Document [original]

Modelling Peptides at Interfaces

in Atomic Detail

vorgelegt von

Dipl.-Phys.

Tobias Daniel Pobandt

aus Meppen

Von der Fakultät II - Mathematik und Naturwissenschaften

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften

- Dr. rer. nat. -

genehmigte Dissertation

Promotionsausschuss:

Vorsitzende: Prof. Dr. Sabine Klapp

Gutachter: Prof. Dr. Martin Schoen

Gutachter: Dr. Volker Knecht

Tag der wissenschaftlichen Aussprache: 13. Dezember 2013

Berlin 2014

D 83

Contents

1 Introduction 1

1.1 Biological membranes and phospholipid bilayers . . . . . . . . 3

1.2 Amyloiddeposits......................... 6

1.2.1 Components and structure . . . . . . . . . . . . . . . . 6

1.2.2 Formation: Misfolding and intermediates . . . . . . . . 8

1.3 Alzheimer’s disease . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3.1 Molecular aspects . . . . . . . . . . . . . . . . . . . . . 12

1.3.2 Amyloid β........................ 15

1.3.3 Interaction of amyloid βwith membranes: Ca2+

dyshomeostasis...................... 17

1.4 Antimicrobial peptides . . . . . . . . . . . . . . . . . . . . . . 20

1.4.1 Properties and modes of action . . . . . . . . . . . . . . 20

1.4.2 NK-2 and its interaction with biological membranes . . 23

2 Methods 25

2.1 Molecular dynamics . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2 Umbrellasampling ........................ 29

2.3 Thermodynamic integration . . . . . . . . . . . . . . . . . . . . 30

2.3.1 Dummy atoms and soft-core-potential . . . . . . . . . . 33

2.4 Analysismethods......................... 35

2.4.1 Lipid order parameters . . . . . . . . . . . . . . . . . . 35

2.4.2 Secondary structure of peptides: DSSP . . . . . . . . . 35

2.4.3 Cluster analysis . . . . . . . . . . . . . . . . . . . . . . 36

3 Amyloid β: Peptide folding at an air-water-interface 39

3.1 Simulationsetup ......................... 40

3.2 Results............................... 42

3.2.1 Aβ40: Secondary structure and cluster analysis . . . . . 43

3.2.2 Aβ42: Secondary structure and cluster analysis . . . . . 49

iii

Contents

3.2.3 Discussion and comparison of Aβ40 and Aβ42 ...... 55

4 Amyloid β: Pore formation in phospholipid bilayers 57

4.1 Simulationsetup ......................... 58

4.2 Results............................... 60

4.2.1 Size and shape of pores . . . . . . . . . . . . . . . . . . 60

4.2.2 Free energy of membrane pores . . . . . . . . . . . . . 63

4.2.3 Influence of Aβ42 on the bilayer tail region . . . . . . . 64

4.2.4 Poredensities....................... 65

4.2.5 Water permeabilities and lipid flip flop waiting times . . 68

4.2.6 Pore closure and pore opening times . . . . . . . . . . . 69

4.3 Discussion and summary . . . . . . . . . . . . . . . . . . . . . 71

5 NK-2: Affinity for phospholipid bilayers 73

5.1 Simulationsetup ......................... 74

5.2 Results............................... 76

5.2.1 Secondary structure and position . . . . . . . . . . . . . 76

5.2.2 Binding affinities from simulations . . . . . . . . . . . 78

5.2.3 Comparison with electrophoresis experiments . . . . . . 79

5.3 Discussion............................. 87

5.4 Conclusion ............................ 89

6 Summary 91

Glossary 95

Acronyms................................ 95

Symbols................................. 97

Appendix 99

A.1 Amyloid β: Time evolution of secondary structure at air-water-

interface.............................. 99

A.2 Amyloid β: Pore densities in phospholipid bilayers . . . . . . . 104

A.3 NK-2: Time evolution of secondary structure at phospholipid

bilayers ..............................107

Bibliography 109

Publication List 133

Danksagung 135

Introduction

The interaction between proteins and biomembranes is crucial for many bio-

logical processes including membrane fusion, selective transport through mem-

branes, or defence mechanisms of the innate immune system. Under pathogenic

conditions this interaction might be strongly involved in the progress of several

severe maladies including neurodegenerative diseases. A prevalent example of

such a neurodegenerative disease is Alzheimer’s disease. Here, the mutual in-

teraction of the so-called amyloid β(Aβ) peptide with cellular membranes is

believed to be essential for the pathogenesis. Cellular membranes might pro-

mote aggregation of the peptide which may result in the formation of amyloid

deposits. On this aggregation pathway the peptide accumulates into various

toxic oligomers which affect the cell membrane by increasing its permeability

for ionic species like Ca2+ions leading to calcium dyshomeostasis and, subse-

quently, cell death. This alteration of the membrane permeability might arise

from peptide mediated membrane pores.

Another class of peptides capable to induce pores in membranes is provided by

antimicrobial peptides. These peptides are part of the innate immune system

of nearly all higher organisms. Antimicrobial peptides attack and kill intrud-

ing prokaryotic cells like bacteria but spare organism innate eukaryotic cells.

Several studies suggest that this selectivity arises from different affinities of the

peptides to prokaryotic and eukaryotic plasma cell membranes due to a different

lipid composition between these two types of membranes. Antimicrobial pep-

tides may play a fundamental role in future health care as they might serve as

a template for the development of peptidomimetic alternatives to conventional

Chapter 1 INTRODUCTION

antibiotics which suffer from increasing inefficiency due to growing resistance

of pathogenic bacteria.

In this study three questions concerning peptide-membrane interactions are ad-

dressed. The first two involve the amyloid βpeptide and its role in Alzheimer’s

disease and the third the selectivity mechanism of antimicrobial peptides.

•How do various factors like the presence of interfaces, pH or the number

of residues influence the folding behaviour of Aβmonomers?

•How does the Aβmonomer affect membrane defects like water pores in

terms of their size, frequency, or stability?

•How does the lipid composition affect the membrane affinity of the an-

timicrobial peptide NK-2?

All three questions are addressed by molecular dynamics (MD) simulations. In

the first case 2µs MD simulations in combination with secondary structure and

cluster analysis methods are employed to study the folding behaviour of Aβ40

and Aβ42 in bulk solution and at an air-water-interface under slightly acidic and

pH neutral conditions. The influence of the Aβ42 monomer on membrane de-

fects is investigated by determining the free energy of water pores within zwit-

terionic phospholipid bilayers by means of MD simulations combined with the

umbrella sampling technique. Finally, the difference in the affinity of NK-2 for

anionic and zwitterionic phospholipid bilayers is estimated by MD simulations

in conjunction with the thermodynamic integration (TI) method. All methods

are introduced in chapter 2.

In the remainder of this chapter the biological background is given. In section

1.1 phospholipid bilayers serving as model systems for biomembranes are in-

troduced. Subsequently, the structure and the aggregation process of amyloids

known to be formed by several different peptides are presented in section 1.2.

Alzheimer’s disease and in particular the Aβpeptide as well as peptide-mediated

calcium dyshomeostasis are described in section 1.3. Finally, antimicrobial pep-

tides, their mode of action, and especially the NK-2 peptide are treated in section

1.4.

Biological membranes and phospholipid bilayers 1.1

1.1 Biological membranes and phospholipid bilayers

Biological cells are categorized as (i) eukaryotes being mostly the building-

blocks of multicellular organisms like animals, land plants, and fungi, or (ii)

prokaryotes occurring mostly as unicellular organisms including bacteria, ar-

chaea, or protozoa. In eukaryotic cells the majority of the genetic material is

stored in a nucleus enveloped by a membrane whereas the genetic material of

prokaryotes is largely bound in a DNA/protein complex, the so-called nucleoid.

In contrast to prokaryotes, eukaryotic cells are furthermore compartmentalized

into organelles like the nuclei, mitochondria, chloroplasts, and the endoplasmic

reticulum.

However, in both cases cell membranes are essential for the existence and via-

bility of the cell. They do not just simply separate the inside from the outside

of the cell but also fulfil many fundamental biological tasks as the importation

of gases, nutrients, or solutes into the cell, as well as the exportation of toxic

waste products out of the cell. The permeability of cell membranes has thus

to be highly selective concerning the molecular species and the direction of the

molecular flux through the membrane. Permeation through membranes is en-

abled by passive diffusion as well as active transport by carrier and channel

proteins. Furthermore cell membranes have to maintain large chemical gradi-

ents between the intra- and extracellular space. This involves especially ionic

species. For instance the extracellular concentration of K+ions is with ∼4 mM

much lower than inside the cell where a K+ion concentration of ∼140 mM is

maintained. The concentration of Ca2+ions outside the cell is typically 1000-

fold higher than in the cytosol [1].

Biological membranes are mainly composed of lipids and integral or peripheral

Membrane Lipid Protein

Myelin Sheath 80% 20%

Plasma Membrane 50% 50%

Mitochondrial Inner Membrane 25% 75%

Table 1.1: Mass content of lipids and proteins of three different mammalian membranes as

taken from [1].

proteins. Here, the protein content strongly depends on the biochemical func-

tionality of the membrane as indicated in table 1.1. Myelin sheaths have a rather

simple biological function as they merely electrically insulate axons whereas mi-

tochondrial inner membranes fulfil several tasks involving the reformation of the

energy carrier adenosine triphosphate (ATP). Lipids can be grouped into func-

tional lipids like phosphatidylinositol, phosphatic acid or gangliosides as well

Chapter 1 INTRODUCTION

as lipids playing a predominately structural role. The latter can furthermore be

categorized into sterols like cholesterol, phospholipids including phosphatidyl-

choline (PC), phosphatidylethanolamine (PE) or phosphatidylglycerol (PG), and

sphingolipids like cerebrosides or glycolipids. Especially phospholipids provide

the main component of biomembranes. The structure of three different phospho-

lipids is exemplary shown in figure 1.1. These lipids contain a polar headgroup

composed of an alcohol group, phosphate, and glycerol and two non-polar tails

each comprising 14 to 24 hydrocarbon groups. Hydrocarbon tails can be satu-

rated as well as mono- or poly-unsaturated.

The amphipathic nature of phospholipids is essential for the formation of lipid

DPPC

DOPC

DOPG

Figure 1.1: Structure of phospholipids considered in this study. Shown are zwitteri-

onic dipalmitoylphosphatidylcholine (DPPC) (chapter 4) and dioleoylphosphatidylcholine

(DOPC) (chapter 5) as well as anionic dioleoylphosphatidylglycerol (DOPG) (chapter 5).

Cationic choline groups are highlighted in light green, anionic phosphate groups in blue,

neutral glycerol groups in red, and acyl groups in yellow.

bilayers being the basis of biomembranes. Lipid bilayers are composed of two

leaflets of phospholipids arranged such that the lipid head groups are aligned in

a plane whereas all hydrocarbon tails point in one direction. Both leaflets are

orientated in opposite direction with the hydrophilic head groups facing water

and the hydrophobic hydrocarbon tails buried in the bilayer interior as shown in

figure 1.2. Lipid bilayers form spontaneously if the concentration of phospho-

lipids solvated in water exceeds a critical value. Depending on the environmental

conditions and the lipid concentration other assemblies like micelles or vesicles

may form. This self assembly process is largely driven by the hydrophobic ef-

fect which results from a entropy loss of water molecules surrounding solvated

non-polar particles. The self assembly of (partially) non-polar molecules into

larger clusters minimizes the described entropy loss due to a decreased contact

surface with the aqueous environment. A well known example for this effect are

oil droplets in water. The lack of covalent bonds stabilizing the bilayer struc-

Biological membranes and phospholipid bilayers 1.2

Figure 1.2: Model of a phospholipid bilayer as taken from [2].

ture allows phospholipids as well as incorporated proteins to rotate and diffuse

almost freely lateral to the bilayer surface which is why a phospholipid bilayer

is described as a two dimensional fluid. Even lipid flip flops denoting the trans-

lation of a phospholipid from one leaflet to the other are possible.

The first biomembrane model proposing the described lipid bilayer structure in-

cluding incorporated integral and peripheral proteins was postulated by Singer

and Nicolson in 1972 and is known as the fluid mosaic model [3]. Their model

was the first to be capable of describing the lateral protein and lipid dynam-

ics. An extension of the fluid mosaic model was provided by Simon and Iko-

nen in 1997 by additionally regarding so called lipid rafts [4]. Lipid rafts are

sphingolipid- and cholesterol-rich relatively tight packed microdomains floating

in the lipid bilayer matrix which might be associated with cellular signalling

processes [5]. Here, cholesterol is believed to serve as glue holding the mi-

crodomain together whereas the higher packing density results from an extraor-

dinarily high content of saturated hydrocarbon tails.

The phospholipid composition of the outer plasma membrane leaflet of eu- and

prokaryotic cells differs in that the plasma membrane of eukaryotes contains

mainly zwitterionic PC lipids and cholesterol whereas prokaryotic membranes

contain phospholipids with anionic PG or zwitterionic PE head groups. Prokary-

otic cells are surrounded by a cell wall which can be either detected as gram-

positive or gram-negative depending on its peptidoglycan, i. e. murein, content.

Chapter 1 INTRODUCTION

1.2 Amyloid deposits

1.2.1 Components and structure

In 1854 the German physician Rudolph Virchow found deposits in abnormal hu-

man brains that showed a characteristic reaction with iodine similar to that seen

for starch. He denominated these deposits ’amyloids’ as this term had been pre-

viously used for starchy (i.e. amylaceous) components of plants by the German

botanist Mathias Schleiden in 1838 [6]. Nowadays it is known that amyloids

are mainly composed of unbranched fibrillar structures of peptides or proteins

as shown in figure 1.3. Amyloid fibrils are associated with several neurodegen-

Figure 1.3: Amyloid fibrils of the islet amyloid polypeptide (IAPP) associated with type II

diabetes visualized by electron microscopy (EM) as taken from [7].

erative diseases like Alzheimer’s, Parkinson’s, and Huntington’s disease as well

as non-neuropathic diseases like type II diabetes. These fibrils arise due to mis-

folding and subsequent aggregation of disease-related proteins or peptides, like

the amyloid β(Aβ) peptide (39 to 43 residues) associated with Alzheimer’s, α-

synuclein protein (140 residues) related to Parkinson’s, or the huntingtin protein

(about 3144 residues) with expanded polyQ stretches associated with Hunting-

ton’s disease. Although formed by many different peptides or proteins with

diverse amino acid sequences as well as chain lengths, the corresponding fib-

rils exhibit similar structures. As revealed by atomic force microscopy (AFM)

and transmission electron microscopy (TEM) they are typically built of two to

six protofilaments with diameters between 2 nm and 5 nm. If these protofila-

ments twist around each other along the fibril axis as shown in figure 1.4 (left)

they form rope-like fibrils with a diameter of 7-13 nm [8,9], whereas they form

ribbon-like fibrils with a thickness of 2-5 nm and a width of up to 30 nm if they

align laterally [10–12].

Amyloid deposits 1.2

Figure 1.4: Sketch of the molecular cross-βstructure of amyloid protofilaments (top) as

taken from [13] and the characteristic X-ray fibre diffraction pattern (bottom) of fibrils con-

sisting of islet amyloid polypeptides (IAPP) as taken from [7].

Polypeptides within a protofilament are arranged in a characteristic cross-β

structure where the polypeptide forms β-strands normal and inter-strand hydro-

gen bonds nearly parallel to the fibril axis indicated in figure 1.4 (middle). Char-

acteristic patterns from X-ray diffraction experiments [7,14] are shown in figure

1.4 (right). A strong meridional reflection at 4.7 ˚

A corresponds to the hydrogen

bonding distance between the β-strands and the more diffuse equatorial reflec-

tion at about 10 ˚

A to the inter-sheet distance as apparent from figure 1.4 (middle).

The latter depends on the side chain lengths of the fibril forming polypeptides

and may vary from 5 to 15 ˚

A [15, 16]. The β-sheets as well as the β-strands

may be in parallel or antiparallel orientation. The relative orientation cannot be

determined from X-ray diffraction but from solid-state nuclear magnetic reso-

nance (SSNMR) [17] and Fourier-transform infrared spectroscopy (FTIR) [18].

Further experimental techniques to illuminate the structure of amyloid fibrils in-

clude circular dichroism (CD) spectroscopy and electron microscopy (EM). The

presence of regular β-sheet and therefore fibril structures can be detected by

the fluorescence of Thioflavin T (ThT) as well as by the binding of Congo red

(CR) [19].

Chapter 1 INTRODUCTION

1.2.2 Formation: Misfolding and intermediates

The aggregation of proteins or peptides into amyloids arises due to their misfold-

ing under specific pathological conditions. A large number of human diseases

is associated with protein misfolding, with the majority of these diseases being

linked to the formation of fibrillar aggregates. Misfolding takes place due to

pathological, non-natural conditions which prevent the folding or refolding of

the corresponding polypeptide into, or support their unfolding out of, their na-

tive, functional state.

Since 1998 an increasing number of proteins not related to amyloid diseases

were found to undergo fibril formation [16, 20–22]. It is furthermore notable

that all amyloid forming proteins show no similarities in sequence, size or na-

tive folding structure [23, 24]. This led to the proposal of the "generic hypoth-

esis" of amyloid formation which states that the ability to aggregate into fibrils

is a generic property of the backbone of all polypeptide chains [25] though the

propensity for fibril formation depends on the particular amino acid sequence.

Amino acid substitution experiments show that the aggregation susceptibility of

a polypeptide can be increased by decreasing its net charge or increasing its hy-

drophobicity as well as its propensity to form β-structures [26]. The folding

of a protein into its native state and its aggregation can be seen as two sepa-

rate but competitive processes. They are distinct as the unique native structure

of a natural protein is determined by its amino acid sequence selected by evo-

lution whereas the aggregation into fibrils occurs for each polypeptide with no

regard of its specific amino acid sequence. The native state is mainly determined

by side chain and the fibrillar conformation by main chain interactions [15,24].

Which of these effects is dominant is determined by the given conditions. In nat-

ural environments the biological relevant conformation state of a protein is its

native state. Several mechanisms in living cells including chaperones or ubiqui-

tination help the protein to find its native state and suppress misfolding. These

control mechanisms can fail in amyloid diseases as they may be saturated due

to an overbalance of misfolded proteins. This may furthermore be caused by the

overproduction of the corresponding protein or the failing of its clearance [27].

The close competition between folding and aggregation is indicated in the free

energy landscape of conformational and oligomerization states shown in figure

1.5. Although the thermodynamically most stable state and thus the global free

energy minimum is assumed to correspond to fibrillar structures these structures

are not readily adopted, as proteins have to overcome large free energy barriers

to escape their native state where they may be kinetically trapped. The shape of

the free energy landscape depends on the amino acid sequence of the polypep-

tide as well as the environmental conditions like pH, temperature, ionic strength,

polarity of the medium, peptide concentration and available space. In general the

Amyloid deposits 1.2

Figure 1.5: Free energy landscape of peptide folding and aggregation as taken from [24].

latter is much larger in vitro than in vivo as the concentration of macromolecules

inside the cell amounts to 20-30 % of the total volume. This ’macromolecular

crowding’ reduces the conformational space available for the polypeptide dra-

matically and favours the occupation of rather compact structures like the native

or the aggregation state [24,28].

An important factor for the folding and misfolding process is the interaction of

the corresponding polypeptide with surfaces. In the native environment, such

surfaces are provided by macromolecules or membranes and can support pro-

tein folding as well as unfolding followed by aggregation. Here the efficiency

and rate of protein folding is enhanced at the surface or the interior of chap-

erones [29] whereas membrane surfaces allow polypeptides to partly unfold

and adopt aggregation prone states. Furthermore, surfaces increase the local

polypeptide concentration accelerating its aggregation [30–32]. Evidence from

sonication experiments suggests that even for in vitro experiments intended to

probe aggregation in solution, interactions with interfaces as provided by ac-

cidentally present gas bubbles determines the kinetics of aggregation and fibril

formation [33,34].

As the aggregation-prone residues of natively folded polypeptides like globular

proteins are usually shielded by side-chains a partial unfolding of the polypep-

tide is often necessary before aggregation takes place. For several natively un-

structured polypeptides, aggregation is preceded by the formation of secondary

structure [22]. In both cases the peptide adopts a partially folded state before

Chapter 1 INTRODUCTION

entering the aggregation landscape as indicated in figure 1.5.

During the aggregation of monomers the number of fibrils grows exponentially

after an initial lag phase as it was observed in vitro by the binding of Thioflavin

T (ThT). This lag phase can be shortened by adding preformed fibrillar struc-

tures [35, 36]. This suggests that the formation of fibrils involves a nucleation

process representing the rate limiting step. The nucleus therefore resides at

a local free energy maximum. Due to their heterogeneity the states of small

oligomers are not as well defined as for fibrils, protofilaments, or natively folded

proteins.

The interplay between different folding and aggregation states of a polypep-

tide can be illustrated in a network of equilibria as shown in figure 1.6. After

synthesis from the ribosome and under natural conditions the initially unstruc-

tured polypeptide folds into its native state. These natively folded peptides may

associate into functional oligomers as it occurs for actins, myosins, or micro-

tubules. Along its folding pathway the polypeptide undergoes several transitions

between partially folded intermediates. Non-natural conditions can cause the

aggregation of these intermediates into more or less disordered, soluble, low-

weight aggregates. For the amyloid-βpeptide such oligomers were found to

assemble and dissolve at very high rates. They typically consist of two to six

mainly unstructured monomers [37,38]. These small oligomers may be precur-

sors of larger, metastable, in general β-sheet enriched protofibrils which adopt

different shapes like spherical beads with a diameter of 2-5 nm, linear or curly

chains consisting of these beads or doughnut-like, annular structures [39, 40].

Several polypeptides including amyloid β,α-synuclein, or polyQ-containing

proteins [23] were found to form protofibrils assumed to precede the aggrega-

tion into fibrils [23,41,42]. Interestingly, in some cases aggregation was found

to take place before the unfolding of the polypeptide. This results in the tem-

porary formation of native-like aggregates where the native structure of the cor-

responding polypeptide is almost retained. Examples are given by the insulin

peptide [43] or the pathogenic form of the ataxin-3 protein [44] associated with

spinocerebellar ataxia type-3 also known as ’Machado Joseph disease’. Beside

these aforementioned on-pathway oligomers several off-pathway products also

occur during the aggregation process.

Nowadays much effort is put into the investigation of these off- and on-pathway

oligomers as they have been found to be the major toxic species along the aggre-

gation pathway. This was observed for several disease- (e.g. amyloid β[45,46]

or αsynuclein [47]) as well as nondisease-associated polypeptides [48, 49].

Their toxicity may be caused by the exposure of residues usually buried in the

native or fibrillar state. This may cause several undesired, harmful interactions

with cell components as for example the plasma membrane resulting in the for-

Amyloid deposits 1.3

Figure 1.6: Aggregation and folding pathways taken from [23].

mation of membrane pores [23]. The proportion of exposed residues is increased

for smaller oligomers.

Chapter 1 INTRODUCTION

1.3 Alzheimer’s disease

Alzheimer’s disease (AD) being the most common form of dementia is an age

related, progressive, fatal, and up to date incurable neurodegenerative disorder.

It affects memory, thinking as well as behaviour and is therefore an extremely

staggering diagnosis for patients and their families. The risk of dementia roughly

doubles every five years for individuals aged over 65 years. In 2010 about 36

million people were suffering from dementia worldwide. The total related costs

were estimated to US$ 604 billion. According to the 2010 annual report of

Alzheimer’s Disease International (ADI) the number of dementia patients is ex-

pected to increase up to 115 million until 2050 due to increasing life expectan-

cies. Especially in the developing countries the number of affected individuals

will increase dramatically [50].

1.3.1 Molecular aspects

In a 1907 published study Alois Alzheimer for the first time described the

disease-typical extracellular deposits accumulating in specific regions of the cor-

tex of the brain as well as the neurofibrillary tangles within neurone cells [51].

He obtained his insights from a post-mortem examination of Auguste Deter who

suffered from an early onset type of the disease showing symptoms like rapid

memory loss, delusion and disorientation [52]. In the 1980s the extracellular

deposits were identified as senile plaques consisting of fibrillar structures of the

peptide amyloid β(Aβ) [53] and the neurofibrillary tangles as aggregates of hy-

perphosphorylated tau proteins [54–56].

Hydrophilic tau proteins primarily occur in neuron cells where they facilitate

the nucleation and stabilization of microtubules. In tauopathic diseases like AD,

hyperphosphorylated tau proteins aggregate in an abnormal way as they form

neurofibrillary tangles which might be neurotoxic. Furthermore the aberrant

aggregation of tau proteins provokes the destabilization and reorganization of

microtubules. This also influences other subcellular components like mitochon-

dria or lysosomes. The number of tangles correlates with the grade of dementia

in AD [57].

The 37 to 43 residues long Aβpeptide is a cleavage product of the type I orien-

tated trans-membrane amyloid precursor protein (APP). The physiological role

of APP is still unclear and a matter of intense research. It might be crucial for the

survival of neurones, plasticity of synapses as well as the adhesion of cells [58],

and furthermore seems to have synapto- and neurotrophic functions [59].

The proteolytic enzymes are called secretases. The cleavage of APP via the sec-

retases proceeds either via a non-amyloidogenic or an amyloidogenic and there-

fore pathological pathway as shown in figure 1.7. In the non-amyloidogenic

Alzheimer’s disease 1.3

pathway the APP is first cleaved by α-secretase releasing the peptide APPsα

into the extracellular space (lumen) and leaving behind the αAPP carboxy-

terminal fragment (CTF). Subsequent intersection of the latter by γ-secretase

within the hydrophobic membrane environment delivers the non disease relevant

peptide P3. In the amyloidogenic pathway the cleavage of APP by β-secretase

leaves the αAPP CTF domain in the membrane whereas the APPsβpeptide es-

capes into the lumen. The following cleavage by γ-secretase generates the Aβ

peptide. In both pathways APP intracellular domains (AICD) are delivered into

the cytosol. These peptides might play a role in nuclear signalling [60]. Both

cleavage pathways compete with each other.

In rare, autosomal, early onset forms of AD gene mutations lead to an overpro-

duction of the 42 amino acids long, most toxic and most amyloidogenic form

of Aβ. This gives strong evidence for the pivotal role of the Aβpeptide and

its aggregation process in the pathogenesis of AD. It is expressed in the preva-

lent ’Amyloid-hypothesis’ [53, 61]. The susceptibility for the most common,

sporadic form of AD is determined by different genes which still have to be

completely identified. One of these genes is located at chromosome 19 and is

responsible for the generation of the apolipoprotein E (ApoE). The gene occurs

in three different alleles which results in the generation of three different iso-

forms of ApoE. A higher risk of AD is associated with the production of the

ApoE-ε4 isoform which might cause an increased cleavage and aggregation as

well as a decreased clearance of the Aβ42 peptide [58].

Figure 1.7: The anti-amyloidogenic (left) and the amyloidogenic (right) pathway of APP

cleavage as taken from [60].

Chapter 1 INTRODUCTION

Several findings support the view that not insoluble mature fibrils but instead

soluble structures like small oligomers [62, 63], Aβderived diffusible ligands

(ADDL) [64] or protofibrils [65,66] are the most toxic forms of the Aβpeptide.

Several different mechanisms may cause the neurotoxicity of Aβ. Patients of

AD exhibit an increased concentration of highly reactive oxygen species (ROS)

in brain cells. This oxidative stress might be correlated with the Aβpeptide

in a vicious circle. On the one hand, the interaction of Aβwith metal ions as

Fe2+or Cu+generates reactive oxygen radicals (ROS) like hydrogen perox-

ide increasing the oxidative stress [67, 68]. On the other hand, oxidative stress

might promote the amyloidogenic cleavage of APP and therefore the generation

of Aβ[58]. The radicals provoke lipid peroxidation and protein oxidation [69].

Furthermore the oxidative stress causes changes in membrane transport, recep-

tor, ion channel, or even tau proteins. The latter might facilitate the formation

of neurofibrillary tangles [58]. In addition, Aβalso directly interacts with tau

proteins leading to a disassembly of microtubules followed by cell death [70].

Another very important aspect of Alzheimer’s disease is the disruption of cal-

cium homeostasis as described in section 1.3.3.

Larger amounts of Aβoligomers are especially found in the vicinity of synapses

as APP is transported along the axons and cleaved at presynaptic terminals. Neu-

ronal death might start at synapses where Aβoligomers cause disruption of

calcium homeostasis, alterations in vesicle trafficking, oxidative stress as well

as the injury of mitochondria and the endoplasmic reticulum. The obstruction

of long-term potentiation by Aβoligomers might be the reason for memory

deficits at an early stage of the disease before degeneration of neurons takes

place [58,71,72].

Several therapeutic approaches against AD are still under development. One of

these approaches is based on preventing the cleavage of toxic forms of the Aβ

peptide by β- or γ-secretase blockers [73]. Other strategies try to reduce the fib-

ril formation and therefore the oligomerization of Aβ. This can be obtained by

binding Aβaggregation provoking copper and iron ions to ligands. The result-

ing complexes additionally reduce oxidative stress [58]. Promising as well are

therapies based on the stimulation of the immune system which consequently

increases the clearance of Aβfrom the brain [74,75].

Alzheimer’s disease 1.3

1.3.2 Amyloid β

The amino acid sequence of the Aβ42 peptide is shown in figure 1.8. The pep-

tide is amphiphilic as it contains a largely hydrophilic domain starting from its

N-terminus and spanning the residues ASP1 to LYS16 and an hydrophobic do-

main spanning the residues LEU17 to ALA42.

ASP

GLU

ASP

GLU

HIS

LYS

HIS

LYS

ARG

SER

TYR

GLN

ASN

ALA

PHE

GLY

VAL

GLU

LEU

VAL

PHE

ALA

VAL

GLY

ILE

ALA

GLY

ILE

GLY

VAL

MET

LEU

GLY

ALA

ILE

VAL

GLY

Nonpolar

Polar

Positive

Negative

Figure 1.8: Amino acid sequence of the Aβ42 peptide and the charge state of its residues at

the isoelectric point.

Several findings indicate that the so called ’self recognition site’ including the

residues Lys16 to Phe20 is crucial for the oligomerization and formation of fib-

rils [76]. It serves as ’glue’ to bind several peptides together. Especially π-

stacking interactions between the aromatic rings of the phenylalanine residues

Phe19 and Phe20 are believed to drive the aggregation and determine the β-

sheet structure [77]. According to this the domains Aβ15−20 [78] as well as

Aβ17−21 [79] have been reported to bind to the full length Aβ42 peptide. The

Aβ16−22 domain assembles into well ordered fibrils [80].

The hydrophobic C-terminal domain of the Aβpeptide which is buried in

the membrane environment before cleavage of APP takes place features three

GlyXXXGly motifs involving the residues Gly25, Gly29, Gly33, and Gly37.

Such glycine patterns are rather common in helical transmembrane channel pro-

teins and believed to drive and determine the packing of these proteins by the

so called glycine zipper mechanism resulting in the formation of membrane

channels [81]. On the other hand glycine is known to destabilize helices in

aqueous environments due to its high flexibility [82]. The direct interaction of

Aβoligomers with the membrane leading to the emergence of ion permeable

membrane channels might play a crucial role in the pathogenesis of Alzheimer’s

disease as described in section 1.3.3. Singular substitutions of Gly25, Gly29,

Gly33 or Gly37 by leucine within the Aβ42 peptide have been shown to reduce

the neurotoxicity of the peptide and concentration of small toxic oligomers in

solution and attached to lipid membranes [83,84]. These findings underline the

crucial role of the GlyXXXGly motif for oligomerization and membrane bind-

ing of Aβand therefore its neurotoxicity.

Chapter 1 INTRODUCTION

The three histidine residues His6, His13, and His14 are double protonated in

slightly acidic and mono protonated in pH neutral environments. This leads to a

change in the net charge of the peptide from -3 e in neutral to 0 in acidic envi-

ronments. Accordingly, the hydrophilicity of the N-terminal residues decreases

which might promote amyloid formation [85]. This may be disease-relevant as

AD patients exhibit a rather acidic environment within the brain compared to the

non diseased case [86].

A still very elusive question about Aβconcerns the much higher neurotoxic-

ity and aggregation propensity of the Aβ42 alloform compared to Aβ40 as both

peptides differ only in two additional residues. Simulation and nuclear mag-

netic resonance (NMR) spectroscopy studies suggest that the additional residues

Ile41 and Ala42 increase the rigidity of C-terminal residues promoting aggrega-

tion [87,88]. By comparing the secondary structures of Aβ40 and Aβ42 at aggre-

gation favouring (T>5◦C) and non-favouring (T<5◦C) conditions by a com-

bination of CD and NMR spectroscopy it was found that both peptides undergo

similar changes from coil to aggregation prone, β-sheet enriched conforma-

tions due to a temperature increase which suggests a similar aggregation mech-

anism. Striking differences were mainly observed for the C-terminal residues

being more structured and prone for β-sheet formation in case of the Aβ42 allo-

form [89].

Despite much effort that had be taken into account the soluble structure of the

full length Aβ40 and Aβ42 peptides in aqueous solution has so far not been iden-

tified. This is due to the peptides’ high tendency to aggregate in water.

NMR experiments indicate that the Aβ10−35 fragment in aqueous solution adopts

a stable collapsed coil structure lacking any significant secondary structure con-

tent but forming a well defined hydrophobic cluster spanning residues Leu17

to Ala21 [90]. Aβ10−35 is more soluble than the full length Aβ40 peptide but

shows comparable chemical shifts in NMR measurements suggesting similar

secondary structure features. The occurrence of a collapsed coil structure could

not be confirmed for Aβ40 and Aβ42 by NMR spectroscopy at low temperatures

(<5◦C) whereas local structure motifs as bends and turns appear similar [91].

More recent NMR experiments showed that Aβ40 in aqueous solution adopts

a partially folded conformation exhibiting a helical structure spanning residues

His13 to Asp23 [92]. Nowadays it is widely believed that the free energy land-

scape of folding for the Aβpeptide is rather flat. This implies a high depen-

dence of the peptide structure on the environmental conditions as well as a rather

high transition rate between different conformations. The latter is confirmed by

NMR [93] as well as replica exchange molecular dynamics (MD) simulations in

implicit [94] and explicit solvent [95]. These simulations predict several differ-

ent peptide conformations featuring structures comprising rather small peptide

Alzheimer’s disease 1.3

segments. Based on similarity the conformations can be classified into a few

clusters between which rapid exchange was found. Hereby it has to be noted

that the results from [94] should be regarded with care as peptide structure pre-

dictions by means of implicit solvent models suffer several shortcomings. For

instance β-structure contents are under- and α-helix contents are overestimated,

and non-native states appear to be overrepresented in replica exchange simula-

tions [96].

In membrane-mimicking environments containing micelles or organic solvents

like fluorinated alcohols (e.g. trifluoroethanol (TFE) or hexafluoroisopropanol

(HFIP)) Aβ40 and Aβ42 were found to adopt mainly α-helical structures [97,98].

The peptides therefore have to undergo a transition from α-helical to β-sheet

conformations on their pathway from the membrane environment to the aggre-

gation state. Although this transition is still poorly understood, it could been

monitored for the Aβ42 peptide solvated in a water/HFIP solution by NMR and

CD spectroscopy [97]. The transition was induced by gradually increasing the

water content of the water/HFIP solution and was shown to be reversible.

1.3.3 Interaction of amyloid βwith membranes: Ca2+dyshomeosta-

sis

Aβ-mediated disruption of Ca2+homeostasis in neuronal cells might provide an

early and crucial step in the pathogenesis of Alzheimer’s disease. The level of

Ca2+ions within the cytosol is rigorously regulated as Ca2+ions play a crucial

role in the functionality of essential enzymes including kinases or phosphatases.

Furthermore, an elevation of the Ca2+concentration within the cell activates

proteolytic enzymes as for example calpain and caspase initiating apoptotic

pathways leading to cell death [99]. Ca2+ions enter into the cytosol via in-

tracellular stores like mitochondria or the endoplasmic reticulum (ER) or from

the extracellular fluid. In the latter case Ca2+ions cross the plasma membrane

via Ca2+exchangers or receptor-, voltage-, or store-operated channels [100].

Ca2+homeostasis might be disrupted by an increased influx of the ions into the

cell induced by Aβoligomers. Primarily three different mechanisms shown in

figure 1.9 have been proposed:(i) the modulation of ion channels, (ii) disrup-

tion of membrane integrity, and (iii) the formation of high conductance cation

pores. As to (i), Aβoligomers were reported to strongly affect the permeability

and activity of several Ca2+associated channels like voltage-gated Ca2+chan-

nels, serotonin receptors, glutamate receptors, dopamine receptors, or nicotinic

acetylcholine receptors [101–105]. The interaction of Aβwith nicotinic acetyl-

choline receptors might result in the activation of several signal pathways lead-

ing to cell death [106].

As to (ii), a direct, non receptor mediated interaction of Aβwith the cell mem-

Chapter 1 INTRODUCTION

Figure 1.9: Schematic model of Ca2+dyshomeostasis caused by the interaction of Aβ

oligomers with cell membranes as taken from [100]. Aβoligomers are part of the aggrega-

tion pathway of the misfolded Aβmonomer.

brane was proposed by Cribbs et al. who investigated the structural and as-

sembly characteristics as well as the toxicity of all-D- and all-L-stereoisomers

of truncated Aβ25−35 and Aβ1−42 peptides towards cultured hippocampal neu-

rons [107]. For both alloforms they found no difference in the structural or toxic

features between both stereoisomers. This suggests that Aβdirectly interacts

with the lipid matrix of the cell membrane as most receptor mediated inter-

actions are stereoisomer-specific. Demuro et al. observed an increase of the

intracellular Ca2+level in human derived SH-SY5Y cells due to the presence

of extracellular Aβ42 oligomers [108]. The enhanced permeability of the mem-

brane for Ca2+ions might be explained by a general disruption of the membrane

lipid integrity as the addition of cobalt known to block various Ca2+-permeable

channels [109] as well as the depletion of intracellular Ca2+stores does not af-

fect the toxicity of the oligomers. Sokolov et al. proposed that an Aβoligomer

mediated increase of membrane ion permeability might arise from a lowering

of the dielectric barrier provided by the non-polar bilayer core region. This

furthermore might be caused by an increase in the area per lipid leading to a

thinning of the membrane [110]. Sokolov et al. investigated the effect of Aβ

oligomers on the electrical current through lipid bilayers solvated in different

aqueous electrolyte solutions including KCl, NaCl, and CaCl2. The electrical

current increases due to the presence of Aβoligomers and shows no jumps in

its time evolution as it would be expected for the appearance of Ca2+permeable

channels. Furthermore they found that the effect of Aβoligomers on the bilayer

washes out rapidly indicating an interaction of the oligomers primarily with the

bilayer surface. However, the membrane thinning observed by Solokov et al.

Alzheimer’s disease 1.3

could also have been caused by hexafluoroisopropanol (HFIP) used to solvate

the Aβoligomers during their preparation as pointed out by Capone et al. [111].

Figure 1.10: Pores induced by Aβin planar lipid bilayers as observed by AFM (left) and

MD simulations (right). The pores are characterized by four to six clumps of Aβmonomers

as apparent from AFM images showing Aβ40 (left,top) and Aβ42 (right,bottom) mediated

pores as taken from [112] and [113], respectively. A similar partition in loosely connected

subunits can be observed by 30 ns MD simulations of an annular oligomer comprising 24

Aβ9−42 monomers located in a lipid bilayer (right) as reported by Jang et al. [114]. Here,

ordered regions characterized by intermolecular β-sheets are depicted as light grey whereas

more disordered regions are coloured dark grey. Each monomer was prepared to adopt

an U-shaped strand-turn-strand motif with the hydrophilic N-terminus exposed to the pore

interior and the hydrophobic C-terminus facing the non-polar bilayer core region (middle).

Here, hydrophobic residues are shown in white, polar ones in green, positively charged ones

in blue and negatively charged residues are depicted in red.

As to (iii), ion channels induced by Aβ40 in planar lipid bilayers were first re-

ported by Arispe et al. in 1993 [115, 116]. These channels turned out to be

highly cation selective as expressed by the magnitudes of membrane perme-

abilities PCs >PLi >PCa =PK>PNa, to survive for minutes up to hours and

to be blocked by Zn2+ions. Furthermore as various single-channel conduc-

tances up to 5 nS were reported it is suggested that several different channel

phenotypes may occur [115–117]. Atomic force microscopy (AFM) shown

in figure 1.10 (left) revealed that pores induced by Aβ40 and Aβ42 are typi-

cally characterized by an outer diameter of 8−12 nm and an inner diameter of

1−2 nm. The rim of the channel is partitioned in four or six subunits which

might themselves be tetra- or hexameric oligomers as suggested by biochemical

analysis [112, 113]. The different sizes of the channels correspond to various

levels of single-channel conductances [113]. As shown in figure 1.10 (mid-

dle), Jang et al. proposed the Aβchannels to consist of monomers adopting

U-shaped strand-turn-strand motifs in the C-terminal residues Aβ17−42 whereas

Chapter 1 INTRODUCTION

the polar N-terminal residues Aβ1−16 are unstructured and solvated in the aque-

ous environment [114, 118, 119]. The described motif resembles the fibrillar

secondary structure. Based on this hypothesis, Jang et al. simulated membrane

pores formed by annular shaped oligomers of 12, 24 or 36 Aβ17−42 or Aβ9−42

monomers exhibiting the according U-shaped conformation. After 30 ns simu-

lation time they found the shape and dimensions of the channel to agree with the

results from AFM microscopy. In particular, the partitioning into subunits could

be reproduced and their rigidity could be explained by intermolecular β-sheets

comprising the inner and the outer β-strands, respectively. The formation of β-

sheets spanning outer β-strands may not be possible in a perfect annular ring as

the large diameter of the outer pore rim corresponds to a relatively large distance

between the single β-strands.

Channels in lipid bilayers, liposomes, neurons, and fibroblasts were also found

to be induced by several other amyloidogenic, disease-relevant peptides and may

play a key role in various different misfolding diseases [120].

1.4 Antimicrobial peptides

In modern health care the increasing resistance of pathogenic bacteria against

antibiotic agents is becoming a challenge of drastically growing importance

[121]. During the last 20 years, the resistance against methicillin and van-

comycin observed in hospitals increased exponentially whereas the number of

new antibiotics decreased markedly [122]. A possible solution to this dilemma

might be provided by antimicrobial peptides.

1.4.1 Properties and modes of action

Antimicrobial peptides represent an ancient part of the innate immune system

of especially higher organisms like vertebrates, insects or plants [123]. As even

one single species may possess more than 24 different antimicrobial peptides,

their number can be expected to be humongous. Nowadays, more than 880 dif-

ferent antimicrobial peptides are known [124]. Besides directly attacking and

killing intruding pathogens like fungi, bacteria, or viruses, antimicrobial pep-

tides are also known to modify the immune system which impacts the infection

and inflammation process [125]. As they are a component of the immune system

they show on the other hand poor activity against eukaryotic cells. Although a

large configurational diversity exists among antimicrobial peptides they can in

general be characterized as cationic, amphipathic (usually they comprise about

50% hydrophobic amino acids) and also as relatively small as they mostly con-

tain only 12 to about 50 residues. Based on their three dimensional structure

and amino acid sequence antimicrobial peptides can be categorized into five

Antimicrobial peptides 1.4

different subgroups [124]. These are (i) anionic peptides, (ii) linear cationic α-

helical peptides, (iii) peptides containing cysteine and forming disulphide bonds,

(iv) peptides containing a high content of certain amino acids including proline,

phenylalanine, arginine or tryptophan, and, (v) peptides occurring as fragments

of larger proteins. The majority of known antimicrobial peptides belongs to the

second or the third group. Many of the about 290 cationic α-helical peptides are

disordered in aqueous solutions but convert to α-helical structures if solvated in

trifluoroethanol (TFE) or in presence of phospholipid vesicles as well as sodium

dodecyl sulphate (SDS) micelles [126,127]. Best studied peptides in this group

include magainin 2 found in the African clawed frog Xenopus laevis as well as

melittin occurring in bee venom. Protegrins appearing in porcine leukocytes are

the primary representatives of the cysteine-containing disulphide bonding group.

This group contains about 380 peptides. Due to the disulphide bonds they are

prone to form stable β-sheets.

Several different killing and lysis modes of antimicrobial peptides have been

Figure 1.11: The barrel-stave (left), carpet (center) and the toroidal (right) models of an-

timicrobial peptide activity as taken from [124]. The peptides’ hydrophilic part is depicted

in red whereas the hydrophobic part is coloured blue.

discovered. On the one hand, they can cause cell death by intracellular mecha-

nisms as for example the flocculation of intracellular contents 1or the binding

of nucleic acids2. Furthermore antimicrobial peptides have been suggested to

inhibit the synthesis of cell walls 3, ribonucleic acids (RNA) 4, or proteins4as

well as the activity of enzymes 5. On the other hand, antimicrobial peptides

address the cell plasma membrane causing the formation of ion channels, trans-

membrane pores, or membrane rupture. Although several mechanisms for mem-

1as observed for anionic peptides [128]

2as observed for Buforin 2 [129]

3as observed for Mersacidin [130]

4as observed for Pleurocidin [131]

5as observed for Histatins [132]

Chapter 1 INTRODUCTION

brane permeabilization mediated by antimicrobial peptides have been proposed

especially three models, namely the barrel-stave-, the carpet- and the toroidal-

pore-model presented in figure 1.11 are nowadays widely assumed. Initially, in

case of low peptide/lipid ratios the peptides are bound parallel to the membrane

surface whereas they change to a transmembrane orientation if the peptide/lipid

ratio exceeds a peptide and membrane specific threshold. In the barrel-stave-

model helical peptides arrange perpendicular to the bilayer surface aligning the

rim of the pore and thus forming the stave of the barrel-shaped pore. Hereby

the hydrophobic side of the peptide faces the apolar bilayer interior and the

hydrophilic side the pore interior. To shield the apolar tail region from wa-

ter the peptides are packed rather tightly. This mechanism has up to now only

been found for the alamethicin peptide derived from the fungus Trichoderma

viride [133]. In the carpet-model the cationic peptides accumulate at the mem-

brane surface and cover its surface like a carpet. At high peptide/lipid ratios

the peptide forms toroidal holes in the bilayer to increase the peptide accessible

surface. This process is succeeded by the disintegration of the membrane and

the formation of micelles. An example for a peptide showing this mechanism

is the model peptide ovispirin [134]. In the toroidal-pore-model the polar sites

of the peptides associate with the polar lipid head groups to form the rim of an

hour-glass shaped pore and shield the bilayer core from water. Toroidal pores

are formed by magainin 2, protregrins, and melittin [124,133].

For both of the above described killing and lysis modes of antimicrobial pep-

tides, the intracellular and the membrane associated mechanisms, the peptide

first of all has to reach the cell plasma membrane. To address the plasma mem-

brane of gram-negative bacteria the peptide has to pass an outer, lipopolysaccha-

ride and phospholipids containing, outer membrane as well as a thin, rather stiff

peptidoglycan layer. The plasma membrane of gram-positive bacteria is merely

enveloped by a rather thick peptidoglycan layer. The peptidoglycan layer and

the corresponding membranes are in each case separated by periplasmic space.

The transit of antimicrobial peptides up to the plasma membrane is still poorly

understood. For gram-negative bacteria a so-called self-promoting uptake pro-

cess has been proposed [135] whereby the peptide initially binds to polyanionic

lipopolysaccharides (LPS) incorporated in the outer membrane. The peptide

displaces salt bridge relevant cations and partly neutralizes the LPS. This causes

the rupture of the outer membrane which enables other peptides to pass. On

the surface of gram-positive bacteria the cationic peptides might bind to teichoic

acids [124].

Antimicrobial peptides 1.4

1.4.2 NK-2 and its interaction with biological membranes

A very promising antibiotic agent may be provided by the NK-2 peptide. It is

derived from the larger NK-lysin polypeptide which is furthermore synthesized

by porcine NK (natural killer) or T-cells [136] 6being part of the innate immune

system of pigs. NK-lysin consists of 78 residues and folds into five amphipathic

α-helices in aqueous [137] as well as in liposome solutions [138]. The peptide

adopts a rather globular shape where the longest, residues 3-18 comprising helix

is surrounded by the four remaining helices. This conformation is stabilized by

three disulfide bridges [139]. NK-lysin has been reported to show lytic activity

against gram-positive and gram-negative bacteria, fungi, and even tumour cells.

On the other hand, it does not target red blood cells [136,140].

In 1999 Andrä and Leippe investigated the antimicrobial and hemolytic activ-

ity as well as the cytotoxicity of two peptides namely NK-1 and NK-2 derived

from the cationic core region of NK-lysin [140]. Thereby they synthesized the

Figure 1.12: The NK-2 peptide highlighted as part of the NK-lysin protein. Polar residues

are coloured in green, non-polar residues as yellow, anionic residues as red and cationic

residues as blue.

NK-2 peptide by extracting the residues 39 to 65 from NK-lysin which corre-

sponds to its third and fourth helix. The residues Leu6, Ser13 and Trp20 are

point mutated by valine, tyrosine and lysine, respectively. The C-terminus is

amidated. This results in an amphipathic peptide with a net charge of +10 e.

Whereas the peptide is unstructured in buffer or water solution it adopts α-

helical conformations in membrane mimicking environments, namely micellar

solutions of anionic, cationic or non-ionic amphiphiles, trifluoroethanol (TFE)

or at the air-buffer-interface [141, 142]. Experimental studies of the interac-

tion of NK-2 with liposomes suggest that the selectivity of NK-2 is based on

the difference in lipid compositions of eu- and prokaryotic cytoplasmic mem-

branes [143, 144]. NK-2 interacts with zwitterionic phosphatidylethanolamine

6The term T-cells arises as they originate in the thymus

Chapter 1 INTRODUCTION

(PE) and much more strongly with anionic phosphatidylglycerol (PG) lipids,

both contained in the outer leaflet of prokaryotic cell membranes. On the other

hand, the outer leaflet of eukaryotic cell membranes contains mainly zwitteri-

onic phosphatidylcholine (PC) lipids to which NK-2 has a low affinity. The

affinity of the cationic peptide for zwitterionic PE lipids suggest that the adsorp-

tion process is not exclusively driven by charge complementary. This founding

was confirmed by von Deuster and Knecht [145,146]. They determined the free

energy for the transfer of NK-2 monomers from palmitoyloleoylphosphatidyl-

choline (POPC) to palmitoyloleoylphosphatidylethanolamine (POPE) as well

as palmitoyloleoylphosphatidylglycerol (POPG) bilayers by means of coarse

grained MD simulations in combination with the thermodynamic integration

(TI) method [145,146]. POPC and POPE lipids are zwitterionic whereas POPG

lipids have a negative net charge. Their results confirm that besides electrostatic

peptide attraction other effects like the release of counter ions or the peptide me-

diated perturbation of lipid-lipid interactions might be crucial for the adsorption

propensity.

Methods

In this chapter employed simulation and analysis techniques are described. First

molecular dynamics (MD) simulation in general and subsequently the umbrella

sampling as well as the thermodynamic integration (TI) method are explicated in

sections 2.1, 2.2, and 2.3, respectively. Finally, in section 2.4 we present analysis

methods to investigate lipid order parameters as well as secondary structures and

peptide conformation clusters.

2.1 Molecular dynamics

Molecular dynamics (MD) simulations provide a powerful tool to study

biomolecular processes like polypeptide folding, peptide-membrane adhesion,

lipid membrane, and micelle formation as well as protein-ligand, DNA-ligand

or protein-DNA complexation. As these processes involve typically energies of

1−10 kBTat physiological temperatures they can sufficiently be described by

classical mechanics. Newton’s second law determines the dynamics of an N

atom system by the equations of motion

∂2ri

∂t2=Fii=1,2,··· ,N. (2.1)

Here, riis the position of the ith nucleus whereas electrons are assumed to

remain in their ground state. The electrons are assumed to follow the nuclei

motions instantaneously. This so-called Born-Oppenheimer-approximation is

Chapter 2 METHODS

justified due to the much lower electron mass compared to the nuclei masses.

As a consequence, the electronic ground state for given nuclei positions yields

the effective potential governing the motion of the nuclei. The force Fi=

Fi(r1,r2,··· ,rN)on the ith nuclei is given by the negative gradient of the po-

tential V=V(r1,r2,··· ,rN), i. e.

Fi=−∇iV i =1,2,··· ,N. (2.2)

Here, ∇i= (∂/∂xi,∂/∂yi,∂/∂zi). After choosing the initial atom positions

and velocities which are commonly set to zero or obtained from a Maxwell-

Boltzmann distribution at a given temperature Tthe forces are computed via

equation 2.2. If the potential energy of the initial system configuration resides

rather far away from a local minimum a MD simulation may fail due to extraor-

dinary large forces as apparent from equation 2.2. This effect might for example

occur if atoms strongly overlap. To overcome this shortcoming the system is first

relaxed to a local energy minimum. In our simulations we employed the steep-

est decent method which changes the configuration of the system in direction

of the negative gradient of the potential, i.e. the force, until a local minimum is

reached. Starting from the initial configuration equation 2.1 is integrated numer-

ically in small time steps ∆tusing methods like the velocity Verlet or the leap

frog algorithm [147,148]. The latter is typically used in the GROMACS1simu-

lation package and computes the atom positions at times t+∆tand the velocities

at times t+∆t/2 which accounts for the term leap-frog algorithm.

Interactions between atoms as occurring in the equations of motion are either

bonded (covalent) or non-bonded. The latter determine to a large extend the

computing time and are described by the Coulomb-Potential accounting for elec-

trostatic interactions between charged particles,

VC=∑

i<j

4πε0εr

qiqj

ri j

, (2.3)

and the Lennard-Jones-potential approximating London dispersion as well as

short-range Pauli repulsion according to

VLJ =∑

i<j

C(12)

i j

r12

i j

−C(6)

i j

. (2.4)

Here, ε0is the vacuum permittivity, εrthe dielectric constant with εr=1 for

explicit solvents, ri j the distance between two particles iand jwith the partial

charges qi,j, and C(12)

i j and C(6)

i j are the Lennard-Jones parameters.

1GROningen MAchine for Chemical Simulations

Molecular dynamics 2.1

Bonded interactions comprise interactions between two, three or four atoms and

are except for dihedral angles described by harmonic functions. The stretching

along the axis connecting two bonded particles at an equilibrium bond length d0

is described by the potential

Vb=

∑

i=1

2di−d0

i2(2.5)

whereas the bond angle potential is given by

Vθ=

Nθ

∑

i=1

kθ

2θi−θ0

i2. (2.6)

Here, θ0

iis the reference angle. The potential associated with the torsion of

proper dihedral angles between two planes spanned by three non-planar bonds

is described by

VΦ=

NΦ

∑

i=1

kΦ

21+cosnΦi−Φ0

i (2.7)

with the reference dihedral angle Φ0

iand n=1,2,.... Improper dihedral angle

potentials expressed as

Vζ=

Nζ

∑

i=1

kζ

2ζi−ζ0

i2(2.8)

with the equilibrium angle ζ0

iare employed to avoid for example the out of plane

bending of aromatic rings or to conserve tetrahedral structures. The summation

in equations 2.5 to 2.8 runs over all Nbcovalent bonds, Nθbond angles θ,NΦ

dihedral angles Φ, or Nζimproper dihedral angles ζ, respectively.

The set of interaction functions comprising the force constants, reference an-

gles or distances, partial charges, and Lennard-Jones parameters in equations

2.5 to 2.8 as well as 2.3 and 2.4 for all combinations of interatomic interactions

provide a so-called force field. Force fields can be categorized into all-atom,

united-atom, and coarse grained descriptions. In the first case all atoms are rep-

resented explicitly whereas in the united-atom force field non-polar hydrogen

atoms are described by treating CH, CH2, and CH3groups as single particles.

Coarse grained force fields treat functional groups of multiple atoms as single

interaction beads to describe a system. Corresponding force field parameters can

be obtained by ab initio quantum chemistry calculations or by experiments pro-

viding macroscopic quantities like dielectric permittivities, diffusion, and vis-

cosity coefficients, heats of vaporization, free energies of solvation or structural

and dynamic properties including crystal structures or vibrational frequencies.

Chapter 2 METHODS

In general, force field parameters are inferred from rather small molecules as

for these data are easier accessible and the derived parameters are transferable

to a wider range of molecular species. Popular force fields for biomolecular

systems comprise the all- and united-atom OPLS2[149], CHARMM3[150],

AMBER4[151] and GROMOS 5[152] as well as the MARTINI6coarse grain

force field [153].

Although MD simulations complement and enlarge experimental findings to a

large extend some shortcomings or inaccuracies associated with MD simula-

tions may occur. This includes the negligence of quantum effects which have to

be taken into account for the description of chemical reactions, relatively light

particles like hydrogens or protons able to tunnel through potential barriers, or

for high frequency covalent bonds with hν&kBT. Here, νis the resonance

frequency of the bond and hthe Planck constant. To minimize artifacts from

the classical treatment as well as for computational efficiency, bond lengths are

often fixed using the SHAKE or the LINCS7algorithm [154,155]. Furthermore,

finite size effects arising due to the relatively small sample size of typically 105

to 106atoms considered in MD studies might cause inaccuracies in the deriva-

tion of macroscopic quantities valid for numbers of particles comparable to the

Avogadro constant. This effect can partly be compensated by surrounding the

simulation box under study by an infinite number of copies of itself which pro-

vides periodic boundary conditions. To investigate macroscopic properties from

a MD simulation the trajectory of the system has to sample all relevant parts

of the phase space sufficiently which might not necessarily be achieved during

accessible computation times. This especially holds true if the free energy land-

scape of the system is rather rough and features comparably high barriers. This

sampling problem might be overcome by advanced techniques like the replica

exchange, umbrella sampling or thermodynamic integration method. The latter

two are explained in more detail in the following two sections.

2Optimized Potential for Liquid Simulations

3Chemistry at HARvard Molecular Mechanics

4Assisted Model Building with Energy Refinement

5GROningen MOlecular Simulations

6Named after a cocktail and the nickname for the city of Groningen

7LINear Constraint Solver

Umbrella sampling 2.2

2.2 Umbrella sampling

The umbrella sampling technique is based on the potential of mean (PMF) first

introduced by Kirkwood in 1935 [156]. The PMF describes the free energy

change of a system along a reaction coordinate λ(q1...qN)which can be a dis-

tance between two particles, an angle or a more complicated function of the

generalized coordinates q1...qN. The averaged probability density, hp(λ)i, that

λ(q1...qN)adopts a certain value λ(q1...qN) = λcan be described by

hp(λ)i=Rδ(λ0(q1...qN)−λ)exp(−βU(q1...qN))dq1...dqN

Rexp(−βU(q1...qN))dq1...dqN

. (2.9)

Here, β=1/(kBT)is defined by the Boltzmann constant kBand the temperature

Twhile U(q1...qN)is the potential energy of the system and δ(·)denotes the

Dirac delta function. The integral runs over the complete configuration space.

The PMF W(λ)with respect to an arbitrary reference reaction coordinate λ∗

can be obtained from

W(λ) = W(λ∗)−kBTloghp(λ)i

hp(λ∗)i.

A sufficient sampling of the configuration space along the reaction coordinate

λis often hindered by large free energy barriers which makes it impossible to

determine hp(λ)iwithin reasonable simulation times. An approach to over-

come this issue is provided by the umbrella sampling technique proposed by

Torrie and Valleau [157]. In this method the potenial of the system is bi-

ased by an additional potential which leads to a change of the potential energy

U(q1...qN)→U(q1...qN) + Wi(λ). The additional bias potential effects a con-

finement of the system in a configuration space region of interest according to a

particular λi. The complete path along λis divided into several windows each

corresponding to a value λi. Often the bias potential is chosen as a harmonic

potential Wi(λ) = k

2(λ−λi)2with the force constant k. According to equation

2.9 the unbiased averaged distribution function hp(λ)iunbias

ifor the ith umbrella

window can be determined from the corresponding biased distribution function

via

hp(λ)iunbias

i=exp(βWi(λ))hp(λ)ibias

ihexp(−βWi(λ))i. (2.10)

In combination with equation 2.2 this leads to the unbiased PMF

Wunbias

i(λ) = W(λ∗)−kBTloghp(λ)ibias

hp(λ∗)i−Wi(λ)+Gi.

Chapter 2 METHODS

including the free energy constant Giwhich is determined from

exp(−βGi) = hexp(−βWi(λ))i

and associated with the introduction of the bias potential Wi(λ). The information

of all umbrella simulations has to be combined in order to construct the unbiased

distribution function hp(λ)ialong the whole path of the reaction coordinate

λ. A very effective approach is provided by the weighted histogram analysis

method (WHAM) proposed by Kumar et al. in 1992 [158]. The method is

similar to the Bennett acceptance method [159] presented in section 2.3 and

based on the histogram method suggested by Ferrenberg and Swendsen [160].

Its central idea is to estimate hp(λ)iby a sum of the weighted unbiased averaged

distribution functions hp(λ)iunbias

idetermined by equation 2.10 and obtained

from restrained simulations. The weighting factors are optimized such as to

minimize the statistical error. In this way Kumar et al. obtained

hp(λ)i=

∑

i=1

nihp(λ)ibias

∑

j=1

njexp(−β(Wj(λ)−Gj))

. (2.11)

Here, NWdenotes the number of umbrella windows and nithe number of inde-

pendent data points used to construct the biased distribution function hp(λ)ibias

The free energy constant Giis determined by

exp(−βGi) = Zdλexp(−βWi(λ))hp(λ)i(2.12)

As Gidepends on hp(λ)ithe two equations 2.11 and 2.12 have to be solved

iteratively until self consistency is reached. The WHAM method is implemented

as g_wham in the GROMACS software package [161].

2.3 Thermodynamic integration

By means of the thermodynamic integration (TI) method the free energy dif-

ference between two system states or even between two different systems is

estimated by integrating over the work required to go along a reversible path-

way from an initial to a final state. In simulations this pathway can also be

non-physical.

The difference in the Gibbs free energy, ∆G, between two systems B and A

described by the Hamiltonian functions HBand HA, respectively, may be calcu-

Thermodynamic integration 2.3

lated via

∆G=∆GB−∆GA=Z1

0dλδG

δλ =Z1

0dλδH

δλ λ

. (2.13)

Hereby the Hamiltonian function H(λ)depending on the continuous coupling

parameter λ= [0,1]is a superposition of the Hamiltonian functions of both

systems with H(λ)→HAfor λ→0 as well as H(λ)→HBfor λ→1. This

holds true for the choice

H(λ) = (1−λ)·HA+λ·HB. (2.14)

Equation 2.13 goes back to Kirkwood in 1935 [156] and provides the basis of the

thermodynamic integration (TI) methods. The brackets h·iλrefer to a thermody-

namic average corresponding to a particular coupling parameter λ. In practice

this parameter is varied in discrete steps.

A very efficient way to compute the free energy difference between two sys-

tems 1 and 2 via their potential energy U1and U2is provided by the Bennett

acceptance ratio method [159] according to

∆G12 =−kBTlog Q1

Q2=−kBTloghWexp(−βU1)i2

hWexp(−βU2)i1. (2.15)

Here, the brackets h·i1and h·i2denote a thermodynamic average over system

1 and system 2, respectively, whereas Q1and Q2represent the corresponding

configurational integrals,

Qi=Zexp−Ui(q1,...,qN)

kBTdq1...dqNwith i=1,2. (2.16)

The potential energies Ui(q1,...,qN)depend on the Nconfigurational degrees

of freedom q1...qNof the system and the integration runs over the complete

configuration space. Bennett optimized the weighting function Wˆ=W(q1...qN)

by means of variational calculus in order to minimize the variance of the free

energy difference ∆G12. Especially for rather poor overlap between the phase

spaces of system 1 and 2 and if the slope of δG

δλ is rather rough, the Bennett

acceptance ratio method provides higher accuracy than the thermodynamic in-

tegration method [162].

To determine the difference in binding free energies ∆∆G=∆GPG −∆GPC for

the association of the NK-2 peptide with anionic DOPG and zwitterionic DOPC

bilayers the thermodynamic cycle shown in figure 2.1 was applied. As the Gibbs

Chapter 2 METHODS

Figure 2.1: Thermodynamic cycle to compute the difference in the affinity of the NK-2

peptide for an anionic DOPG and a zwitterionic DOPC bilayer. Carbon tails are presented

in grey and nitrogens of the phosphocholine (PC) headgroup in orange. The latter, as de-

scribed in section 2.3.1, transformed into oxygens of the phosphoglycerol (PG) headgroup

which are depicted in tan. For the peptide, colours distinguish between hydrophilic (green),

hydrophobic (yellow), cationic (blue), and anionic (red). The snapshots where taken after

100 ns of simulation.

free energy is a state function the relation

∆G0+∆GPG =∆GPC +∆GP

and therefore

∆∆G=∆GP−∆G0

holds. Hence, the desired free energy difference ∆∆Gmay be computed from

the free energy changes ∆G0and ∆GPupon the alchemical transformation of

DOPC to DOPG in absence and presence of NK-2.

In this work, the free energy differences ∆G0and ∆GPwere determined using

thermodynamic integration according to equation 2.13. The step size of λwas

chosen as ∆λ=0.05 for λ∈[0.1,0.9]whereas ∆λ=0.01 was applied for λ∈

[0,0.1]as well as for λ∈[0.9,1.0]. The smaller step size for λ→0 and λ→1

was necessary due to appearing and vanishing atoms, so-called dummy atoms,

involved in the performed alchemical transformation. These dummy atoms are

Thermodynamic integration 2.3

described in more detail in section 2.3.1.

2.3.1 Dummy atoms and soft-core-potential

To transform a DOPC to a DOPG lipid merely the phosphocholine (PC) head-

group has to be converted into a phosphoglycerol (PG) headgroup whereas the

hydrocarbon tails remain unchanged. Therefore several atomic species have to

be replaced by others as shown in figure 2.2. As the lipid headgroups differ in

the number of atoms and in the binding structure some atoms have to be cre-

ated or annihilated during the alchemical transformation. This is achieved by

so-called dummy atoms. In one of the two states (λ=0 or λ=1) these dummy

atoms can be considered as mass points assuming neither Lennard-Jones nor

Coulomb interactions with other particles of the system. The weight of both

interaction terms increases due to the transformation of the Hamiltonian to the

other state. The Coulomb interaction between two particles iand jis described

→

Figure 2.2: The alchemical transformation of the phosphocholine (PC, left) of DOPC to the

phosphoglycerol (PG, right) headgroup of DOPG. Carbon atoms are shown as cyan, oxygen

as red, nitrogen as blue, phosphor as tan, and dummy atoms as pink spheres. Transformed

hydrogens are coloured dark grey.

by the potential

VC(λ) = 1

4πε0εrri j (1−λ)qA

iqA

j+λqB

iqB

j(2.17)

Here ε0is the vacuum permittivity, εr=1 (explicit solvent) the dielectric con-

stant, qA,B

i,jthe charge of particle ior jin system A or B, and ri j the distance

between the particles. The Lennard-Jones potential features an attractive and a

repulsive part and is given by

VLJ (λ) = (1−λ)C(12)

A,i j +λC(12)

B,i j

r12

i j

−(1−λ)C(6)

A,i j +λC(6)

B,i j

i j

(2.18)

Chapter 2 METHODS

TheC(6)andC(12)coefficients are characteristic for each atom type and obtained

from quantum mechanical calculations (C(6)) or fits to experimental data (C(12)).

For the interaction between two atoms of different types, combination rules are

usually applied. For weak Lennard-Jones interactions, dummy atoms might

come very close to other particles of the system. Increasing the weight of the

Coulomb and Lennard-Jones interaction terms simultaneously might therefore

lead to extraordinarily high attractive forces leading to unstable simulation runs.

Hence, two separate simulations are necessary. In the first alchemical trans-

formation, only the Lennard-Jones potentials of the dummy atoms are turned

on (no potential →Lennard-Jones potential) and in the second transformation,

Coulomb potentials are added (Lennard-Jones potential →Lennard-Jones and

Coulomb potential).

As the Lennard-Jones and the Coulomb interaction terms given in equation 2.18

and 2.17 depend linearly on λ, the corresponding partial derivatives δV/δλ are

independent of the coupling parameter λ. For small distances between the par-

ticles (ri j →0) as it might occur for appearing and vanishing atoms (λ→0 and

λ→1) this leads to large fluctuations in δV/δλ during the simulations. Ac-

cording to equation 2.13 and due to the fact that the Hamiltonian function is

given by the sum of the potential and kinetic energy, large statistical uncertain-

ties in the free energy calculations have to be expected [163]. To overcome this

issue, for 0 <λ<1 the Lennard-Jones and Coulomb potentials are replaced by

so-called soft-core potentials

VSC = (1−λ)VArA

i j+λVBrB

i j

i j =ασ6

Aλp+r6

i j1

i j =ασ6

B(1−λ)p+r6

i j1

(2.19)

Here VArA

i jand VBrB

i jare the Lennard-Jones and Coulomb potentials

given in equation 2.18 and 2.17, whereas the distances between the particles

ri j are shifted depending on λ. In this way the derivative δVSC/δλ still depends

on λand the singularities for ri j →0 are avoided. The radius of interaction σis

given by C(12)/C(6)1/6if these coefficients do not vanish. Otherwise it is given

by an input parameter which is often chosen to be σ=0.3 nm. The soft-core

power pwas originally set to p=2 [163] whereas p=1 might lead to better

results due to a smoother shape of δH(λ)/δλ. If atoms have to be annihilated

and created, the soft-core parameter should be α≈0.7 for p=1 or α≈1.5 for

p=2 to obtain reasonable accuracies. In our simulations α=0.5 and p=1

was used. This choice was validated by performing the alchemical transforma-

tion from DOPC to DOPG in steps of ∆λ=0.5 for a single lipid solvated in

Analysis methods 2.4

SPC8water [164]. Here we compared the statistical uncertainties in the free

energy differences for the parameter combinations p=1 and α=0.5−0.8 as

well as p=2 and α=1.4−1.6. For each value of λ, data were collected from

two 10 ns simulations according to the separated transformations of Lennard-

Jones and Coulomb interactions. For each λvalue the system was first energy

minimized using the steepest descent method and subsequently equilibrated for

1 ns.

2.4 Analysis methods

2.4.1 Lipid order parameters

The order of lipid bilayer hydrocarbon tails is measured by the parameters

z=3

2cos2Θn

z−1

2. (2.20)

In this study only the denoted z-component of the order parameter was consid-

ered. The x- and y-components are defined in a similar way. The brackets cor-

respond to an average over simulation time as well as molecules while Θn

zis the

angle between the bilayer normal and the vector connecting the carbon atoms

Cn−1and Cn+1. Whereas Sn

zvanishes for isotropic orientations it adopts the

value -1/2 if all carbon atoms are parallel orientated to the bilayer surface, and

z=1 if they are perpendicular orientated. Order parameters were determined

using the script g_order from the GROMACS software package [165–167].

2.4.2 Secondary structure of peptides: DSSP

In 1983 Kabsch and Sander proposed the rather simple but effective DSSP

9method to categorize the up to then over 100 known protein structures by

means of hydrogen bond patterns and geometrical aspects [168]. First the

structure is searched for hydrogen bonds within the main chain by determin-

ing the Coulomb interaction between partially charged CO (+q1,−q2)and NH

(−q1,+q2)groups via

V=q1q2

4πε01

r(ON)+1

r(CH)−1

r(OH)−1

r(CN).

Here, rdenotes the distance between two atoms and ε0the vacuum permit-

tivity. Partial charges are set to q1=0.42 e and q2=0.20 e. Ideal hydro-

8Simple Point Charge

9Define Secondary Structure of Proteins

Chapter 2 METHODS

gen bonds are characterized by a dipole-dipole distance of d=2.9˚

A and an

alignment angle of θ=0◦corresponding to an antiparallel orientation yielding

V≈ −3 kcal/mole. To define hydrogen bonds, Kabsch and Sander chose a rather

generous cut-off for the electrostatic potential. They assumed hydrogen bonds

for V≤ −0.5 kcal/mole corresponding to alignment angles up to θ≤63◦at

ideal distance and distances up to d≤5.2˚

A at ideal alignment. In this way also

bifurcated hydrogen bonds are taken into account. Based on hydrogen bonds

so-called turns and β-bridges were defined. A n-turn corresponds to a hydrogen

bond between residue iand i+nwith n=3,4,5, and a β-bridge corresponds to

two hydrogen bonds between two residue stretches i−1,i,i+1 and j−1,j,j+1

(strands). These strands can be parallel or antiparallel. Turns and bridges are the

building blocks of higher structures, namely helices and β-sheets. A β-sheet

consists of several consecutive β-bridges of identical type. The three different

turn types can also form three different kinds of helices. Accordingly, 310,α, or

π-helices contain at least two consecutive 3-, 4- or 5-turns, respectively. Bends

are peptide segments of high curvature. They are defined by the angle between

the first (i-2,i-1,i) and the last three residues (i,i+1,i+2) of a five residue peptide

section. A segment is called a bend if the angle between these two segments is

larger than 70◦. In the GROMACS simulation package this algorithm is imple-

mented as do_dssp [165–167].

2.4.3 Cluster analysis

Similar structures adopted by a peptide during a simulation run are clustered by

a method proposed by Daura et al. based on the root mean square deviation

(RMSD) of peptide structures [169]. The RMSD of a peptide structure at the

time t1with respect to a reference structure at time t2is defined as

RMSD(t1,t2) = 1

∑

i=1

mikri(t1)−ri(t2)k21/2. (2.21)

Here, Nis the number of atoms of the peptide, miis the mass of atom i,riits

position, and M=∑N

i=1mithe mass of the peptide. Before evaluating equation

2.21 the structure at t1is fitted to the reference structure at t2by means of the

least square method.

In the method proposed by Daura et al. first the RMSD(t1,t2)for all pairs of

(t1,t2)is calculated and, subsequently, for each peptide structure, the number of

neighbouring structures is counted. Here, two structures at t1and t2are consid-

ered as neighbours if the corresponding RMSD(t1,t2)is below a chosen cut-off

value. The structure with the largest number of neighbours forms the center of

the first cluster and all corresponding structures belong to this cluster. After re-

Analysis methods 2.4

moving the structures of the first cluster from the complete pool of structures the

second cluster is found in the same manner and so on.

Amyloid β: Peptide folding at an

air-water-interface

A central question regarding Alzheimer’s disease addresses the fact that the

amyloid βpeptide aggregates in the brain although it only occurs in relatively

low concentrations. Whereas a peptide concentration in the micromolar range

is required to induce fibril formation in vitro the peptide already aggregates at

submicromolar concentrations in vivo [170–172]. Prevalently, it is assumed

that this discrepancy might at least partly be caused by a cell membrane

mediated increase of the peptide aggregation propensity in vivo [173, 174].

Circular dichroism spectroscopy (CD) experiments indicated that the presence

of phospholipid vesicles exhibiting zwitterionic headgroups does not largely

affect the peptide structure whereas phospholipid vesicles featuring anionic

headgroups significantly increase the amount of β-sheet conformations even at

low peptide concentrations comparable to in vivo conditions [170,175].

Several mechanisms might play a role in membrane mediated peptide aggre-

gation: (i) formation of aggregation prone monomer structures, (ii) increase of

peptide concentration due to the lower dimension or local peptide attracting

inhomogeneities, (iii) alignment of the peptide to aggregation favouring

orientations, and (iv) local environmental changes in the vicinity of mem-

branes [174]. The latter may for example arise due to the presence of anionic

lipids whose negative headgroup charge attracts cations which results in a

decrease in the local pH. Accordingly, slightly acidic environments have been

reported to increase the oligomerization, aggregation, and neurotoxicity of Aβ

Chapter 3 AMYLOID β: PEPTIDE FOLDING AT AN AIR-WATER-INTERFACE

peptides [176–178]. Furthermore a change of the pH from neutral to slightly

acidic in extracellular space has been reported to accompany Alzheimer’s

disease [86].

In this chapter we investigate the influence of air-water-interfaces on the early

steps of Aβ40 and Aβ42 peptide folding under physiological as well as slightly

acidic environments mimicking conditions. The two major alloforms of the Aβ

peptide show different aggregation behaviours as described in section 1.3.2 of

the introduction. Air-water-interfaces serve as hydrophobic/hydrophilic model

systems for biological membranes which allow a relatively fast sampling of the

peptides’ configurational space due to the lack of lipid-peptide-interactions.

We investigated peptide folding on a time scale of 2 µs by means of molecular

dynamics (MD) simulations. The required time tin nanoseconds to find the

peptides’ native or equilibrium state can be roughly estimated from the number

of residues N(with N≤100) [179] according to

exp N2/3

2!≤t≤exp 3N2/3

2!.

For Aβ40 and Aβ42 we obtain 347 ns ≤t≤42 ms and 420 ns ≤t≤74 ms, re-

spectively. Hence, we address rather early steps of peptide folding by our sim-

ulations. On the other hand, MD simulations of the Aβ40 and Aβ42 monomer

on the 1.5µs time scale have been shown to reproduce chemical shifts obtained

from NMR spectroscopy. This suggests that the Aβmonomer long-term struc-

ture can sufficiently be described by µs-simulations [85,91].

3.1 Simulation setup

The simulations described in this chapter are summarized in diagram 3.1. To

imitate the peptides’ folding behaviour directly after release from the membrane

the initial configuration of both peptides was chosen as to exhibit mainly

helical motifs adopted under conditions mimicking water-membrane-interfaces

or membrane core environments. Accordingly, the initial structure of the

Aβ40 peptide was obtained from NMR spectroscopy in aqueous sodium

dodecyl sulphate (SDS) micelles at slightly acidic pH [98] whereas the initial

structure of Aβ42 was obtained from NMR spectroscopy in a nonpolar water-

hexafluoroisopropanol (HFIP) solution [97]. Both structures were downloaded

from the RCSB1protein data bank (PDB entries: 1BA4 for Aβ40 and 1Z0Q for

Aβ42) [180]. The N-termini of the peptides contain the three histidine residues

His6, His13, and His14 whose protonation states are strongly affected by the

1Research Collaboraty for Structural Bioinformatics

Simulation setup 3.1

pH. To mimic physiological conditions corresponding to pH 7.4 the histidine

residues were modelled neutral with only one of the imidazolyl nitrogens

protonated resulting in a peptide net charge of −3 e. The protonation of both

imidazolyl nitrogens of each histidine residue leads to a zero net charge of the

peptide in slightly acidic environments (4 <pH <7) [85]. Each peptide was

simulated at both of these histidine protonation states. Hereby glutamic and

aspartic acid residues were modelled as deprotonated (negatively charged) and

arginine as well as lysine residues as positively charged.

Aβ40/42

Bulk

4<pH <7 pH =7.4

Air-Water-Interface

4<pH <7 pH =7.4

Table 3.1: Systems simulated to study the folding of Aβ40

and Aβ42 at various conditions.

Figure 3.1: Initial con-

figuration of the Aβ40

monomer at an air-

water-interface.

Each peptide was centered in a simulation box with an initial size of 6.53nm3

and solvated with 8870 explicit SPC2water molecules [164]. Subsequently,

Na+and Cl−counter- and co-ions were added in order to obtain an electrical

neutral system with a physiological NaCl concentration of 100 mM. The energy

of the system was minimized using the steepest descent method [181]. The

aqueous NaCl solution was equilibrated via 1 ns NPT-simulations. To avoid

non-equilibrium effects the peptide atoms were kept close to their initial position

via a harmonic potential with a force constant of 1000 kJ/(mol ·nm2)during

the equilibration process. The set-ups for the air-water-interface simulations

were obtained by extending the simulation box in z-direction and subsequently

recentering the water-peptide system in the simulation box as shown in figure

3.1.

In all simulations the peptide, ions, and water molecules were separately

2Simple Point Charge

Chapter 3 AMYLOID β: PEPTIDE FOLDING AT AN AIR-WATER-INTERFACE

coupled to a velocity rescaling thermostat [182] with a relaxation time of

0.1 ps maintaining a temperature of T=300 K. The simulations in bulk

solution were performed at a constant pressure of 1 atm by coupling the system

isotropically to a Berendsen barostat [183] with a relaxation time of 0.5 ps.

Long-range electrostatic interactions were calculated using particle mesh Ewald

(PME) summation [184, 185]. The peptides was described via the united-atom

GROMOS96 force field ffG53a6 [186]. This force field has been shown to

reproduce chemical shifts of HN, N, Cα, and Cβatoms of the Aβ40 and Aβ42

peptide as obtained by NMR spectroscopy [85,91].

3.2 Results

For all systems the secondary structure of the peptide was determined using the

DSSP method [168] described in section 2.4.2 whereas similar conformational

states adopted by the peptide during the sampling time were clustered using the

method by Daura et al. [169] described in section 2.4.3. To this end, the final

1.5µs of the 2 µs simulation runs were analyzed. The time course of the sec-

ondary structure for each residue is shown in the section A.1 of the appendix.

During all simulations involving the presence of an air-water-interface the pep-

Figure 3.2: z-component of the center of mass for the first 40 ns as well as mass density

profiles averaged over the final 100 ns of the 2 µs simulation for an Aβ40 peptide at an air-

water-interface at neutral pH. The N-terminus corresponds to residues Asp1-Lys16 and the

C-terminus to Gly29-Val40.

tide attached to the interface within 10−25 ns as illustrated for Aβ40 at neutral

pH in figure 3.2 (left). Hereby the hydrophilic N-terminus is buried in the water

phase whereas the hydrophobic C-terminus tends to face air. This holds true over

the whole simulation time as indicated from the mass density profiles shown in

figure 3.2 (right). In the following we describe the results for each Aβ40 system

and subsequently compare the results with each other. After reporting the results

Results 3.2

for Aβ42 in a similar manner we compare these with a related study performed

by Olubiyi and Strodel [85]. We conclude with a discussion and the comparison

of both peptides.

3.2.1 Aβ40: Secondary structure and cluster analysis

The secondary structure content for each residue can be found in figure 3.4

whereas the most present hydrogen bonds as well as the coil and β-motif

contents averaged over time are shown in table 3.2. Representatives of the

three main clusters are depicted in figure 3.3 while the time evolution of the

secondary structure for individual residues is presented in figures A.1 and A.2

attached to the appendix.

If Aβ40 is placed in a slightly acid bulk solution, its initial helical struc-

ture dissolves within 120 ns as shown in figure 3.5 (left). Whereas the

hydrophilic N-terminal part consisting of residues Asp1 to Lys16 is mainly un-

structured (figure 3.4) the hydrophobic core residues Leu17-Ala21 and residues

Ile31-Met35 in the C-terminal region adopt a two-stranded β-sheet after around

500 ns as apparent from figure A.1 (top) of the appendix. These β-strands are

parallel to each other and accompanied by a small antiparallel β-strand formed

by residues Asn27 and Lys28. This β-strand and the C-terminal β-sheet are

separated by a turn in residues Gly29 and Ala30 stabilized by hydrogen bonds

between Lys28 and Ile31 (stable over 68% of the sampling time). The parallel

β-sheet is stabilized by the most present hydrogen bonds between residues

Phe19-Ile32, Leu34-Phe19 and Ala21-Leu34 listed in table 3.2. The described

motif dominates the secondary structure during the sampling time as apparent

from the content of secondary structure as well as the results of the cluster

analysis shown in figure 3.4 (top, left) and figure 3.3 (first row), respectively.

At the surface of an acidic aqueous solution the initial N-terminal helix dis-

solves more quickly than in bulk water, namely after about 20 ns (figure 3.5

(left)). The peptide’s secondary structure is dominated by bends or coils and its

coil content averaged over sampling time is with 80% listed in table 3.2 com-

parably high. As in absence of an air-water-interface this holds especially true

for the N-terminus. The peptide forms only a rather small number of stable

hydrogen bonds. The only exception are two hydrogen bonds between Gly33

and Val18 as well as Phe20 and Ile31. These hydrogen bonds stabilize a β-

bridge formed by residues Ile32 and Phe19 which arises after about 100 ns and

extends after about 1.2µs to a β-sheet covering mainly residues Leu17-Phe20

and Ile31-Leu34 as apparent from figure A.1 (bottom) of the appendix. This

motif resembles the corresponding motif found for Aβ40 in acidic bulk solution

Aβ40 in bulk water at acidic pH:575 clusters

23% 10% 5%

Aβ40 at an air-water-interface at acidic pH:385 clusters

17% 12% 9%

Aβ40 in bulk water at neutral pH:1420 clusters

9% 7% 3%

Aβ40 at an air-water-interface at neutral pH:451 clusters

18% 14% 10%

Figure 3.3: Three main conformations of Aβ40 at an air-water-interface and in bulk solution

at slightly acidic and neutral pH as obtained from a cluster analysis of the final 1.5µs of

a 2 µs simulation. Peptides are represented as ribbons and Cαatoms of ASP1 as spheres.

Residues are colored according to their secondary structure. Coil structures are represented

in silver, turns in cyan, β-sheets in yellow, β-bridges in tan, α-helices in purple, and π-

helices in red. Residues 17 and 21 marking the boundary of the hydrophobic core region are

highlighted as ice blue spheres and sticks while residue 29 is colored orange to indicate the

hydrophobic C-terminus. At the air-water-interface the oxygen atoms of the water molecules

are displayed as red spheres. The air-water-interface is shown in side view.

Results 3.2

and characterizes the first two main clusters shown in figure 3.3 (second row) as

well as the secondary structure content of individual residues depicted in figure

3.4 (top,right).

Aβ40 in bulk solution at acidic pH

Secondary Structure Content

0.2

0.4

0.6

0.8

Residue

0 5 10 15 20 25 30 35 40

Aβ40 at air-water-interface at acidic pH

0.2

0.4

0.6

0.8

Residue

0 5 10 15 20 25 30 35 40

Aβ40 in bulk solution at neutral pH

Secondary Structure Content

0.2

0.4

0.6

0.8

Residue

0 5 10 15 20 25 30 35 40

Coil

Turn

Sheet

Bridge

Helix

Aβ40 at air-water-interface at neutral pH

0.2

0.4

0.6

0.8

Residue

0 5 10 15 20 25 30 35 40

Figure 3.4: Content of secondary structure motifs during the final 1.5µs of 2 µs simulations

for individual residues of Aβ40 under various conditions. The corresponding time is given

as fraction of the sampling time. Coils are represented in light gray, β-bridges in blue,

β-sheets in green, turns in red and helices in cyan.

In pH neutral bulk solution the decay of the initial N-terminal helix is rather

slow and takes nearly 500 ns (figure 3.5 (left)). A part of an initial C-terminal

π−or 5-helix, spanning the section Val24-Gly33, survives for about 750 ns (

figure A.1 (bottom) of the appendix). It has to be noted that the DSSP program

does not recognize this helix properly and interprets it as a pattern of turns and

small β-sheets as evident from the time evolution of the secondary structure

(figure A.2 (top) of the appendix). Visualization with the VMD3program [187]

reveals the helical structure of this motif. The helix is thus not considered in

3Visual Molecular Dynamics

Chapter 3 AMYLOID β: PEPTIDE FOLDING AT AN AIR-WATER-INTERFACE

figure 3.5 (left) which rather shows the time evolution of the initial N-terminal

helix as C-terminal helices either decay very fast or are not recognized properly.

During the simulation the peptide assumes a large number of various structures

as indicated by the large number of clusters (3.3 (third row)). These structures

include many β-motifs. Interestingly, especially the C-terminus exhibits a sta-

ble sheet-turn-sheet motif arising after about 800 ns (figure A.2 (top) of the ap-

pendix). The two β-strands are antiparallel and span residues Gly9-Val12 and

Lys16-Phe19 while a turn is located at His14 and Gln15. This motif is stabilized

by mainchain hydrogen bonds between Glu11 and Val18 as well as Phe20 and

Gly9 (table 3.2). In addition the residues Glu3-Asp7 and Met35-Val39 form a

two-stranded antiparallel β-sheet. This motif arises after about 450 ns, survives

for about 1250 ns (figure A.2 (top) of the appendix) and is stabilized by a hy-

drogen bond between Asp7 and Met35 (stable for 55% of the simulation time).

Both described motifs dominate the two main clusters presented and also deter-

mine the secondary structure content in the corresponding residues as apparent

from figure 3.3 (third row) and 3.4 (bottom, left), respectively. In contrast to

the systems described before we thus observe that the hydrophobic core region

forms β-sheets with the hydrophilic N-Terminus which furthermore adopts a β-

sheet conformation with the hydrophobic C-Terminus.

At the surface of a pH neutral aqueous solution we observe that the N-terminal

helix dissolves rather quickly after about 20 ns (figure 3.5 (left)) whereas a π-

helix comprising residues Ser26-Met35 is present in the C-terminus for the first

500 ns (figure A.2 (bottom)). As in the case before this is not recognized by the

DSSP method. During the sampling time a small parallel two-stranded β-sheet

was found between Gly37-Gly38 and Gln15-Lys16, stabilized by a hydrogen

bond between Lys16 and Gly37 shown in table 3.2. A small helix or turn-bridge-

turn-bridge motif is adopted by the segment Asp23-Lys28. This motif is fixed

to the aforementioned β-sheet by the hydrogen bond Val24-Gln15 (table 3.2).

Both described motifs occur in the three main clusters depicted in figure 3.3

and determine the secondary structure content in figure 3.4 (bottom, right). In

the latter the aforementioned helix in the residues Asp23-Lys28 occurs as turn-

bridge-turn-bridge motif.

Results 3.2

Hydrogen Bonds Secondary Structure

>60% Bond Durability Coil β-motifs

Phe19-Ile32 72%

Bulk water Leu34-Phe19 71% 69±9% 24±9%

at acidic pH Ala21-Leu34 69%

Gly33-Val18 93%

Air-water Phe20-Ile31 92% 80±9% 15±11%

at acidic pH His13-Asp7 65%

Glu11-Val18 75%

Bulk water Val18-Glu11 71% 53±11% 37±13%

at neutral pH Phe20-Gly9 71%

Val24-Gln15 81%

Air-water Gly25-Lys28 79% 70±9% 15±6%

at neutral pH Lys16-Gly37 77%

Table 3.2: Intramolecular hydrogen bonds and temporal structure content of Aβ40 in dif-

ferent environments. Data were collected from the final 1.5µs of 2 µs simulations. Shown

are the number of hydrogen bonds existing longer than 60% of the time, the three most

common hydrogen bonds and their durability in terms of their content in time as well as the

averaged percentage of coils and β-motifs. Hereby, „coil“denotes the sum of coil and bend

content from the DSSP method. In the same way the sum of β-sheet and β-bridge content

is denoted as „β-motif “.

Conclusion Aβ40

Our simulation show that a slightly acidic environment leads to a destabiliza-

tion of the initial helical structure. This holds especially true for the C-terminal

helix in pH neutral environments. The position of the helix coincides with the

threefold GlyXXXGly pattern located between the residues Gly25-Gly37 as de-

scribed in section 1.3.2. Furthermore the peptide and especially the hydrophilic

N-terminus assumes rather unstructured conformations at acidic pH as reflected

by the coil content presented in table 3.2 and the secondary structure content

depicted in figure 3.4. On the other hand, the number of different conformations

and hence the number of clusters is larger in pH neutral environments which

comes along with an increased β-sheet content in bulk solution (table 3.2). The

latter does not hold true at an air-water-interface where the β-sheet content is

rather not affected by the pH. In bulk solution and at an air-water-interface the

tendency to form β-structures comprising N-terminal residues is increased at

neutral compared to acidic conditions. This effect appears much stronger for

the bulk systems. A more detailed analysis reveals that the histidine residues

Chapter 3 AMYLOID β: PEPTIDE FOLDING AT AN AIR-WATER-INTERFACE

HIS hydrogen bonds

>10% total

Bulk water at acidic pH 16 94

Air-water at acidic pH 20 177

Bulk water at neutral pH 5 157

Air-water at neutral pH 14 174

Table 3.3: Total number of hydrogen bonds and hydrogen bonds existing more than 10% of

the sampling time involving histidine residues of the Aβ40 peptide.

which are especially affected by changes in pH form a larger number of hydro-

gen bonds existing longer than 10% of the sampling time at acidic conditions.

On the other hand, the total number of histidine involved hydrogen bonds de-

creases. As shown in table 3.3, this holds especially true for the simulations in

bulk water where the pH has a much stronger effect on the N-terminal structure.

In a pH neutral environment the N-terminus exhibits rather transient hydrogen

bonds which correlates with a larger number of different peptide conformations

as reflected in the different cluster sizes. This might also accelerate the reor-

ganization into β-sheet conformations. Under acidic conditions the peptide’s

N-terminus adopts a rather stable coil and bend structure during the sampling

time as apparent from figure A.1 presented in the appendix.

By comparing the peptide’s folding behavior in bulk solution and at an air-

0100 200 300 400 500

Time (ns)

0.2

0.4

0.6

0.8

Helix Content

Bulk, acidic pH

Air-Water, acidic pH

Bulk, neutral pH

Air-Water, neutral pH

0 200 400 600 800 1000 1200 1400 1600

Time (ns)

0.2

0.4

0.6

0.8

Helix Content

Bulk, acidic pH

Air-Water, acidic pH

Bulk, neutral pH

Air-Water, neutral pH

Figure 3.5: Time evolution of helical content for Aβ40 (left) and Aβ42 (right) under various

conditions.

water-interface we observe that the initial helical structure dissolves faster in

the presence of the interface (figure 3.5 (left). Furthermore an increased coil

but decreased β-bridge and -sheet content was observed compared to the bulk

systems (table 3.2). Schladitz et al. determined the secondary structure con-

tent of Aβ40 in a pH neutral aqueous solution by means of circular dichroism

Results 3.2

(CD) and at an interface between air and an acidic aqueous solution (pH ≈5)

using infrared reflection-absorption spectroscopy (IRRAS) [188]. They reported

aβ-sheet content of about 32% in the bulk system which agrees well with our

simulations. On the other hand they found an increased β-sheet content of about

75% at the interface while we obtained merely 15±11% . Comparing both stud-

ies suggests that rather a cooperative effect due to the increased peptide density

at the air-water-interface than its intrinsic hydrophobicity plays the key role in

the promotion of β-sheet structures.

The β-sheets in sections Lys16-Phe20 and Met35-Val39 found for Aβ40 in pH

neutral bulk solution agree partly with results from NMR spectroscopy [189]

proposing β-sheets for residues Lys16-Val24 and Ile31-Val40 as well as with

MD simulations reporting β-sheets in sections Phe19-Asp23 and Ile32-Gly37

[85].

3.2.2 Aβ42: Secondary structure and cluster analysis

Representatives of the three main clusters are shown in figure 3.6, the secondary

structure content for each residue can be found in figure 3.7 whereas the most

present hydrogen bonds as well as the coil and β-motif contents averaged

over sampling time are tabulated in table 3.4. Time evolutions of secondary

structures are shown in section A.1 of the appendix.

The N-terminal secondary structure of the Aβ42 peptide in slightly acidic

bulk solution is dominated by an α-helix comprising residues Ser8-Val18 and

surviving the first 1.6µs of the simulation as evident from figures 3.5 (right)

and figure A.3 (top) in the appendix. The most present hydrogen bonds stabilize

this helix (table 3.4). In the C-terminal we observe rather transient patterns and

the β-sheet content is accordingly low. A bridge-turn-bridge motif in residues

Lys28-Ile31 is stable for about 1.3µs (figure A.3 (top) of the appendix).

At the surface of a slightly acidic aqueous solution the initial N-terminal helix

vanishes after about 650 ns (figure 3.5 (right). In the sampling period the sec-

ondary structure is dominated by a three-stranded antiparallel β-sheet includ-

ing residues Phe19-Glu22, Leu34-Val39, and Ala30-Ile31 and stabilized by the

hydrogen bonds Ile31-Leu34 (stable for 43% of the sampling time) and Phe20-

Gly38 (table 3.4). This motif is accompanied by a β-bridge in Gln15 stabilized

by the hydrogen bond Gln15-Ala21. The three stranded β-sheet dominates the

three main clusters and the β-sheet content of the corresponding residues as de-

picted in figure 3.6 (second row) and 3.7 (top, right), respectively.

Aβ42 in bulk water at acidic pH:459 clusters

40% 6% 5%

Aβ42 at an air-water-interface at acidic pH:492 clusters

38% 6% 5%

Aβ42 in bulk water at neutral pH:369 clusters

40% 9% 8%

Aβ42 at an air-water-interface at neutral pH:411 clusters

27% 7% 5%

Figure 3.6: Three main conformations of Aβ42 at air-water-interface and in bulk solution at

slightly acidic and neutral pH as obtained from a cluster analysis of the final 1.5µs of 2 µs

simulations. The representation is the same as chosen in figure 3.3. The air-water-interface

is shown in top or side view with its normal orientated in x- or z-direction, respectively.

Results 3.2

In a pH neutral bulk solution the initial N-terminal α-helix dissolves after

about 375 ns (figure 3.5 (right)). During the sampling time the peptide assumes

a stable five-stranded β-sheet spanning the sections Glu3-Arg5, Leu17-Phe20,

Val36-Ile41, Ala30-Ile32 and Gly9-Tyr10. Accordingly, the β-sheet content of

the whole peptide (table 3.4) as well as of the corresponding residues depicted

in figure 3.7 (bottom, left) are quite high. The five-stranded β-sheet occurs in all

three main clusters shown in figure 3.6 (third row) and stabilized by the hydrogen

bonds Arg5-Phe20 (present for 46% of the time), Gly38-Ile31 (present for 75%

of the time) and Gly9-Met35 (present for 54% of the time). The most robust one

of these motifs is the β-sheet with the strands Leu17-Phe20 and Val36-Ile41 as

the most stable hydrogen bonds maintain this pattern as tabulated in table 3.4.

Aβ42 in bulk solution at acidic pH

Secondary Structure Content

0.2

0.4

0.6

0.8

Residue

0 5 10 15 20 25 30 35 40

Aβ42 at air-water-interface at acidic pH

0.2

0.4

0.6

0.8

Residue

0 5 10 15 20 25 30 35 40

Aβ42 in bulk solution at neutral pH

Secondary Structure Content

0.2

0.4

0.6

0.8

Residue

0 5 10 15 20 25 30 35 40

Aβ42 at air-water-interface at neutral pH

0.2

0.4

0.6

0.8

Residue

0 5 10 15 20 25 30 35 40

Figure 3.7: Content of secondary structure motifs during the final 1.5µs of 2 µs simulations

for individual residues of Aβ42 under various conditions. The representation is the same as

that chosen in figure 3.4.

At an air-water-interface at neutral pH the initial α-helix dissolves within

80 ns (figure 3.5 (right)). The peptide’s secondary structure during the sampling

Chapter 3 AMYLOID β: PEPTIDE FOLDING AT AN AIR-WATER-INTERFACE

time is dominated by a three-stranded β-sheet formed by Phe4-His6, Asn27-

Ile31, and Leu34-Val36 which is present in all three clusters shown in figure

3.6 (fourth row). Hereby the former two β-strands are parallel to each other

whereas the third is antiparallel to both. This pattern is stabilized by the three

most present hydrogen bonds shown in table 3.2 and indicated by the secondary

structure content depicted in figure 3.7 (right, bottom).

Hydrogen Bonds Secondary Structure

>60% Bond Durability Coils β-motifs

Val12-Asp7 87%

Bulk water Lys16-Glu11 70% 53±10% 15±8%

at acidic pH Gln15-Tyr10 64%

Phe20-Gly38 90%

Air-water Val40-Val18 86% 50±10% 35±11%

at acidic pH Gln15-Ala21 85%

Phe19-Val39 97%

Bulk water Ile41-Phe19 92% 57±9% 39±9%

at neutral pH Val39-Leu17 90%

Lys28-Phe4 93%

Air-water His6-Lys28 93% 57±9% 32±7%

at neutral pH Val36-Gly29 82%

Table 3.4: Hydrogen bonds and secondary structure content of Aβ42 in different environ-

ments as obtained from a 2 µs simulation. Data were collected from the final 500 ns. Rep-

resented are the number of hydrogen bonds existing longer than 60% of the time, the three

most common hydrogen bonds and their durability in terms of their content in time as well

as the averaged percentage of coils and β-motifs comprising sheets and strands. Hereby, as

both are not stabilized by hydrogen bonds, we summarize coils and bends as obtained from

the DSSP method in the column termed coils.

Conclusion Aβ42

In contrast to Aβ40 we found that the initial N-terminal helix of Aβ42 is much

more stable at slightly acidic compared to pH neutral conditions as apparent

from figure 3.5 (right). This holds especially true for the bulk simulations. In

accordance with this rather slow unfolding behavior a larger number of stable

but smaller content of transient hydrogen bonds involving the histidine residues

were observed as presented in table 3.5. The latter effect appears less distinctly

in presence of an air-water-interface but corresponds to the influence of the pH

Results 3.2

HIS hydrogen bonds

>10% total

Bulk water at acidic pH 17 108

Air-water at acidic pH 15 139

Bulk water at neutral pH 9 156

Air-water at neutral pH 13 162

Table 3.5: Total number of hydrogen bonds and hydrogen bonds existing longer than 10%

of the sampling time involving histidine residues of the Aβ42 peptide.

on the Aβ40 alloform. Furthermore a reduction of the β-sheet content in slightly

acidic bulk solution but not in presence of an air-water-interface occurs (table

3.4). In both systems, in bulk solution, and at an air-water-interface, the pos-

itive charge of the histidine residues at acidic conditions seems to impede the

N-terminal residues to form β-strands. Especially the section Glu3-His6 shows

a higher propensity for β-sheet formation in case of electrically neutral histi-

dine residues as apparent from the secondary structure content shown in figure

3.7. The corresponding β-sheets involve the hydrophobic core region or the hy-

drophobic C-terminus. This behavior was partly also found for the Aβ40 peptide.

The positively and negatively charged residues His6 and Asp7 might have a large

dipole moment and therefore their high polarity might decrease the interaction

with hydrophobic sequences at acidic conditions. From 1 µs MD simulations

under very similar conditions Olubiyi and Strodel reported a comparable effect

of the histidine protonation state on the persistence of the Aβ42 N-terminal he-

lix [85]. On the other hand, they observed an increase in the β-sheet content

due to the positive charge of the His residues in slightly acidic environments.

It cannot be excluded that the observed discrepancies are caused by insufficient

sampling.

For both pH conditions the presence of an air-water interface results in a faster

dissolution of the initial helix in the N-terminus (figure 3.5 (right)). The pres-

ence of the interface effects the folding behavior much more strongly at acidic

conditions where it induces C-terminal β-sheets as reflected by the secondary

structure content of the corresponding residues depicted in figure 3.7. This is

as well expressed by the number of hydrogen bonds existing longer than 60 %

of the time (table 3.4). At pH neutral conditions the presence of an air-water-

interface leads to a reduction in the amount of β-sheet conformations in the

hydrophobic core residues Leu17-Phe20 which turns into a bridge-turn-bridge-

motif in residues Val18-Glu22 as evident from figure 3.7. Much more distinct

than in case of Aβ40 the formed β-sheets mainly located in the hydrophobic se-

Chapter 3 AMYLOID β: PEPTIDE FOLDING AT AN AIR-WATER-INTERFACE

quence sections are parallel to the air-water-interface (compare figures 3.3 and

3.6 (second and fourth row)). This β-sheet plane might bind similar structured

peptides by hydrogen bonds explaining the increased β-sheet content at the air-

water-interface observed in experiment as suggested from the aforementioned

study of Schladitz et al for Aβ40 [188].

Comparison with other MD simulations

Our results might be compared with the aforementioned study by Olubiyi and

Strodel [85]. In this work the effect of the atomistic force fields GROMOS43a2

[190] and GROMOS53a6 [186] on the folding behavior of the Aβ40 as well as

the Aβ42 peptide was investigated. The authors found that simulations with

GROMOS53a6 as also employed in our study reproduce chemical shifts for

both peptides measured by NMR spectroscopy [91]. From their simulations us-

ing GROMOS53a6 Olubiyi and Strodel predicted the initial N-terminal helix of

Aβ40 at physiological pH spanning roughly residues Tyr10-Lys16 to persist for

about 600 ns. This agrees partly with our simulations where the helix comprises

residues Glu11-Lys16 and dissolves after about 500 ns (figure 3.5 (left)). On

the other hand they predict the N-terminus to be rather bend or coil dominated

after dissolution of the initial N-terminal helix whereas we observe a very high

β-sheet content featuring a relatively stable sheet-turn-sheet motif in the section

Tyr10-Phe19 occurring after about 800 ns (figure A.2 (top) of the appendix). In

both studies the section Phe19-Ile32 (Phe19-Gly33 in our case) adopts rather

coil and bend motifs although in our case this section is dominated by a π-helix

comprising residues Val24-Ile32 during the first 750 ns as apparent from figure

A.2 (top) of the appendix. Interestingly, a similar helix was found by Olubiyi

and Strodel for GROMOS43a2 spanning residues Lys28-Val36 and decaying af-

ter 1.4µs.

Both simulation studies regarding Aβ42 under pH neutral conditions described

by GROMOS53a6 predict a quite different β-sheet content. Whereas we ob-

serve a large and stable β-sheet motif spanning four or partly five β-strands as

described in section 3.2.2, Olubiyi and Strodel report a mainly unstructured con-

formation featuring only temporary β-sheets. In the latter case, the most stable

β-sheets arise after about 650 ns, comprise the strands Lys28-Ile31 as well as

Gly38-Ala42 and survive for the remaining 850 ns. Interestingly, they found an

increased amount of β-sheets at slightly acidic compared to neutral pH whereas

we observe a decrease (table 3.4).

It has to be mentioned that our simulations were performed under marginally

different conditions as applied in the referenced study. Olubiyi and Strodel cou-

pled their system to a Nosè-Hoover thermostat and a Parinello-Rahman barostat

and solvated the Aβpeptide in a water-salt solution exhibiting a NaCl concen-

Results 3.2

tration of 150 mM whereas we applied a velocity-rescale thermostat [182] and

a Berendsen barostat [183]. We performed our simulations at a NaCl concentra-

tion of 100 mM.

3.2.3 Discussion and comparison of Aβ40 and Aβ42

In course of our simulations an in general increased content of β-sheets pro-

voked by slightly acidic conditions could not be observed. On the other hand,

experimental findings report extraordinary high aggregation propensities as well

as cytotoxicities for both major Aβalloforms at pH values close to the pep-

tide’s isoelectric point [176–178]. Guo et al. investigated the influence of pH

on the oligomerization as well as the fibril formation of Aβ40 variants modified

by point mutations of charged residues [191]. They substituted the negatively

charged Asp, Glu or the positively charged His residues by the electrical neutral

Ala amino acid resulting in an increase or decrease in the peptide’s net charge

by ±3 e, respectively. By means of turbidity assays, thioflavin T (ThT) bind-

ing as well as electron microscopy (EM) they found a maximal propensity of

the peptide to form octamers, larger oligomers, very large oligomers, or amy-

loid fibrils at the isoelectric point of the peptide (pH where its electrophoretic

mobility and hence its net charge vanishes). This indicates that instead of the

charge of a specific residue the net charge of the peptide plays a crucial role

in the pH dependence of amyloid formation, oligomerization, and therefore its

toxicity. The results of our simulations support this view as we observed that the

β-sheet content of the Aβmonomer does in general not depend on the protona-

tion state of the histidines. The comparably high aggregation rate of both major

Aβalloforms at slightly acidic environments might therefore not be explained

by extraordinarily high amounts of aggregation prone monomer conformations

but rather by the lack of intermolecular electrostatic repulsion.

Interestingly, we found that the durabilities of initial helical structures of the

two alloforms are affected in different ways by changes in the pH. Under slightly

acidic environments mimicking conditions the N-terminal helix of the Aβ40 pep-

tide dissolves more quickly whereas in case of the Aβ42 peptide it dissolves more

slowly than at physiological pH. At all conditions and for all peptide lengths the

most stable section of the N-terminal helix is roughly located between residues

Ser8 and Leu17. This section contains His13 and His14 as well as the positively

charged Lys16 and the negatively charged Glu11 residue. The net charge of this

section vanishes therefore at the isoelectric point. This might explain the corre-

sponding higher stability of the N-terminal α-helix in case of Aβ42. In case of

Aβ40 at physiological pH conditions we observe that especially the C-terminal

helix retains over an extraordinary long time. As mentioned before this helix

spans the GlyXXXGly patterns located in the section Gly25-Gly37. The addi-

Chapter 3 AMYLOID β: PEPTIDE FOLDING AT AN AIR-WATER-INTERFACE

tional two hydrophobic residues in Aβ42 increase the C-terminal’s tendency to

minimize its exposure to the aqueous environment and therefore to interact with

other peptide sections which furthermore might destabilize the C-terminal helix.

This illustrates the flatness of the folding free energy landscape as described in

section 1.3.2 of the introduction.

The β-sheet content, especially at the hydrophobic C-terminus of Aβ42 is, in

particular at the air-water-interface, remarkably higher than for Aβ40. Addition-

ally, these β-sheets are rather parallel to the interface and allow the hydrophobic

C-terminus to minimize its exposure to the aqueous solution. This tendency is

more distinct for Aβ42 due to its additional two hydrophobic residues. Nev-

ertheless, do we not observe a general increase in β-sheet content at the air-

water-interface. This is in accordance with replica exchange MD simulations

of the Aβ42 monomer at anionic and zwitterionic phospholipid bilayers per-

formed by Davis and Berkowitz [192]. At both types of bilayers the peptide

adopts secondary structures strongly dominated by coil and bend motifs. The

authors proposed that lipid bilayers catalyze the aggregation of Aβ42 peptides

rather by an increased peptide-peptide interaction than by provoking the tran-

sition of monomers to aggregation prone conformations. This is also indicated

from our simulations as the alignment of β-sheets parallel to the interface as

especially observed for Aβ42 might facilitate the formation of intermolecular

β-sheets and therefore dramatically increase the β-sheet content as observed in

experiment [188].

On the other hand, the higher β-sheet content of Aβ42 compared to Aβ40 at an

air-water-interface might indicate a higher aggregation propensity and thus cy-

totoxicity of Aβ42 in vivo where membranes and interfaces are comprehensively

present.

Amyloid β: Pore formation in phospholipid

bilayers

A key aspect regarding the neurotoxicity of Aβis its high propensity to inter-

act with cell membranes leading to the formation of ion channels [116, 193],

insertion of peptides [194, 195], or disruption of membranes [196]. Especially

small oligomers are reported to represent the most toxic species of Aβ. In this

chapter, as a first step the influence of Aβ42 monomers on small membrane de-

fects as provided by water pores is addressed. In this way we try to gain insight

into the basic mechanisms of peptide-membrane interactions causing the distur-

bance of membrane integrity. Water pores within membranes are severe local

defects which are capable to increase the permeation of ions, water, or lipids

through the membrane [197, 198]. They can form spontaneously by thermal

fluctuations [199, 200] or be induced by electrostatic [201], mechanical [202],

or chemical stress as arising from peptides [203].

In this chapter we employ molecular dynamics (MD) simulations in combination

with the umbrella sampling technique to investigate the influence of an adsorbed

Aβ42 monomer on the free energy of water pores within a zwitterionic phospho-

lipid bilayer serving as model membrane. From our simulations we are able to

determine closure and formation rates as well as densities of membrane pores.

In addition our results are compared with a peptide-free reference system. For

this system computed water permeabilities and lipid flip flop waiting times are

furthermore compared to results reported from experiments.

Chapter 4 AMYLOID β: PORE FORMATION IN PHOSPHOLIPID BILAYERS

4.1 Simulation setup

The free energy of small water pores in zwitterionic phospholipid bilayers

with and without an Aβ42 monomer attached to each leaflet of the bilayer is

determined using the potential of mean force (PMF) as obtained from MD

simulations combined with the umbrella sampling technique [204] as described

in section 2.2 of the introduction. The investigated bilayers contain 128

1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipids depicted in figure

1.1 presented in section 1.1 of the introduction. Pores were induced in the

bilayer by pulling a single phosphatidylcholine (PC) headgroup in z-direction

to the center of the bilayer. The z-component of the distance between the

headgroup and the center of the bilayer was chosen as reaction coordinate λ.

Thus, pore formation takes place for λ→0 as depicted in figure 4.1. Two

systems were compared: a pure DPPC bilayer and a DPPC bilayer with an

Aβ42 monomer attached to each bilayer leaflet. Hereby, the initial configuration

of the Aβ42 monomer attached to a DPPC bilayer was taken from replica

exchange simulations [205, 206] performed by Davis and Berkowitz [192]. In

advance of the cited study Davis and Berkowitz estimated the free energy of

peptide binding by pulling one unstructured Aβ42 monomer to the surface of

a DPPC bilayer using the umbrella sampling method [207]. Starting from the

obtained final configuration of these simulations they investigated the structure

of the peptide adsorbed to the bilayer surface by means of the replica exchange

method [192]. Due to the enhanced sampling provided by the replica exchange

technique the peptide configuration should likely reside in a local free energy

minimum at the start of our simulations. To obtain a symmetric setup with one

peptide attached to each of the bilayer leaflets we copied and rotated the peptide

containing leaflet around the x-axis parallel to the bilayer surface. We compared

our simulations with a peptide-free reference system.

To each system about 5700 SPC1[164] water molecules and to the peptide

containing system Na+counter ions were added. The protonation of Aβ42

was chosen such as to correspond to a physiological pH of 7. That is, the

arginine and the lysine residues were modeled as cationic, aspartic and glutamic

acid residues as anionic, the histidine residues as neutral, the C-terminus

as deprotonated, and the N-terminus as protonated. This leads to a peptide

net charge of -3 e. All systems were energy minimized using the steepest

descent method. The peptide-free system was equilibrated for 10 ns and the

peptide-bilayer system for 20 ns. The initial configurations for each reaction

coordinate were obtained by pulling one lipid headgroup from its equilibrium

position normal to the bilayer surface to the center of the bilayer. To locate

1Simple Point Charge

Simulation setup 4.1

the equilibrium position within the potential of mean force (PMF), in an

additional simulation, the corresponding lipid headgroup was pulled about

3−4◦

A out of the bilayer into the aqueous solution. Both simulations were

carried out with a pulling rate of 0.02 nm/ps and an umbrella potential of

500 kJ/(mol·nm2). From these simulations we took about 70 snapshots serving

as initial configuration for each particular umbrella window. In each window

the distance between the pulled lipid headgroup and the center of the bilayer

were restrained normal to the bilayer surface using an umbrella potential with

a force constant of 5000 kJ/(mol ·nm2). Each setup was equilibrated for 10

ns and data were collected from additional 100 ns simulation runs. The PMF

was calculated using the weighted histogram analysis method (WHAM) [158]

described in section 2.2 whereas the statistical errors were estimated by the

Bayesian bootstrap method [208]. Both methods are implemented in the

Gromacs software package [161] and described in section 2.2.

To determine pore closure rates the umbrella window with the lipid headgroup

restrained at the center of the bilayer (λ=0) was employed. In both cases, with

and without peptide, ten configurations at separate times with a pre-formed pore

were taken. After releasing the restrained lipid headgroup the simulations were

extended until the pore had closed.

For all simulations a temperature of 323 K was maintained by separately cou-

pling lipids, water, peptides, and ions to a velocity rescaling thermostat [182],

with a relaxation time of 0.1 ps. At the chosen temperature the bilayer is in

the biologically relevant fluid phase. Furthermore the system was coupled

semi-isotropically to a Berendsen barostat [183] with a relaxation time of

0.5 ps in order to maintain an average pressure of 1 atm. Van der Waals and

electrostatic short range interactions were truncated at 0.9 nm whereas for

long range electrostatics the particle mesh Ewald method [185] was applied.

All bonds of the lipids and peptides were constrained using the LINCS algo-

rithm [209]. The lipids were described by parameters from Berger et al. [210]

while the Aβ42 peptide was treated using the united-atom GROMOS96 force

field ffG43a1 [165, 166]. The simulation time step was 2 fs. All simulations

were performed using the GROMACS 4.0 software package [165–167].

It has to be mentioned that we also determined the PMF of an asym-

metric peptide-bilayer system with an Aβ42 peptide attached to only one

of the bilayer leaflets as obtained from the referenced study [192]. For

this system an extraordinarily high free energy barrier of pore formation

(∆G≈94 kJ/mol) was obtained. This is presumably caused by a discrep-

ancy in the effective areas per lipid ALip between both leaflets. For the

peptide-free system ALip =0.689 ±0.011nm2whereas for the symmetric

system featuring one attached Aβ42 monomer at each leaflet a smaller area

Chapter 4 AMYLOID β: PORE FORMATION IN PHOSPHOLIPID BILAYERS

per lipid of ALip =0.660 ±0.008 nm2was found. In case of the asym-

metric system this results in an expansion of the peptide containing and a

compression of the peptide-free leaflet. For this system an area per lipid of

ALip =0.669±0.012 nm2was observed. This finite size effect is the presumed

reason for the observed extraordinarily high free energy barrier. Consequently,

we did not analyze this system in more detail.

4.2 Results

In this section we first describe the influence of the Aβ42 peptide on the size

and shape of induced pores as well as on the order of the bilayer’s hydrocarbon

tails described in section 2.4.1 of the introduction. Subsequently, we determine

the free energy of membrane pores and explain the results partially by the Aβ42

mediated disturbance of the nonpolar bilayer tail region. After computing pore

densities, water permeabilities, and lipid flip flop waiting times and comparing

the latter with experimental results, pore closure and pore opening times are

estimated. We conclude with a summary and a discussion.

4.2.1 Size and shape of pores

Pores were induced by pulling one lipid headgroup along the bilayer normal to

the center of the bilayer. For the peptide-free system a pore forms after about

70 ns whereas in presence of bilayer attached Aβ42 peptides a pore was induced

already after about 5 ns. In the latter case the propensity of pore formation

strongly depended on the position of the pulled lipid. We observed pore for-

mation by pulling a lipid headgroup in the vicinity of the hydrophilic segment

Ser8-His13. On the other hand, no pore was formed when a lipid headgroup

close to the hydrophobic tail region Val40-Ala42 or between the hydrophobic

segments Lys16-Phe19 and Ile31-Leu34 was pulled to the bilayer center. Pore

formation in the vicinity of hydrophobic segments increases their exposure to

water and might therefore be unfavored.

The size and shape of the induced pores are apparent from the snapshots shown

in figure 4.1 as well as from the water density maps depicted in figure 4.2. In

case of the peptide-free system a relatively large, hour glass shaped pore can

be observed whereas the induced pore in case of the peptide containing system

is rather small and exhibits a disordered toroidal shape. Hereby it has to be

noted that the density maps are averaged over time. In this way the size of the

pore in case of the peptide attached bilayer appears much larger in the density

map 4.2 (right) than in the snapshot 4.1 (bottom). This does not hold true for

the peptide-free system and indicates that the small pore induced in the Aβ42

Results 4.2

Figure 4.1: Pore formation for λ→0 in absence (top) and presence (bottom) of Aβ42. The

water oxygens are shown as cyan spheres and the lipid restrained by the umbrella potential

as purple sticks. The phosphor atoms of the other lipids are shown in tan. The peptides

are depicted in ribbon presentation; here, colors distinguish between anionic (blue), cationic

(red), hydrophobic (white), and hydrophilic (yellow) residues.

attached bilayer is rather mobile parallel to the bilayer surface whereas the com-

parably large pore formed in the pure bilayer more or less keeps its position.

The number of water molecules inside the pore and the flux of water molecules

Figure 4.2: Number density map of water molecules in the x−zplane averaged over the

90 ns where a pore is formed. The densities are averaged over 2 nm in y-direction with the

pulled lipid headgroup centered in the slices (without (left) and with Aβ42 (right)).

Chapter 4 AMYLOID β: PORE FORMATION IN PHOSPHOLIPID BILAYERS

through the pore were calculated using the scripts g_count and g_flux by Oliver

Beckstein [211]. To determine the number of water molecules inside a pore the

number of molecules residing between the two polar headgroup regions in pres-

ence and absence of a pore were counted. Both results were subtracted from

each other. The position of each headgroup region normal to the bilayer was

determined from the center of mass of its phosphor atoms. This yielded 375 wa-

ter molecules in the pore for the peptide-free and 195 for the peptide containing

system. The flux was estimated from the number of water molecules entering

the interior of the bilayer through one headgroup region and leaving it through

the other headgroup region. For the peptide-free system a unidirectional flux of

j=20 ns−1and for the peptide containing system j=0.4 ns−1was obtained.

It has to be noted that in case of the pure bilayer three lipid flips during the 30

ns simulation time during which a stable pore was present were observed. Lipid

flips describe the translation of a lipid through the bilayer from one leaflet to

the other as shown in figure 1.2 depicted in section 1.1 of the introduction. Our

finding agrees well with results from earlier MD simulation studies of vesicle

formation [212] and pore mediated lipid flip flops [213]. Similar lipid flips did

not occur within the peptide attached bilayer.

We computed lipid order parameters of the pure and the peptide attached bi-

0 2 4 6 8 10 12 14

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Carbon atom

Order Parameter

no Aβ42, no pore

no Aβ42, pore

Aβ42, no pore

Aβ42, pore

Figure 4.3: Order parameters averaged over 10 ns with and without pore.

layer in presence and absence of a pore by means of equation (2.20) described

in section 2.4.1 of the introduction. The results are shown in figure 4.3. Lipid

tails in vicinity of the water pore are more parallel to the bilayer surface and the

order parameters decrease accordingly as if compared to the case where no pore

is formed. In general the attachment of the Aβ42 peptides leads to an increase of

the lipid order parameters which might be explained by the decreased area per

Results 4.2

lipid as described in the method section 4.1. Interestingly, we found that for the

peptide-free system the segments of the hydrocarbon tails with a carbon number

≥8 are more strongly orientated normal to the bilayer surface than in absence

of a pore. We thus observe a crossover of the corresponding graphs.

4.2.2 Free energy of membrane pores

The potentials of mean force being the main result of this study are shown in

figure 4.4. In case of the trajectories where pore formation occurs (λ→0) only

the part of the trajectory featuring an already formed pore was considered. The

reason for this approach is given in the discussion (section 4.3). To describe

the profile of the PMF we start from the equilibrium position of the pulled lipid

headgroup located in the free energy minimum. An increase of λcorresponds

0 0.5 1 1.5 2 2.5

Distance from bilayer center [nm]

PMF [kJ/mol]

with Aβ42

without Aβ42

Figure 4.4: Potential of mean force (PMF) governing the motion of a lipid vertically to the

bilayer surface for a pure and an Aβ42 monomer attached DPPC bilayer. Pore formation

takes place in the range of the plateau at λ→0.

to pulling the lipid out of the bilayer and therefore exposing its hydrophobic tail

to an aqueous environment and consequently to an increase of the free energy.

Decreasing λand thus pulling the lipid headgroup into the bilayer causes an

increase of the free energy as it forces the polar headgroup into the nonpolar

tail region. If a hydrophilic pore forms (λ→0) the free energy only slightly

changes by further decreasing λ.

This holds especially true for the peptide-free system and can be explained by

the geometry of a hydrophilic, hour glass shaped pore. In this shape the nonpolar

tails of the pulled lipid are placed within the tail region of the bilayer whereas

its hydrophilic headgroup faces water. Dragging the lipid headgroup further into

the lipid bilayer (decreasing λ) corresponds to its translation lateral to the curved

bilayer surface. Here, the pulled lipid headgroup remains exposed to water and

Chapter 4 AMYLOID β: PORE FORMATION IN PHOSPHOLIPID BILAYERS

its nonpolar tail buried in the hydrophobic tail region. This process is similar

to pore mediated lipid flips which occurs rather spontaneously once a pore is

formed. Accordingly, the potential of mean force exhibits a rather flat shape in

this region. For the peptide containing system this effect could not be observed

as in this case no real hydrophilic pore is formed. We obtain a free energy of

membrane pores of

∆Gwo =63.7±1.8 kJ/mol for the pure DPPC bilayer and

∆GAβ=54.5±2.0 kJ/mol for the Aβ42 attached bilayer.

4.2.3 Influence of Aβ42 on the bilayer tail region

The mass density profiles given in figure 4.5 B indicate that the Aβ42 monomers

deeply intrude into the hydrophobic tail region of the bilayer. Furthermore the

attachment of the peptides leads to a broadening of the phosphor and nitrogen

densities along the bilayer normal as apparent from figure 4.5 A, B. This

012345678

200

400

600

800

1,000

z[nm]

Mass density kg/m3

DPPC

Carbon tails

Phosphor

Nitrogen

0123456789

200

400

600

800

1,000

z[nm]

Mass density kg/m3

DPPC

Carbon tails

Phosphor

Nitrogen

Aβ42

Polar res.

Apolar res.

012345678

−0.6

−0.4

−0.2

0.2

0.4

0.6

z[nm]

Charge density e/nm3

System

DPPC

0123456789

−0.8

−0.6

−0.4

−0.2

0.2

0.4

z[nm]

Charge density e/nm3

System

DPPC

Aβ42

Figure 4.5: Mass and charge densities of the pore-free lipid bilayer without peptide (A, C)

and attached by an Aβ42 peptide (B, D) averaged over 40 ns.

corresponds to an increased roughness of the polar headgroup region and thus

an effective decrease in the thickness of the nonpolar region of the bilayer. To

Results 4.2

validate this assumption we calculated the standard deviation of the z-positions

of the lipid phosphor atoms along the bilayer surface.

In case of the bottom leaflet a standard deviation of 0.03 nm for the peptide-free

and 0.3 nm for the peptide-containing system was obtained. The reduction

in the effective thickness of the nonpolar region within the bilayer is even

amplified by the intrusion of polar and charged residues of the Aβ42 peptide into

the hydrophobic bilayer core. This effect is indicated by the charge distributions

shown in figure 4.5B. Whereas the bilayer center in the peptide-free system

shows no charge density variations over a range of about 2 nm, this region is

reduced to about 0.5 nm in the peptide containing system. A broaden increase in

the electron density in the nonpolar core region of synaptic plasma membranes

due to the presence of Aβoligomers observed by small angle X-ray diffraction

spectroscopy was as well reported by Mason et al. [214].

Furthermore the thickness of the bilayer as given by the distance between

the two headgroup regions determined by the center of masses of the lipid

phosphor atoms was determined. For the pure bilayer a thickness of 3.64±0.05

nm and for the peptide attached bilayer a larger value of 3.75 ±0.04 nm was

obtained. The corresponding error was estimated from the standard deviation

over simulation time. We can therefore exclude that the higher propensity for

pore formation in case of the peptide containing system is caused by a general

thinning of the bilayer mediated by the peptide.

4.2.4 Pore densities

In our simulations we observed that a membrane pore is induced by pulling a

single lipid headgroup normal to the bilayer to the center of the bilayer. If the

distance zbetween the lipid headgroup and the bilayer center falls below a crit-

ical value zp, a pore forms. In unrestrained systems this happens spontaneously

due to thermal fluctuations. The probability Ppthat the distance between a lipid

headgroup and the bilayer center is smaller than zpand thus that a pore is induced

is given by

Pp=exp−β·Gp. (4.1)

Hereby β=1/(kBT)is given by the Boltzmann constant kBand the temperature

Twhereas Gpdenotes the free energy of membrane pores as given by

Gp=−kBT·logZp/Z. (4.2)

Chapter 4 AMYLOID β: PORE FORMATION IN PHOSPHOLIPID BILAYERS

Here, Zdenotes the partition function

Z=Zzc

0exp(−β·G(z))dz(4.3)

where zcdenotes the z-position of the phosphocholine group above which the

lipid is desorbed from the bilayer and Zpthe partition function of all lipid states

involving pore formation (z≤zp) according to

Zp=Zzp

0exp(−β·G(z))dz. (4.4)

The symbol G(z)denotes the potential of mean force (PMF) along zdetermined

from umbrella sampling as described in section 2.2 of the introduction. The

density of pores, i.e., the number of pores per area, is computed from

ρp=Pp

Nl·a. (4.5)

Here we took into account that Nllipids reside in each existing pore and that

these lipids are not available for the formation of new pores. From our simula-

tions Nlwas determined by counting all lipid phosphor atoms with z≤zpin a

given pore. In equation 4.5 ais the area per lipid. This equation holds only true

for the peptide-free system as in this case the bilayer surface is homogeneous.

If on the other hand a peptide is attached to the bilayer a lipid can be in contact

with the peptide or not. The corresponding pore density depends on the number

of lipids in contact with a peptide ncnpep. Here, npep denotes the number of pep-

tides per lipid and ncthe number of lipids in contact with a single peptide. For

peptide attached bilayers we obtain

ρP=Pc·ncnpep

Nl,ca+Pn1−ncnpep

Nl,na. (4.6)

A more detailed derivation of this equation can be found in section A.2 of the

appendix. The probabilities for a lipid to reside close to the bilayer center de-

termined by equation 4.1 are denoted as Piwhereas Nl,istands for the number

of headgroups fulfilling z≤zp. Hereby we took lipids in contact with a peptide

(i=c) and lipids not affected by any peptide (i=n) into account.

The density of pores within a pure lipid bilayer was computed via equation (4.5)

and within a peptide attached bilayer via equation (4.6). Hereby it is necessary

to integrate the Boltzmann factor in equation 4.3 up to zcassociated with lipid

desorption. As this state is not included in our simulations we extrapolated the

PMF by means of a harmonic function. Hereby we neglected the plateau in the

Results 4.2

PMF corresponding to the pore state. Results from a comparable study pub-

lished by Tieleman and Marrink [215] suggest that the description of the PMF

profile by a harmonic function is appropriate. Figure 4.6 shows the extrapolated

Boltzmann factors b(z) = exp(−β·G(z)) occurring in equation 4.3 and 4.4 for

the peptide containing (left) and the peptide-free system (right). The Boltzmann

factor in equation (4.3) was integrated up to a z-coordinate corresponding to a

lipid desorption free energy of ∆Gc=63 kJ/mol. Lipid desorption free ener-

gies of ∆Gc=75−80 kJ/mol and ∆Gc=63±4 kJ/mol have been reported for

pure DPPC lipid bilayers by Tieleman [215] and Grafmüller [216], respectively.

Here, it has to be noted that the results are rather insensitive to this choice as the

Boltzmann weight already drops below 10−4for a z-coordinate value associated

with G(z→zc) = 30 kJ/mol. For the pure bilayer we observed pore formation

0123

0.2

0.4

0.6

0.8

Distance from bilayer center [nm]

Boltzmann factor b(z)

Data

Extrapolation

0123

0.2

0.4

0.6

0.8

Distance from bilayer center [nm]

Boltzmann factor b(z)

Data

Extrapolation

Figure 4.6: Boltzmann factors occurring in equation 4.3 and 4.4 for the peptide-free (left)

and the peptide containing system (right).

for z≤0.3 nm and in case of the peptide attached bilayer for z≤0.1 nm. By

means of phosphor atom number densities we computed the number of lipids in-

volved in a single pore averaged over time to NL,n =2.5 for the peptide-free and

NL,c =0.1 for the peptide containing system. In case of the peptide containing

system we estimated the number of lipids in contact with the peptide to Nc=35.

Hereby we counted all headgroup phosphor atoms residing closer to the peptide

than the headgroup phosphor atom of the pulled lipid. In vicinity of Aβ42, pore

formation only occurred for one out of three pulled lipids as described in section

4.2.1. The probability Pcwas thus divided by three. With the ratio of peptides

per lipid npep =1/64 we obtain

ρp=1.8±3.6·103cm−2for the peptide-free system and

ρp=1.2±1.4·105cm−2for the peptide containing system.

Thus the attached Aβ42 peptides increase the density of membrane pores by a

factor of about 102.

Chapter 4 AMYLOID β: PORE FORMATION IN PHOSPHOLIPID BILAYERS

4.2.5 Water permeabilities and lipid flip flop waiting times

The permeability of molecules through a membrane can be calculated by their

flux Jthrough the membrane divided by the permeation driving concentration

difference, namely the osmotic gradient, ∆C, as

P=J

∆C.

The flux Jis given by the pore density ρpand the flux jof molecules through

a single pore according to J=j·ρp. In our case the net flux of water through

the bilayer vanishes as the concentrations on both sides of the bilayer coincide

and the translation of water molecules through the membrane is driven by self-

diffusion. Thus only the uni-directional flux can be considered where the water

number density can be assumed to be ∆C=55 M [215]. With j=20 ns−1for

the peptide-free and j=0.4 ns−1for the peptide containing system obtained in

section 4.2.1 we obtained

P≈1.1·10−9cm/s for the pure DPPC bilayer and

P≈1.4·10−9cm/s for the peptide containing system.

Hence, for the peptide attached and the pure bilayer similar water permeabilities

are obtained. For pure DPPC bilayers water permeability coefficients were re-

ported to cover a range of P=102−104cm/s from MD simulations [217,218]

as well as by H2OD2O exchange light scattering experiments [199]. Water per-

meation seems therefore not to be mediated by nanopores as already suggested

earlier [219].

A lipid flip as described in section 4.2.1 is in general accompanied by the re-

verse process, a lipid flop, as both leaflets contain the same number of lipids in

equilibrium. The corresponding lipid flip flop waiting time can be determined

τ=1

J. (4.7)

For the peptide-free system three lipid flips were observed during 30 ns and thus

j=0.1 ns−1. This leads to a flip flop waiting time of τ=2.71·102−8.12·102s.

Accordingly, flip flop times are in the range

5 min ≤τLip ≤14 min.

By means of sum-frequency vibrational (SFV) spectroscopy Liu and Conboy

determined the half-life of lipid flip flops for a planar supported bilayer of DPPC

lipids at about 310 K to 9.2 min [220]. It should be noted, though, that our

simulations were carried out at 323 K and thus above the phase transition of free

standing DPPC bilayers at 314 K [221]. The SFV spectroscopy experiments

Results 4.2

were conducted at 310 K and thus below but close to the phase transition of

free standing DPPC bilayers. However, supported bilayers are typically under

tension which is expected to lower the main transition temperature such that the

DPPC bilayers probed in Ref. [220] were most likely in the fluid phase. Hence,

the good agreement of the flip flop times between these experiments and our

simulation may not be coincidental. Our results confirm that pore formation is

the rate determining factor of lipid flip flops [213].

4.2.6 Pore closure and pore opening times

The bilayer attached Aβ42 peptide dramatically increases the pore closure time.

Whereas pores within the pure bilayer close after 17 ns to 303 ns, in case of the

peptide attached bilayer closure times of 40 ns up to over 1.2 µswere observed.

In the latter case pore closure took only place in six out of ten simulations.

From the number qcl(t)of simulations featuring a closed pore at time tand the

total number of performed simulations nthe probability Pcl (t)for a pore to be

closed at time tis estimated as

Pcl (t)≡P(t≥τcl) = qcl(t)

n. (4.8)

Thereby it is assumed that the pore opened at time zero. The corresponding

closure time is denoted as τcl. The probability Pcl (t)is furthermore related to

0 100 200 300 400 500

0.2

0.4

0.6

0.8

t[ns]

Pcl (t)

Simulation

Fit

0 500 1000 1500 2000 2500

0,2

0,4

0,6

0,8

t[ns]

Pcl (t)

Simulation

Fit

Figure 4.7: Probability of a pore open at t=0 being closed at time t,Pcl (t), from simulation

and fitted for the peptide-free (left) and the peptide containing system (right).

the probability of a pore being still open at time t,Pop ≡P(t<τcl), according to

Pcl (t) = 1−Pop (t).

Chapter 4 AMYLOID β: PORE FORMATION IN PHOSPHOLIPID BILAYERS

Assuming a Markovian process for pore closure leads to

Pop (t) = exp−t

τcl 

and thus

Pcl (t) = 1−exp−t

τcl . (4.9)

We estimated the confidence interval P−

cl ,P+

cl via the Wilson score method

[222],

P±

cl (t) =

Pcl (t)+ z2

1−α/2

2n±rPcl(t)(1−Pcl(t))

n+z2

1−α/2

4n2

1+z2

1−α/2

. (4.10)

Hereby z1−α/2denotes the critical value of the normal distribution with an error

α. This says that in case of normal distributed data around a mean value ¯xthe

quantile 1 −αof the data lies within the interval ¯x−z1−α/2,¯x+z1−α/2. To

obtain a confidence level of 95% we used α=5% resulting in z1−α/2=1.96.

The probabilities Pcl (t)according to equation (4.9) fitted to the simulation data

are depicted in figure 4.7. Using the confidence interval P−

cl ,P+

cl obtained from

equation (4.10) in combination with the fitting function (4.9) yields

51.4 ns ≤τcl ≤91.8 ns for the peptide-free system

296.1 ns ≤τcl ≤1789.2 ns for the peptide containing system.

On the basis of the pore closure rates kcl =τ−1

cl the pore formation rates, kf, may

be derived from the detailed balance condition

kf=kcl ·exp(−β∆G)

with β=1/(kBT). This yields

4.0·1010 s−1cm−2≤kf≤2.8·1011 s−1cm−2in absence and

6.2·1010 s−1cm−2≤kf≤1.7·1012 s−1cm−2in presence of Aβ42.

Hence, the attached Aβ42 peptide considerably stabilizes nanopores and further-

more tends to slightly increase pore formation rates.

Discussion and summary 4.3

4.3 Discussion and summary

In this chapter it was demonstrated that Aβ42 monomers strongly affect zwitte-

rionic phospholipid bilayers leading to thermodynamic and kinetic stabilization

of bilayer defects as given by small membrane pores. According to this, the

adsorption of Aβ42 on the one hand leads to an increase of the pore density by

a factor 102as well as a dramatic stabilization of nanopores as in terms of in-

creased pore closure times (life times of pores). On the other hand, the size of

membrane pores involving peptides is decreased compared to peptide-free pores.

Pore opening rates and water permeabilities were not considerably affected by

adsorbed Aβ42 monomers. The higher propensity of the peptide attached bilayer

to form nanopores might be explained by the peptide mediated disturbance of

the nonpolar bilayer region resulting in an effective thinning of this region. This

furthermore might facilitate the intrusion of water into the bilayer and thus pro-

mote the formation of nanopores. On the other hand, the interaction of lipid

headgroups with the peptide might prevent the complete reorganization of the

lipids into larger hydrophilic pores. Instead we observe a comparably small

pore exhibiting a rather disordered shape.

Our results for the peptide-free reference system might be compared to a simi-

lar study by Tieleman and Marrink [215]. Whereas we obtain a free energy of

membrane pores of about 64 kJ/mol, Ref. [215] reports a free energy change

upon pulling a lipid headgroup from its equilibrium position to the bilayer cen-

ter of 75 −80 kJ/mol. We believe that the main reason for this discrepancy is

the underestimation of the pore state due to the shorter production runs of the

simulations performed in Ref. [215]. If a lipid is restrained close to the center

of the bilayer, a hydrophilic pore forms after several nanoseconds. In this case

the free energy of the state characterized by the presence of a hydrophilic pore

is lower than the ”no pore“ state. Hence, the former is more likely and more sta-

ble. Accordingly, we obtain a much higher free energy of 78 kJ/mol if we only

consider the part of each trajectory in which no pore is formed yet. In contrast,

regarding merely the trajectory sections featuring a hydrophilic pore we obtain

64 kJ/mol. Consequently, for long time scales the initial absence of a pore can

in terms of the potential of mean force be neglected as the system will strongly

prefer the ”pore“ state. Tieleman and Marrink collected their data from a 50 ns

production run. In our study we observe that pore formation takes place after 45

ns in four of nine windows. Therefore the state of the system with an already

formed pore is apparently underestimated in the study of Tieleman and Marrink.

As a counter check we computed the potential of mean force using only the first

50 ns of our simulations and obtained a free energy of 76 kJ/mol in accordance

with the results of Marrink and Tieleman. In addition we extended the particular

trajectory in which the lipid headgroup is restrained as close as possible to the

Chapter 4 AMYLOID β: PORE FORMATION IN PHOSPHOLIPID BILAYERS

bilayer center z≈zpwithout formation of a pore. No pore formation was ob-

served within a 500 ns simulation. In this way we ensured that the whole range

of the reaction coordinate where pore formation takes place is included.

Furthermore, it has to be noted that Tieleman and Marrink simulated a smaller

bilayer patch of 64 DPPC lipids. The different size of the bilayer patches,

though, might not play a crucial role for the discrepancy observed in the re-

sults as the previous analysis showed that this can sufficiently be explained by

the difference in simulation timescales.

Tieleman and Marrink also determined lipid flip flop waiting times. Their re-

sults seem to overestimate the waiting times as they obtain 4 −30h, whereas

our values are with 5 min ≤τLip ≤14 min much closer to results reported from

experiment.

This study might serve as starting point to investigate the influence of more toxic

species like dimers or small oligomers of Aβ42 on pore formation and closure.

NK-2: Affinity for phospholipid bilayers

In this chapter the mechanisms determining the selectivity of antimicrobial pep-

tides between eu- and prokaryotic plasma cell membranes are studied. To this

end the affinities of the antimicrobial peptide NK-2 for zwitterionic 1,2-dioleoyl-

sn-glycero-3-phosphocholine (DOPC) and anionic 1,2-dioleoyl-sn-glycero-3-

phosphoglycerol (DOPG) bilayers are investigated. These serve as model sys-

tems for the corresponding membranes as described in section 1.1 of the in-

troduction. The difference in the binding affinities is determined by means of

molecular dynamics (MD) simulations in combination with the thermodynamic

integration (TI) method. Our studies were performed at atomistic resolution.

In a related work von Deuster and Knecht [145] employed a simplified coarse-

grained description and dissected various entropic and enthalpic contributions

determining the binding free energy. In the present study, the focus is on the

accuracy and the comparability of the computational method with experimen-

tal results. After describing simulation details the peptide structure as well as

the system composition in terms of density profiles are briefly outlined. Sub-

sequently, our results are compared with the simulations from von Deuster and

Knecht [145]. Finally, corresponding experimental binding free energies are

inferred from zeta potentials estimated for DOPC, DOPG, and DOPC/DOPG

vesicles by means of electrophoresis experiments performed by Karmakar et

al. [223].

Chapter 5 NK-2: AFFINITY FOR PHOSPHOLIPID BILAYERS

5.1 Simulation setup

The difference in the affinities of NK-2 for anionic DOPG and zwitterionic

DOPC bilayers in terms of a shift in the binding free energy, ∆∆G, was de-

termined by means of the thermodynamic integration (TI) method according to

the thermodynamic cycle described in section 2.3 of the introduction. The tran-

sition from DOPC to DOPG was performed by increasing the coupling param-

eter λin steps of ∆λ=0.05 for λ∈[0.1,0.9]while ∆λ=0.01 was chosen for

λ∈[0,0.1]∪[0.9,1.0]. To avoid possible singularities due to required dummy

atoms, Lennard-Jones and Coulomb interactions were transformed in separate

simulations as described in section 2.3. For λ∈[0,0.1]∪[0.9,1.0]data were

collected from 180 ns simulations whereas the larger step size of ∆λ=0.05

for λ∈[0.1,0.9]made longer simulation times of 360 ns necessary to assure

proper sampling. Each particular simulation was first energy minimized using

the steepest descent method and equilibrated for 20 ns.

The initial configuration of NK-2 was derived from the solution structure of

NK-lysin as obtained from NMR spectroscopy and stored in the RCSB 1pro-

tein data bank (PDB entry: 1NKL [137,180]). Its initial structure features two

α-helices separated by a kink as shown in figure 5.1. This configuration was

chosen as the peptide is, as many antimicrobial peptides, known to reorganize

into α−helical configurations if adsorbed to a bilayer surface [140, 142]. The

peptide was added to a DOPC bilayer by placing it within a hole with a radius of

1.5 nm pervading the bilayer as depicted in figure 5.1 (left). Hereby the peptide

was orientated such that its hydrophobic side chains face the bilayers’ nonpolar

hydrocarbon tails whereas the hydrophilic side chains pointed toward the polar

headgroups. The corresponding bilayer coordinates were downloaded from the

lipid bilayer library of the CHARMM2graphical user interface [224,225]. Ini-

tially the system was simulated for 20 ps restraining the coordinates of all pep-

tide atoms, succeeded by an additional 9 ns simulation with the peptide helicity

being stabilized using distance restraints. The N-terminus of the peptide was

pulled towards the upper bilayer leaflet during 600 ps. Finally, the system was

equilibrated for 100 ns resulting in the configuration shown in figure 5.1 (right).

This configuration served as starting point for the alchemical transformation of

DOPC to DOPG in presence of the NK-2 peptide. Several times during build-

ing up the initial setup water molecules had to be removed manually from the

bilayer interior. In several previous attempts with the peptide initially located in

the aqueous solution the peptide showed little tendency to attach to the DOPC

bilayer indicating a very small affinity for DOPC.

1Research Collaboraty for Structural Bioinformatics

2Chemistry at HARvard Macromolecular Mechanics

Simulation setup 5.2

The bilayer consisting of 128 DOPC or DOPG lipids, respectively, was sol-

Figure 5.1: NK-2 peptide in helix-kink-helix structured state positioned in a water pore

within a DOPC bilayer (left) chosen as the initial configuration and after 100 ns equilibration

(right). Lipids are shown in gray, headgroup nitrogens in orange, polar residues in green,

nonpolar residues in yellow, cationic residues in blue and anionic ones in red. The peptide

is depicted in ribbon representation.

vated by adding 8956 SPC3water molecules in presence and 5354 SPC3water

molecules in absence of the peptide. Both systems include 128 solvated dummy

atoms which were transformed to Na+ions for λ=1, then serving as counter

ions of the anionic DOPG bilayer. The electric charge of the cationic peptide

was compensated by ten Cl−ions.

The NK-2 peptide and the phospholipids were described using the united-atom

GROMOS964force field ffG53a6 [186] and separately coupled to a velocity

rescale [182] thermostat with a relaxation time of 0.1 ps maintaining a temper-

ature of 310 K. An average pressure of 1 atm parallel and normal to the bi-

layer was maintained using a Berendsen barostat [183] with a relaxation time

of 0.5 ps. For all simulations a time step of 2 fs was applied. Long-range

electrostatic interactions were calculated using particle mesh Ewald summa-

tion [184,185].

3Simple Point Charge

4GROningen MOlecular SIMulations

Chapter 5 NK-2: AFFINITY FOR PHOSPHOLIPID BILAYERS

5.2 Results

5.2.1 Secondary structure and position

Although the peptide is assumed to organize into α-helical structures in the lipid

bilayer environment the preformed helical structure was observed to partially or

completely unfold as shown in figure 5.2. In case of DOPC the unwrapping

comprised the residues Val6-Thr13 and started after 60 ns whereas for DOPG

the complete peptide adopts only coil, bend and turn conformations after about

380 ns. Time evolutions of the peptide’s secondary structure are shown in sec-

tion A.3 of the appendix. The unfolding of the peptide could be an artifact of

the chosen force field, GROMOS53a6, which is known to artificially destabi-

lize α-helical conformations whereas, on the other hand, it is parameterized to

match solvation free enthalpies of polar amino acid side chains which might be

important for the accuracy of our free energy calculations. [186].

As indicated from the mass density profiles of the peptide attached and pure

Figure 5.2: Snapshots of NK-2 attached to a zwitterionic DOPC (left) and an anionic DOPG

bilayer (right) after 400 ns of simulation. Lipids are depicted in gray, hydrophobic residues

in yellow, hydrophilic ones in green, cationic ones in blue and anionic residues in red. Pep-

tides are shown in ribbon presentation.

DOPC and DOPG bilayers shown in figure 5.3 we observe stable bilayers for all

four systems with no water molecules being present in the bilayer core region.

The profiles show well defined hydrocarbon tail and lipid headgroup regions

as indicated from the mass densities of the headgroup phosphor atoms. Inter-

estingly, only for the DOPC bilayer in absence and presence of the peptide, a

shoulder in the water density was found. Its position corresponds to the peak of

the phosphor atom density indicating a higher hydration of the PC head groups.

This effect is accompanied by a corresponding enlarged area per lipid as well

as a decrease in the bilayer thickness shown in table 5.1 and may be explained

by the larger polarity of the PC headgroup as the negatively charged phosphor

group is screened by the positively charged choline nitrogen group in a distinct

distance. On the other hand, in case of DOPG, the charge of the phosphor group

is directly neutralized by the Na+counter cations as indicated by the large over-

lap in the corresponding density profiles. The peptide density shows a very large

Results 5.2

overlap with the phosphor atoms. This holds especially true for the hydrophilic

residues whereas the hydrophobic residues rather reside in the nonpolar carbon

tail region. For DOPC the peptide density exhibits a slightly broader shape com-

pared to DOPG suggesting more translational freedom along the bilayer normal

for the peptide. This may at least partially be explained by the peptide’s weaker

electrostatic interactions with the zwitterionic PC head group.

Figure 5.3: Mass density profiles for DOPC (top) and DOPG (bottom) in absence (left) and

presence (right) of NK-2 averaged over 50 ns. Water is shown in black, DOPC and DOPG

in red, headgroup phosphor atoms in blue, carbon tails in light green, Na+ions in brown

and NK-2 in orange. In addition, hydrophobic residues (isoleucine, leucine, glycine, valine,

cysteine, methionine, and phenylalanine) are colored purple, hydrophilic ones (lysine, argi-

nine, threonine, serine, and asparagine) are depicted in cyan, and the cationic residues lysine

and arginine in magenta.

Interestingly, only for DOPG, a broadening of the phosphor density peak cor-

responding to an increased roughness and therefore a spatial disturbance of the

headgroup region was caused by the adsorption of NK-2. An explanation might

be given by the strong interaction of the cationic peptide residues with the an-

ionic PG head group. During the folding and organization processes the corre-

sponding peptide residues may partially drag the lipid head groups leading to an

increased disorder in their spatial distribution normal to the bilayer. At high pep-

tide concentrations this might lead to bilayer disruption in accordance with the

Chapter 5 NK-2: AFFINITY FOR PHOSPHOLIPID BILAYERS

alin nm2dP-P in nm

DOPC pure 0.73±0.001 3.45±0.06

NK-2 0.76±0.001 3.49±0.05

DOPG pure 0.65±0.002 3.84±0.15

NK-2 0.65±0.003 3.75±0.05

Table 5.1: Area per lipid, al, and bilayer thickness as obtained by the distance between the

center of masses of the phosphor atoms of the two leaflets, dP-P.

carpet model [226]. This suggests that the higher antimicrobial activity of NK-2

towards anionic lipid bilayers may not only be explained by its larger binding

affinity but also by an increased capability to disrupt anionic rather than zwitte-

rionic bilayers and therefore a larger propensity to intrude into anionic bilayers.

Additionally, we observed, in accordance with experimental results [143] a very

slight thinning of the DOPG bilayer due to the attached NK-2 peptide whereas

the thickness of the DOPC bilayer remains unchanged within the error margins.

5.2.2 Binding affinities from simulations

Our simulations indicate that the cationic NK-2 peptide binds much more

strongly to the anionic DOPG than to the zwitterionic DOPC bilayer. The TI

calculations yield a difference in the binding affinity of NK-2 for DOPG and

DOPC bilayers of

∆∆GPC→PG =∆GPG −∆GPC =−54.4±21.8 kJ/mol.

Here, the difference in the free energy between two neighboring states asso-

ciated with a particular λwas calculated using the Bennett acceptance ratio

method [159] as described in section 2.3 whereas the statistical error was

determined by dividing the trajectory in 20 ns blocks and determining the

corresponding standard error. This method refers to as block averaging.

In a comparable study von Deuster and Knecht estimated the difference

in the binding affinity ∆∆Gof the NK-2 peptide for anionic palmitoyl-

oleoyl-phosphatidyl-glycerol (POPG) compared to zwitterionic palmitoyl-

oleoyl-phosphatidyl-choline (POPC) lipid bilayers using MD simulations in

conjunction with the thermodynamic integration (TI) method [145]. Differing

from our atomistic description von Deuster and Knecht applied a rather simple

coarse grained representation by use of the MARTINI force field. They obtained

a value of ∆∆G=−56±6 kJ/mol which is in good agreement with our results.

Both investigated systems are quite similar as the POPC and DOPC as well as

Results 5.2

POPG and DOPG lipids are only slightly distinguished in their hydrocarbon

tail composition. DOPC as well as DOPG lipids exhibit two mono-unsaturated

allyl tails featuring 18 hydrocarbons whereas one of the alkyl tails of POPC

and POPG is completely saturated and merely contains 16 hydrocarbons. The

comparably large statistic uncertainty of our results is based on the more

detailed and therefore more complex description of our system. Here, in

particular the use of dummy atoms which were not required in the coarse grain

model play a crucial role as described in section 2.3.1 of the introduction.

5.2.3 Comparison with electrophoresis experiments

The difference in the binding affinities ∆∆GPC→PG obtained from our sim-

ulations might be compared to zeta potentials inferred from electrophoretic

mobilities of lipid vesicles at various NK-2 concentrations. The electrophoretic

mobility is the drift velocity of a particle suspended in a liquid due to an external

static and homogeneous electric field, normalized by the field intensity. The

drift of the particle arises due to its surface charge. The surface charge of the

dispersed particle is partially screened by a layer of rather tightly bound counter

ions. This layer refers to as the Stern plane and is furthermore surrounded by

a diffusive layer of a majority of counter and a minority of co-ions. The zeta

potential is the electrostatic potential at the shear plane with respect to the bulk

phase. At the shear plane the Stern plane turns into the diffusive layer of counter

and co-ions. According to the Smoluchowski equation the zeta potential is

proportional to the electrophoretic mobility [227].

Karmakar et al. investigated the effect of NK-2 on zeta potentials of large

unilamellar DOPG, DOPC, and DOPC/DOPG (4:1) vesicles (LUV) with a

diameter of about 20 nm [223]. The zeta potentials in dependence of NK-2

concentrations are depicted in figure 5.4. For zwitterionic DOPC as well as for

anionic DOPG vesicles negative zeta potentials are observed in absence of the

peptide where the value for DOPG (ζ=−61.1±17.9 mV) is much lower than

for DOPC (ζ=−10.6±9.9 mV) as expected from the negative charge of the

DOPG lipids. The slightly negative value within the range of error for DOPC

may be explained by negative ions binding to positive choline groups represent-

ing the most solution exposed moiety of the lipid. Willumeit et al. reported

zeta potentials of ζ=2.3±2.0 mV for pure DPPC and ζ=−56.0±2.2 mV

for pure DPPG vesicles [143]. The completely saturated hydrocarbon tails of

DPPG and DPPC (16 hydrocarbons per tail) are slightly shorter than the ones

of DOPC and DOPG (18 hydrocarbons per tail). It has to be noted that DOPC

and DPPC as well as DOPG and DPPG differ remarkably in their main phase

transition temperature, Tm. For DPPC and DPPG Tm=314 K whereas Tmis

Chapter 5 NK-2: AFFINITY FOR PHOSPHOLIPID BILAYERS

much lower for DOPC (Tm=253 K) and DOPG (Tm=255 K). As the study

from Karmakar as well as from Willumeit were performed at room temperature

(T=298.15 K), DOPC and DOPG vesicles were investigated in the liquid but

DPPG and DPPC liposomes in the gel phase.

For anionic DOPG, DPPG and DOPC/DOPG as well as for zwitterionic

Figure 5.4: Zeta potential for DOPC, DOPG, and DOPC/DOPG vesicles attached by NK-2

peptides inferred from electrophoresis experiments by Karmakar et al. [223].

DOPC vesicles charge neutralization and even charge overcompensation and

saturation is observed upon addition of cationic NK-2 peptides [143,223]. The

lipid bilayer-peptide interaction thus seems to be driven by electrostatic as well

as hydrophobic interactions. Charge overcompensation was not reported for

DPPC.

In this section we use these zeta potentials to determine the binding free

energies of NK-2 for DOPC, DOPG and DOPC/DOPG vesicles. We first

describe the corresponding ansatz published by von Deuster and Knecht [146]

and subsequently present inferred binding free energies and area densities of

membrane bound peptides. The latter give insight about the interaction between

membrane bound peptides. The results are finally discussed and compared with

results obtained from our simulations.

Results 5.2

Ansatz

The ansatz to determine the binding affinity of a charged peptide for particular

lipid vesicles or membranes is based on the change of the membrane surface

charge ∆σas mediated by peptide adsorption. The change of the surface charge

∆σis obtained from the inferred zeta potential as described below. By means

of ∆σit is possible to determine the concentration of bound peptides cswhich

depends on the peptide concentration in the bulk solution, c, and the binding free

energy, ∆G. In the following we first derive this relation and then describe the

estimation of ∆σfrom zeta potentials.

The relation between the number of peptides adsorbed to the bilayer surface, Ns,

and the number of peptides in the bulk, Nb, can be described by the free energy

difference between both corresponding thermodynamic states as

Ns=Nb·exp(−β(∆G−T∆S)). (5.1)

Here, ∆Gdenotes the binding affinity, β=1/(kBT),kBthe Boltzmann constant,

and T=298 K the temperature. The term −T∆Srefers to the contribution aris-

ing from the difference in the translational entropy of the peptide in bulk and

adsorbed at the bilayer. This term can be estimated from the peptide accessible

volume in bulk, Vb, and at the membrane, Vs, according to

−T∆S=−kBTlogVs

Vb. (5.2)

Assuming that the vast majority of peptides within the sample resides in the bulk

phase,

c≈cb, (5.3)

with the average peptide concentration c= (Ns+Nb)/Vand the sample volume

V≈Vb. Equations 5.1 and 5.2 result in

cs=c·exp(−β∆G)

⇔∆G=−kBTlogcs

c.(5.4)

The concentration of bound peptides, cs, can be expressed as cs=Ns/Vs=Γ/∆z

with the area density of bound peptides Γ=Ns/A. Here, Adenotes the complete

vesicle surface and ∆zthe accessible space of the peptide normal to the surface.

The latter might be taken as the standard deviation of the peptides’ center of

mass position normal to the bilayer as obtained from MD simulations. The de-

scribed ansatz implies that an adsorbed peptide is not restricted in its translation

along the bilayer surface. Thus, especially if the peptides are prone to aggrega-

tion the surface area available for each peptide, Ap, has to be large compared to

Chapter 5 NK-2: AFFINITY FOR PHOSPHOLIPID BILAYERS

the surface area covered by a single peptide, ap. Hence,

Apap. (5.5)

The adsorption of charged peptides results in a change of the vesicle surface

charge, ∆σ, depending on the area density of bound peptides, Γ, and the charge

of the peptide, qp, according to

∆σ=qpΓ=qpcs∆z. (5.6)

The surface charge, σ, and the surface potential, ψ0, are related via

σ=p8ε0εrkBTcel sinhzeψ

2kBT. (5.7)

This relation is denoted as Grahame equation and obtained from the Gouy-

Chapman theory (Poisson-Boltzmann theory in one dimension) [228]. Here,

εris the relative permittivity of the solution, ε0the vacuum permittivity, cel the

electrolyte concentration, ethe elementary charge, and z= +1 the charge num-

ber of counter ions. Approximately we determined the surface charge, σ, by

the electrostatic potential at the shear plane, the zeta potential, replacing the

potential at the surface, ψ0. For phospholipid vesicles in alkali metal chloride

solutions the shear plane was found to be located in about 2 ˚

A distance from

the bilayer surface as obtained by fitting the Stern equation to zeta potentials in-

ferred from electrophoresis experiments [229]. This approach to determine the

surface density, σ, from the Zeta potential, ζ, has recently been verified by MD

simulations by Knecht and Klasczyk [230,231].

Evaluation

Understanding the binding affinities from zeta potentials via equation 5.4 re-

quires to account for the partial compensation of the vesicle surface charge by

counter ions bound to the lipids. The adsorption of a peptide whose charge is

complementary to that of the surface leads to a release of counter ions which de-

creases the effective charge, qp, of the peptide. The number of released counter

ions per peptide, Nri, may be estimated from the fraction of lipids binding a

counter ion, α, and the number of lipids covered by a peptide, Nlc, as

Nri =αNlc. (5.8)

To compute Nlc we assume that the peptide adopts an α-helical structure at the

membrane. The thickness of an α-helix is typically D=0.54 nm whereas the

average length per amino acid is L=0.15 nm. Thus, the area covered by a 26

residue peptide as NK-2 adsorbed to the membrane can be estimated as

Results 5.2

ap=26·D·L≈2.1 nm2. The number of lipids covered by the peptide, Nlc, can

be determined by the area per lipid, al, from

Nlc =ap/al.

The fraction of lipids being charge neutralized due to the binding of a counter

ion, α, might be computed by the number of lipids, Nlq, including exactly one

lipid featuring an unscreened charge

α=Nlq −1

Nlq

. (5.9)

The next step is to estimate the surface concentration, Γlq, of lipid charges, ql,

Γlq =σ

. (5.10)

Equation 5.10 allows to calculate the surface area alq =1/Γlq exhibiting exactly

the charge of one lipid. The surface charge σis determined from the zeta poten-

tial via equation 5.7 applied for the peptide-free case c=0 mM. From the area

per lipid, al, and Nlq =alq/al, the fraction of lipids absorbing a counter ion, α,

can be computed via equation 5.9. The number of counter ions released upon

binding of a peptide is then estimated by equation 5.8 while the effective charge

of the peptide, qeff

p, is estimated as qeff

p=qp−Nriqiwith the peptide net charge

qpand the charge qi= +eof a single counter ion.

For DOPG we found αPG =0.98±0.01, leading to a net change of the vesicle

charge upon binding of a peptide of qeff

p= +6.8 e while for the ratio of ion ad-

sorbing lipids, DOPG, within the DOPC/DOPG mixture αPC/PG =0.94 ±0.03

corresponding to qeff

p= +7.3 e is obtained. In the latter case it has to be taken

into account that only 1/5 of the lipids are charged and thus the area per charged

lipid, alq, has to be multiplied by this factor. The applied zeta potentials in ab-

sence of peptides were inferred as ζPG(c=0 mM) = −61.1(±17.9)mV for

DOPG and ζPG/PC(c=0 mM) = −43.3±(20.3)mV for DOPC/DOPG. Fur-

thermore the areas per lipid, al, as obtained from our MD simulations shown in

table 5.1 were employed. To calculate the area per lipid for DOPC/DOPG we

averaged over the according values for DOPC and DOPG considering the mix-

ture ratio 4:1. For the uncharged DOPC vesicles qeff

p=qp= +10 e holds.

The binding affinities inferred from zeta potentials are given in table 5.2. The

accessible space of the peptide normal to the surface, ∆z, as required in equation

5.6 was estimated to ∆zPC =0.192 nm for DOPC, ∆zPG =0.163 nm for DOPG,

and ∆zPC/PG =0.186 nm for DOPC/DOPG. Hereby, ∆zPC/PG was evaluated by

averaging the values ∆zPC and ∆zPG according to the mixture ratio. Experiments

Chapter 5 NK-2: AFFINITY FOR PHOSPHOLIPID BILAYERS

were conducted at room temperature, T=298 K, in an aqueous solution ex-

hibiting a NaCl concentration of cel =0.6±0.2 mM.

The relative permittivity, εr, in equation 5.7 was set to the value for water at

cin mM ζin mV ∆Gin kJ/mol

DOPC 0−10.6±9.9−14.7±1.0

0.0312 25.4±10.4

DOPG 0.0312 −56.7±8−15.3±0.4

0.1248 12.7±4.1

DOPC/PG (4:1) 0.0156 −21.6±4.02 −18.2±0.4

0.0312 29.4±6.4

Table 5.2: Zeta potentials, ζ, for different NK-2 concentrations, c, as taken from [223] as

well as binding free energies, ∆G, obtained from equation 5.7 and 5.4.

room temperature, εr=78.

In order to validate condition 5.3, the total concentration of bound peptides

within the sample, cts, was computed from

cts =Γ·al·cl

Here, cl=0.65 mM is the concentration of lipids within the sample and althe

area per lipid. The second term alcl/2 is the concentration of accessible lipid

area within the sample. The factor 1/2 takes into account that the inner lipid

monolayer of the vesicle is inaccessible to the peptide. For all investigated

systems the ratio between the concentration of peptides in bulk, cb=c−cts,

and the concentration of peptides within the whole sample, c, was found to be

cb/c>0.96. The condition 5.3 is therefore always fulfilled.

The prerequisite 5.5 was tested by computing the lipid area containing exactly

one adsorbed peptide Ap=1/Γand comparing it to the surface area covered

by a single peptide, ap=2.1 nm2. Hereby apwas estimated by considering an

α-helix consisting of 26 residues as described above. For all systems and for

all studied peptide concentrations Ap/ap>111 was found. Condition 5.5 is

therefore fulfilled.

Area density of bound peptides

The interaction between membrane bound peptides is crucial for the activity of

antimicrobial peptides. As described in section 1.4 of the introduction depends

the propensity of antimicrobial peptides to induce membrane pores and mem-

brane disruption strongly on the corresponding peptide/lipid ratio.

Results 5.2

The interaction between membrane bound peptides may be described by a po-

tential, V(r) = γq2

pv(r), depending on the charge of the peptide, qp, a positive

factor, γ>0, scaling the strength of the interaction, and a positive strictly mono-

tonically decreasing function, v(r)>0, which depends on the distance between

two peptides, r. Furthermore v(r)→0 for r→∞is assumed. A potential which

fulfills these conditions and which is physically plausible would be provided

by the Coulomb potential with an effective dielectric constant for the water-

membrane interface. The peptide-peptide interaction can be neglected for low

concentrations of membrane bound peptides. This is crucial for the determina-

tion of peptide binding affinities for particular vesicle species and is expressed

in the condition 5.5. The concentration of membrane bound peptides increases

with its bulk concentration until it saturates. In this case the concentration of

membrane bound peptides is maximal. We assume for simplicity that in satu-

ration the peptides arrange on a quadratic lattice and that each peptide is sur-

rounded by four nearest neighbors in a distance of rmin. Under these conditions

the equation

∆G+4γq2

pv(rmin) = 0 (5.11)

holds. Thus, rmin can be determined via

rmin =v−1 −∆G

4γq2

p!. (5.12)

The inverse function v−1(·)of v(·)is strictly monotonically decreasing. Further-

more we assume v−1(·)>0. As ∆G<0 on the right side of equation 5.12, rmin

decreases if the charge of the peptide qpdecreases. For a quadratic lattice the

area density of membrane bound peptides Γsmay then be estimated from

Γs=1

min

. (5.13)

As described in section 5.2.3 the adsorption of NK-2 to the DOPG vesicles leads

to a release of counter ions bound to the lipids and hence to a decrease in the

effective net charge of the peptide, qeff

p= +6.8 e. As the distance rmin decreases

with the peptide charge an increase of the area density of membrane bound pep-

tides Γsin saturation may be expected. The area density Γscan be determined

via equations 5.6 and 5.7 using the zeta potentials obtained in absence of pep-

tides (c=0 mM) and in saturation.

In absence of peptides ζPG =−61.1(±17.9)mV was inferred for DOPG and

ζPC =−10.6(±9.9)mV for DOPC as apparent from figure 5.4. For saturation

Karmakar et al. found ζPG =47.3(±8.4)mV for DOPG at c=0.312 mM and

ζPG =25.3(±8.9)mV for DOPC at c=0.065 mM.

Chapter 5 NK-2: AFFINITY FOR PHOSPHOLIPID BILAYERS

Hence, we estimated

Γs

PG =6.8(±1.8)·10−3nm−2for DOPG and

Γs

PC =1.3(±0.5)·10−3nm−2for DOPC.

According to equation 5.13 this corresponds to rmin =12.1(±1.6)nm for DOPG

and rmin =27.6(±5.3)nm for DOPC.

In simulations the peptide may be affected by long-range interactions with its

periodic image. The distance between the peptide and its closest periodic images

is given by the length of the simulation box parallel to the bilayer, dx,y. While

for simulations of charged peptides in water the interaction between the peptide

and its periodic images may be neglected due to ionic screening as well as the

comparably high relative permittivity of water (εr≈80) and V(r)∝1/εrfor the

Coulomb potential this does not necessarily hold true for a peptide located at

the interface between the polar headgroup and the nonpolar hydrocarbon region

of a bilayer. The former exhibits a rather high relative permittivity parallel to

the bilayer, εr,k≈210(±30), while the relative permittivity of the latter is quite

low, εr,k≈4(±3), as determined from MD simulations for DPPC [232]. Under

these conditions the interaction between the peptide and its periodic image might

have to be taken into account. According to this, instead of the binding free

energy ∆Gat infinite low concentrations of membrane bound peptides the free

energy ∆Gbc including the interaction between the peptide and its four nearest

periodic images are computed by our simulations. In accordance with the ansatz

described above this leads to

∆Gbc =∆G+4γq2

pv(dx,y).

Hence, for the difference in the binding free energy of NK-2 at DOPG and

DOPC the relation

∆∆Gbc

PC→PG =∆Gbc

PG −∆Gbc

PC =∆∆GPC→PG +4γv(dx,y)(qeff

PG)2−(qeff

PC)2

is obtained. Hereby, qeff

PG and qeff

PC = +10 e are the effective net charge of

the peptide bound to the DOPG and DOPC bilayer, respectively, as obtained

from our simulations. For DOPG we inferred qeff

PG = +8.5 e as will be de-

scribed in section 5.3. As γ>0 and γv(dx,y)>0 our simulations yield a

difference in the binding free energy, ∆∆GPC→PG, reduced by a subtrahend of

4·8.52−102e2γv(dx,y) = −111 e2γv(dx,y)due to the peptide’s interaction

with its periodic images. As furthermore dx,y≈6.5 nm <rmin for DOPC as

well as for DOPG and the potential v(r)decreases strictly monotonically it can

be assumed that the contribution of the peptide-peptide interaction to the deter-

mined ∆∆Gbc

PC→PG is rather high.

Discussion 5.3

5.3 Discussion

The difference between the affinities of NK-2 for DOPG and DOPC vesicles as

obtained from electrophoresis experiments is determined to

∆∆GPC→PG =∆GPG −∆GPC =−0.6(±1.12)kJ/mol.

At first sight this result appears rather surprising as NK-2 is highly cationic

and the peptide is thus expected to strongly favor complementarily charged

DOPG over DOPC vesicles. Instead, NK-2 appears to exhibit the same bind-

ing affinity for both vesicle types. Furthermore, our simulations indicate a

much higher adsorption propensity of NK-2 for DOPG bilayers, ∆∆GPC→PG =

−54.4±21.8 kJ/mol. On the other hand, we estimate that in experiment the

negative charge of αPG =98(±1)% lipids is neutralized by positive counter ions

bound to the lipids. This effect dramatically diminishes the electrostatic attrac-

tion of the peptide to the vesicles originated by charge complementarity.

To determine the ratio αPG in our simulations the Na+number density was in-

tegrated over the bilayer region confined by the Gibbs-dividing surfaces of the

two leaflets. The Gibbs-dividing surface approximately corresponds to the shear

plane as suggested by MD simulations of a zwitterionic phospholipid (POPC)

bilayer exposed to an electric field parallel to the bilayer surface [230]. It is

given by the plane where the water density is equal to half of its bulk value. This

plane is closely located to the phosphor group region as indicated by the den-

sity profiles shown in figure 5.3. In the described manner, from simulations, we

found that merely 58.3 Na+ions bind to a DOPG bilayer comprising 128 lipids.

Thus αPG =58.3/128 =0.46 corresponding to an effective peptide net charge

of qeff

p= +8.5 e was estimated.

The obtained comparably low ratio of bound counter ions might result from

force field inaccuracies as for example mediated by the underestimation of the

charge of PO−

4groups within the PG head groups. Tolokh et al. reported a ratio

of 27% of membrane bound Na+ions using the CHARMM force field [233]

whereas for the GROMOS force field a ratio of about 60% was found [234]. On

the other hand, it has to be taken into account that the number of lipids charge

neutralized by bound counter ions depends on the concentrations of ions, ci,s,

at the membrane surface as a higher concentration, ci,s, increases the binding

probability. The concentrations ci,s are different in experiment and simulations.

The effect of ci,s given by a possible difference in boundary conditions should

be dissected from the possible difference in the intrinsic binding affinity aris-

ing from possible force field inaccuracies. To this aim, the intrinsic binding

constant, Kint, [235] was compared between simulation and experiment. The in-

trinsic binding constant Kint is related to the fraction of lipids binding an ion, α,

the fraction of ion-free lipids, 1−α, and the concentration of counter ions at the

Chapter 5 NK-2: AFFINITY FOR PHOSPHOLIPID BILAYERS

surface, ci,s, according to

Kint =α

ci,s(1−α). (5.14)

In experiment, the concentration ci,s can be estimated from the Boltzmann rela-

tion [229] as

ci,s =ci,b exp(−zeβψ0). (5.15)

Hereby, ci,b =0.6±0.2 mM is the concentration of ions in the bulk, z= +1 the

charge number of the counter ions, ethe elementary charge, β=1/(kBT),kB

the Boltzmann constant, and Tthe temperature. The value of ci,s was estimated

by replacing the surface potential ψ0in equation 5.15 by the zeta potential. For

DOPG with ζ(c=0 mM) = −61.9(±17.9)mV in the absence of peptides (also

employed to determine αas described above) ci,s =3.8(±3.0)·10−3nm−3was

obtained. With α=0.98 (±0.01)the experimental intrinsic binding constant is

estimated as Kint =1.27(±1.17)·104nm3. For our simulations, ci,s might be

approximated by the number density of Na+ions at the aforementioned Gibbs-

dividing surface. Here, a Na+concentration of ci,s ≈1.9 nm−3and thus with

α=0.46 as described above Kint ≈0.45 nm3is obtained.

Two effects are therefore identified to cause the large discrepancy between

∆∆GPC→PG obtained from simulations and experiment: on the one hand, the

interaction of the peptide with its periodic images as described in section 5.2.3,

and on the other hand, the underestimation of the intrinsic binding constant for

the association of counter ions with the lipids. Furthermore it has to be noted that

in experiment the charge of the peptide itself might be compensated by counter

ions which would decrease its effective charge even further.

Interestingly, we found that NK-2 binds even more strongly to DOPC/DOPG

than to pure DOPG vesicles,

∆∆GPC/PG→PG =∆GPG −∆GPC/PG = +2.9(±0.6)kJ/mol.

This might result from a slightly lower fraction of DOPG lipids charge neutral-

ized by bound counter ions. For DOPG we obtained αPG =98 ±1% and for

the fraction of DOPG lipids within DOPC/DOPG (4:1) vesicles α=94 ±3%.

Although both values agree within the error range the values suggest that α

might be slightly lower for DOPC/DOPG. This may result from the lower sur-

face charge of the vesicle and therefore a smaller density of cations at its shear

plane, leading to a decrease in the probability of counter ion binding.

Conclusion 5.4

5.4 Conclusion

We have investigated the affinity of the antimicrobial NK-2 peptide for anionic

DOPG and zwitterionic DOPC lipid bilayers by means of MD simulation in

combination with the thermodynamic integration (TI) method. Furthermore we

compared our results with the affinities of NK-2 for DOPC, DOPG and mixed

DOPC/DOPG vesicles as obtained by analysis of zeta potentials inferred from

electrophoresis experiments. Interestingly, we found that simulations predict

a much stronger adsorption of the peptide to DOPG bilayers whereas elec-

trophoresis experiments indicate a similar propensity of the peptide to attach

to DOPC or DOPG vesicles. We explain this unexpected finding by counter

ions bound to the charged lipids which largely compensate the anionic charge of

the DOPG vesicles, an effect which appears to be underestimated by the simu-

lations.

Our findings might be of large importance for the understanding of the modes of

action of antimicrobial peptides as they suggest that the selective activity of the

peptides against pro- but not eukaryotic cells may not simply be explained by

different binding affinities of the peptides for pure plasma cell membranes. On

the other hand, in saturation we inferred an about fivefold higher area density of

membrane bound peptides for DOPG compared to DOPC. This increased area

density results from a lower peptide-peptide-interaction due to the compensation

of cationic peptide charges by anionic lipids. The area density of membrane

bound peptides correlates with the peptide/lipid ratio which is crucial for the

propensity of antimicrobial peptide mediated pore formation in membranes as

described in section 1.4 of the introduction.

Another crucial aspect which differentiates prokaryotic from eukaryotic cell

membranes is the cholesterol content. Cholesterol accounts typically for 20 −

25% of all lipid molecules within plasma cell membranes of vertebrate eukary-

otes whereas it is not present in prokaryotes [236]. It strongly interacts with

the surrounding lipids inducing a higher lateral lipid order and increased pack-

ing density. This decreases the lipid fluidity and the membrane permeability for

small polar molecules as for example water. These effects might as well decrease

the pore formation propensity of eukaryotic cell membranes yielding an addi-

tional explanation for the reduced activity of antimicrobial peptides here [237].

Summary

In this PhD thesis molecular dynamics simulations (MD) have been employed

to investigate the mutual influence between peptides and model membranes.

In particular the impact of (i) air-water interfaces on the folding behavior of

Aβmonomers associated with Alzheimer’s disease, (ii) the effect of these

monomers on the formation and stability of phospholipid bilayer defects like

water pores, and (iii) the difference in the affinity of the antimicrobial peptide

NK-2 for zwitterionic and anionic phospholipid bilayers have been studied.

As to (i), the secondary structures of the alloforms Aβ40 and Aβ42 at pH 5

and pH 7 in presence and absence of an air-water-interface were examined.

Here, for both peptides we observe a decrease in the amount of β-structures

in aqueous solution at pH 5 compared to physiological pH conditions. A

comparable decrease was not observed at an air-water-interface where the

fraction of β-structures does not remarkably change upon a decrease in pH. On

the other hand, for all systems especially the hydrophilic N-terminus shows a

comparable low propensity to form β-sheets or -bridges at pH 5. The N-termini

of both peptides contain three histidine residues whose positive charge at pH

5 might promote the interaction between nearby residues resulting in stable

helical motifs (Aβ42) or increase the polarity and thus the segment’s water

solubility (Aβ40). Our findings confirm studies indicating that the higher

aggregation propensity of Aβunder slightly acidic compared to pH neutral

conditions is rather caused by the peptide’s vanishing net charge and thus the

absence of electrostatic repulsion than by the formation of aggregation prone

Chapter 6 SUMMARY

monomer structures [191].

For Aβ40 the presence of an air-water-interface diminishes the formation of

β-sheets and -bridges which suggests that the higher β-sheet content of Aβ40 at

air-water-interfaces as detected by infrared reflection-absorption spectroscopy

(IRRAS) by Schladitz et al. [188] is provoked by peptide-peptide interactions

promoted by adjusted peptide orientations or increased peptide densities at

the interface. In case of Aβ42 the β-structure content is either higher (pH 5)

or similar to the one in bulk solution (pH 7). This difference to Aβ40 may

be explained by the additional two hydrophobic residues which increase the

peptide’s tendency to locate its hydrophobic C-terminus directly at the interface

and might play a role in the difference in aggregation propensities between the

peptides in membrane environments and thus their toxicities in vivo.

As our studies indicate that peptide-peptide interactions might be crucial for the

adoption of aggregation prone conformations provoked by air-water-interfaces

or pH conditions close to the peptide’s isoelectric point it would be enlight-

ening to perform similar studies for small oligomers like dimers or trimers.

Hereby it might be necessary to employ enhanced sampling methods like

accelerated [238] and discrete [239] MD simulations or the replica exchange

method [206].

As to (ii), the free energy of water pores in zwitterionic phospholipid

bilayers (DPPC) attached by an Aβ42 monomer was determined by means of

the umbrella-sampling method. The comparison with a peptide-free reference

system revealed that the adsorption of an Aβ42 monomer dramatically increases

the pore density and durability but also decreases the pore size. The latter is

indicated from a diminished unidirectional flux of water molecules through

the pore. Pore mediated water permeabilities as well as pore opening rates are

comparable for both systems.

Furthermore for the peptide-free reference system we determined lipid flip-flop

waiting times which were found to be in accordance with experimental results.

For this system we argued that the evaluation of our simulations are an

improvement to a former similar study by Tieleman and Marrink [215].

The higher propensity for pore formation observed for the Aβ42 adhered bilayer

might be explained by an effective lowering of the dielectric barrier provided

by the nonpolar bilayer core region. This finding is in accordance with studies

from Sokolov et al. [110,240] who suggested that rather the general disturbance

of membrane integrity than the formation of single calcium channels might

play the major role in Aβmediated calcium dyshomeostasis. Sokolov et al.

proposed that surface attached Aβoligomers increase the area per lipid leading

to a penetration of water molecules into the nonpolar bilayer region and thus to

6.0

an increase of its effective dielectric constant. Our simulations rather indicate

that the Aβpeptide locally dislocates polar head groups into the bilayer tail

region which furthermore facilitates the intrusion of water molecules into the

membrane indicated from comparably high densities and stabilities of small

water pores. These both effects decrease the effective dielectric constant of the

bilayer core region mediating a higher ion permeability of the bilayer. Here, it

has to be noted that Sokolov et al. observed an increased ion current through

lipid bilayers only in presence of Aβoligomers (∼90 −110 kDa [240]) but

not monomers (∼4.5 kDa). As we already observed a strong effect of Aβ42

monomers on the integrity of the bilayer as well as the frequency and stability

of water pores it would be very interesting to perform comparable simulation

studies with small toxic Aβ-oligomers like tetramers or pentamers.

Furthermore the role of the lipid composition of the bilayer on the free

energy and stability of water pores might be investigated. Here especially the

interaction between Aβand anionic phosphatidylinositol (PI) lipids might be

important for a deeper understanding of Alzheimer’s disease as a higher PI

content has been observed in membranes within disease affected brain regions

like the frontal and temporal cortex or the hippocampus [241].

As to (iii), the free energy difference for the transfer of the peptide NK-2

from an anionic (DOPC) to a zwitterionic (DOPG) phospholipid bilayer was

determined by means of atomistic MD-simulations in conjunction with the ther-

modynamic integration (TI) method. Our simulations indicate a much higher

affinity of the antimicrobial peptide to anionic compared to zwitterionic bilay-

ers. Hereby our results agree well with a comparable simulation study by von

Deuster and Knecht [145] using a coarse grained description.

Furthermore we determined the affinity of NK-2 for DOPC, DOPG as well as

DOPC/DOPG (4:1) vesicles from zeta potentials inferred from electrophoretic

mobilities by Karmakar et al. [223]. Unexpectedly, NK-2 showed similar affini-

ties for DOPC and DOPG vesicles which is not in accordance with results from

our simulations. This discrepancy may be explained by force field inaccuracies

like the underestimation of bilayer adsorbed counter ions or by finite size effects

like the interaction between the peptide and its periodic images.

Our interpretation of the experimental results indicate that the comparable affini-

ties of NK-2 for anionic and zwitterionic vesicles are accounted for by the ad-

sorption of counter ions which largely neutralize the charge of the anionic lipids.

Thus a higher density of bilayer adsorbed peptides in case of DOPG may rather

be explained by weaker peptide-peptide repulsion than by higher membrane

binding affinities. This decrease in the electrostatic repulsion between peptides

arises due to the partly screening of the positive net charge of the peptide by the

Chapter 6 SUMMARY

anionic lipids.

In a similar way it might also be desirable to analyze the affinity of NK-2 for

other vesicle species like DOPE/DOPG (4:1) or DOPC/DOPE (4:1). The cor-

responding zeta potentials were already inferred by Karmakar et al. [223]. The

corresponding areas per lipid, al, and the standard deviations of the z-position ,

∆z, of the membrane attached peptide may be obtained by comparably simple

MD simulations. In this simulations it would also be interesting to investigate

the influence of the attached peptide on the formation of lipid domains within

the mixed bilayer.

Additionally it has to be mentioned that the Grahame equation 5.7 employed

to determine surface charges from zeta potentials is strictly only valid for 1:1

electrolytes. Hence in our analysis we neglected the impact of solvated cationic

peptides on the strength of the electrolyte. Especially for large peptide concen-

trations further analysis might be necessary to validate this approximation. An

appropriate ansatz was already provided by Grahame in 1947 [242].

It would also be very enlightening to study the role of cholesterol on NK-2 me-

diated membrane disruption or pore formation within phospholipid bilayers. As

a starting point a single NK-2 peptide attached to a pure phospholipid and a

phospholipid-cholesterol bilayer may be considered. For both systems the free

energy for the transition of the peptide from a parallel to a normal surface ori-

entation might be determined by MD simulations in conjunction with the um-

brella sampling technique. Similar simulations were performed by Irudayam

and Berkowitz for the antimicrobial peptide melittin within a pure zwitterionic

phospholipid bilayer (POPC) [243]. To enhance the sampling of the conforma-

tional space of the peptide it might be necessary to employ more sophisticated

techniques like the replica exchange umbrella sampling (REUS) instead of the

common umbrella sampling method [244].

Glossary

Acronyms

AβAmyloid beta

AD Alzheimer’s disease

ADDL Amyloid beta derived diffusible ligands

ADI Alzheimer’s disease international

AFM Atomic force microscopy

AICD Amyloid precursor protein intracellular domains

AMBER Assisted model building with energy refinement

ApoE apolipoprotein E

APP Amyloid precursor protein

CD Circular dichroism

CHARMM Chemistry at Harvard molecular mechanics

CR Congo Red

CTF Carboxy-terminal fragment

DNA Deoxyribonucleic acid

DOPC Dioleoylphosphatidylcholine

DOPC Dioleoylphosphatidylglycerol

DPPC Dipalmitoylphosphatidylcholine

DSSP Define secondary structure of proteins

EM Electron microscopy

FTIR Fourier-transform infrared spectroscopy

GROMACS Groningen machine for chemical simulations

GROMOS Groningen molecular simulations

Acronyms

HFIP Hexafluoroisopropanol

IRRAS Infrared reflection-absorption spectroscopy

LINCS Linear constraint solver

LPS Lipopolysaccharides

LUV Large unilamellar vesicle

MD Molecular dynamics

NK Natural killer

NMR Nuclear magnetic resonance

OPLS Optimized potential for liquid simulations

PC Phosphatidylcholine

PDB Protein data bank

PE Phosphatidylethanolamine

PG Phosphatidylglycerol

PI Phosphatidylinositol

PME Particle mesh Ewald

PMF Potential of mean force

POPC Palmitoyloleoylphosphatidylcholine

POPE Palmitoyloleoylphosphatidylethanolamine

POPG Palmitoyloleoylphosphatidylglycerol

RCSB Research collaboraty for structural bioinformatics

REUS Replica exchange umbrella sampling

RMSD Root mean square deviation

RNA Ribonucleic acid

ROS Reactive oxygen species

SDS Sodium dodecyl sulphate

SFV Sum-frequency vibrational

SPC Simple point charge

SSNMR Solid-state nuclear magnetic resonance

TEM Transmission electron microscopy

TFE Trifluoroethanol

Symbols

ThT Thioflavin T

TI Thermodynamic integration

WHAM Weighted histogram analysis method

Symbols

aArea per lipid

αSoft-core parameter or fraction of lipids binding a counter

ion

bBoltzmann factor

cConcentration

C(12)

i j C(12)coefficient scaling the repulsive term of the

Lennard-Jones potential between particles iand j

C(6)

i j C(6)coefficient scaling the attractive term of the Lennard-

Jones potential between particles iand j

δDirac delta function

dBond length or distance

eElementary charge

ε0Vacuum permittivity

εrRelative permittivity

FForce vector

GGibbs free energy

HHamiltonian function

hPlanck constant

kBBoltzmann constant

Kint Intrinsic binding constant

λCoupling parameter (TI) or reaction coordinate (umbrella

sampling)

mMass

NNumber

νResonance frequency

PProbability

pProbability density or power of the soft-core potential

ΦProper dihedral angle

Ψ0Surface potential

QConfigurational integral

qElectric charge or generalized coordinate

rPosition

tTime

Symbols

ρDensity

ri j Distance between the particle iand j

SEntropy

σRadius of interaction

Szz-component of the lipid order parameter

TTemperature

∆tDiscrete time interval

θBond angle

UPotential energy

VPotential or volume

WBias potential

WPotential of mean force

ZPartition function

zCharge number or coordinate

ζImproper dihedral angle

Appendix

A.1 Amyloid β: Time evolution of secondary structure at

air-water-interface

On the following pages the time evolutions of the secondary structures of the

peptides Aβ40 and Aβ42 under different conditions as discussed in chaper 3 are

shown.

400 800 1200 1600 2000

Residue

Time (ns)

0 500 1000 1500 2000

Residue

Time (ns)

Figure A.1: Time evolution of secondary structure for individual residues of Aβ40 at slightly acidic pH in bulk solution (top) and at air-water-interface

(bottom).

0 500 1000 1500 2000

Residue

Time (ns)

0 500 1000 1500 2000

Residue

Time (ns)

Figure A.2: Time evolution of secondary structure for individual residues of Aβ40 at neutral pH in bulk solution (top) and at air-water-interface

(bottom).

101

400 800 1200 1600 2000

Residue

Time (ns)

0 500 1000 1500 2000

Residue

Time (ns)

Figure A.3: Time evolution of secondary structure for individual residues of Aβ42 at slightly acidic pH in bulk solution (top) and at air-water-interface

(bottom).

400 800 1200 1600 2000

Residue

Time (ns)

0 500 1000 1500 2000

Residue

Time (ns)

Figure A.4: Time evolution of secondary structure for individual residues of Aβ42 at neutral pH in bulk solution (top) and at air-water-interface

(bottom).

103

Appendix A

A.2 Amyloid β: Pore densities in phospholipid bilayers

In this section equation 4.5 and 4.6 employed in section 4.2.4 to determine the

density of membrane pores in case of pure and peptide attached lipid bilayers

are derived. To estimate pore densities, first a peptide-free lipid bilayer shall

be considered. The distance of the phosphate group of a given lipid from the

center of the bilayer in z-direction shall be denoted as z. If zis fixed below a

critical value zpusing an umbrella potential in a MD simulation, a pore forms

spontaneously. It is intuitive to denote a lipid with z<zpas to reside in the

”center“ of a pore. The probability that a given lipid resides in the center of a

pore, Pp, is given by

Pp=exp−β·Gp. (A.1)

Here, β=1/kBTwhere kBdenotes Boltzmann’s constant and Tthe absolute

temperature. The free energy Gpis

Gp=−kBT·logZp/Z(A.2)

where

Z=Zzc

0b(z)dz(A.3)

is the full partition function for a bilayer-inserted lipid and zcdenotes the posi-

tion above which the lipid is desorbed from the bilayer. The symbol Zpdenotes

the partition function for the state ”lipid resides in pore center“ which is given

Zp=Zzp

0b(z)dz(A.4)

with the Boltzmann factor

b(z) = exp(−β·G(z)). (A.5)

Here, G(z)is the potential of mean force (PMF) along zas obtained from the

umbrella sampling simulations of the peptide-free system. Now a macroscopic

bilayer patch at macroscopic time scales shall be considered. If Ndenotes the

number of lipids of one leaflet, Npthe number of pores averaged over time, Nl

the number of lipids in the center of a given pore coming from one leaflet, and

hNlithe average number of lipids in the center of pores averaged over time, the

equation

hNli=Np·Nl=Pp·N

holds. Here, Nlmay be obtained from a MD simulation of a bilayer exhibiting

a pore by determining the corresponding number of phosphate groups with dis-

104

Amyloid β: Pore densities in phospholipid bilayers A.2

tances 0 to zpfrom the center of the bilayer. If A denotes the area of the (now

macroscopic) patch, a=A/Nthe area per lipid, and

ρp=Np

the number of pores per area, this leads to

ρp=exp−β·Gp

Nl·a. (A.6)

If, in contrast, a peptide is present, we assume that (i) the probability of a lipid

residing in the center of a pore is equal for all lipids in contact with the peptide

and that (ii) pores always involve lipids in contact with peptides. Admittedly,

assumption (i) is a rather crude approximation due to the inhomogeneity of the

peptide. Accordingly, in our case, pulling different lipids in contact with the

peptide induced pore formation in one out of three cases only as described in

section 4.2.1. This effect was taken into account as described in the result section

4.2.4. Assumption (ii) might lead to a lower or upper bound of the corresponding

pore density depending on the free energies of pores in absence and presence of

the peptide. The probability that a given lipid in contact with the peptide resides

in the center of a pore, Pp,c, is given by equation (A.1) with Gpin equation

(A.1) and (A.2) replaced by Gp,cand G(z)in equation (A.5) by Gpep(z), where

Gpep(z)denotes the PMF obtained from the umbrella sampling simulations in

the presence of the peptide. If hNl,cidenotes the number of lipids in contact with

a peptide and residing in the center of a pore averaged over time, Ncthe number

of lipids in contact with a peptide, and Nl,c the number of lipids in contact with

a peptide and residing in the center of a single pore, the equation

hNl,ci=Np·Nl,c =exp−β·Gp,c·Nc

holds. If Npep is the number of peptides, nc=Nc/Npep the number of lipids in

contact with a single peptide, and npep =Npep/Nthe molar ratio of peptides and

lipids, the pore density is

ρp=exp−β·Gp,c·nc·npep

a·Nl,c

In the presence of a peptide, two types of pores will be present: c-type pores

denoting pores involving lipids in contact with a peptide, and n-type pores *not*

involving lipids in contact with a peptide. If the average number of c-type pores

is hNp,ci, the average number of n-type pores hNp,ni, and the total number of

105

Appendix A

pores hNpi, then

hNpi=hNp,ci+hNp,ni.

The number of lipids in the center of a c-type pore shall be called Nl,c, and the

number of lipids in the center of a n-type pore as Nl,n. Then the number of c-type

pores is given by

hNp,ci=Nc

Nl,c ·exp(−β·Gp,c)

and the number of n-type pores by

hNp,ni=N−Nc

Nl,n ·exp(−β·Gp,n).

Here,

Gp,i=−kBT·logZp,i

Zii=c,n

with the partition function for the pore state

Zp,i=Zzp

0bi(z)dz i =c,n

and the full partition function for the membrane-inserted lipid

Zp,i=Zzc

0bi(z)dz i =c,n.

Here, as before, zcdenotes the position from which the lipid is desorbed from

the bilayer and bi(z)the Boltzmann factor

bi(z) = exp(−β·Gi(z)) i=c,n,

with Gn(z)denoting the PMF for the peptide-free and Gc(z)the PMF for the

bilayer with peptide. With

Pi≡exp−β·Gp,ii=c,n

and ncnpep =Nc/N, the number of pores per area, ρP, is given by

ρP=hNpi

A=hNpi

Na =Pc·ncnpep

Nl,ca+Pn1−ncnpep

Nl,na. (A.7)

106

NK-2: Time evolution of secondary structure at phospholipid bilayers A.3

A.3 NK-2: Time evolution of secondary structure at

phospholipid bilayers

Here, the time evolution of the peptide NK-2 attached to a zwitterionic DOPC

and an anionic DOPG bilayer as discussed in section 5.2.1 are shown.

0 100 200 300 400

Residue

Time (ns)

Secondary structure

Coil B-Bridge Bend Turn A-Helix 5-Helix 3-Helix

Figure A.5: Time evolution of secondary structure of the NK-2 peptide attached to DOPC

(top) and a DOPG (bottom) bilayer.

107

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Publication List

Parts of this thesis have also been published in the following publication

T. Pobandt and V. Knecht. Free energy of lipid bilayer defects affected by

Alzheimer’s disease associated amyloid-β42 monomers. J. Phys. Chem. B,

2014. Doi: 10.1021/jp410477x.

133

Danksagung

Abschließend möchte ich mich bei all jenen bedanken, die mich während meiner

Promotion begleitet und unterstützt und somit maßgeblich zum Gelingen dieser

Arbeit beigetragen haben.

Ganz besonders möchte ich mich bei meinem Betreuer Dr. Volker Knecht

bedanken, der mir zu jeder Zeit geduldig mit Rat und Tat zur Seite stand, auch

wenn dies teilweise aufgrund äußerer Umstände nicht immer ganz einfach war.

Er ermöglichte mir die Arbeit an äußerst interessanten und spannenden Themen

und war jederzeit bereit meine Forschung in richtige Bahnen zu lenken. Vielen

Dank.

Weiterhin möchte ich mich recht herzlich bei Prof. Dr. Martin Schoen von

der Technischen Universität Berlin bedanken, der es mir ermöglichte meine

Arbeit in seiner Arbeitsgruppe “Theoretische Chemie“ zu Ende zu führen. Hier

wurde ich sehr freundlich empfangen, was mir gerade die letzten, doch eher

schwierigen Monate des Zusammenschreibens deutlich erleichtert hat.

Die Zeit meines Aufenthaltes an der University of North Carolina at Chapel

Hill habe ich sehr genossen und ich habe wissenschaftlich und persönlich

interessante und schöne Erfahrungen sammeln können. Hierfür danke ich

insbesondere Prof. Dr. Max Berkowitz und seiner Arbeitsgruppe für das

hervorragende Arbeitsklima . Ausdrücklichen Dank gebührt dabei Dr. Sheeba

Irudayam, die mir mit zahlreichen Diskussionen geholfen hat einen anderen

Blick auf meine Forschung zu erhalten.

Weiterhin möchte ich mich bei Petra Erdmann bedanken, die mir bei organi-

satorischen Anliegen, gerade bezüglich des USA Aufenthaltes, stets behilflich

war.