 4 -10 0 10 ∆ f 5 /5 (Hz) A B C D 66 4.5.4. The A mount of A dso rbed P ro tein Determ ined by the I o nic Stren gth The S auerbr e y equatio n (see sect ion 3.3.4.2. ) was used to ex tr act th e changes of th e mass density (Δm) of t he brus h at each step of th e ex periments described above (see Fig ure 49 ) to estimate the amount of HSA adsor bed per PAA chain. The obse rved brush response in steps VIII, IX and X corresponds to the swelling/deswell ing of the PAA brush induced b y ch anging pH. The calcul ated value s of Δ m upon i onic strength - and pH - chan ges as w ell as the Δ m val ues upon pH induced swelling of a p rotein - free brush are presented in T ab les 6 , 7 and 8 , respect ivel y. Figure 49 . Top panel: cal culated ch anges of t he m ass density upon ionic s tren gth and pH in duced response of pro tein - complexed PAA brush deriv ed from t he Sauerbrey equation. An al y zed steps are indicated by Ro m a n num erals. pH and ion ic strengt hs corresponding to each step are highlighted by red and blue color, respectively . (I) 7.2; 20 m M with 5 g /L HSA suspens ion (II) 7.2; 20 m M (III) 7.2; 5 0 m M (IV) 7.2; 75 m M (V) 7.2; 100 m M (VI) 7.2; 120 m M (VII) 7.2; 20 mM (VIII) 6.5; 20 m M (IX) 7.6; 20 m M (X ) 7.2; 20 mM. Ste ps I t o VII: c onstant pH = 7.2. S teps: V III to X : con stant I = 20 mM. Lowe r panel: cal culated m a ss de nsi t y upon pH induce d response of prot ein - free PAA brush deriv ed from th e Sa uerbre y eq uation . Analyzed steps are in d icated by capital lett ers. The QC M cryst als were ca libr ated i n buff er solut ion with ionic str ength of 120 mM and pH of 7.2. pH an d ionic str engt hs corres pondi ng t o each step are highlight ed b y red and blu e color, res pectiv ely. (A) 7.2; 20 m M (B) 6.5; 20 m M (C) 7.6; 20 m M (D) 7. 2; 20 m M. St ep A: c onst ant p H = 7.2. St eps B, C and D: c onstant I = 20 m M. 0 1 2 3 4 -20 0 20 40 Time (hrs) ∆ m (5 th overtone) (Da/A 2 ) Time (hrs) A B C D 02468 0 200 400 I II III IV V VI VII VIII IX X 67 Tab le 6. Calcula ted value s of chan ge s of the mas s d ensi t y (Δ m) upo n incr eas in g ioni c st re ngt h ( IS ). Ro man numerals refer to the steps described in th e paragraph. Ion ic stren gth in crease pH I ( mM) Mass density (Da/A 2 ) St ep I 7.2 20 372 S t ep II – initial sta te of the IS - incre ase 7.2 20 353 S t ep II I 7.2 50 297 S t e p IV 7.2 75 256 St ep V 7.2 100 239 St ep V I 7.2 120 217 S t ep V I I – fi nal st ate o f t he I S - i ncre ase 7.2 20 235 Tab le 7. C alculated values of changes of t he m ass d ensity (Δ m ) upon changin g pH. Roman numerals refer to the steps described in t he paragraph. pH cha nge pH I ( mM) Mass density (Da/A 2 ) S t ep V I I – initial state o f the pH - change 7.2 20 235 Step VIII 6.5 20 196 S t e p IX 7.6 20 220 St ep X – final sta te of th e pH - chang e 7.2 20 220 Tab le 8. C alculated values of changes of the mass density ( Δ m ) upon pH induced swelling of a protein - free PAA brush. C ap ital letters refer to the st eps described in the paragraph. pH - indu ced p rotein f ree PAA bru sh sw ell in g pH I ( mM) Mass density (Da/A 2 ) St ep A 7.2 20 33 St ep B 6.6 20 -16 St ep C 7.6 20 1 St ep D 7.2 20 30 The chan ges of the m ass den sit y bet ween each ste p of t he pH - in fluen ce ex peri ment (se e Fi gure 49: Top panel) compared well to the changes of the mass densit y b etween analogous steps of the pH induced swelling of the protein - free PAA b rush (see Figure 43: Lower panel), indicating that protein desorption d uring the pH - change is m arginal. Consequently, during the pH - chan ge only the swelling of the protein - complexed brush was observed. From t he difference in the changes of the mass densit y recorded upon swell ing of the protein - fre e bru sh ( Ta bl e 6 ) th e effect of the c oupled solvent in the ex periments can be e stimate. The larg est Δ f sh ift can be observed between steps A and B thus t he coupled solvent c an be expressed as ± 49 Da/A 2 . In 68 this way the obta ined results can be corr ected to determine with grea ter accurac y the amount of HSA adsorbed per PAA chain and lost du ring inc rease of the ionic streng th. The difference in Δ m be tween the initial and the final step s of inc reasing ionic str ength (step s II and VII in Table 6) is of a bout 118 ± 49 Da/A 2 . This ref lects the amount of desor bed HSA, and thus highlig hts the major influence of counterions in the process of poly electrol yte mediated protein adsorption / desorption. 1 75, 354,3 55 The re maining 220 ± 49 Da/ A 2 can th erefo re be a ttribute d to the H SA molecule s that a re attac h ed to the PA A brus h with higher affinity than the proteins desorbe d during the increa se of the ionic strength. This mig ht indicate the existence of two fractions of HSA molecules within the PAA brush: those with hig h - and low binding affini t y (see F i gure 50 ). The pres en ce of hi gh - and low binding affinity sites for proteins within a PE brush was previously observed for β - Lactoglobulin ( B LG ) binding onto SPBs and discussed in section 4.4.3. 80 H ere, due to the planar geometr y of the PE brush, the pr esence of high - and low bindin g affinity si tes can be attri buted to pol y dispersity of brush chains. While, high graftin g density occurs close t o t he su rfa ce, th e ch ain s egment de nsi t y d ec reas es to wards t he distal end of the brush as presented in Figure 50. Figure 50 . Sch e m atic il lustra tion of HSA mol ecule s ads orbed onto PA A brus h wit h th e high - an d lo w bin ding af fin ity . The presence of a HSA f raction with low binding affinit y indi cates that thi s phenomenon is an ex ampl e of a negativ e co operat ivi t y . The refo re hi gh - and low binding affinit y ma y reflect the differe nce i n protein adsorption ont o free - and al read y preo ccup ied p ol yelect rol y t e chain s. A similar result was observe d in the case of HSA adsor ption onto PAA - based SP Bs (see s ectio n 4.4.3. ). 4.5.4.1. Number of HSA Molecules per PAA Chain Fro m the c hange of the mass density at Step II (the initial state of the incr easing ionic stre ngth) with correc tion for the effect of coupled solvent and from the molecular weight of H SA (see secti on 3.2.2. ) the number of HSA molecules per nm 2 can be det erm ine (s ee Tab le 9 ). Comparing this number to the inverse grafting densit y σ -1 = 2.9 ± 0.5 nm 2 of PAA brush allows to estima te the amount of HSA initially adsor bed per PA A chain. 69 Tab le 9. The calcu lated numb er of HSA m olecules adsorbed per po ly elec trol yte chain. Con sid ered s tep ∆ m (D a / A 2 ) HSA/nm 2 a N p/c b S t ep II 353 ± 49 0.53 ± 0.07 1.5 ± 0.2 St ep X 220 ± 49 0.33 ± 0.07 0.9 ± 0.2 a) N um ber of prot ein mole cules per nm 2 . b) Num ber of protein molecules p er polyelect r olyte chain. In th e s ame w a y it can be verif y that at Step X (the final state of pH - change) approxim ately one HSA m olecu le is adso rb ed per on e PAA chai n (s ee Tabl e 9 ) – th e evalu at ion of th ese dat a are presented in the suppor ting material. Therefore approx imately 40% of initiall y adso rbed HSA molecules are desorbed during the increase of the ionic strength. These numbers are consistent with results reported b y Yu et al . 52 and agree also with work of Wittemann et al. in which bovine serum albumin ( BSA ) mole c ules we re r eleased fro m P AA - based SPBs by washing them off with solution of higher ionic strength. 32 The y reduced the number of attac hed BSA mol ecules fr om two per PAA chain to about one per two PAA chains. In w ork of HSA adsorption onto SPBs (see section 4.4.3.1. ) the influ enc e of ionic strength on the binding was also v erified. With increasing salt con centration the repulsion between investigated protein and PE brush become operative thus suppressing the adsorption process. 4.5.5. Conclusion Pres ent st ud y demonst rat es a successful ARGET ATRP pol y meriz ation of PAA brushes gra fted from a planar gold surfa ce of QCM cr ystals. The adsorption of HSA onto and the desorption from PAA brush as a function of ionic strength and pH was investigated b y QCM - D. Conformational change s of the PAA brush were obser ved and used to cor rect the va lues measured f or HSA adsorpti on. By r eleasing a part of initiall y adsorbed protein molecules upon increasing salt concentration we demonstra ted the dominant role of counterions in the process of polye lectrol yte me diated protein adsorption / desorption. B y comparison wit h the results of rec ent calorimetr ic studie s on the prote in inter action with po l y electroly tes 52 along with t he result s of S PB - HSA inter action discussed in section 4.4. ,this study present a new approach in which QCM data are anal y z ed based on the results of thermody namic studies. Finally , it can be conclu de that QCM crystals modified throug h p resente d method based on ARGET ATRP reaction are full y functional. A comparison with large nu mber of other brush sys tems inte racting with prote ins 3 2,52 ,73,1 73 l ead to a full agreement in the number of adsorbed protein molecules per pol y ele ctrol y te ch ain at low and hi gh ionic strength. Thus, the present findings extend the understanding of interaction between protein and pol y e lectroly te brush b y comparison of systematic studi es of protein adsorption / desorption driv en b y incr eased salt concentration with calorimetric studies of the same problem. 70 5. Sum m a ry and Outlook The studies presented in this t hesis are f ocused at the understanding of the mechanism and the underly ing driving forces upon pol ye l ectrolyte - prot ein (P E - P) interaction. The combination of experimental techniques and theoretical approach enables insight into the binding process b y combinin g ther mody namics with struc tural in formation. PEs emp l oyed in this work such as lin ear - , low molecular weight - , dendritic - , and brush - like PEs offer s a matrix that include s differen t st ruct ural featu res e.g. flexibilit y and surface area for bi nding with proteins. The adsor ption studie s were s y stematically performed using s alt conce ntratio n c s , tem pe ratur e T , and pH as th e main variables allo wing a d etaile d t hermody namic analy sis. o The f irst investiga ted PE is a highl y char ged, dendritic pol y gl y c erol sulphate (dPGS). To explore counterion condensation to dPGS , the ion specific effects and the competitive adsorption betwee n mono - and divale nt counterions, the isothermal titration calori metr y (ITC) an d th eo retica l app roach based on the non - linear penetrable Poisson- Boltz man n (P PB) mo del are empl o y e d. The calor im etri c measu rem ents sho w that the ion- specific effects upon binding of Mg 2+ and Ca 2+ ions to dPGS are marg inal. The overall number of Mg 2+ ions adsorbe d per dPGS molecule obtained b y ITC experiment stands in a very god agreement with theore t ical predictions of the PPB model. Since PP B model giv es a rel at ivel y accu rate pi cture o f th e dPG S - counter ion electrostatic binding affinity, the r ep ort ed appro ach is envi sioned to become applied in t he future anal y sis of counterion condensation and interactions between various different P Es and proteins. o In the second part, ITC is used to investiga t e interaction of l y soz yme ( L ys ) with linea r and low molec ular weig ht PEs: heparin (Hep) and β - CD - S, respecti vely. The depend en ce on temp erat u re in case of Lys - Hep i nterac tion allows to dissect the binding free en erg y ∆ G b int o the respect ive en th alp ies ∆ H b and entropies ∆ S b tog et her with the speci fic h eat c apa cit y ∆ C p . A strong enthalpy - entro py canc ell ati on (EEC ) w as ob serv ed. The binding free energ y ∆ G b could be dissected into a part ∆ G ci due to counterion release and a res idual p art ∆ G res . The dependence on salt concentration c s i n β - CD - S inter action with Lys lea d to the net n umber of released counterions ∆ n ci and K b (1 M ). Th e in teracti on between Lys and β - CD - S should be extended in order to verif y the dependence on temp eratur e in the sam e m anner as i n th e cas e of Lys -H ep bindin g. The i n teracti on o f L ys with β - CD - S may be then directly compared to the Ly s - Hep binding as well as to the wel l - studied bindin g of proteins to DNA. Th e reported approach is en visioned to become a pplied in the future ana l ysis of inter actions betwee n various different GAGs and signaling proteins (cytokines, chemokines, growth fac tors), pavin g the way for the fabrication of GAG - based pol y mer h y d rogel networks with rationally desi gned protein binding characteristics. It may also become applied in the future fabrication of pol y me r dru gs wi t h enhanced solubili ty . o In the third part, ITC and quar tz crysta l microbalanc e with dissipa tion monitor ing ( QCM -D) are used to investigate adsorption of human serum albumin (H SA) to pol y(acr ylic acid) ( PAA ) - based P E b rus hes. Calo ri met ric meas u rement s sho w that HSA adsorption onto spher i cal pol yelectr ol yte b rush es ( SPBs ) is a two - step pr ocess. The therm od ynami c anal y s is reve al t hat t he count eri on r eleas e en trop y is th e mai n contribution to the binding free energ y ( Δ G b ). ITC measurements, performed over a range of temperatures bet ween 25 a nd 37°C show a strong temperature dependence of the c alorime tric entha lp y ( Δ H ITC ) alo ng with a nearl y temp erat ure - inv ari an t Δ G b . As 71 well as for t he in teracti on bet ween Lys and Hep, t his sy st em ex hib its a marked E EC. The performed anal y sis thus allows a s ystematic comparison of the present results with Hep - Ly s int eraction along with a large set of data from other s yste ms. Such comparison demo nstr ates t hat a s tron g EEC is a general featu re occu rri ng in s ystems in wh ich t he binding is dominated by counterion release. o Prior to investigate HSA adsorption to plan ar PE brush an ARGET ATR P polymerization of PAA brushes grafted from a planar gold surface of QCM cr ystals wa s employe d. The adsorption of HSA onto and the desorption from P AA brush as a function of ionic streng t h and pH was then investiga t ed b y QCM - D. Conformational cha n ge s of the PAA brush wer e observe d and used to correct the va l ues measure d for HSA adsorption. B y rel easing a part of initially adsorbed protein molecules upon increasing salt concentration, the dominant role of c ounterions in the process of polyelectroly t e mediated protein adsorption / desorption is de m onstarte. By comparison with the results of calor imetric studie s on the HSA - SPB interaction, this stud y present a new app roach in which QC M dat a are an al yzed b as ed on th e res ult s of t h erm od ynamic studies. Thus, the present findings extend the understandin g of interaction between protein and PE brush by comp arison of s y ste matic studies of protein adsorption / desor ption dr iven b y incr ease d salt concen tration with calo rimetr ic studies of the same problem. In conclusion, this thesis provides a deeper insi ght into the PE - P int erac tion. In particular, a combination of experimental methods with theor y have been applied to identif y the mechanism and the thermodynamic driving f orces of protein binding. Moreover, an important contribution to a more complete understanding of PE st ructure along with counterion - condensation and rele as e upon binding w ith proteins is ma de which is essentia l for many biomedica l applicatio n. It d emon str ates that EEC is a gen eral f eatu re o ccurring in s y stems in which the bin ding is d riven b y co unt eri on rel eas e . 72 6. Materia ls and Methods 6.1. Ma teria ls For the s y nthesis of spherical pol y electrol y t e brushes ( SPBs ) ; the monomers: st y rene, acr y l ic acid (AAc) a nd the initiator potassiu m pero xodisulfa te (KPS) as w ell as the emulsifie r sodium dodecyl sulfate (SDS) were purchased form Sigm a - Aldrich . St yrene con tai ns a s mall amou nt of 4 - tert - butylc atechol as sta bilizer to pr event from autopolimerisation. The refore for the purpose of poly m erization reaction styrene was destabilized by flushin g over a column filled with inhibito r remov er ( Sigma - Aldrich). AAc was distilled under reduc ed pressure (1 mbar, 40- 45°C) in a rotar y evaporator to remove the stabili zer hydr oquinone monometh y l ether. The cleaned mono mers w ere st ored at - 4°C. KPS a nd S DS as well a s photoiniciator 2- [p - (2 - hydroxy- 2-methylpropiop henone) ] - ethyl ene gl ycol - meth acryl ate (HMEM) f or the s y nthesis of core - shell pa rticl es w ere u sed as r ecei ved. For the synthesis of pl anar po l yelect rol y te b ru shes ( PPBs ) ; the tert - b ut yl acr y l ate ( t BA ) mon omer as well as the cat al yst: Cu Br 2 ; the complexing liga nd: N,N,N’,N’,N”- Pentame th y ldieth y lene triamine (PMD ETA) ; red ucing ag ent: L- asco rbic aci d; aceto ne; s odi um dodecyl sulfate (SDS); and trifuoroacetic acid were purchased from Sigma - Aldrich. Anh y drous dichloromethane was purchased from Merck. The surface bond initiator Bis[2 - (2 - bromoisobut y r yloxy)undecyl]disulfide (DTBU ) was synthesized according to the published procedure. 77 t B A contains a small amount of mon ometh y l ether h y d roquin one as inhibitor to prevent fr om autopolimerisation. Therefore for the purpose of polymerization reaction t BA wa s destabilized by flushing over a column filled with ac tivated basic aluminum oxide ( Al 2 O 3 from Sigma - Aldr ich). All other substra tes wer e used as receiv ed . Gol d QCM sen so rs were purch as ed from QSense and c lean p rior t o us e (se e secti on 4. 5.1.1. ). The buffer components: 3 - (N -morpholino)propane sulfo nic a cid (MOP S) was re ceiv ed from Sigma - Aldrich and used direc tl y . Sodium phospha te dibasic (Na 2 HPO 4 ) a nd sodium phosphate monobasic (NaH 2 PO 4 ) we re purchased from Fluka and used without further purifica tion. 6.2. Pro tein s and Bu ffer s Human serum albumin (HSA) and ly soz yme (Ly s ) were used in this wor k to stud y the intera ctions with heparin, β - CD - S, SPBs and PPBs . Essential details about used proteins are listed in Table 10 . Tab le 10. Overvie w of pr o tei ns used in t hi s st ud y. Protei n Origin Suppli er Cat. - No. LOT. - No. Pu ri ty Human Serum Albumin Human serum Sigma - Aldr ich A3782 S L BT8667 ≥ 99% L ys o z ym e Chicken egg- white Sigma - Aldr ich L6876 S L BZ2146 ≥ 90% The proteins listed above were received as l y ophil ized powders containing low amount of additional impurities. These proteins were used in binding studies with SPBs and dendr itic polygl y cerol sulfate ( dP GS ) without further purifica tion. Two buffer s y s tems were use d in presented studies: 10 mM MOPS buffer pH 7.2 and 10 mM phosphate buffer pH 7.4. The 73 MOPS buffer was pr epared by dissolving 10 mM 3 - (N - morpholino) propane sulfonic ac id (MOPS) in w ater (Millipo re Milli - Q). For the phosphate buffer; sodium phosphate dibasic (8 mM; Na 2 HPO 4 ) and sodi um phos phate monobasic (2.8 mM; NaH 2 PO 4 ) were d iss olv ed in water (Millipor e Milli - Q) . The ionic strength of the buffers was adjusted b y addi tion of a proper amount of sodium chloride (Na Cl). The pH w as very care f ull y adjust ed by drop wise addition of 1 M sodium hydrox ide (NaOH) w ith consideration of temperature - dependent acid dissociation of MOPS. 6.3. S ynth esi s and C harac ter izat ion of SPBs 6.3.1. Synthesis of Polys tyrene (PS) Core Latex The s y nthesis of PS cor e particles with a thin la yer of photoinitiator (HME M) on their surf ace was accomplished b y co nventional emulsion poly merization usi ng a 2 L three - necked glas s reacto r whi ch was heat e d t hrough a t hermostat and equipped with thermometer, stirrer and reflux condenser. The s ynthesis wa s carried out as foll ows, 208.3 g (2. 0 mo l) of f reshl y puri fied styre ne was added to a continuously stirred (at 320 rpm) solution consisting of 2.1 g (0. 0073 mol) of SDS emulsifier in 700 ml of water. B y s everal vacuum/nitrogen purge c y cl es the whole mixture was deoxyge nat ed and gradually brought to the temperature of 80°C under nitrogen atmosphere. The pol y me rization process was initiated b y addition of 0. 44 g (0. 0016 mol) of KPS initiator dissolved in 125 ml of wate r. After 1h of stirring at 80°C the turbid suspension was cooled to 70°C. To c over the PS cor e particles with a thin la ye r of photoinitiator a solution of 5.34 g (0.0 144 mol) of HMEM dissolved in 6.0 ml (0. 0816 mol) o f aceto ne w as added dropwise (0.19 ml/min) to the suspension. HMEM was adde d under starved conditions to achiev e a wel l - defined core - brush morpholog y . The reactor was shielded from light and the reac tion was continued for a further 1h. Prior to t he grafting of the brushe s all PS - co - HMEM latex wa s filtra ted ( after cooling to 40°C) by dia l y sis ag ainst water. Tab le 11. Weight po rt io ns of t he ed ucts use d fo r s ynthe si s o f PS co re s. PS - co - HME M m(st yrene) [g] 208.30 m(SDS ) [ g] 2.10 m(K PS) [g] 0.44 m(H 2 O) [ g] 825 m(HMEM ) [g] 5.34 weight percentage (in % w/w) 18.55 hy drod y namic ra dius a R h,core [ n m] 57. 5 a Before mo dify ing t he PS c ore late x by HM EM p hotoiniti at or a small sample of PS core l atex was taken f or th e purpos e of R h,core measure men ts. 74 6.3.2. Synthesis of Core- Brush Parti cles The brush of the SPB - PAA was pol ymerized onto PS - co - HMEM late x as follow s: Given amounts of a PS core latex modified with a thin l a y e r of HMEM (see Table 12 ) were d ilu ted with wa ter to ~2. 5 wt% and char ged in a UV rea ct or ( TQ 150; Heraeus, 650 cm 3 vol ume, r ang e of wavelength 200 -600 nm ). After addition of destabiliz ed monomer the whole r eactor was degassed by repeated evacuation and subseque nt additi on of nitroge n. The amounts of used monom ers wer e cho s en t o ob tain a well - defined brush as well as to avoid aggregation of particles during pol y m eriz ation process. Photopol y m erization was done b y use of UV/vis radiat ion at a temp erat u re of 25 o C . Vi gor ous st irring (at 400 rpm) ens ured homogeneous conditions during the photopol y m erization. Small samples were dr awn repeatedly to follow the extent of reaction. After 1h of irr adiation the UV/vis lap was switched off and the photopol y merization ended. The latex was purifie d ex haustively b y serum replacement using pure wat er u nti l th e cond uct ance o f th e eluat e d id no t chan ge an ymor e. Tab le 12. Weight po rt io ns of t he ed ucts use d fo r s ynthe si s o f SP Bs . S PB - PA A m(PS - co - HMEM) a [g ] 106.0 m(PS - co - HMEM) b [g ] 19.6 m(H 2 O) [ g] 600.0 m(AAc) [ g] 5.8 a latex, b solid 6.3.3. Purification of SPB Part icles SPB particles were purif ied b y ul trafiltration in order to remove unreac ted monomers, dissolved poly mers and s urfactant molec ules f rom partic les dispers ion. Ultr afiltr ation was car ri ed out in serum repl acem ent c ell s wh ich con tai n cel lul ose ni trat e memb ran e. Fo r t he purp ose of S PB s purification membrane s with pore size of 100 nm were chosen. The serum was replaced against wate r (Milli - Q) under ov erpres su re of nit rogen (1 . 2 bar) until the conductivity o f el uate h ad reac hed the conductivit y of pure water (κ < 1 µS). 75 Figu re 51. Schem atic rep resentation o f an ultra filtratio n cell. Afte r purific ation the mole cula r weight of SPB particles M w, SPB was calcu lat ed b y t he us e of the fo llowing formula: 𝑀𝑀 𝑤𝑤 , 𝑆𝑆𝑃𝑃𝐵𝐵 = ( 𝑚𝑚 𝑐𝑐𝑡𝑡𝑐𝑐𝑒𝑒 + 𝑚𝑚 𝑏𝑏 𝑐𝑐𝑏𝑏𝑠𝑠 ℎ ) 𝑁𝑁 𝐴𝐴 = 𝜌𝜌 𝑐𝑐𝑐𝑐𝑟𝑟𝑟𝑟 4 3 𝜋𝜋𝑅𝑅 ℎ 3 , 𝑐𝑐𝑐𝑐𝑟𝑟𝑟𝑟 𝑤𝑤 𝑐𝑐𝑐𝑐 𝑟𝑟𝑟𝑟 𝑁𝑁 𝐴𝐴 (56 ) Becaus e of th e m ass b alance of S P Bs dis persi on before and afte r ult rafil t rati on th e mass of monomers unpolymerized into the brush can be determined and so the mass fraction of the core can be calcul at ed vi a 𝑤𝑤 𝑐𝑐𝑡𝑡 𝑐𝑐𝑒𝑒 = 𝑚𝑚 𝑐𝑐𝑡𝑡𝑐𝑐𝑒𝑒 /( 𝑚𝑚 𝑏𝑏𝑐𝑐𝑏𝑏 𝑠𝑠 ℎ + 𝑚𝑚 𝑐𝑐𝑡𝑡𝑐𝑐𝑒𝑒 ) . The ρ core and R h,cor e denotes, respect ivel y, t he den sit y of th e PS core (ρ core = 1. 055 x 10 - 21 g nm -3 ) and the hydr od y n amic radiu s of t he PS core d eter min ed b y DLS. Tab le 13. The respectiv e values of molecular weight and size of SPB p articles. AAc a [%] w core Mw [g mol -1 ] R h,core [n m] L c [n m] SPB - PAA 40 0.909 5.56 x 10 8 57.5 231 a amount of AAc adde d for pol ymer izat ion (mol ar per cent of s tyrene) 6.3.4. Dynamic Light Scattering (DLS) Part icle s iz e can be det er min ed b y the meas ur em ent o f tim e - dependent fluctuations in the intensit y of the scattere d light from a suspensi on or solution. This te chnique is known as Dynam ic Li ght Scatt eri ng (DLS), a.k.a. Quasi - Elastic L i gh t Scattering (Q ELS) . B rownian motions of the macromolecules in solution imparts a randomness to th e phase of scattered li ght, as li ght scat ters f rom t he mov ing macro mol ecul es. Th erefor e when t he scat t ered l ight fro m two or mo re parti cles i s add ed to gether, t here w ill occur a co nst ructi ve or d estru ctiv e int erferen ce leading to the random changes in the intensit y of scattered light. Those ran dom changes in the intensit y are directl y related with the rate of the molec ul e diffusion through the solvent, which in turn is r elated to the h y d rod y n amic r adii of the partic les. The D LS meas ur ement s were p erfo rmed b y usin g a com pact A LV/CGS - 3 instrument, which is equipped with a He- Ne laser (wavelength of λ = 632. 8 nm ). This instrument allows to perform 76 simultane ousl y , d yna mic and sta tic light s catter i ng ex peri ment s. P seud o cross corr el atio n function are received b y using an A LV 5000/E multiple - τ co rrelato r. Th e setu p permi ts to measu re at an gle ran gin g from 17 ° to 150° , th erefore cover in g a scatt eri ng vector r an ge of 0.0039 – 0.0256 nm -1 . T he temperature of the samples was controlled using a tempered bath containing toluene as index matching substance. All measurements performed on this instrument were done at a sc attering angle of 90° and at temperature of 29 8 K. For the pu rpos e of those me asurem ents S PBs as w ell as PS - cores were dispersed in buf fer sol ution (see section 1.2), therefore there were diluted to a concentration of 0. 01 g / L. All samples w ere filte red throug h a syr inge filter (polye th e rsulfone (PES) membrane with 1.2 µm por e width) in order to avoid the prese nce of dust. To obtain thermal equilibr ium, before the mea s urement, all samples were i ncub ate d at th e des ired t emp erat ur e fo r 5 min utes . Fo r each ex peri ment a s et o f 3 measu rement s w as perfo r med and ea ch on e of it co nsi sts o f 10 single runs. The DL S data were anal y zed with the software AfterALV to obtain the hydrodynamic radius of measured particles . The fluctuations in the scattered light are quantifie d via second order c orrelation function: 𝑔𝑔 ( 2 ) ( 𝜏𝜏 ) = <𝐼𝐼 ( 𝑡𝑡 ) 𝐼𝐼 ( 𝑡𝑡 +𝜏𝜏 ) > <𝐼𝐼 ( 𝑡𝑡 ) > 2 (57 ) where I (t ) refer s to the intensity of the scatter ed light a t time t , an d the bracket s den otes avera ging over all t . The correlation function depends on the d ela y τ , which is the a mount th at a duplic ate intensity tra ce is shifte d from the orig inal one before the averagin g is performed. The correlation func tion for a monodisperse sample can be analy z ed by the equation: 𝑔𝑔 ( 2 ) ( 𝜏𝜏 ) = 𝐵𝐵 + 𝛽𝛽 exp ( − 2 𝛤𝛤𝜏𝜏 ) (58 ) where B refers to the baseline of the correlation function at infinite de lay , β repr es ents the corre lation function at z ero dela y an d Γ denotes th e deca y rat e. In order to obtain the correlation function deca y rate Γ , the measured correlation fun ction is fitted to equ at ion (58 ) by a nonlinear squar es fittin g a l gorith m. From this poin t, Γ ca n be c onverted to the diffusion constant D for the pa rticle via the relation: 𝐷𝐷 = 𝛤𝛤 𝑞𝑞 2 (59 ) Here, q is the ma gnitude of the scatter ing vector, a nd is given b y : 𝑞𝑞 = 4𝜋𝜋 𝑛𝑛 𝑐𝑐 𝜆𝜆 𝑐𝑐 sin ( 𝜃𝜃 2 ) (60 ) where n o is the solvent index of refraction, λ o is t he vacuum wavelength of the incident light and θ is the scattering angle. Finall y , the dif fusion constant can be interprete d as the hydrodynamic ra dius R h of a diffusin g sphere via Stokes-Einstein equation: 𝑅𝑅 ℎ = 𝑘𝑘 𝐵𝐵 𝑇𝑇 6 𝜋𝜋𝜂𝜂𝜋𝜋 (61 ) Wh ere, k B is Boltzman’s constant, T is t he tem peratu re in K an d η is the solvent visc osity . 77 6.3.5. Conductometric and Potentiometr ic Titration Conducto metric and Potentiometr ic titration me as urements we re perfor me d simultan eously b y using Mettler Toledo SevenCompactTM pH/Ionnmeter S220 and a conductometer WTW Cond 197i. For this titration experiment, the SPB dispersion was diluted with water to a total concentration of 0.5 wt %. Then, 30 mL of the SPB suspension were titrated with 0.01 M NaOH. The titration were run i n a thoroughl y cl eaned 50 m L beaker fitted with the pH and the conductivity electrode. The NaOH solution was sl owly added to the SPB dispersion with a rate of 0.1 mL/min. The conductometr ic and potentiometric titration curve s of SPB are show n in Figure 52. The amount of acr y li c acid polymer ized into the brus h of SPB particles was determined from the equivalent point of both titration curves. 048 12 16 20 24 28 2 4 6 8 10 12 V NaOH (mL) pH 0,0 0,2 0,4 0,6 0,8 1,0 Conductivity (mS cm -1 ) Figu re 52. Conductometric and po tentiometric titratio n curv es of SPB in millipo re w a ter. In addition, the dissociation degree α diss of the carb ox y li c aci d fun ctio nal gro ups w as calcu lated as a func tion of the amou nt of added NaOH and thus, as a function of the pH acco rdi ng to: α diss = [ 𝑉𝑉 ] 𝑝𝑝𝑝𝑝 [ 𝑉𝑉 ] 𝑟𝑟𝑒𝑒 (62 ) Wh ere [ V] pH and [ V] eq are the vo lum e o f ad ded Na OH at a giv en pH value and at the equivalent point, respectively . To c alculate the apparent pK a value of the c arbox ylic acid functional groups as a func tion of dissociati on degree , t he followin g equation was used: pK a = pH – log ( 𝛼𝛼 𝑑𝑑𝑐𝑐𝑠𝑠𝑠𝑠 1−𝛼𝛼 𝑑𝑑𝑐𝑐𝑠𝑠 𝑠𝑠 ) (63 ) 78 6.3.6. Determination of the Molec u lar Weight of the Tethere d Polye lectrolyte Chains The grafted PAA chai ns were cle aved o ff f rom the P S core p arti cles d ue to the fa ct t hat t he ester bond of the photoinitiator ca n be hy drol y z ed in alkaline conditions. In order to do so, a sample of purified SPB latex was heated to 97°C in 2.0 M aqueous NaOH for 17 d a y s. S uch a treatm ent i s neces sar y si nce ne gativ e coion s su ch as t he h y drox i de ion s are repel led f rom anionic brushes. 356 Due to the loss of the steric sta bilization b y PAA chains the latex coag ul ated. The amount of the PAA chains in the s upernatant serum was calculated due to the info rmations obtained from the c onducto metric an d p otentiome tric tit rati on ex peri ment (se e s ectio n 6.3 .5. ). The kinematic visc o s i t y [ u ] o f PAA chains was m easured b y us i ng a Laud a iV isc Vi scos imet er Versi on 1 .01 with Mikr o -Ubblohde capillary i n 2.0 M NaOH at 25°C. Tab le 14. T he kinematic viscosit y [ u ] and the de nsit y [ d ] o f PA A chai ns so luti o n and 2 . 0 M aqueo us N aOH (solute). u [nm 2 /s] d [g/ cm 3 ] PAA in 2 .0M NaOH a 1.34982 1.07870 2.0 M NaOH b 1.24401 1.07253 a, b measur ements w ere per formed at 25°C Toge ther with the kinem atic viscosity of the solvent and with the measured densities of both solute and solvent the intrinsic viscosity [ η ] was d etermi ned. The vi scos it y avera ge mol ecul ar weig ht ( Mη ) of th e PAA chai ns w as calcul at ed acco rdin g to the M ark - Houwink relation ( K = 4.22 x 10 -2 m L/ g , α = 0,6 4) 357 [η ] = KM α (64 ) The deter mination of the molec ular weight Mη tog ether with the known amount of PAA on the surfac e all ows t he calcu lati on o f t he graft in g dens it y ( σ ) via: 𝜎𝜎 = 𝑤𝑤𝑝𝑝 % 𝑏𝑏𝑟𝑟𝑏𝑏𝑠𝑠 ℎ 𝑤𝑤𝑝𝑝 % 𝑐𝑐𝑐𝑐 𝑟𝑟𝑟𝑟 𝜌𝜌 𝑐𝑐𝑐𝑐𝑟𝑟𝑟𝑟 4 3 𝜋𝜋𝑅𝑅 ℎ 3 , 𝑐𝑐𝑐𝑐𝑟𝑟𝑟𝑟 𝑀𝑀 𝜂𝜂 4𝜋𝜋 𝑅𝑅 ℎ 2 , 𝑐𝑐𝑐𝑐𝑟𝑟𝑟𝑟 𝑁𝑁 𝐴𝐴 (65 ) In order to prove a brush structure, the aver a ge dist ance ( D ) between neighboring grafted points of polymer chains should be smaller than two times of the gy ration radius ( R g ) of a free pol ymer chain ( D < 2 R g ), which can be calculated via through: 𝑅𝑅 𝑔𝑔 = � 3𝑀𝑀 𝜂𝜂 [ 𝜂𝜂 ] 10 𝜋𝜋𝑁𝑁 𝐴𝐴 � 1 3 (66 ) 79 Tab le 15. The respectiv e values of the structural param eters of synthesized s pherical PAA br ush . initiator I a (%) AAc b [%] Mη [g mol -1 ] σ [n m -2 ] R g [n m] D [nm] SPB - PAA HMEM 0.8 14 96000 0.013 9.97 8.77 a amount of photoi niti ator (m olar perc ent of styrene) . b amount of AAc mon omer polyme riz ed into brus h (molar percent of styrene) 6.3.7. Cryogenic Transm i ssion Electron Microscopy (Cryo- TEM) Cryoge nic Transmission Electron Microscop y wa s perfor med on a J EOL J EM -2100 transmission electron mic roscope (JEO L GmbH, Eching, Germany). T he Cr y o - TE M sam ples were prepared by placing a 4 µL drop of SPB dispersion on a lace y ca rbon - coated co pp er TEM grid ( 200 mesh, Electron Microscop y Sciences, Hatfield, PA), and frozen in liquid ethane at its free zin g point with an FEI vitrobot Mark IV with setting condition of: 4 °C and 95% humidity. All grids befo re ex p eri ment were pr etreat ed b y gl ow - dischar ged and inserted into the microscope holder (Gatan 914, Gatan, Munich, German y ). Examination of samples was carried out at tem peratu re o f 90 K. Th e TEM w as op erat ed at an a ccel erati on vo ltag e of 200 kV. T he C r yo - TEM micrographs were recor ded at a number of mag nifications with a bottom -mount ed 4*4k CMO S camer a (Te mC am -F416, TVIPS, Gauting, German y ). T h e C r yo - TEM ima ge of S P B’s is shown in Figure 53 . Figu re 53. Cr yo - TEM imag e of a 0.1 w t% of SPB particl es s uspens io n i n MOPS bu ffer s oluti on. 80 6.4. S ynth esi s and C harac ter izat ion of PPBs 6.4.1. Immobilization of DTBU Initiator on the Surf ace of QCM Cryst als The functionaliza tion of the surface of QCM crystals w ith DTBU in itiator was ca rried out as follows; QCM crysta ls were thoroughl y cleaned b y rinsin g them with 1% SDS solution, D I water, and ethanol and b y soni cating them for 5 minut es in each of the subst rates mentioned above. Each sonication was performed at constant temperature of 50°C. In the final step of the cleaning procedure the QCM crystals were dried under nitrogen and exposed to air plasma (Ha rric Plasma C leaner ) for 2 minu tes to activa te their s urfac e. Right aft er cleani ng th e QCM crystals were immersed for 24 h at room tempe rature in solution containing 35 mL of ethanol and 80 µL of DTBU init iator. 6.4.2. ARGET ATRP Polymerization of poly( ter t -butyl acrylate) (P t BA) The polymerization of P t BA brush on the surface of gold QCM cr ystals bearing a thin layer of DTB U initiator w as accomplished tow ards surface initiate d “graf ting from” method with activ ator r e generat ed b y electr on trans fer (AR G ET) ato m tr ans fer radi c al pol ymeri z atio n (ARGET ATRP ) . The reaction was performed according to the following procedure: 12.0 m L (82. 7 mmol ) of freshl y p uri fied t ert - but yl acrylate monomer was added to a 100 m L glass flask that cont ai ned the solution of ac etone (35.0 mL ; 0.48 mol), CuBr 2 (67.1 m g; 0.30 mmol) and PM DETA (64.7 µL ; 0.3 1 mmol). The flask was sealed with rubber septum and purge d with nitrogen f or 1 h. Then 0.7 g of a scorbic acid (4.0 mmol) was add to the monome r solution in a glovebox under the argon atmosphere and the w hole mix ture was stirred for 5 min utes until color changed. The Q CM crystals functionalized with DTB U initiator were dried under nitrogen and transferre d to the flask containin g the polymer i zation solution. The pol y merization proceed ed fo r 22 h at roo m t emp erature. Aft erw ard s th e QCM cr yst als were removed and rinsed with DI water , ethanol and dried under nitrogen. Tab le 16. Overvie w of t he a m ount of t he e d uct s u sed for s ynt hesi s o f P t B A. P t BA V( tert - but y l acr ylat e) [m L ] 12.0 V(acet one) [ m L] 35.0 V(PMDETA) [ µ L ] 64.7 m(C u Br 2 ) [ m g] 67.1 m(asco rbic acid ) [g] 0.7 6.4.3. Conversion of poly( tert -butyl acrylate) Brush in to poly(acrylic acid) Brush The conversion of P t BA - int o PAA brush was accomplished by acid h y drol ysis that wa s carried out as f ollows; the QCM cry stals modif i ed with P t BA brus h wer e ex p osed to trifluoroacetic acid (3.0 mL; 39.2 mmol) in the presence of dichloromethane (35 m l; 0.55 mol). The deprot ecti on pro ced ur e was all owed to pr oceed for 18 h at t emp erat ure of 0 °C. Afterw ards QCM cr y st al s wer e cle an ed wi th et hano l, D I water and dried under nitrogen. 81 Scheme 1. Synthetic route for p olymerization of poly(acrylic acid) bru sh from a gold substrate. (CH 2 ) 10 CH 2 O C H 2 O C H Br O O n S (CH 2 ) 10 CH 2 O Br O S (CH 2 ) 10 CH 2 O C H 2 O C H Br O n OH S i. ii. i) tert - butyl acrylate, aceton e, CuBr 2 , PMDETA, asc orbid aci d, room temp. , 22 h. ii) trifl uoroac etic acid, dic hlorom etan e, 0°C , 18 h. 6.4.4. Static Water Contact A ngle (SWCA) Con tact an gles were de term ined usi ng a R am e Hart NR L - 100 contact an gle goniomete r equipped with fiber optic illuminator, 3 - axis specimen stag e with leveling , U1 Series SuperSpeed dig ital camera which operates at 100 fps and micros y rin ge for manual dispensing. The con tact an gle m eas uremen ts wer e su ppor te d b y DROP im age Adv anced soft war e that allo ws th e stat ic con tact angl e meas ur ement in a ran ge of 0 - 180° with accurac y of ±0.1° and r esolution of ±0.01°. The m easure ments were performed by m anual dispensing of 3 µL of DI water on th e in vest igat ed surfac e and fol low ed b y DR OPi mage anal ysis. The meas ur ed con ta ct angl e (85°) co rrel at es we ll wit h th e literatu re valu es for P tBA la y e r ass emb led at th e surfac e of poly(styrene) substrate. 358 Afte r h y drol y sis the measured static conta ct angle decreased to 16°. This proves the increased hydr ophilicit y due to the presence of the PAA la yer. Tab le 17. Static w a ter contact angle data for the sa mples stu died in this work. Sam ple Static water contact angle a (deg) poly( tert - but y l a cryla te ) 85 pol y(acr ylic acid ) 16 a) T he stan d ard deviation of contact angles was < 3°. 6.4.5. Ellips om etry Ellipsome tric me asur ements we re per forme d an a J. A. Wollam M - 88 V ariabl e An gle Spectr oscopic Ellipso meter with Hg - Xe laser wi th a wav el ength in a ran ge of 30 0 -800 nm and a fix ed angle o f i ncid en ce o f 70 °. Thickness of a film applied to the surface of a given substrate can be determined b y ellipsometr y which measu res the chan ge i n po larization of the l ight refle ct ed f rom a materia l struc ture. The 82 measu rables i n th is t ech niqu e are Ψ , the amplitude ratio and ∆ , th e ph as e d iffer ence betw een the p - and s - components of the polarized light. Those parameters are related by the complex refle cti on coef fici ent ρ : 𝜌𝜌 = tan ( 𝛹𝛹 ) 𝑒𝑒 𝑐𝑐 ∆ (67 ) In th e cas e of a mul ti - film la y e rs at a given substra te the equations derived fo r a si n gle refl ectio n can be directly inverte d to provide a pseudo dielect ric function < 𝜀𝜀 > : < 𝜀𝜀 >= sin 2 𝜑𝜑 tan 2 𝜑𝜑 � 1−𝜌𝜌 1+𝜌𝜌 � 2 (68 ) Wh ere 𝜑𝜑 is t he an gle of i nci dence. The thickness of the la yer underl ying the P t BA /PAA films was deter mi ned exper imentally based on the optical constants of the materials provi ded in the instrument software , and were then used to build a model. After a m easu remen t a model is const ruct ed to descri be th e measu red sa mpl e. That mod el is then used t o calcu late t h e predi cted r esp onse fr om Fresnel ’s equ at ion s whi ch des cribe e ach material in regard of the optical constants and the thickness. The qualit y of the data fit to t he mod el is evalu ate b y the mean s quar e er ror (MS E) : 𝑀𝑀𝑆𝑆𝑃𝑃 = 1 2𝑁𝑁− 𝑀𝑀 ∑ [ � 𝛹𝛹 𝑐𝑐 𝑚𝑚 𝑐𝑐𝑑𝑑 −𝛹𝛹 𝑐𝑐 𝑟𝑟𝑒𝑒 𝑝𝑝 𝜎𝜎 𝛹𝛹 𝑟𝑟 𝑒𝑒 𝑝𝑝 � 2 + � ∆ 𝑐𝑐 𝑚𝑚𝑐𝑐𝑑𝑑 −∆ 𝑐𝑐 𝑟𝑟𝑒𝑒 𝑝𝑝 𝜎𝜎 ∆𝑐𝑐 𝑟𝑟𝑒𝑒𝑝𝑝 � 𝑁𝑁 𝑐𝑐 =1 2 (69 ) Wh ere N represents the numbe r of used pairs of Ψ and ∆ , M represents the number of variable paramet ers in t he re gressi on anal ysis and σ represent s the standard de viation of the experimental data p oint s. T he mi nim um MSE ind icates the s atisf ying cor respo nden ce o f calcu lated res ult s with the measured ones. The P t BA/PA A film thic kness were the n determined usin g a Cau chy lay e r logarithm. Meas ured thickness depends on the optical consta nts of the measure d material, therefore to obtain th e cor rect results from a n ellipsometry the re fractive inde x n and the extinction coeffi cien t k of a given material must be known or determined as well. I n the c as e of a transp arent film (where k is neglig ible) a Cauch y r elatio nship for n can b e us ed to anal y z e th e ellipsome tr y data: 𝑛𝑛 ( 𝜆𝜆 ) = 𝐴𝐴 + 𝐵𝐵 𝜆𝜆 2 + 𝐼𝐼 𝜆𝜆 3 ( 7 0 ) Wh ere λ is the w avelen gt h and t he th ree pa ramet er s A , B a nd C are adjust ed t o fit the refract ive ind ex o f a given m aterial . From ellipsometry the dr y thickness of the pol ymer film was found to be 18 nm. After hy d roly s is t he polyme r brush thickness in a dry state decreased to 8 nm. The drop in the brush thickness ca n be attributed to the re moval of the bulk y t ert - butyl groups. A sim ilar observ atio n was r epo rted r ecent l y. 3 59 83 Tab le 18. El lipsom etry dat a for the sam ples of pl an ar polym er brush studi ed in thi s work. Sam ple Thickne ss a (n m) poly( tert - but y l a cryla te ) 18 pol y(acr ylic acid ) 8 a) Thick ness w as det ermined by el lips ometry as an average of thr ee s amples , typ ical e rror for the th ickne ss meas urem ent is ± 1 nm. 6.4.6. Determination of the G rafting Density The graf tin g de nsit y σ of the PAA brush was determined from the following e quation: σ = hρN A /M n (71 ) Here h is t he dry pol ymer thickness, ρ the de nsity o f PAA (= 1.1 g /cm 3 ) 3 60 , N A Avog adro’s number, and M n the pol y mer molecular weight. To estima te M n we us ed a s ystemat ic comparison b y W u et al. on PAA brush es anchored to a flat sili con wafer with variation of the graf tin g de nsities a t several ionic str engths. 76 As a res ult we can pr edi ct th e thi ckness of th e wet PAA brush H as it should present the dry thickness mul tiplied b y the factor of 6.5 ± 0.5 (se e Table 19 ). Tab le 19. Param eters used for determinati o n of the m o lecular w ei ght of grafted PAA chains M n . Paramet er Value h (nm) 8 ± 1 H (nm) 52 ± 11 N m.u. 208 ± 44 M m.u. (g /mol) 72.07 M n (g /mol) 15000 ± 3171 Assuming that each monomer unit is a bea d with diameter of 0.25 nm we can de t ermine the number of monomer units N m.u. within a sing le PAA c hain. Multiply in g the molecu lar weig h t of a monomer unit M m.u . b y N m.u. we can est im ate the mo lecul ar wei ght M n of a s ingle gr afted PAA ch ain. The graft in g densi t y was estim ated t o be σ = 0.35 ± 0.13 nm -2 . Such hig h graftin g densitie s were also reported for PAA brushes achieved b y a simi lar pol y me rization procedure on a fl at si lico n su rface 76 whe re PAA brushes w ith grafting de nsit y up to 0.85 nm - 2 have been achiev ed. Howev er, i n th e p res ent cas e t he mo lec ular wei ght of th e s in gle grafted PAA chai n as we ll as the g rafting densit y is only estimate d. The we t thickness H of the PAA brush does not represe nt the total length of the pol y el ectrol yte cha i n. The refo re the e sti mat ed σ refers to the m ax imal graftin g den si t y o f the an al y z ed b rus h . 6.5. Four ier Tra nsfo rm I nfrared (FT - IR) Spe ctrosc opy The anal ysis of t he P t B A and P AA br ushes as wel l as the seco nd ar y st ructu re o f free an d immobili zed HSA onto SP Bs were performed b y us in g a Fourier T rans form Infrared – Attenu ated T otal Refle ction (FTI R - ATR) spe ctroscopy setup including an ABB FT LA 2000 84 spect romet er eq uip ped w it h the P IKE MIRa cle A TR s ampl ing access o r y i n s et wi th a d iamo nd cr ystal pl ate. In Fi g u r e 5 4 th e M I R acl e ATR setu p i s s chemat icall y presen ted . Figu re 54. MIRacl e - A T R samp ling acce sories . 6.5.1. FT- I R of HSA Adsor bed onto SP Bs The measurements of the secondar y structure of HSA were conducted in 10 mM MOPS buffer pH 7.2 at 298 K. To stud y the structure of the fre e p rotein, HSA was dissolved in 10 mM MOP S buffer pH 7.2 to a conc entration of 5.0 g/L. The effect of immobi lization on the secondar y stru cture w as an al y z ed u si ng prot ein - load ed SPB samples adjusted with 10 m M M OPS b uffer to a conce ntration of 0.5 wt%. I n order to avoid an y f ree HSA in SPB - HSA sample the molar ratio betwee n protein and SPB - particles was a djust based on the I TC results obtained at 298 K. Measu rement s o f th e pu re S PB par ticl es wer e acc omp lis hed at concentration of 0.5 wt% of the SPB suspension. All sample s were f iltered thr ough a me mbrane syr inge f ilter ( 0.8 µm pore width, PALL , Acrodisc) in order to remove an y dust contamination. Then the sample soluti on was injected onto the crystal plate ful ly cov erin g the cr ystal. Th e buffe r so lut ion was meas ured as wel l and used as ref eren ce sp ectru m. The res ult s are di s cussed in s ectio n 4.3.1. 6.5.2. FT- IR o f PPB s Spect ra wer e reco rded at 2 cm -1 resolution and 2 2680 scans were collected. A represe ntative samples of surface functionalized with P t BA/PAA brush were thoroughl y c l eaned with 1% SDS solution, D I water and ethanol and then dried unde r nitrogen. The samples were placed at the sample slot of FTI R instr ument and pressed with a swivel pressure tower. A gold surfa ce that was a fterwards func tionalized with P t BA/PAA brush was meas ur ed as wel l and u sed as background f or furth er measurements. The F T - IR sp ectru m (s ee Figure 55 ) contai ns the e x pect e d peaks at 1731 cm -1 (C =O st retch ) 141 and 2973 cm -1 (a symmetr ic CH3 str etch ing vibration) 141 and a doublet a t 1370/1395 cm -1 (sy mmetric meth y l deformation mod e), sh owing the presence of the t BA moiety . 141 The P t BA chain s wer e convert ed t o P AA vi a acidic h y drolysis. This wa s achieve d b y immers ing the 85 samples in a solution containing 35 mL of dichlor omethane and 3 mL of trifluoroacetic acid for 18 h in an ice bath (~ 0 °C ). 4000 3000 2000 1000 0,000 0,001 0,002 0,003 Absorbance Wavenumbers (cm -1 ) poly( t -butyl acrylate) poly(acrylic acid) Figure 55 . FT - IR spectra of poly (tert - but y l acr ylate) (PtBA) and poly (acrylic acid) (PAA). The F T - IR spectrum after h ydr ol ysis showed a broad peak at 3000 – 3500 cm -1 , a broadening of the peak a t 1731 cm -1 and the loss of the peaks associated with the pendant methyl groups (see Figure 1), thereb y d ocumenting the successful cleavage of the t B A moiety . 141 A similar procedu re w as used re cently in s ynthe sis of pol y( methacr y l ic acid) brush from silica nanop articl es. 361 6.6 . ITC Me asu rement s The I T C meas ur ement s were co ndu cted on a VP - ITC ins trum ent (Micro Cal, GE Heal thcare, Freibur g, Ger man y) and on a Mic rocal iTC 2 00 inst rume nt (MicroCal, Northampton, M A), booth cont roll ed b y the VP Vie wer so ftw are (Micro Cal) . The r efer ence - and th e sa mpl e cell o f t he ITC m ac hi nes ar e comp osed o f H ast ell o y ® Al lo y C - 276. The working vol ume of the sample cell is 1. 43 m L ( V P - ITC) and 200 μ L (iTC 200 ) w h i le string s yring e allows to inject 2 80 µL (VP - ITC) o r 39 μ L ( i T C 200 ) of react an t in tot al. For the experiments conducted on a V P - ITC in stru ment the refer ence p owe r was set to 15 µcal l/s ec with the stirring speed in the sa mple cell of 307 rpm. For the experiments conducted on a iTC 200 ins trum ent t he referen ce power w as set to 10 µcal l/sec wi th t he st irrin g speed i n the s ampl e cell of 750 rpm. After thermal equilibration the protein solution was titrated dropwise into the samp le cell an d Q was evalu ated for each in jec tio n st ep (see s ect ion 3. 3.2.3. ). During the experime nt the injection vo lume as well a s the ti me interva l betwe en the injections w ere kep t const ant. The s am e ex peri ment al pr oced ur e was ap pli ed in ord er to det erm in e the h eat o f dil uti on. A fter each m eas uremen t bo th s ampl e cell s as well as the s yrin ge were ve r y thoro u ghly cleane d usin g 2% of Dec on90 solution and ultrapure Milli- Q water. 86 Tab le 20. Ex p eriment a l parameters for dP GS - divale nt io n me as ure me nt s, conduc ted on a VP - ITC instrume nt. Sys tem Bu ffer/ Ion ic stren gth T [ K] c (++) [ mM] a) c (dPGS) [ mM] Ca 2+ /dP GS MOPS/16.5 mM 303 5.1 0.032 Mg 2+ /dPGS MOPS/16.5 mM 303 5.0 0.032 MOPS/19.1 mM 303 5.0 0.020 MOPS/16.4 mM 303 10.0 0.039 MOPS/14.0 mM 303 15.2 0.064 a) conc entr ation of div alent io ns in the i njectant. Tab le 21 . Ex periment al parameters for Hep - Lys mea s ure m ent s, c ond uc te d o n a V P - ITC instr ument. Sys tem Bu ffer/ Ion ic stren gth T [ K] c (prot ein) [ mM] c (Hep ) [mM] L ys / H e p Phosphate buffer/25 mM 288, 293, 298, 303, 308, 310 1.4 x 10 -2 2.0 x 10 -4 Phosphate buffer/35 mM 288, 293, 298, 303, 310 1.2 x 10 -2 2.4 x 10 -4 Phosphate buffer/5 0 m M 288, 293, 298, 303, 310 1.4 x 10 -2 2.9 x 10 -4 Phosphate buffer/75 mM 288, 293, 298, 303, 310 7.8 x 10 -2 6.6 x 10 -4 Phosphate buffer/100 mM 288, 293, 298, 303, 310 15.6 x 10 -2 22.7 x 10 -4 Tab le 22 . Experim enta l parameters for β - CD -S - Lys m eas ure m ents, conducted on a VP - IT C instrume nt. Sys tem Bu ffer/ Ion ic stren gth T [ K] c (prot ein) [ mM] c (β - CD -S ) [ mM] L ys / β - CD -S Phosphate buffer/20 mM 310 1.3 0.08 Phosphate buffer/30 mM 310 1.3 0.08 Phosphate buffer/40 mM 310 1.8 0.10 Phosphate buffer/60 mM 310 3.0 0.18 Phosphate buffer/100 mM 310 3.0 0.18 87 Tab le 23 . Experim enta l parameters for SPB - HS A measurements, con ducted on a VP - ITC in strume nt. Sys tem Bu ffer/ Ion ic stren gth T [ K] c (prot ein) [ mM] c (SPB) [mM] HSA/ SPB - PAA MOPS/20 mM 298 0.359 3.64 x 10 -6 300 0.363 3.13 x 10 -6 302 0.362 2.91 x 10 -6 304 0.525 3.50 x 10 -6 306 0.519 2.91 x 10 -6 308 0.686 3.43 x 10 -6 309 0.682 3.05 x 10 -6 310 0.681 2.70 x 10 -6 MOPS/50 mM 310 0.680 2.70 x 10 -6 6.7 . QCM - D M easu rem ents HSA adsorption onto planar PAA brush as a function of ioni c strength and pH w as studied using the quar tz cr y stal microba lance with dissipation ( QCM - D) from Q S ense wh i ch me asu res f and D for the first four odd harmonic of the cr y st als. The cr y st als used in the ex peri ment s were gold co ated and h ad a n om in al cent er freq uen c y of 5 M Hz. Thoroug hl y cleaned and dried under nitrogen QCM sensors functionalized with PAA brush were placed inside of the QCM removable flow modules. Then the available 40 µ L volume above the sensors was f ill ed with starting buf fer and the sensors we re allowed to equilibrate within for 10 minutes. Af terwards at constant temper ature of 25°C and at constant pump rate of 5 µL/min the frequency and dissipation were measured in order to establish the baseline. 6.7.1. Deter mina tion of the N umber of HS A Mol ecul es per PAA Chai n For an arbit ra r y area of S = 20 nm with grafting densit y of σ = 0,35 ± 0,13 nm -2 we hav e approx i mat el y N c = 7 ± 3 PAA chains. Mass densi t y at St ep II of ion ic st ren gth c ycle i s 35 3 Da/Å 2 (see Tab le 7 in s ect ion 4.5.4. ), which for an arbitra r y area S giv e 706000 Da . B y taking into account the mol ecular weight of a single HSA m olecu le ( M w, HS A = 66,5 kDa ) w e get N p = 11 H SA m olecul es pe r area S . K eepi n g in min d th at area S is occupied b y ap prox im atel y 7 PAA cha ins brings us to the number of HSA mol ecules per PA A ch ain ( N p/c ) which in this ca se is 1,5 . I t m eans t hat app ro x imat el y th ree HS A mol ecules are ad sorb p er tw o PAA chain s. In the sam e fas hio n we c an evalu ate t hat at Step X of t he pH c ycle N p /c = 1 , meaning that one HSA molecule is adsorb per one PAA chain. 88 7. Supplement 7.1 . Calcu lati on of the Bulk C oncentra tion c i 0 for the Ion - Speci fic PPB Mo del The bulk concentration of divalent and monovalent counterions c i 0 (see sect ion 3.3.4.2. ) is updated during each injection in the following way . : A. Solve PB equation ( Eq. (49)) (Unknown parameter c i 0 is gue ssed from the outcome of previous injection.) B. Find c 0 ++ and it erate Total known molar concentration of Mg 2+ per molar concentra t ion of dPGS : c tot ++ The total amount of Mg 2+ i s conserved w ithin the t itration volume V (spheric al cell of radius R ). � 𝑐𝑐 ++ ( 𝑟𝑟 ) 4 𝜋𝜋 𝑟𝑟 2 𝑑𝑑𝑟𝑟 𝑅𝑅 0 = 𝑐𝑐 ++ 0 � 𝑒𝑒 −2𝛷𝛷 ( 𝑐𝑐 ) −𝛽𝛽 ∆𝜇𝜇 𝑐𝑐 𝑛𝑛𝑝𝑝 , ++ ( 𝑐𝑐 ) 4 𝜋𝜋 𝑟𝑟 2 𝑑𝑑𝑟𝑟 𝑅𝑅 0 = 𝑐𝑐 ++ 𝑡𝑡𝑡𝑡𝑡𝑡 � 4 𝜋𝜋 3 𝑅𝑅 3 � ⇒ 𝑐𝑐 ++ 0 = 𝑐𝑐 ++ 𝑡𝑡𝑡𝑡𝑡𝑡 � 4 𝜋𝜋 3 𝑅𝑅 3 � ∫ 𝑒𝑒 −2𝛷𝛷 ( 𝑐𝑐 ) −𝛽𝛽 ∆𝜇𝜇 𝑐𝑐𝑛𝑛𝑝𝑝 , ++ ( 𝑐𝑐 ) 4 𝜋𝜋 𝑟𝑟 2 𝑑𝑑𝑟𝑟 𝑅𝑅 0 Substitute c 0 ++ back in E q. (49) and repeat steps A and B till c 0 ++ is converged. C. Calculate bound Mg 2+ ions aft er conv er gence o f c 0 ++ using Eq. (48), and use c 0 ++ as initial gue ss for next injection. Follow the same steps f or the conver ge nce of the bulk Na + concentration c 0 + . 7.2. Mate rial s and the ITC I sot herm s for dP GS - Diva lent Ion Inter action Desc ribed in Sec t ion s 4. 1.2.1. and 4. 1. 2.2. 7.2. 1. Mat er ials Sodium phosphate dibasic (N a 2 HPO 4 ) and sodium phosphate monobasic (NaH 2 PO 4 ) were purchase d from Fluka and used dir ectl y . S odium chloride (NaCl), m agnesium chloride hex ah y drat e (MgCl 2 ∙ 6H 2 O) and Lysozy me from chicken egg - w hite (M Lys =14,3 kDa) were receiv ed fro m S i gm a -Ald rich and used without further purifica tion. dPGS was obtained by sulfation of a fr actionated h y pe rbranched pol y gl y c erol. 362 Ta bl e S1 gives t he mol ecul ar wei ght M n,dPG S and the degree of sulfation (DS) of dPGS as determined from the weight percentag e of sulfur. 278 89 Table S1 . Stru ctural proper tie s of dP GS. dPGS M n,dP G (kDa) 2.6 DS (%) 97 N ter 34 M n,dPGS (kDa) 6.5 DS : the degree of s ulfation deter mined f r om elem ental analysis. N ter : the nu mbe r o f te r minal sul fa te gr o ups. T he num ber - average molecular weig h t M n of t he dPG core as well as for dPGS was determined by g el permetation chr o matogr ap h y. 7.2. 2. ITC Is otherm s 0 10 20 30 40 50 0.0 0.2 0.4 0.6 0.8 1.0 0 50 100 150 200 0.0 0.5 1.0 1.5 T i me ( mi n) µcal / sec T=30 o C dPGS + Ca 2+ Ca 2+ di l ut i on n( Ca 2+ )/n(d P G S ) kcal / m ol e of Ca 2+ 0 5 10 15 20 25 30 35 40 45 0 200 400 600 800 1000 Q in cal/mol of Ca 2+ n(Ca 2+ )/n(dPGS) 0 5 10 15 20 25 30 35 40 45 10 100 1000 Q in cal/mol of Ca 2+ n(Ca 2+ )/n(dPGS) Figur e S1 . (a) I TC data f or th e bindi ng of Ca 2+ ions to dPG S at pH 7.2 and tem perat ure of 30°C in 10 m M MOPS buf fer . T he upp er p anel s ho ws t h e ra w data of the binding ( red spikes) a nd t he dilutio n o f Mg 2+ by buf fer (bl ac k spikes ). T he in tegrated heats of each in j ection are shown i n the lower panel. (b) Bind ing i s o ther ms for Ca 2+ - d P G S interaction, p rese nted o n a typ ical IT C plo t (left - hand ed ) and se mi - logar ith mic plot ( right - ha nd ed ). Resul t ing [Ca 2+ ] tot : 0,8 mM . Plots r efer to sectio n 4.1.2.1. a) b) 90 0 10 20 30 40 50 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 0 50 100 150 200 0. 0 0. 5 1. 0 1. 5 T i me ( mi n ) µcal / sec T=30 o C dPGS + Mg 2+ Mg 2+ di l ut i on n ( Mg 2+ )/n(d P G S ) kcal / m ol e of M g 2+ 0 5 10 15 20 25 30 35 40 45 0 200 400 600 800 1000 1200 Q in cal/mol of Mg 2+ n(Mg 2+ )/n(dPGS) 0 5 10 15 20 25 30 35 40 45 10 100 1000 Q in cal/mol of Mg 2+ n(Mg 2+ )/n(dPGS) Figur e S2 . (a) I TC data for th e bindi ng of M g 2+ ions to dPG S at pH 7.2 and tem perat ure of 30°C in 10 m M MOPS buf fer . T he upp er p anel s ho ws t he ra w d ata o f t he b ind i ng ( bla ck sp i kes) a nd t he d il utio n of M g 2+ b y buffer (re d spikes ). T he integ rated heats of each injection are shown in the lower panel. (b) Binding isotherms for Mg 2+ - dP GS interaction, p resented on a ty p ical IT C plo t (left - handed ) and se mi - logarit hmi c pl ot ( right - ha nde d) . Res ulti ng [ M g 2+ ] tot : 0,8 m M . Plo ts refer to sectio n 4.1.2.1. a) b) 91 0 10 20 30 40 50 60 0. 0 0. 2 0. 4 0. 6 0. 8 0 50 100 150 200 0. 0 0. 5 1. 0 T i me ( mi n ) µcal / s ec T =30 o C dPGS + Mg 2+ Mg 2+ D ilu tio n n ( Mg 2+ ) / n ( dPGS) kcal / m ol e of M g 2+ 0 10 20 30 40 50 60 0 200 400 600 800 1000 Q in cal/mol of Mg 2+ n(Mg 2+ )/n(dPGS) 0 10 20 30 40 50 60 10 100 1000 Q in cal/mol of Mg 2+ n(Mg 2+ )/n(dPGS) Figur e S3 . (a) I T C dat a f or the bin din g of M g 2+ io ns to dPGS at pH 7.2 an d tem peratur e of 30°C in 10 m M MOPS buf fer . T he upp er p ane l sho w s the ra w da ta o f the bind ing ( b lue sp ikes) and the d ilution of Mg 2+ by buff er ( black spikes ). T he integ rated heats of each injection are shown in the lower panel. (b) Binding isotherms for Mg 2+ - dP GS interaction, p resented on a ty p ical IT C plo t (left - handed ) and se mi - logarit hmi c pl ot ( right - ha nde d) . Res ulti ng [ M g 2+ ] tot : 0 ,8 mM. Plo ts refer to section 4.1.2.2. a) b) 92 0 10 20 30 40 50 60 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 0 50 100 150 200 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 T i me ( mi n ) µcal / sec T=30 o C dPGS + Mg 2+ Mg 2+ di l ut i on n ( Mg 2+ ) / n ( d PGS) kcal / m ol e of M g 2+ 0 10 20 30 40 50 60 0 200 400 600 800 1000 1200 Q in cal/mol of Mg 2+ n(Mg 2+ )/n(dPGS) 0 10 20 30 40 50 60 10 100 1000 Q in cal/mol of Mg 2+ n(Mg 2+ )/n(dPGS) Figur e S4 . (a) I T C dat a f or the bin din g of M g 2+ io ns to dPGS at pH 7.2 an d tem peratur e of 30°C in 10 m M MOPS buf fer . T he upp er p anel s ho ws t h e ra w data of the binding ( red spikes) a nd t he dilutio n o f Mg 2+ by buf fer (bl ac k spikes ). T he integ rated heats of each injection are shown in the lower panel. (b) Binding isotherms for Mg 2+ - dP GS interaction, p resented on a ty p ical IT C plo t (left - handed ) and se mi - logarit hmi c pl ot ( right - ha nde d) . Res ulti ng [ M g 2+ ] tot : 1 ,6 mM. Plo ts refer to section 4.1.2.2. a) b) 93 0 10 20 30 40 50 0. 0 0. 5 1. 0 0 50 100 150 200 -1 0 1 2 3 4 5 T i me ( mi n ) µcal / s ec T=30 o C dPGS + Mg 2+ Mg 2+ di l ut i on n ( Mg 2+ ) / n( d PGS) kcal / m ol e of M g 2+ 0 10 20 30 40 50 60 0 200 400 600 800 1000 1200 1400 Q in cal/mol of Mg 2+ n(Mg 2+ )/n(dPGS) 0 10 20 30 40 50 60 10 100 1000 Q in cal/mol of Mg 2+ n(Mg 2+ )/n(dPGS) Figur e S5 . (a) I T C dat a f or the bin din g of M g 2+ io ns to dPGS at pH 7.2 an d tem peratur e of 30°C in 10 m M MOPS buf fer . T he upp er p anel sho ws th e ra w data o f t he bi nding ( yello w spi ke s) a nd the di l utio n o f Mg 2+ by buff er (black spikes ). T he integ rated heats of each injection are shown in the lower panel. (b) Binding isotherms for Mg 2+ - dP GS interaction, p resented in a typical IT C plo t (left - hand ed ) and se mi - lo garithmic plot ( rig ht - han ded). R esu lting [Mg 2+ ] tot : 2,5 mM. Plots refer to section 4.1.2.2. a) b) 94 7.3. Det ails on Hep - Lys I nteraction Described in Chapter 4. 2. 7.3.1. ITC Data Measu remen ts f or i oni c stren gth of 25 mM: Temper atur e: 1 5 o C Temper atur e: 2 0 o C 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 95 Temper atur e: 25 o C Tem peratu re: 30 o C 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) Temper atur e: 35 o C 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 96 Measu remen ts f or i oni c stren gth of 35 mM: Temper atur e: 1 5 o C Tem peratu re : 20 o C 0 4 8 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 0.2 0.4 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 048 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 0.2 0.4 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 048 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 4 8 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) Temper atur e: 2 5 o C Temper atur e : 30 o C 0 4 8 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 4 8 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 4 8 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 4 8 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 97 Temper atur e: 37 o C 048 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 4 8 12 -60 -40 -20 0 0 20 40 60 80 0 20 40 60 80 -0.4 -0.2 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) Measu remen ts f or i oni c stren gth of 50 mM: Temper atur e: 1 5 o C Tem peratu re: 20 o C 02468 10 -60 -40 -20 0 0 20 40 60 80 -0.6 -0.4 -0.2 0.0 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 -60 -40 -20 0 0 20 40 60 80 -0.6 -0.4 -0.2 0.0 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 98 Temper atur e: 2 5 o C Temper atur e: 3 0 o C 02468 10 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.2 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) Temper atur e: 3 7 o C 02468 10 -60 -40 -20 0 0 30 60 90 120 -0.4 -0.2 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 -60 -40 -20 0 0 30 60 90 120 -0.4 -0.2 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 99 Measu remen ts f or i oni c stren gth of 75 mM: Temper atur e: 1 5 o C Temper atur e: 2 0 o C 0 5 10 15 20 25 -60 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 20 25 -60 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 20 25 -60 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 20 25 -60 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) Temper atur e: 2 5 o C Tem peratu re: 30 o C 0 5 10 15 20 25 -60 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 20 25 -60 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 20 25 -60 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 20 25 -60 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 100 Temper atur e: 37 o C 0 5 10 15 20 25 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 0 5 10 15 20 25 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) Measu remen ts f or i oni c stren gth of 100 mM: Temper atur e: 1 5 o C Temper atur e: 2 0 o C 02468 10 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 12 -60 -40 -20 0 0 20 40 60 80 -0.4 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 12 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 12 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 101 Temper atur e: 2 5 o C T emperat ur e: 30 o C 02468 10 12 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 12 -40 -20 0 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 12 -40 -30 -20 -10 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 12 -40 -30 -20 -10 0 20 40 60 80 -0.3 -0.2 -0.1 0.0 0.1 0.2 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) Temper atur e: 37 o C 02468 10 12 -30 -20 -10 0 30 60 90 120 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 02468 10 12 -30 -20 -10 0 30 60 90 120 -0.2 -0.1 0.0 0.1 kJ/mol of Lys n Lys /n Hep µ cal/sec Time (min) 102 Figur e S6. ITC da ta f or the adsorpt ion of Lys to He p (bl ack color ) and c orrespondi ng dat a for th e heat of di luti o n of Ly s by buff er (red color ). The u pper panel s sh o w the raw data of adsorpt ion (black curv es) and dilution (red curv es). T he integ r ated heats of in j ect ion are s hown in the low er pan els. Me asurem ents w ere condu cted in ph osphat e buff er pH 7.4 w ith ion ic s trengths: 25, 35, 50, 75 a nd 10 0 mM at dif fe rent tem peratu res as in d icated above each plot . 103 02468 10 12 14 -60 -40 -20 0 Q in kJ/mol of Lys n Lys /n Hep 15 o C 20 o C 25 o C 30 o C 35 o C 37 o C 25 mM 0 2 4 6 8 10 -60 -40 -20 0 Q in kJ/mol of Lys n Lys /n Hep 15 o C 20 o C 25 o C 30 o C 37 o C 35 mM 0 2 4 6 8 -60 -40 -20 0 Q in kJ/mol of Lys n Lys /n Hep 50 mM 15 o C 20 o C 25 o C 30 o C 37 o C 0 5 10 15 20 -60 -40 -20 0 Q in kJ/mol of Lys n Lys /n Hep 15 o C 20 o C 25 o C 30 o C 37 o C 75 mM 02468 10 12 -60 -40 -20 0 Q in kJ/mol of Lys n Lys /n Hep 15 o C 20 o C 25 o C 30 o C 37 o C 100 mM Figur e S7. ITC i sothe rms for th e adsorpti on of Ly s to Hep i n ph osphate buffer pH 7.4 w ith i onic s treng ths: 25, 35, 50, 7 5 and 100 mM at diff erent temperatures. T he solid lin es presents the fits by the SSIS m o del. 104 Table S2 . T h e r mo dynami c properties of ly sozyme bin ding to hepa rin unde r diff ere nt condition s of tem perature an d ionic st rength . I ( mM ) Tem perature ( o C) N b K b x 10 -7 (M -1 ) ∆ H ITC (k J/mol) ∆ G b (k J/m ol) ∆ H b (k J/m ol) ∆ S b (k J/m ol K) T∆S b (k J/ m ol) ∆ Cp vH (k J/mol∙ K) a) 25 15 5.7 39 ± 6 - 52. 0 ± 1.3 - 47. 4 ± 0.3 - 53. 2 ± 6.1 - 0.020 0 ± 0.020 8 - 5.8 ± 6. 0 1.3 ± 0. 5 20 5.9 28 ± 4 - 52. 4 ± 1.3 - 47. 5 ± 0.2 - 47. 0 ± 3.7 0.0 016 ± 0. 0127 0.5 ± 3. 7 25 6.4 20 ± 2 - 52. 5 ± 1.3 - 47. 4 ± 0.2 - 40. 7 ± 1.7 0.0 229 ± 0. 0057 6.8 ± 1. 7 30 6.5 17 ± 2 - 51. 2 ± 1.3 - 47. 7 ± 0.2 - 34. 4 ± 1.9 0.0 438 ± 0. 0063 13. 6 ± 1.9 35 6.5 13 ± 1 - 50. 5 ± 1.2 - 47. 9 ± 0.1 - 28. 1 ± 4.1 0.0 643 ± 0. 0132 19. 8 ± 4.1 37 6.4 13 ± 2 - 51. 6 ± 1.3 - 48. 1 ± 0.2 - 25. 6 ± 5.0 0.0 725 ± 0. 0163 22. 5 ± 5.0 35 15 6.4 16.1 8 ± 1.68 - 52. 7 ± 1 .2 - 45. 3 ± 0.2 - 50. 3 ± 8.9 - 0.017 7 ± 0.030 5 - 5.1 ± 8. 8 1.2 ± 0. 7 20 6.1 11.1 6 ± 0.71 - 52. 1 ± 1.1 - 45. 1 ± 0.2 - 44. 2 ± 5.6 0.0 034 ± 0. 0191 1.0 ± 5. 6 25 6.2 8.93 ± 0. 49 - 52. 4 ± 1.1 - 45. 4 ± 0.1 - 38. 1 ± 2.8 0.0 242 ± 0. 0095 7.2 ± 2. 8 30 6.2 6.45 ± 0. 51 - 54. 4 ± 1.2 - 45. 3 ± 0.2 - 31. 9 ± 3.0 0.0 446 ± 0. 0099 13. 5 ± 3.0 37 7.0 5.34 ± 0. 30 - 50. 6 ± 1.1 - 45. 9 ± 0.1 - 23. 3 ± 7.2 0.0 727 ± 0. 0235 22. 5 ± 7.3 50 15 6.5 6.06 ± 0. 35 - 51. 4 ± 1.2 - 42. 9 ± 0.1 - 70. 9 ± 6.0 - 0.097 1 ± 0.020 6 - 28. 0 ± 5.9 3.5 ± 0. 6 20 6.5 6.06 ± 0. 35 - 49. 8 ± 1.1 - 42. 7 ± 0.1 - 53. 5 ± 3.4 - 0.037 1 ± 0.011 7 - 10. 9 ± 3.4 25 6.0 4.08 ± 0. 16 - 51. 7 ± 1.1 - 42. 5 ± 0.1 - 36. 1 ± 2.3 0.0 218 ± 0. 0077 6.5 ± 2. 3 30 6.9 2.84 ± 0. 10 - 51. 4 ± 1.3 - 42. 8 ± 0.2 - 18. 6 ± 4.1 0.0 797 ± 0. 0135 24. 2 ± 4.1 37 6.4 2.36 ± 0. 19 - 51. 8 ± 1.4 - 43. 7 ± 0.2 5.7 ± 7. 9 0.1 593 ± 0. 0259 49. 4 ± 8.0 75 15 6.1 1.46 ± 0. 10 - 47. 9 ± 1.3 - 39. 5 ± 0.2 - 58. 7 ± 3.8 - 0.066 6 ± 0.013 1 - 19. 2 ± 3.8 1.9 ± 0. 3 20 6.5 0.97 ± 0. 07 - 47. 2 ± 1.4 - 39. 2 ± 0.2 - 48. 9 ± 2.3 - 0.033 1 ± 0.008 0 - 9.7 ± 2. 3 25 6.2 0.70 ± 0. 06 - 47. 1 ± 1.5 - 39. 1 ± 0.2 - 39. 2 ± 1.1 0.0 002 ± 0. 0037 - 0.1 ± 1. 1 30 6.6 0.59 ± 0. 04 - 50. 5 ± 1.6 - 39. 3 ± 0.2 - 29. 5 ± 1.3 0.0 321 ± 0. 0041 9.7 ± 1. 2 37 6.2 0.47 ± 0. 03 - 46. 5 ± 1.6 - 39. 6 ± 0.1 - 15. 9 ± 3.2 0.0 766 ± 0. 0103 23. 7 ± 3.2 100 15 6.5 0.83 ± 0. 05 - 41. 1 ± 1.1 - 38. 2 ± 0.1 - 71. 2 ± 21.4 - 0.114 3 ± 0.073 6 - 32. 9 ± 21.2 3.8 ± 2. 1 20 6.1 0.62 ± 0. 03 - 37. 8 ± 1.2 - 38. 1 ± 0.1 - 52. 3 ± 12.2 - 0.049 4 ± 0.041 8 - 14. 5 ± 12.2 25 6.0 0.37 ± 0. 02 - 29. 9 ± 1.2 - 37. 5 ± 0.1 - 33. 5 ± 8.2 0.01 45 ± 0. 0276 4.3 ± 8. 2 30 6.2 0.41 ± 0. 03 - 24. 7 ± 1.2 - 38. 5 ± 0.2 - 14. 5 ± 14.5 0.0 770 ± 0. 0480 23. 3 ± 14.5 37 6.0 0.31 ± 0. 03 - 15. 8 ± 1.3 - 38. 8 ± 0.2 11. 8 ± 28.2 0.1 635 ± 0. 0926 50. 7 ± 28.7 105 N b is t he number of adsor bed Ly s molec ules as dete rm ined by ITC . K b , ΔH ITC , ΔG b ar e the e xperi ment al val ues of the bindi ng co nstant, calor ime tric e nthal py and bindi ng fr ee ene rgy, r es pec tivel y as dete rm ine d by ITC. ΔH b , ΔS b and Δ Cp vH are t he bindi ng ent halpy, bi ndi ng ent ro py and t he heat capac ity ch ange, r espec tive ly as fitted by eq. ( 20). Wit h respec t to i onic s trength onl y 106 7.3.2. Effec t of Dif fere nt Conc ent rat ions of Lys and Hep on the Binding C ons tant K b 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 Q in kJ/mol of Lys n Lys /n Hep a) µ cal/sec Time (min) 0 5 10 15 -60 -40 -20 0 0 30 60 90 120 -0.3 -0.2 -0.1 0.0 0.1 Q in kJ/mol of Lys n Lys /n Hep b) µ cal/sec Time (min) Figur e S8. ITC dat a of th e ads orption of Ly s to H ep (a) and corres ponding data of the Ly s hea t of dilut ion (b) . Measurements were perform e d at pH 7.4, I = 25 mM an d T = 37 o C, [ Hep] = 2 x 10 -4 m M . T he upp er p ane l sho ws the raw data of the a dsorpt ion a nd the dilut ion of Lys by buf fer. Pres ented m easureme nts w e re perf ormed wit h iTC 200 calorimeter. 02468 10 12 14 -10 -5 0 5 0 100 200 300 400 -1. 5 -1. 0 -0. 5 0. 0 0. 5 Ti me ( mi n) µcal / sec n Lys /n Hep kcal / mol e of Lys a) 02468 10 12 14 -10 -5 0 5 0 100 200 300 400 -1. 5 -1. 0 -0. 5 0. 0 0. 5 Ti me ( mi n) µcal / sec n Lys /n Hep kcal / mol e of Lys b) Figur e S9. ITC dat a of th e ads orption of Ly s to H ep (a) and corres ponding data of the Ly s hea t of dilut ion (b) . Measurements were perform e d at pH 7.4, I = 25 mM an d T = 37 o C, [ Hep] = 7 x 10 -4 m M . T he upp er p ane l sho ws the raw data of th e adsorpti on and th e dil ut ion of Lys by buffer. Prese nt ed me asure ments were p erform ed with VP - IT C calorimeter. 107 For measure ment with iTC 200 calor imeter: A total of 39 µ L o f L ys – buf f er solution was ti trated into the sample c ell with 39 successive injections, with stirring rate at 750 rpm and a tim e interval of 180 s b etween each injection. The sample cell containe d 200 µ L of Hep solut ion in the matching buf fe r . For measure ment with V P - I TC calorimete r: A total of 280 µL of L ys – buf fer solution was titrated i nto the sa mple c ell with 70 s uccessi ve injec tions, with st ir ring rate at 307 rpm and a time interval of 360 s b etween each injection. The sample cell containe d 1.43 m L of Hep soluti on in a matching buf fe r . 02468 10 12 14 -60 -50 -40 -30 -20 -10 0 K b x 10 -7 (M -1 ) 13 ± 2 10 ± 3 Q in kJ/mol of Lys n Lys /n Heparin Figu re S10. Int egr ated he ats of adsorption o f Lys to Hep at const a nt ionic streng th of 25 mM and t e mpera tu re of 37 o C. Red data points represen t the bin d ing measured by VP - ITC calorimet er with Hep concentration o f 7 x 10 -4 m M. Black data points represent the binding measured by iTC200 calorim eter with Hep concentration of 2 x 10 -4 mM. Solid line s presents t he single set o f ide ntical sites (S SIS) fit. Table S3 . T he rmod yna mic d ata o f the L ys - Hep bindi ng. E ffe ct of dif fe rent con centrat ions and c o mpa rison be twee n tw o t y pe s of calorim e ters , VP - IT C an d iTC200. [Hep] ( mM) [Lys] ( mM) K b x 10 -7 (M -1 ) ∆ H ITC (kJ/mol) N b c* Calo rimet er typ e 0.0002 0.0115 13 ± 2 -51.6 ± 1.3 6.4 167 iTC200 0.0007 0.0437 10 ± 3 -56.6 ± 1.2 6.2 442 VP - IT C * W ize man parameter c = [Hep ] * K b *N b 108 Figure S 10 an d th e the rm od ynamic d ata gath ere d in Table S3 shows that at the same condition of ionic streng th and tem perature, the measured binding constant, K b is independent of the concentration of reagents. Moreover, measured binding is not affected by the dif ference in the technical c onditions of ex periments run by diff erent t ype s of calorimeters. 7.3.3. Fracti ona l Ch arge of Hep ari n According to Manning 302, 324 , the f raction of charge along a linea r pol y ele ctrolyte with monovalent counter ions is give n b y : 𝑓𝑓 ( 𝑠𝑠 ) = 1 2𝜉𝜉 � 1 − 𝑙𝑙𝑛𝑛 ( 𝜅𝜅𝑏𝑏 ) 𝑙𝑙 𝑛𝑛 ( 𝑠𝑠 𝑏𝑏 ⁄ ) � , (S1) where 𝜉𝜉 is the d imen sio nless ch arge dens it y parame ter , κ -1 is the Deb ye lengt h, s the d istance fr om the end, and b the spacing between ne ighboring cha rged groups. The parameter 𝜉𝜉 is given by 302,3 24 : 𝜉𝜉 = 𝑒𝑒 2 4 𝜋𝜋𝜀𝜀 𝑘𝑘 B 𝑇𝑇𝑏𝑏 = 𝑙𝑙 B 𝑏𝑏 , (S2) where e i s th e elemen tar y cha r ge, ε the pe rmittivit y of the solve nt, k B the Boltzmann constant, T the t emper atu re, and l B the Bjerrum len gth. Chain end effects on the ch arge of hep arins of different molecular we ights (num ber of struc tural charges) were calcula ted on the basis of Eqs. (S1) and (S2) assuming 3 sulfa te a nd 1 carboxyl groups per disaccharide unit ( Figure S11 ). Figur e S11 . Fractional ch ar ge v s. stru ctural charge calculated for heparin acco rding to Eqs. ( 1 ) and (2) using t he follo wing para meters: c s = 25 mM, 50 m M, 75 m M, an d 100 m M (indi cate d), b = 0.25 nm, a nd T = 310. 15 K (37° C). The horizontal and vertical dashed lines i ndicate the structural charge and the range of t he resulting fractional charge of the he p ar in us ed in t hi s st ud y ( 22 d isa ccha ri de uni ts wit h, i n ave ra ge , 3 sul fat e gro ups an d 1 ca rbo x yl group ) f or sa l t concentrati ons in the range 25 mM to 100 m M. 109 7.3.4. Ionization of H eparin The ionization of the hep arin was calculated as a f unction of the pH and sa lt concentration in the electro l yte appl ying the t heoret ical f ram ewo rk de velo ped b y Paolet ti et al . 323,3 63 – 365 . According to this approach, the apparent p K a of a monoprotic polyacid is g iven b y : 𝑝𝑝𝐾𝐾 a ( 𝛼𝛼 ) = 𝑝𝑝 K o + Δ p 𝐾𝐾 a ( 𝛼𝛼 ) , (S3) where th e p K o repres ents the intrin sic p K of the isolated ionisable repe at u nit. The chang e in the apparent p K a , Δp K a , is determined b y the change in the ionic Gibbs free energ y w ith the variation of the degree of dissocia ti on α of the poly m er: Δ p 𝐾𝐾 a ( 𝛼𝛼 ) = 1 2 . 303 𝑛𝑛 p 𝑅𝑅𝑇𝑇 𝜕𝜕 𝐺𝐺 𝑐𝑐𝑐𝑐 𝑛𝑛 𝜕𝜕𝛼𝛼 = 𝑓𝑓 �𝛼𝛼 , 𝜉𝜉 , 𝐶𝐶 p , 𝐶𝐶 s , 𝜖𝜖 , 𝑇𝑇 � (S4) where ξ is a d imen sio nl ess p aram eter char acte riz in g the pol yelect rol y te ch arge densi t y, C p t h e concentration of ionisable uni ts, C s t he sal t concen trat ion (1:1 electro l y te ), ε th e diel ectric co nst ant, and T th e temp erature 3 23,36 3,365 . Full expressions for Δp K a ( α ) under conditions without ion condensation ( ξ ≤ ξ cr it = 1) and with ion condensation ( ξ > ξ crit = 1) can be found in Ref. 323 . Paoletti et al . have fur ther shown that for he t erogeneous polye lectrol y t es consist ing of N different monoprotic acids with the molar fraction X i and the intrinsic 𝑝𝑝𝐾𝐾 o 𝑐𝑐 the overa l l intrinsic p K o is a function of the overall degree of ionization α according to 364, 365 : Δ p 𝐾𝐾 o ( 𝛼𝛼 ) = 𝑝𝑝𝐾𝐾 o 𝑐𝑐 + 𝑙𝑙𝑚𝑚𝑔𝑔 � 𝛽𝛽 𝑐𝑐 1−𝛽𝛽 𝑐𝑐 1−𝛼𝛼 𝑎𝑎 � (S5) where β i is the ioniz ation degr ee of the i- th functional group and α is g iven by: 𝛼𝛼 = ∑ 𝑋𝑋 𝑐𝑐 𝛽𝛽 𝑐𝑐 𝑁𝑁 𝑐𝑐 =1 (S6) with 𝑋𝑋 𝑐𝑐 = 𝐼𝐼 𝑐𝑐 ∑ 𝐼𝐼 𝑐𝑐 𝑁𝑁 𝑐𝑐=1 (S7) For the ionisation of i - th functional group, the Henderson - Hassel balch eq uat ion can b e writ ten i n the form : p 𝐾𝐾 𝑐𝑐 ( 𝛽𝛽 𝑐𝑐 ) = 𝑝𝑝𝐻𝐻 + log � 1− 𝛽𝛽 𝑐𝑐 𝛽𝛽 𝑐𝑐 � for i = 1,…, N (S 8) Defining Δ p 𝐾𝐾 𝑐𝑐 = p 𝐾𝐾 1 − 𝑝𝑝 𝐾𝐾 𝑐𝑐 = 𝑙𝑙 𝑚𝑚𝑔𝑔 � 𝛽𝛽 𝑐𝑐 ( 1−𝛽𝛽 1 ) 𝛽𝛽 1 ( 1−𝛽𝛽 𝑐𝑐 ) � for i = 2,…, N (S9) and 110 𝑞𝑞 𝑐𝑐 = 10 Δ p𝐾𝐾 𝑐𝑐 for i = 2,…, N ( S 1 0 ) it is possible to obtain β i as a function of β 1 365 : 𝛽𝛽 𝑐𝑐 = 𝑞𝑞 𝑐𝑐 𝛽𝛽 1 1+ ( 𝑞𝑞 𝑐𝑐 −1 ) 𝛽𝛽 1 for i = 2,…, N (S11) This set of equations was used to calculate the ionization of the sulphate and carbox y l groups of the heparin and the solution pH as a function of α for the conditions in the ITC experiments taking into account cha in end effects on the fractional charge of the heparin used in this stud y ( Fig u r e S12 ). Figur e S12 . I oni zat io n de gre e of t he sul fa te gr oup s ( le ft) a nd ca rb o xyl gro up s ( r ig ht) o f he pa rin a s a f unct io n o f t he solutio n pH for differ ent salt c oncentratio ns o f the ele ctrol yte . T he ionizati on curves were calculated for a te m p erature of 37°C tak ing into account chain end effects on the f ractio nal charge. 111 7.4. Det ails on SPB - H S A Inter action De scrib ed in C hapt er 4. 4. 7.4.1. ITC Data 0 5000 10000 15000 20000 25000 -2 0 2 4 6 8 0 100 200 300 400 500 600 -0, 2 0,0 0,2 Ti me ( mi n ) µcal / sec I =20m M T=25 o C H S A D ilu tio n HSA + SPB n( HSA) / n ( SPB) kcal / mol e of i nj ec t ant 0 5000 10000 15000 20000 25000 0 1 2 3 4 5 6 7 8 9 10 0 100 200 300 400 500 600 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 Ti me ( mi n ) µcal / sec I =20m M T=27 o C HSA + SPB H S A D ilu tio n n( HSA) / n ( SPB) kcal / mol e of HS A 0 5000 10000 15000 20000 25000 30000 0 2 4 6 8 10 12 0 100 200 300 400 500 600 0,0 0,1 0,2 0,3 0,4 0,5 Ti me ( mi n ) µcal / sec I =20m M T=29 o C H S A D ilu tio n HSA + SPB n( HSA) / n ( SPB) kcal / mol e of i nj ec t ant 0 5000 10000 15000 20000 25000 30000 35000 0 2 4 6 8 10 12 0 100 200 300 400 500 600 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 Ti me ( mi n ) µcal / sec I =20m M T=31 o C H S A D ilu tio n HSA + SPB n( HSA) / n ( SPB) kcal / mol e of i nj ec t ant a) b) c) d) 112 0 10000 20000 30000 40000 0 2 4 6 8 10 12 0 100 200 300 400 500 600 0,0 0,2 0,4 0,6 Ti me ( mi n ) µcal / sec I =20m M T=33 o C H S A D ilu tio n HSA + SPB n( HSA) / n ( SPB) kcal / mol e of i nj ec t ant 0 10000 20000 30000 40000 50000 0 2 4 6 8 10 12 0 100 200 300 400 500 600 0,0 0,2 0,4 0,6 0,8 Ti me ( mi n ) µcal / sec I =20m M T=35 o C H S A D ilu tio n HSA + SPB n( HSA) / n ( SPB) kcal / mol e of i nj ec t ant 0 10000 20000 30000 40000 50000 0 2 4 6 8 10 12 14 0 100 200 300 400 500 600 0,0 0,2 0,4 0,6 0,8 1,0 Ti me ( mi n ) µcal / sec I =20m M T=36 o C H S A D ilu tion HSA + SPB n( HSA) / n ( SPB) kcal / mol e of i nj ec t ant 0 10000 20000 30000 40000 50000 60000 0 2 4 6 8 10 12 14 16 0 100 200 300 400 500 600 0,0 0,2 0,4 0,6 0,8 1,0 1,2 Ti me ( mi n ) µcal / sec I =20m M T=37 o C H S A D ilu tion HSA + SPB n( HSA) / n ( SPB) kcal / mol e of i nj ec t ant Figu re S13. I T C dat a for th e a dsorption of HSA onto S P B at pH 7.2, I = 20 m M, an d tem peratur es: (a) 25°C , (b) 27° C, (c) 2 9°C, (d ) 31° C, (e) 33°C , (f) 35° C, (g) 36°C, (h ) 37°C , res pecti vely . T he u pper panel sh ows t he raw data of th e adsorpt ion of HSA onto S P B (bl ack c ur ve s) and dil utio n o f HS A b y buf fer (c yan c ur ves) . T he inte gra ted hea ts o f eac h injection are sh o wn in the lower panel. e) f) g) h) 113 0 5000 10000 15000 20000 25000 -1000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 25 o C: HSA + SPB (after subtracti on of the heat of dilution of HSA) SPB Dilution Q cal/mole of HSA n(HSA)/n(SPB) 0 5000 10000 15000 20000 25000 -1000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 27 o C HSA + SPB (after subtracti on of the heat of dilution of HSA) SPB Dilution Q in cal/mol of HSA n(HSA)/n(SPB) 0 5000 10000 15000 20000 25000 30000 -1000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 29 o C: HSA + SPB (after subtracti on the heat of dilution of HSA) SPB Dilution Q cal/mole of HSA n(HSA)/n(SPB) Figu re S14. Integrat ed heats of each injection af ter first subtraction (corrected for protein h ea t of dilution) (black circles) and th e heat of dilution of SP B by buffer (red squares) in the case of low pro tein co ncentratio n (24 g/ L). a) b) c) 114 0 5000 10000 15000 20000 25000 0 2000 4000 6000 8000 10000 12000 Q in cal/mol of HSA n(HSA)/n(SPB) 25 o C 0 5000 10000 15000 20000 25000 30000 0 2000 4000 6000 8000 10000 12000 Q in cal/mol of HSA n(HSA)/n(SPB) 27 o C 0 5000 10000 15000 20000 25000 30000 0 2000 4000 6000 8000 10000 12000 Q in cal/mol of HSA n(HSA)/n(SPB) 29 o C 0 5000 10000 15000 20000 25000 30000 35000 0 2000 4000 6000 8000 10000 12000 Q in cal/mol of HSA n(HSA)/n(SPB) 31 o C 0 10000 20000 30000 40000 0 2000 4000 6000 8000 10000 12000 Q in cal/mol of HSA n(HSA)/n(SPB) 33 o C 0 10000 20000 30000 40000 0 2000 4000 6000 8000 10000 12000 Q in cal/mol of HSA n(HSA)/n(SPB) 35 o C 0 10000 20000 30000 40000 50000 0 2000 4000 6000 8000 10000 12000 Q in cal/mol of HSA n(HSA)/n(SPB) 36 o C 0 10000 20000 30000 40000 50000 0 2000 4000 6000 8000 10000 12000 Q in cal/mol of HSA n(HSA)/n(SPB) 37 o C 115 Figu re S15. The in tegrate d heats Q of ads orption of HSA ont o SPB at tem perature s betw een 25°C and 37°C for I = 20 mM. The respectiv e fits ( TSIS model) are display ed as solid red lin e. The HSA co ncent rations were as follows: 24.0 g /L (f or m easureme nts a t temp. 25 – 29°C); 35.0 g/ L (for m easurem ent at t e m p. 31°C) a nd 4 5.0 g/ L (for measure ment at temp. 33 – 37 °C ). The con cent rati on of SPB var ied f ro m 1.38 to 1.84 g /L. 0 10000 20000 30000 40000 50000 60000 1 2 3 4 5 6 0 100 200 300 400 500 600 0,0 0,1 0,2 0,3 0,4 0,5 Ti me ( mi n ) µcal / sec I =50m M T=37 o C H S A D ilu tion HSA + SPB n( HSA) / n ( SPB) kcal / mol e of i nj ec t ant Figu re S16. I T C dat a f or t he adsorpt ion of HSA onto S P B at pH 7.2, I = 50 m M, an d temperatu re of 37° C. The u pper pane l show s the ra w data of t he adsorpt ion of HSA onto S P B (bl ack curve s) an d dilut ion of HSA by buffer (cy an curves). The integ r ated heats of each injection are shown in the lower panel . Plot refer to section 4.4.3.1. 7.4.2. Th ermodyn amic Da ta 298 300 302 304 306 308 310 0 100 200 300 400 ∆ H 1 ITC ∆ H 2 ITC ∆ H i ITC (kJ/mol) Temperature (K) Figu re S17. Total c alorimetric enthalpie s ( ∆H i ITC ) for HSA ads orption on to SPBs at diff e rent tempera t ures at I = 20 mM a nd pH 7.2. Plot ref er to se ction 4.4.3.2. 116 300 305 310 -26 -24 -22 ∆ G b (kJ/mol) Temperature (K) Figu re S18. Temperature dependence of the ∆ G b in th e second s tep of bi ndi ng of HS A ont o SPB. Solid re d lin e represents th e fitting obtained fro m the integrated form of t he nonl inear van’t Hoff equ at ion (eq. 20). Plot ref er to section 4.4.3.2. 298 300 302 304 306 308 310 -40 -20 0 20 40 60 ∆ G 2 T ∆ S b2 ∆ H b2 Contribution to ∆ G b2 (kJ/mol) Temperature (K) Figu re S19. C ha nge s in the t h er mod ynamic pa ra me ter s ( ∆G b , ∆H b , T∆S b ) that accom panie s th e second step of binding of HSA onto SPB as a function of temperature. Black squares sho ws t he binding free energy. Solid black line shows the theoretical fit o f ∆G b (eq. 20). T∆S b is sho wn as da s hed or ange li ne. ∆H b i s sh o wn as dashed blue l ine. Characteristic tem peratu res for the s eco nd s t ep of bi nding ( T 2S = 284 ± 7 K and T 2H = 298 ± 7 K ) are n ot displ ay ed in the plot in order to maintain t he better clarit y. Plo t refer to section 4.4.3.2. 117 20 25 30 35 40 45 0 5 10 15 20 second step of binding ∆ H b2 (kJ/mol) T ∆ S b2 (kJ/mol) Figu re S20. Energeti cs of HSA binding to SPB: dependence of the enthalpy, ∆H b on the entrop y factor, T∆S b i n th e second step of bindi ng. Solid blac k line shows the li near fi t resultin g in equation 5 1. P lot refer to sec tion 4.4.3.3. 118 Table S4 . Therm od yn a mi cs param eters f or the f irst and s ec ond bi nding of HSA ont o SPB. T (K) N 1 ∆ H 1 IT C (kJ / mol) K b1 ∙ 10 -5 ( mo l -1 ) ∆ G b1 (kJ / mol) ∆ H b1 (kJ / mol) ∆ S b1 (kJ / mol / K) N 2 ∆ H 2 IT C (kJ / mol) K b2 ∙ 10 -4 ( mo l -1 ) ∆ G b2 (kJ / mol) ∆ H b2 (kJ / mol) ∆ S b2 (kJ / mol / K) 298 663 ± 58 143 ± 15 2,24 ± 0.38 - 30.5 ± 0, 4 - 110 ± 17 - 0.27 ± 0. 06 493 ± 26 0 71 ± 38 0.9 ± 0.2 - 22.5 ± 0. 5 - 1 ± 6 0.07 ± 0.02 300 787 ± 24 0 133 ± 37 1,55 ± 0.26 - 29.8 ± 0, 4 - 84 ± 12 - 0.18 ± 0. 04 600 ± 29 0 60 ± 37 0.9 ± 0.3 - 22.6 ± 0. 7 3 ± 4 0.08 ± 0.01 302 944 ± 12 0 219 ± 33 1,34 ± 0.12 - 29.6 ± 0, 2 - 59 ± 8 - 0.10 ± 0. 03 627 ± 33 0 110 ± 29 0.9 ± 0.3 - 22.8 ± 0.7 6 ± 3 0.09 ± 0.01 304 689 ± 13 0 247 ± 55 1,25 ± 0.20 - 29.7 ± 0, 4 - 33 ± 7 0.01 ± 0.02 558 ± 47 0 144 ± 34 0.9 ± 0.3 - 23.0 ± 0. 8 9 ± 2 0.11 ± 0.01 306 650 ± 28 0 252 ± 50 1,20 ± 0.34 - 29.8 ± 0, 7 - 7 ± 10 0.07 ± 0.03 450 ± 26 0 126 ± 32 1.0 ± 0,4 - 23.4 ± 1.0 12 ± 4 0.12 ± 0.01 308 760 ± 32 0 285 ± 65 1,36 ± 0.62 - 30.3 ± 1, 3 19 ± 15 0.16 ± 0.05 633 ± 39 0 137 ± 28 0.9 ± 0.6 - 23.3 ± 2. 0 16 ± 6 0.13 ± 0.02 309 612 ± 30 0 278 ± 52 1,23 ± 0.50 - 30.1 ± 1, 1 32 ± 18 0.20 ± 0.06 433 ± 27 0 133 ± 52 1.0 ± 0.4 - 23.6 ± 1 .0 17 ± 8 0.13 ± 0.02 310 541 ± 16 0 296 ± 70 1,08 ± 0.32 - 29.9 ± 0, 8 44 ± 21 0.24 ± 0.07 470 ± 24 0 154 ± 45 1.0 ± 0.6 - 23.7 ± 1. 8 19 ± 9 0.14 ± 0.03 N i - number of adsorbed proteins d etermined from titrations at each tem per ature. K bi , ∆H i ITC and ∆G bi values are the experimental values determined from titrations at each te mperature. ∆H bi , ∆S bi , ∆C p1vH = 12.1 ± 2.7 kJ·mol -1 ·K -1 and ∆C p2vH = 1.7 ± 1.1 kJ·mol -1 ·K -1 - bi ndi ng e ntha lp y, e ntr op y and heat ca p ac it y cha nge , r esp ec ti vel y a s o bt aing t hr ou gh ap pl ic a tion o f equa tion (20). ∆C p1ITC = 13.7 ± 1.6 kJ· mo l -1 ·K -1 and ∆C p2ITC = 6.9 ± 1.7 kJ·mol -1 ·K -1 - obtained from linear tem p erature dependence of ∆H i ITC . 119 Table S5 . T he calcu lated gain of entrop y ∆G ci and the residual part (T∆S res ) of the tota l bindin g entrop y T∆S b. T ( K) ∆ G ci (k J / m ol) T∆S res (k J / m ol) 298 - 24.6 - 105.1 300 - 24.8 - 78.8 302 - 25.0 - 55.2 304 - 25.1 - 22.1 306 - 25.3 - 3.9 308 - 25.5 23.8 309 - 25.5 36.3 310 - 25.6 48.8 Aver age error on ∆G ci and T∆S res is 4 a nd 14 kJ·m ol -1 , respectively . 7.5. Det ails on PPB - HSA Inter action De scri bed in C hap ter 4. 5. 7.5.1. QCM -D Data for I- and pH Cyc le upon H SA Adsorpt ion 02468 -80 -70 -60 -50 -40 -30 -20 -10 0 10 ∆ f n /n (Hz) Time (hrs) ∆ f 3 /3 ∆ f 5 /5 ∆ f 7 /7 02468 -6 -4 -2 0 2 4 ∆ D (10 -6 ) Time (hrs) ∆ D 3 ∆ D 5 ∆ D 7 120 Figur e S21 . I - an d pH in duced respon se of pr otei n pre - compl ex ed PAA brush m o nit ored by QCM - D. T op pan el: QCM - D nor maliz ed fre que nc y signa l . Lo we r p ane l: Q CM - D d issipation s ignal. Re sults for the third , the fifth, and the s e venth overtone are displayed. Plots refer t o s ection 4.5.2. -10 0 10 -70 -60 -50 -40 -30 ∆ f 3 ∆ f 5 ∆ f 7 ∆ f (Hz) ∆ D(10 -6 ) Figur e S22 . Distrib ution of ∆ f as a fu nct io n o f t he co r re sp o ndi ng ∆ D . Res ult s fo r the t hir d, the fi ft h, a nd t he seventh overton e are displayed. P lot ref er to section 4.5.2. 121 7.5.2. QCM -D Data for pH In du ced Sw elli ng /Desw ellin g of a Protein - Free PAA B rush 01234 -10 -8 -6 -4 -2 0 2 4 6 ∆ f n /n (Hz) Time (hrs) ∆ f 3 /3 ∆ f 5 /5 ∆ f 7 /7 01234 -2 -1 0 1 2 3 4 ∆ D (10 -6 ) Time (hrs) ∆ D 3 ∆ D 5 ∆ D 7 Figur e S23 . pH in duc ed res ponse of protei n - free PAA brus h m o nit ored by Q CM - D . T o p pa nel: QCM - D normalized f req uency signal. Lower panel: QCM - D dissip atio n signal. Res ults for the th ird, the fifth, and t he seventh overton e are displayed. P lots refer t o section 4.5. 3. 122 -10 0 10 -40 -30 -20 -10 0 10 20 30 ∆ f 3 ∆ f 5 ∆ f 7 ∆ f (Hz) ∆ D (10 -6 ) Figur e S24 . Distrib ution of ∆ f as a fu nct io n o f t he co r re sp o ndi ng ∆ D . Res ult s fo r the t hir d, the fi ft h, a nd t he seventh overton e are displayed. P lot ref er to section 4.5.3. 123 BIBLIOG RAPHY (1) Manning, G. S. The Mo lecula r T heory of Polyelec trol yte Solution s with Applicatio ns to th e Electr ostatic Propert ies of P oly nucleot ides. Q. Rev. 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