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Computational Investigation of the Pore Formation Mechanism of Computational Investigation of the Pore Formation Mechanism of

Beta-Hairpin Antimicrobial Peptides Beta-Hairpin Antimicrobial Peptides

Richard Lipkin The Graduate Center, City University of New York

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COMPUTATIONAL INVESTIGATION OF PORE FORMATION BY BETA-HAIRPIN

ANTIMICROBIAL PEPTIDES

by

RICHARD LIPKIN

A dissertation submitted to the Graduate Faculty in Chemistry in partial fulfillment of the

requirements for the degree of Doctor of Philosophy, The City University of New York

2017

ii

© 2017

RICHARD LIPKIN

All Rights Reserved

iii

Computational Investigation of the Pore Formation Mechanism of Beta-Hairpin Antimicrobial

Peptides

By

Richard Lipkin

This manuscript has been read and accepted for the Graduate Faculty in

Chemistry in satisfaction of the dissertation requirement for the degree of

Doctor of Philosophy.

Date Themis Lazaridis

Chair of Examining Committee

Date Brian Gibney

Executive Officer

Supervisory Committee:

Lei Xie

Marta Filizola

Emilio Gallicchio

THE CITY UNIVERSITY OF NEW YORK

iv

ABSTRACT

Computational Investigation of the Pore Formation Mechanism of Beta-Hairpin Antimicrobial

Peptides

By

Richard Lipkin

Advisor: Themis Lazaridis

β-hairpin antimicrobial peptides (AMPs) are small, usually cationic peptides that provide innate

biological defenses against multiple agents. They have been proposed as the basis for novel

antibiotics, but their pore formation has not been directly observed on a molecular level. We

review previous computational studies of peptide-induced membrane pore formation and report

several new molecular dynamics simulations of β-hairpin AMPs to elucidate their pore formation

mechanism. We simulated β-barrels of various AMPs in anionic implicit membranes, finding

that most of the AMPs’ β-barrels were not as stable as those of protegrin. We also performed an

optimization study of protegrin β-barrels in implicit membranes, finding that nonamers were the

most stable, but that multiplicities 7–13 were almost equally favorable. This indicated the

possibility of a diversity of pore states consisting of various numbers of protegrin peptides.

Finally, we used the Anton 2 supercomputer to perform multimicrosecond, all-atom molecular

dynamics simulations of various protegrin-1 oligomers on the membrane surface and in

v

transmembrane topologies. We also considered an octamer of the β-hairpin AMP tachyplesin.

The simulations on the membrane surface indicated that protegrin dimers are stable, while

trimers and tetramers break down because they assume a bent, twisted β-sheet shape. Tetrameric

arcs remained stably inserted, but the pore water was displaced by lipid molecules. Unsheared

protegrin β-barrels opened into long, twisted β-sheets that surrounded stable aqueous pores,

whereas tilted barrels with sheared hydrogen bonding patterns were stable in most topologies. A

third type of observed pore consisted of multiple small oligomers surrounding a small, partially

lipidic pore. The octameric tachyplesin bundle resulted in small pores surrounded by 6 peptides

as monomers and dimers. The results imply that multiple protegrin configurations may produce

aqueous pores and illustrate the relationship between topology and pore formation steps.

However, these structures’ long-term stability requires further investigation.

vi

ACKNOWLEDGMENTS

Acknowledgments are given for the helpful support and assistance of the following:

Themis Lazaridis

Marta Filizola

Emilio Gallicchio

Lei Xie

Almudena Pino-Angeles

John M. Leveritt III

Yi He

Jorge Ramos

Joel Koplik

Shanan Leeman

Jolinos Vartan Ngilahpong

Maksim Boyko

Brian Gibney

Maria Tamargo

The National Science Foundation

The National Institutes of Health

D.E. Shaw and Associates

Pittsburgh Supercomputing Center (Anton 2 Supercomputer)

Amanda Meyer

Terrance I, Rousey I, Terrance II, and Rousey II (cats)

Satoshi Nakamoto, Vitalik Buterin, and all contributors to the blockchain economy

vii

TABLE OF CONTENTS

1. Introduction 1

2. Implicit membrane investigation of the stability of antimicrobial peptide β-barrels and arcs 27

3. Computational prediction of the optimal oligomeric state for membrane-inserted β-barrels of protegrin-1 and

related mutants 64

4. Transmembrane pore structures of β-hairpin antimicrobial peptides by all-atom simulations 90

5. Conclusions 127

6. Bibliography 130

viii

LISTS OF TABLES, ILLUSTRATIONS, CHARTS, FIGURES, DIAGRAMS

Figure 1.1 4

Figure 1.2 8

Figure 1.3 11

Figure 1.4 19

Figure 1.5 23

Figure 2.1 37

Figure 2.2 39

Figure 2.3 40

Figure 2.4 41

Figure 2.5 52

Figure 2.6 56

Figure 2.7 58

Figure 3.1 69

Figure 3.2 76

Figure 3.3 78

Figure 3.4 81

Figure 3.5 81

Figure 3.6 83

Figure 3.7 84

Figure 3.8 86

Figure 3.9 86

Figure 4.1 95

Figure 4.2 96

Figure 4.3 103

Figure 4.4 106

Figure 4.5 107

ix

Figure 4.6 108

Figure 4.7 110

Figure 4.8 113

Figure 4.9 114

Figure 4.10 114

Figure 4.11 116

Figure 4.12 119

Table 2.1 48

Table 2.2 48

Table 2.3 49

Table 2.4 49

Table 2.5 50

Table 3.1 68

Table 3.2 78

Table 3.3 79

Table 3.4 81

Table 3.5 82

Table 4.1 99

Table 4.2 118

1. Introduction

This dissertation is based on four peer-reviewed publications. Chapter 1 is based partially on the

review paper “Computational studies of peptide-induced membrane pore formation” [1]. In

Chapter 1, we first summarize research and knowledge on the general class of antimicrobial

peptides (AMPs), and then we describe what is known about β-hairpin AMPs and set the goals of

the dissertation in that context. Chapters 2–4, respectively, are identical to three research papers:

“Implicit membrane investigation of the stability of antimicrobial peptide β-barrels and arcs” [2],

“Computational prediction of the optimal oligomeric state for membrane-inserted β-barrels of

protegrin-1 and related mutants” [3], and “Transmembrane pore structures of β-hairpin

antimicrobial peptides by all-atom simulations” [4].

Computational studies of peptide-induced membrane pore formation

A variety of peptides induce pores in biological membranes; the most common ones are naturally

produced AMPs, which are small, usually cationic, and defend diverse organisms against

biological threats. Because it is not possible to observe these pores directly on a molecular scale,

the structure of AMP-induced pores and the exact sequence of steps leading to their formation

remain uncertain. Hence, these questions have been investigated via molecular modelling. In this

chapter, we review computational studies of AMP pore formation using all-atom, coarse-grained,

and implicit solvent models; evaluate the results obtained; and suggest future research directions

to further elucidate the pore formation mechanism of AMPs.

Pore formation in lipid bilayers occurs in important biological processes, such as apoptosis [5-7],

immunity [8, 9], bacterial toxin function [10, 11], viral infection [12], and protein translocation

[13]. In most of these processes, a soluble protein reconfigures and assembles into a membrane-

embedded oligomer. Some available structures [14-16] show a completely proteinaceous pore.

2

However, in other cases, lipids are speculated to participate in the pore’s construction [17]. Pores

can also be induced in pure lipid bilayers by applying electric fields (i.e. electroporation; [18]).

The antibacterial defence mechanisms of a broad range of organisms also seem to involve

membrane pore formation. Antimicrobial peptides (AMPs, or host defense peptides) are usually

small, cationic peptides that provide a diverse array of immunological functions [19-22]. These

amphipathic peptides, which assume various secondary structures, can permeabilize lipid

bilayers in vivo [23-25] and in vitro [26-28]. This, together with the observed lack of dependence

on amino acid chirality [29, 30], led to the suggestion that they target the bacterial membrane,

either by forming pores [31] or by dissolving the membrane in a detergent-like fashion (i.e. the

carpet mechanism; [32]). Their cationic charge is thought to impart selectivity for bacterial

membranes, whose exterior lipid leaflet is negatively charged [33]. Whether membrane

permeabilization is the actual lethal event is still actively debated [34, 35]. Other proposed

mechanisms include clustering of ionic lipids [36] and targeting intracellular components, such

as DNA [37-39]. Nevertheless, the occurrence of AMP-induced membrane poration is

unquestionable, and understanding peptide stabilization of membrane pores has fundamental

value independent of its precise role in AMP action. In this chapter, we will focus on AMPs’

membrane-permeabilizing function.

Extensive experimental effort has been invested in characterizing AMPs’ membrane interactions

and the nature of the pore state. For example, fluorescence measurements have been used to

quantify membrane binding and leakage from vesicles [40, 41]; fluorescence applied to giant

unilamellar vesicles (GUVs) has allowed direct imaging of permeation [42-44]; and fluorescence

imaging of live cells has elucidated the sequence of events [34, 45]. Calorimetry has provided

the thermodynamic properties of membrane binding [46]. Oriented CD has provided information

3

on peptide orientation with respect to the bilayer normal [47, 48]. X-ray diffraction has shown

reduced membrane thickness upon peptide binding [49, 50] and illustrated the shape of peptide-

induced pores [51]. Neutron scattering has provided information on pore size [52].

Electrophysiology studies have described pore ion conductance and its voltage dependence [53-

55]. Solution NMR in detergent micelles has provided structures and sometimes described

oligomerization propensities [56]. Solid-state NMR (ssNMR) has provided structural and

dynamic information in native environments [57, 58]. Atomic force and electron microscopy

have shown AMP-induced membrane damage [59-61]. However, these pores’ lability and

transience have prevented the acquisition of an experimental high-resolution structure of an

AMP-stabilized pore.

A summary of experiments on the dozens of previously investigated AMPs would be beyond the

scope of this review; therefore, we will mostly focus on a few well-studied peptides. Alamethicin

is a 20-residue helical peptide of the peptaibol family with charge 0 or −1 [62]. Melittin is a 26-

residue cytolytic peptide isolated from bee venom that has low target selectivity [63]. Magainin-

2 (hereafter, magainin) is a 23-residue AMP isolated from frog skin that preferentially targets

bacterial membranes [64]. The latter two peptides are cationic, and as expected, they bind more

strongly to membranes containing anionic than zwitterionic lipids [65, 66]. Alamethicin appears

to form cylindrical barrel-stave pores, in which the pore lumen is completely lined by peptides

[67], whereas melittin and magainin appear to form toroidal pores, in which the two membrane

leaflets curve together and the peptides are adjacent to lipid headgroups [52, 68, 69] (Figure 1.1).

Magainin exhibits synergy with another AMP from the same family, PGLa [70], which has also

been the subject of ssNMR studies [71]. Dye leakage from vesicles usually does not proceed to

completion in the presence of AMPs, suggesting that the pores are transient [72]. However,

4

simple mutations to melittin generate peptides that form pores detectable long after equilibration

[73]. Electrochemical impedance spectroscopy has shown the transience of melittin bilayer

permeabilization [74], in sharp contrast to the behavior of its MelP5 mutant [75].

Figure 1.1. Schematics of a) barrel-stave, b) toroidal, and c) semitoroidal pores.

Key questions

Despite valuable information provided by over four decades of experimental investigations, our

understanding of membrane pore formation, and therefore our predictive abilities, are severely

limited. Presently, it is not possible to predict a peptide’s pore-forming ability given its sequence.

To generate such predictions, we would need to resolve the following key questions:

1. Pore vs. carpet mechanisms. Do well-defined pores form [31], or is the membrane dissolved in

a detergent-like fashion [32]? There is evidence supporting both models. In favour of the pore

mechanism, many experiments using GUVs show permeation without membrane dissolution [44,

76]. However, in other cases, the GUV bursts, supporting the carpet model [77]. Also in favour

of the carpet model, some peptides seem unable to adopt transmembrane orientations [78],

although, whether such orientations are necessary for pore formation remains to be determined.

The carpet model implies quite high peptide concentrations in the membrane, and membrane

partitioning measurements suggest that such concentrations are attainable at typical solution

concentrations [79, 80].

5

2. Pore structure. When well-defined pores are formed, what is their detailed structure? The most

common proposed models are the classical barrel-stave pore—where the pore is cylindrical and

lined by peptides [81]—and the toroidal pore, where the two membrane leaflets bend and join

together [52, 82]. Although toroidal pores’ overall lipidic shape has been visualized [31], the

number, position, and orientation of the peptide constituents with respect to the pore is unknown.

Some computational studies have suggested highly disordered pores [83, 84] (see below).

3. Pore lifetime. Are the pores long-lived or transient, and what determines their lifetime? What

peptide features lead to pore stability or transience? Electrophysiological techniques are the

primary sources of direct information on pore lifetime; however, AMP-induced membrane pores

seem to change dynamically. For example, time-lapse AFM has shown lateral pore expansion

with time [85].

4. Aggregation. Do the peptides need to aggregate (i.e. directly contact each other) during the

pore formation process? Numerous biophysical studies over the past decades have looked for

signs of such aggregation (e.g. [86-89]. Direct contact is implied in the barrel-stave model but is

not necessary in the toroidal model; indeed, most toroidal-pore-forming peptides’ high charge

levels would discourage direct peptide–peptide contact [90]. However, dimerization has been

detected for magainin [91] and other AMPs in detergent micelles.

5. Pore formation pathway. Do the peptides adsorb to the membrane surface as monomers and

then oligomerize? Is the reverse possible? At what point does pore opening occur? The exact

sequence of steps and the factors that influence their interaction have not been completely

elucidated for any peptide.

6. Selectivity and toxicity. What is the origin of most AMPs’ selectivity toward bacterial

membranes and other AMPs’ toxicity towards mammalian cells? The prevalent explanation is

6

that most AMPs’ positive charge directs them towards negatively charged bacterial membranes

as opposed to the largely neutral outer leaflet of mammalian membranes. However, the situation

is somewhat more complex. For example, both melittin and magainin are positively charged and

bind anionic membranes more strongly than zwitterionic ones. However, melittin

preferenentially permeabilizes zwitterionic membranes [92], whereas magainin does so for

anionic membranes [93]. This shows that there is no simple correlation between membrane

affinity and permeabilization. Other contributions to selectivity include the effects of cholesterol

(which is present in mammalian but not bacterial membranes) and the magnitude of the

transmembrane voltage [33]. The dominant determinant of toxicity seems to be hydrophobicity,

which is usually positively related to binding strength to neutral membranes and hemolysis; e.g.

[94].

Computational investigations

The lack of an experimental atomic-level picture of peptide-stabilized pores has prompted

numerous molecular modelling studies. The standard computational technique in molecular

biophysics is classical molecular dynamics (MD) simulations: all peptide, lipid, and water atoms

are represented by particles interacting according to an empirical energy function, and Newton’s

equations of motion are solved to provide an atomic-level view of the system on a timescale

dependent on the available resources, currently limited to the microsecond range. Because pore

formation typically occurs on much longer timescales, a single MD trajectory normally cannot

show the entire sequence of events from water-soluble (usually unfolded) peptides to folded,

membrane-inserted oligomeric pore. Hence, researchers have resorted to the following courses of

action:

7

a) Study putative initial steps of the pore formation process, such as monomer binding to a lipid

bilayer [95] or association between two peptides in water or on the membrane surface [96].

b) Use free energy calculation techniques, such as umbrella sampling [97] or adaptive biasing

force [98], to compute the free energy profiles (or potentials of mean force, PMFs) for these

elementary steps. These calculations are time-consuming and expensive, with slow convergence

reported [99].

c) Start the simulation closer to the putative final pore state (e.g. with preformed pores [100] or

several inserted transmembrane peptides [101]). Sufficiently long simulations should remove the

initial bias and allow the system to relax to a local free energy minimum, which hopefully will be

the desired pore state.

An alternative way to address the limitations of atomistic simulations is to simplify the model.

One popular direction is to employ coarse-grained (CG) simulations, which represent the lipids,

water, and often the peptide itself with particles corresponding to more than one atom [102-104].

Several procedures to devise CG representations have been implemented: interactions between

CG ‘beads’ can be calibrated to reproduce forces between corresponding groups of atoms in

atomistic simulations [105], or the CG system’s density, phase transitions, or structure can be

adjusted to match the physical system’s characteristics [106]. CG modelling speeds up the

computations considerably, but the added approximations can cause problems. For example, the

representation of groups of four water molecules by one particle may not be appropriate for

small pores [107], and peptide secondary structure is usually fixed, preventing conformational

adaptation.

Even greater simplification is attained by implicit solvent simulations, which represent water and

lipids implicitly through extra terms in the energy function. Implicit solvent models were first

8

created for water-soluble proteins [108-110] and were extended to membranes soon afterwards

[111-114]. Such models can easily account for surface charge using Gouy–Chapman theory

[115]. Implicit membrane models typically describe intact membranes, but one model permits

dynamic changes in membrane thickness [116], and Implicit Membrane Model 1 (IMM1),

developed in our lab, has been extended to pores [117, 118]. In IMM1, pore shape is specified by

making the radius R dependent on vertical position within the membrane, z′, according to a

desired curvature k [2, 118, 119] (Figure 1.2). Transmembrane voltage [120], membrane dipole

potential [121], and lateral pressure effects [122] can also be included in IMM1. Because Gouy–

Chapman theory is restricted to modelling flat anionic membranes, the electrostatic potential in

anionic membrane pores is found by numerical solution of the Poisson–Boltzmann equation,

with the bilayer’s dielectric properties represented by a five-slab model accounting for solvent,

lipid headgroup, and lipid tail regions [2, 119]. The work published as [2] is included as Chapter

2 below.

Figure 1.2. Dependence of solvation parameters on internal pore radius (R0), vertical position

(z′), and pore curvature (R = R0 + k × z′2). a) k = 0 in cylindrical pores. b) k > 0 in toroidal pores.

9

Below, we review the available computational results on AMP pore formation obtained by all-

atom, CG, and implicit modelling. Earlier general reviews of this topic can be found in [123-

127].

All-atom modelling

In addition to AMP studies, atomistic simulations have been used to study pore formation in pure

lipid bilayers. Because this is not a spontaneous process, it has to be induced, either by

application of an electric field (as in the experimental electroporation process; [128-131]) or by

constraining collective variables [132-134]. However, many of the latter approaches suffer from

slow convergence and hysteresis [135]. In addition, pronounced force field dependence has been

noted in the calculated free energy of pore formation [136], which impacts interpretation of the

AMP simulations mentioned below. Strong force field dependence of results has also been

reported in another study [137].

The simplest objective of AMP simulation research has been to examine monomer binding,

usually parallel to the membrane surface but also in a transmembrane orientation. This has been

done for numerous peptides, such as melittin [138-141], alamethicin [142], magainin [143], and

others [144-147]. The peptide is usually placed on the membrane interface with the more

hydrophobic side towards the membrane, but it can also be placed a small distance from the

membrane, in which case it usually binds rapidly, e.g. [148]. Simulations have also been

performed in micelles [149, 150], because they are the standard medium in solution NMR.

Simulations like these reveal details of AMPs’ orientation, depth of membrane insertion, and

lipid interactions but give no information about the permeabilization mechanism.

Spontaneous pore formation starting from peptides dissolved in the water phase has rarely been

observed in simulations. The only reported examples in AMPs are a study of a magainin

10

derivative [83] and a similar subsequent study of melittin [84], which inspired the ‘disordered

toroidal pore’ model. The exceedingly fast insertion observed in those studies may have been

caused by the systems’ lack of counterions. A similar issue was noted in a simulation of

spontaneous translocation of an arginine-rich peptide [151]. Recent microsecond-scale atomistic

MD simulations of multiple melittin–membrane systems showed bent U-shaped conformations

of melittin without any transmembrane insertion or pore formation [152].

The difficulty of observing spontaneous pore formation has led to efforts to circumvent the

timescale problem by starting from preformed pores or preinserted peptides. An early example is

simulations of transmembrane helical alamethicin bundles [153, 154]. Similar studies have been

done on other peptides; for example, a transmembrane melittin tetramer was found to decay to a

trimer and generate a toroidal pore in 5.8 ns [155]. Increases in available computational power

have gradually allowed much longer simulations. Work in our laboratory compared alamethicin

with melittin in preformed pores and confirmed their preference for cylindrical and semitoroidal

pores, respectively [118]. Further work examined the influence of intrapeptide charge position

and imperfect amphipathicity (i.e. the presence of polar or charged sidechains within a peptide’s

hydrophobic part) on pore character [156].

Other groups have studied melittin tetramers, either half-inserted [157] or fully inserted [158] in

preformed pores. The latter study found that antiparallel arrangement and reduced peptide

folding yielded stable toroidal pores. Another group studied various oligomers on the surface or

in transmembrane orientation [159]. Our group’s much longer atomistic simulations of a melittin

tetramer conducted on the Anton supercomputer revealed a classical toroidal pore characterized

by dynamic orientation change of one or two peptides (Figure 1.3a) [101]. Similar simulations of

magainin and PGLa in lipid membranes showed a different picture: highly tilted peptides around

11

a very small pore, with tilt angles in agreement with ssNMR experiments (Figure 1.3b) [160].

This work also provided insights into the synergy between these two magainin-family peptides:

more transmembrane orientations, stronger interactions, and a larger and more ordered pore were

seen in the 1:1 heterotetramer with antiparallel helix arrangement than in homogeneous peptide

mixtures [160]. Starkly different results were obtained for another AMP called piscidin: a 26-μs

Anton simulation starting from 20 peptides in 4 barrel-stave pores resulted in almost all peptides

moving to a surface-bound state, suggesting a non-pore mechanism for this peptide [145].

Figure 1.3. Snapshots from all-atom simulations of α-helical antimicrobial peptides. a) Melittin

tetramer at 8.3 µs [101]. b) Magainin–PGLa heterotetramer at 9 µs [160].

In addition to standard MD simulations, attempts have been made to obtain thermodynamic

information for putative steps in the pore formation pathway via free energy calculations. The

free energy of melittin binding and reorientation in phospholipid bilayers has also been

calculated [95, 161, 162], as well as the free energy of membrane binding of a lipopeptide at the

CG level [163] (see next section).

Coarse-grained modelling

12

CG modelling of AMP pore formation can offer unique insights, as it allows longer simulation

times and larger systems than all-atom modelling. Most CG studies so far have used the

MARTINI model [103, 107], but models that employ coarser graining have also appeared [164].

MARTINI-based studies have included: a study of PAMAM dendrimers that showed

unacetylated molecules forming pores ; a study of alamethicin that showed aggregation and some

transitions to an interfacial state [165]; a study of the synthetic LS3 peptide that showed the

spontaneous formation of mostly hexameric barrel-stave pores [166]; a study showing

spontaneous pore formation by a hydrophobic magainin derivative [167]; a study of magainin

and melittin that found U-shaped conformations for melittin and disordered toroidal pores for

magainin [168, 169]; studies of antimicrobial lipopeptides that found clustering of anionic lipids

but no pore formation [170, 171]; a dissipative particle dynamics study of eight AMPs

employing a MARTINI-like model showing pore formation and translocation [172]; and a study

of the AMP maculatin that found that an increased peptide-to-lipid ratio caused an interfacial–

transmembrane orientation change and cooperative membrane insertion of peptide aggregates

without a well-defined central pore lumen [173]. The last authors also observed maculatin-

induced spontaneous membrane curvature and used that evidence to suggest that pore formation

may not be responsible for maculatin’s activity. In a larger-scale setting, beyond the practical

limits of all-atom simulations, up to 1600 magainin peptides added to only one side of the bilayer

induced spontaneous buckling and vesicle budding of the lipid bilayer [174].

While these results sound very promising, some issues interfere with their applicability. The

pores observed in CG simulations often contain no water [123, 165, 168], and coarse graining the

water to a spherically symmetric particle corresponding to four water molecules limits

reproduction of the pore’s structural details. A detailed comparison of CG with atomistic

13

simulations revealed deficiencies in the CG pore structures [175]. Models that employ

polarizable CG water models provide improvements [107, 176], although they still have

difficulties forming aqueous pores under standard parameterization. Coarse graining of the

abundant water molecules is generally a quite important factor in the computational efficiency

gains offered by CG: one study estimated a speedup factor of 50 from coarse graining the water

molecules [177].

Implicit solvent modelling

In the 1980s and 1990s, when atomistic simulation of peptides in membranes was out of reach,

researchers were forced to develop simple ways to account for the membrane environment [178-

182]. The newer generation of implicit membrane models [111, 112, 114] are extensions of

implicit aqueous solvation models [108-110] and thus account for the energetics of both

membrane insertion and conformational changes. The Poisson-Boltzmann continuum model can

also be used to study peptide–membrane interactions [183, 184], but usually for static peptide

configurations. Even with modern computational power, implicit membrane modelling allows

studies that are impossible with all-atom and CG methods and facilitates unique insights because

of its fast convergence and simple energetic interpretation.

Modern implicit membrane models are routinely and trivially used to determine the

configurations and membrane binding energetics of AMP monomers (e.g. [185, 186]). More

sophisticated approaches have included the effects of transmembrane voltage, dipole potential,

and lateral pressure profile [120-122]. For example, using such simulations we showed that

voltage induces the interfacial–transmembrane orientation change in alamethicin [120] and the

addition of a membrane dipole potential term reduced the membrane binding affinity of

magainin [121]. Negative lateral pressure at the water–lipid interface stabilized interfacial

14

binding and yielded an interfacial–transmembrane orientation shift with an increased

peptide:lipid ratio, in accord with experiment. Further, with the inclusion of a lateral pressure

term, an increased DOPE mole fraction in mixed DOPC:DOPE bilayers stabilized interfacial as

opposed to transmembrane orientations [122].

Additional results of interest have been produced by implicit pore modelling [115, 119, 186].

When we compared peptide binding to pores of different shapes, we found that most AMPs bind

more favourably to both zwitterionic and anionic toroidal pores than to flat membranes [119,

186]. Alamethicin exhibited similar transfer energy to cylindrical and toroidal pores, whereas

toroidal pore-forming peptides, such as melittin, exhibited a preference for toroidal pores. One

factor driving these favourable transfer energies appears to be imperfect amphipathicity, which

reduces binding strength to flat membranes but does not affect binding to membranes with

positive curvature. Melittin and protegrin are examples of this type of amphipathic structure.

(Note that the term ‘imperfect amphipathicity’ has a broader meaning in Wimley’s independently

developed interfacial activity model [187].)

A large-scale computational study using IMM1 analysed activity determinants of 53 α-helical

AMPs [188], testing the hypothesis that antimicrobial and haemolytic activity correlate with

binding affinity to anionic and zwitterionic membranes, respectively. Antibacterial and

haemolytic activity were found to correlate best with transfer energy to membranes with anionic

lipid fractions of >30% and 10%, respectively. Surface area occupation, insertion depth, and

structural fluctuation were significantly correlated with antibacterial, haemolytic, and both

activity levels, respectively. Peptides active at low membrane surface coverage ratios tended to

be those identified in the literature as pore-forming. Further, the transfer energy to toroidal pores

was negative in almost all cases, while that to cylindrical pores was more favourable in neutral

15

than anionic pores, and pore transfer energy correlated with deviation from the predictions of the

carpet model. There were significant correlations of hydrophobic quadrupole moment (a

biophysical descriptor related to imperfect amphipathicity) with lethality against both E. coli and

red blood cells.

Implicit simulations in our laboratory that accounted for the free energy cost of acyl chain

exposure showed that certain antiparallel alamethicin bundles have lower free energy than

parallel ones and could be present under experimental conditions [189]. Multiple combinations

of radius and oligomeric number were investigated, with all oligomeric numbers 5–9 forming

open pores at their optimal radii. All oligomers 6–9 had comparable energies, consistent with

multiple experimentally observed conductance levels [190] and the barrel-stave model. The N-

terminal part was less tilted than the C-terminal part, resulting in hybrid funnel/hourglass pore

shapes; this shape was not affected by transmembrane voltage, but pore stability was. The

presence of a pore raised the total effective energy, suggesting that alamethicin pores may

correspond to excited states stabilized by voltage and ion flux.

Conclusions and Future Directions

Computational studies have provided a wealth of insights on pore-forming peptides, some of

which have been listed above. However, the limitations and uncertainties of the calculations have

not allowed definitive conclusions. Moreover, many studies focus on certain stages of the pore-

forming process, such as early membrane binding and dimerization or the final pore state. Thus,

a picture of the entire process is still lacking. In some cases, modelling results seem to conflict

with each other: in the example case of melittin, one study found disordered pores with half-

folded peptides [84], and another found mostly helical peptides around a classical-type toroidal

pore [101]. The origin of these discrepancies—whether the force field or other technical

16

details—needs to be clarified, and convergence needs to be achieved. As always, experimental

validation will be necessary for reliable conclusions.

The ‘to-do’ list in this field is long and exciting. The ability to perform multi-microsecond MD

simulations on Anton or other powerful computers has started to provide better-equilibrated pore

structures and detailed views of peptide–lipid interactions. Extending the timescale to a

millisecond, which is now conceivable with Anton II [191], may bring into view processes like

spontaneous aggregation, pore formation, expansion, contraction, and annihilation. This will start

to provide information on not only on pore structure but also dynamics. Additional PMF

calculations of higher-order oligomer insertion into lipid membranes, similar to those available

for monomers and dimers, are also needed to obtain the complete energetic landscape for pore

formation. It would also be useful to increase the diversity of lipid membrane compositions

simulated, because activity and toxicity are clearly dependent on membrane lipid composition.

CG simulations face some challenges to reproduce the details of peptide-stabilized pores. One

possible way forward could be mixed-resolution models that represent system components at

different resolution levels according to importance (e.g. [192-194]) or adaptive resolution models

whose resolution depends on location [195]. However, application to membrane pores will not

be trivial. An additional challenge is that peptide conformation is usually restrained in CG

simulations, which is not ideal, as considerable evidence indicates that conformational changes

in AMPs are possible during the poration process [196]. A challenging solution to this problem

could come from the development of CG peptide models that correctly reproduce the

environment-dependent conformational distribution. Because of the above-mentioned

difficulties, the investigation of large-scale membrane remodelling effects (e.g. membrane

bilayer buckling and vesicular budding [174]) may be a more fruitful application of CG models.

17

Significant work remains to be done, e.g. to understand the effects of the dependence of area per

lipid on the peptide:lipid ratio and how this determines the properties of both quasispherical

vesicular buds and their narrow necks.

Implicit membrane models could also be further developed. Extensions to curved membranes

would allow a more systematic exploration of the effects of curvature, especially Gaussian

curvature [197], on peptide binding. One significant limitation of most implicit models is the

assumption that the membrane is fixed. Large-scale changes, like bilayer buckling or vesicular

budding, are very difficult—and perhaps counterproductive—to pursue via implicit solvent

methods. However, making pore radius or shape dynamic simulation variables is feasible. Some

of these developments are in progress in our laboratory.

Eventually, to enable quantitative predictions, we need to develop a detailed molecular

thermodynamic model of peptide-induced pore formation. That would require quantitative

characterization of contributions to the pore state’s free energy from peptide–peptide, peptide–

lipid, and lipid–lipid interactions. Implicit solvent models are best positioned to provide the first

two terms; however, their quantitative accuracy needs to be ascertained by comparison with

atomistic PMF calculations. Although we have previously done this by computing PMFs

between ionisable side chains in solution [198] and at the bilayer–water interface [198], it is also

necessary to consider free energy profiles for entire peptides, as has been done for glycophorin A

[199] and model peptides [43]. A critical ingredient in this energetic landscape is the free energy

of opening a pore in a pure bilayer (i.e. lipid–lipid interactions in the above scheme). This

contribution has previously been estimated roughly from line tension measurements [200], but

such values suffer from large experimental uncertainty and correspond to the lowest free energy

state of a pore in a pure bilayer. Although we need to know the free energy of lipidic pore

18

formation as a function of radius, shape, and lipid headgroup distribution, existing approaches do

not provide this level of detail [132-134].

Beyond thermodynamics, dynamic models of pore creation, growth, and annihilation would also

be useful. For example, the pore could represent a dynamic state constituted by a growing

number of peptides: AMP pores may be able to expand laterally, even to the micrometre scale,

until the membrane disintegrates [85]. Future multiscale approaches could integrate atomistic

MD simulations, mesoscale models of single-pore electrodiffusion, and models of transient

bacterial cell ion transport [201].

Integrated multiscale computational models could not only provide a general understanding of

AMPs’ pore formation mechanism but facilitate the development of efficient antimicrobial

pharmaceutical products. In addition to ones based on protegrin (discussed below), several

AMPs are in clinical development as drugs, such as thanatin and heliomycin [202], but the lack

of detailed understanding of AMPs’ mechanisms of action has limited the rational design of

AMP-based therapeutics. A bottleneck has been most AMPs’ high toxicity levels at therapeutic

doses [203]. Future insights from computational studies could facilitate efficient drug design by

identifying peptides with the desired pharmacological properties.

Protegrin and the β-hairpin AMP family

Protegrin-1 (hereafter, protegrin) is an 18-residue β-hairpin derived from porcine leukocytes that

is stabilized by two disulfide bonds [204]. It is the most-studied member of the larger family of

β-hairpin AMPs. In this section, we summarize the experimental and computational techniques

that have been applied to protegrin and the rest of the β-hairpin AMP family, their results, and

their shortcomings.

19

Several experimental studies have measured the minimal inhibitory concentrations (MICs)

against Gram-positive and Gram-negative bacteria for both protegrin and other β-hairpin AMPs,

and other studies have verified biological effects on other types of cells. Both MIC and other

biological activity results are listed in detail in Chapter 2. Although a detailed experimental

review would be beyond the scope of this dissertation, a few previous experimental results

specifically guided the present research on protegrin, and many other experimental studies of

protegrin are also mentioned in Chapters 2–4. A crystallization study of protegrin pores in

membranes suggested that protegrin forms toroidal pores [69], and ssNMR evidence indicates

that protegrin oligomerizes into a closed β-barrel composed of 4–5 dimers in anionic bacterial

membrane mimetics [205]. Dimerization of protegrin has also been detected in detergent

micelles [206]. Protegrin-1 dimers have been suggested to assume NCCN parallel topology on

the basis of NMR evidence [205] (Figure 1.4a), although solution NMR in detergents yielded

NCCN antiparallel topology (Figure 1.4b) [206]. Further, protegrin-3 adopts NCCN antiparallel

topology in DPC micelles [207]. These studies have provided a rudimentary picture of

protegrin’s pore state, even though such pores are impossible to observe directly on an atomic

scale. Those experiments also provided useful information on topology from which we can draw

comparisons with our results.

20

Figure 1.4. Three possible topologies of protegrin-1 dimerization. a) NCNC parallel; b) NCCN

parallel; c) NCCN antiparallel. Yellow bridges represent disulphide bonds, which point inward

only on the right side of b). Arrows point N→C.

Other β-hairpin AMPs besides protegrin have not been experimentally studied as extensively as

protegrin has. However, there have been some experimental investigations of several other

peptides in this family, and those have revealed some structural and mechanistic insights.

Although a detailed experimental review would be beyond the scope of this section, the

subsections for each AMP studied in Chapter 2 contain additional notes on experimental

research. Here, we mention some experimental results that are interesting or relevant to the

investigations in the present dissertation. The β-hairpin AMP θ-defensin has relatively low

antimicrobial activity [208, 209], but it can prevent the entry of HIV into cells, possibly by

inhibiting the gp120:gp41 membrane binding/fusion process [210]. A crystallization study of a θ-

defensin AMP found a mixed-topology trimer wherein one dimer had NCNC parallel and the

other NCCN antiparallel topology [211]. Tachyplesin is structurally similar to protegrin, but

solid-state NMR results have indicated that tachyplesin orients in a surface rather than

transmembrane orientation [212, 213], leading to doubt that it could function by the same pore

formation mechanism as protegrin. Experimental studies of β-hairpin AMPs have shown

targeting of not only the bacterial inner membrane, but also components of the outer membrane:

a study using polyphemusin analogs indicated binding to divalent cation binding sites on

lipopolysaccharide (LPS) molecules [214]. Tachyplesin has also been shown to interact with

LPS micelles via NMR [215]. A study using giant unilamellar vesicles (GUVs) showed that

gomesin made the GUVs burst suddenly; stable pores were not observed, indicating that gomesin

21

may affect GUVs by the carpet mechanism [77]. Androctonin is a β-hairpin AMP that has a

structural twist in its backbone; ATR-FTIR experiments indicated that androctonin stays on the

membrane surface without destabilizing the bilayer structure [216]. Androctonin binds only to

negatively charged lipid vesicles and adopts a -sheet structure but leaves the acyl chain order

unaffected, suggesting a detergent-like mechanism [216].

Experimental results obtained using the β-hairpin family have not only provided the fundamental

knowledge listed above, but also led to their identification as a possible basis for the

development of novel antimicrobial therapeutics. Iseganan IB-367, a protegrin AMP designed

for activity against microflora associated with oral mucositis [217], was granted fast-track status

in both the United States and European Union for a Phase-II/III trial for prevention of

nosocomial pneumonia [218]. However, those trials were discontinued in 2004, as they failed to

show improvements over existing treatments, and no AMP-based drugs have ultimately been

given final approval, despite these compounds’ promisingly low in vitro minimum inhibitory

concentrations.

Besides the lack of progress in therapeutic development, the experimental work on β-hairpin

AMPs has limitations. For example, deconvolution of NMR signals does not always produce

definitive information about pore structure and topology, and NMR signal processing would

make it difficult to distinguish the characteristics of a diverse population of pores. Although the

previous NMR study of a protegrin pore yielded reasonable conclusions about the number of

peptides in the pore (8–10 peptides), it came to a suspect conclusion about the topology of the

peptides within the pore (NCCN parallel; [205]). That study could not definitively determine

whether the peptides formed a closed β-barrel or were arranged as a β-sheet. In addition, the

numerous experimental studies of protegrin have sometimes resulted in contradictory evidence.

22

While NCCN parallel topology was favored by the previously mentioned NMR study, other

studies have revealed a mixed or NCCN antiparallel topology (see above). There has also been

contradictory evidence regarding protegrin’s pore size: despite numerous predictions of a pore

diameter of approximately 20 Å, one experiment suggested a much larger pore of diameter 30–

40 Å [219]. Finally, experimental techniques generally do a poor job of revealing detailed

information about intricate processes such as the pore formation pathway, which tend to occur on

short timescales.

Because of those experimental shortcomings, protegrin has also been the subject of many

computational studies. Although a comprehensive review of protegrin simulations would be

beyond the scope of this section, we briefly mention a few of the most relevant results here;

further, a previous review of computational studies of protegrin is available [203]. Monomers of

protegrin have been subject to all-atom simulations in both surface and transmembrane

orientations [220]. In addition, complete β-barrel models of protegrin-1 based on the

experimentally suggested NCCN parallel β-barrel structure have been subjected to all-atom

simulations [59, 221-223]. Our laboratory observed that the intrinsic tilt and twist values of

NCNC parallel tetramers formed protegrin-1 into an arc shape, which formed stable pores on a

timescale of 300 ns [100] (Figure 1.5). However, those explicit simulations showed that a lipid

entered the pore lumen, displacing water; this implies that a single NCNC parallel tetrameric arc

may be insufficient for a stable conductive pore. Our laboratory has also investigated complete

NCNC parallel protegrin β-barrel models [100, 224], which concluded that the barrels were

stable in simulations shorter than the present dissertation’s all-atom investigations.

23

Figure 1.5. Snapshot from simulation of single NCNC parallel protegrin-1 tetrameric arc [100].

Our laboratory has also proposed implicit models of protegrin β-barrels, which show the highest

octameric β-barrel stability in NCNC parallel topology [224]. Although ssNMR results had

suggested NCCN parallel topology [205], in that topology, the barrels were much less stable in

implicit pores than those in NCNC parallel or NCCN antiparallel topologies, because the latter

two topologies allow all monomers’ hydrophobic sides to face the membrane [224]. Explicit

simulations also showed the NCNC parallel topology to be more stable. Therefore, simulation

studies have provided information regarding topology that has been difficult to generate using

experimental methods.

Protegrin has also been the subject of free energy calculations to determine the favorability of

dimerization, insertion, and tilting within the membrane. PMFs have been calculated for

protegrin dimerization [96], adsorption of monomers and dimers to membrane bilayer interfaces

[225], and insertion into a lipid bilayer [226] in an effort to clarify the major steps in protegrin

pore formation. Another study also calculated PMFs for protegrin’s orientation within membrane

bilayers, finding a significant tilt angle at the optimal orientation [227]. This is information that

has been difficult to obtain experimentally.

24

The rest of the β-hairpin AMP family has not been studied computationally as thoroughly as

protegrin has. Some peptides from the β-hairpin family, such as androctonin, had not been

simulated at all until the investigations reported in Chapter 2. However, some computational

investigations of β-hairpin AMPs besides protegrin have been performed. For example, the sum

frequency generation spectroscopy results used to assert that tachyplesin orients parallel to the

membrane surface were also backed by MD studies verifying the results [212]. An MD study of

three C-terminal analogues of human β-defensin 3 indicated the accretion of well-defined

structures that compacted positive charges together within peptide oligomers, which was

correlated with antimicrobial activity [228]. That study offered a picture of aggregation leading

to toxicity, which is attractive in light of the present dissertation’s goals. Zhou et al. performed

equilibrium and restrained MD simulations of bovine lactoferrin, which should show a transition

from a mixed α-helical β-strand region in the protein to a twisted antiparallel β-sheet in the

peptide [229]. Although the peptide as released from the protein was relatively unstable, a

directional force had to be exerted on the peptide for the change to a β-strand to be observed in

60 ns. Rausch et al. formed a combinatorial library of β-sheet-forming peptides [230, 231],

arriving at insights regarding structure–function relationships. That information could be useful

when designing future β-hairpin AMP-based therapeutics. Although some of the peptides from

their combinatorial library are studied in Chapter 2, those peptides differ from the rest of the β-

hairpin family in their larger size and absence of disulfide bonds. The absence of disulfide bonds

may make the formation of those combinatorial library peptides entropically unfavorable.

Although previous computational studies of β-hairpin AMPs have yielded some promising

results, those results also have limitations. For example, some previous authors may have

assumed that their results applied uniformly or generally when such assumptions were not

25

warranted: one study estimated that 100 total protegrin pores are necessary to kill an E. coli cell

[232], but this estimate was made using a rough, static estimate of pore size. Other studies have

also made analogous assumptions about the uniformity of protegrin pores. For example, although

previous computational studies of protegrin β-barrels have employed only 8 or 10 peptides, it is

not clear that protegrin pores comprise a uniform population, and some have speculated that the

pore population is nonuniform [205]. Further, there has been a lack of β-hairpin AMP

simulations at time scales that could determine the pores’ lifetime or long-term stability. For

example, our laboratory’s previous all-atom simulations of protegrin β-barrels [224] and arcs

[100] have been limited by computational resources to a few hundred ns. Therefore, we have

been unable to make any definitive determinations about the stability of the previously simulated

pore structures. Such simulations by our laboratory have also been limited by computational

resources to only a few initial configurations and oligomeric multiplicities, and we have not been

able to run any simulations using a tilt angle from vertical. The PMF calculations run on

protegrin have investigated only limited situations, such as dimerization on the membrane

surface and membrane insertion of a monomer, and no PMF calculations have been run on other

β-hairpin AMPs. The simulations necessary for PMF calculations are expensive and complicated

to run, contributing to this lack of information about these peptides’ energetic landscape of pore

formation.

Aims of Dissertation

In view of the lack of authoritative knowledge about the pore state of β-hairpin AMPs, in this

dissertation, we performed MD simulations to clarify both the final pore state and its formation

pathway. In addition to exploring various possibilities for the protegrin pore state, we aimed to

compare the results with analogous ones found using different β-hairpin AMPs. We did this

26

using both implicit membrane and all-atom simulations; the all-atom simulations reported here,

to the author’s knowledge, are the longest ones yet reported on β-hairpin AMPs.

In Chapter 2, we report simulations of β-barrels and arcs of several β-hairpin AMPs in anionic

implicit membranes. The goal was to determine the relative favorability of β-barrels, which have

been proposed as the basis of protegrin pores, for the rest of the β-hairpin AMP family.

In Chapter 3, we perform an optimization study of protegrin β-barrels in implicit membranes and

compare the results with those for various mutants. The goal was to determine the range of the

number of monomers per pore that would result in the most stable β-barrels. This was predicted

to indicate whether the β-barrel pore state may consist of a diverse population of sizes.

In Chapter 4, we report all-atom simulations of various protegrin-1 oligomers on the membrane

surface and in transmembrane topologies, which were executed on the Anton 2 supercomputer.

We also compared the results with those for the β-hairpin AMP tachyplesin. The goal was to

illustrate β-hairpin AMP pores using longer all-atom simulations than had been available

previously, which was predicted to show the feasibility of putative pore structures. In this

chapter, we varied the peptides’ initial topology and configuration to gain insights about peptide

aggregation and how it affects the final pore state. The overall aim of the dissertation was to

elucidate the pore state and formation pathway of β-hairpin AMPs.

27

2. Implicit membrane investigation of the stability of antimicrobial peptide β-barrels and

arcs

Published as: [2]

Summary

Previous simulations showed that the β-hairpin antimicrobial peptide (AMP) protegrin-I can

form stable octameric β-barrels and tetrameric arcs (half barrels) in both implicit and explicit

membranes. Here, we extend this investigation to several AMPs of similar structure: tachyplesin,

androctonin, polyphemusin, gomesin, and the retrocyclin θ-defensin. These peptides form short

β-hairpins stabilized by 2‒3 disulfide bonds. We also examine synthetic β-sheet peptides selected

from a combinatorial library for their ability or inability to form pores in lipid membranes. When

heptameric, octameric, and decameric β-barrels and tetrameric arcs of these peptides were

embedded in preformed neutral or anionic lipid pores (i.e., pores in neutral or anionic

membranes, respectively), a variety of behaviors and membrane binding energies were observed.

Due to the cationic charge of the peptides, more favorable transfer energies and more stable

binding were observed in anionic than neutral pores. The synthetic peptides bound very strongly

and formed stable barrels and arcs in both neutral and anionic pores. The natural AMPs exhibited

unfavorable or marginally favorable binding energy and kinetic stability in neutral pores,

consistent with the lower hemolytic activity of some of them compared with protegrin-I. Binding

to anionic pores was more favorable, but significant distortions of the barrel or arc structures

were sometimes noted. These results are discussed in light of the available experimental data.

The diversity of behaviors obtained makes it unlikely that the barrel and arc mechanisms are

valid for the entire family of β-hairpin AMPs.

Introduction

28

Antimicrobial peptides (AMPs) are small (12‒50-amino-acid), usually cationic peptides that

provide immunological defenses [19, 196, 233] against bacteria, fungi, parasites, the HIV virus,

and even cancer cells [19, 21, 78, 82, 233-235]. They could serve as the basis of novel antibiotics

[236]. Their mechanism of action is not known precisely, but there is considerable evidence that

they target cell membranes [70, 237].

The positive charge of AMPs offers an explanation for their selectivity for prokaryotic over

eukaryotic cells [33, 238]. Bacterial membranes tend to be anionic, (i.e., rich in acidic

phospholipids like phosphatidylglycerol [PG] and cardiolipin [239]). In mammalian cells, acidic

phospholipids are usually sequestered in the inner plasma membrane leaflet, whereas the outer

leaflet is usually comprised of zwitterionic phosphatidylcholine and sphingomyelin molecules

[200]. Although the anionic composition of bacterial inner membranes varies widely, 30%

anionic content is typical [239]. For example, the composition of Escherichia coli inner

membrane was found to be 70%‒75% phosphatidylethanolamine (PE), 18%‒22% PG, and 6%‒

8% cardiolipin [240], depending on temperature. Bilayers of PE and PG at a 7:3 ratio are

commonly used to mimic bacterial cell membranes [241].

AMPs may micellize and/or disintegrate the membrane (i.e., the carpet mechanism; [237]) or

aggregate to form pores that cause fatal ion leakage [31, 242]. The pores may be cylindrical,

lined by peptides (i.e., the barrel-stave model) or toroidal, stabilized by peptides and lined

partially by lipids. There is evidence that alamethicin forms barrel-stave pores, whereas melittin

and magainin form toroidal pores [52, 68]. Both cylindrical and toroidal pores were classically

viewed as ordered structures, but molecular dynamics (MD) simulations have suggested that

some AMPs may form disordered pores [83, 84, 165].

29

Most AMPs are helical when membrane-bound. However, some are disordered, and some form

β-hairpins. The best-studied of the latter family are the protegrins, small β-hairpins stabilized by

2 disulfide bonds; the face with the disulfide bonds contains charged or polar residues, and the

opposite face has a hydrophobic cluster flanked by charged residues. They are active against

Gram-positive and Gram-negative bacteria and fungi in vitro [243, 244]. A large number of

variants [245, 246] and synthetic analogs [247] have been synthesized. Other β-hairpin AMPs

include the retrocyclin θ-defensin [248], tachyplesin [249], polyphemusin [250], gomesin [251],

and androctonin [252].

Protegrin-1 (hereafter called protegrin) is the best-studied AMP of this family, both

experimentally [49, 61, 253] and computationally [203]. It forms ion channels in membranes

[254, 255]. MD simulations have been performed of protegrin monomers in micelles (e.g., [256])

and of monomers and dimers in bilayers with transmembrane and interfacial orientations [149,

220, 257-259]. Tilting within the membrane [227] and association with and insertion into an

anionic membrane [226] have also been calculated. The evidence that it oligomerizes into a

closed β-barrel [205] inspired simulations of β-barrel models [59, 221-224].

Previous computational studies from this laboratory in implicit and explicit membranes

examined the interaction of protegrin monomers with membranes and pores and the relative

stability of different β-barrel topologies [224]. The NCNC parallel topology was most stable,

because it allows immersion of the hydrophobic cluster of each peptide into the nonpolar

membrane interior. Further, incomplete barrels (arcs) formed kinetically stable pores for 300 ns

[100]. Thus, the barrel or arc structures seem to constitute viable pore formation mechanisms for

protegrin.

30

We presently ask whether the other β-hairpin AMPs could work by the same mechanism. While

that would be an attractive proposal, experimental studies have suggested the carpet mechanism

for gomesin [77], non-pore-forming internalization for polyphemusin [260], and an orientation

parallel to the membrane plane for tachyplesin [213]. It would be interesting to rationalize these

differences through molecular modeling; we do this here using an implicit membrane approach

[117, 186]. We construct tetrameric arcs and heptameric, octameric, and decameric β-barrels of

θ-defensin, tachyplesin, polyphemusin, gomesin, and androctonin, insert them into implicit

toroidal pores of varying radii, and subject them to MD simulations. We observe their kinetic

stability and estimate their thermodynamic stability by computing their transfer energies from the

pores to bulk water. Our goal is to determine how structural differences are associated with

differences in pore-forming ability.

In addition to the AMPs, we studied two 26-residue peptides selected from a combinatorial

library based on known structures of membrane-spanning β-sheet peptides [231]. The first is a

good pore former and contains the residues YGKRGF in the combinatorial sites; it has sterilizing

antimicrobial activity and low activity against mammalian cell membranes [230]. The second

peptide lacks pore-forming ability and contains AGGKGF in the combinatorial sites. Rausch et

al. [231] noted that the interfacial, hydrophobic sites in the library peptides support a membrane-

spanning mechanism. However, fluorescence spectroscopy showed that the peptides were

partially exposed to water on the bilayer surface rather than being in a membrane spanning-state,

which suggested a carpet mechanism [230]. The authors also speculated that carpet model pores

might be formed on a mechanistic pathway toward more structured β-barrel pores [231].

Methods

Energy Functions

31

The simulations in this study employed Implicit Membrane Model 1 (IMM1; [112]), which is an

extension of Effective Energy Function 1 (EEF1) for soluble proteins [108]. IMM1 extends

EEF1 to heterogeneous membrane-water systems by making the solvation parameters dependent

on vertical position. These are modeled as linear combinations of the values for water and

cyclohexane; further, the dielectric’s dependence on vertical position accounts for strengthening

of electrostatic interactions within the membrane. IMM1 has been extended to account for

surface charge due to anionic lipids using Gouy-Chapman theory [115], transmembrane voltage

[120], membrane dipole potential (Zhan and Lazaridis 2012), and lateral pressure effects [122].

IMM1 can also accommodate pores [117, 118], whose shape can be adjusted by making the

radius dependent on vertical position:

R = Ro + kz2; z = |z| / (T / 2)

where Ro is the pore radius at the membrane center, R is the radius at a given z-level, T

represents the hydrophobic thickness of the membrane, and k (curvature) determines pore shape.

For example, Ro = 15 Å and k = 0 defines a cylindrical pore of radius 15 Å, whereas Ro = 15 Å

and k = 20 Å defines a toroidal pore with radii of 15 and 35 Å at its center and rims, respectively.

Because Gouy-Chapman theory can no longer be used in pore geometries, the electrostatic

potential in anionic pores (i.e., ones comprised of anionic lipids) is obtained by solution of the

Poisson-Boltzmann (PB) equation [119]; those potential values are applied as a static field in

MD simulations. We solve the PB equation and use it similarly to the analytical Gouy-Chapman

equations by adding an extra term to the effective energy function representing the interaction

between solute charges and the electrostatic potential ⃑ :

∑ ⃑

32

This simple approximation gives acceptable results compared with the full nonlinear PB

treatment [183]. The bilayer’s dielectric properties are represented by a five-slab model (see

Figure 2 from [119]), whereby ε(d) depends on distance (d) to the hydrophobic core’s surface:

{

where εmemb (the dielectric constant inside the membrane), εhead (that inside the interfacial

region), and εwater (that in water) are 2, 10, and 80, respectively [119]. Width D was set to 3.0 Å,

localizing the boundary around the phosphate group. The ion accessibility factor is assigned

values of

{

so that ions cannot penetrate below the phosphate groups; the ions were taken as monovalent

with radius 2.0 Å. To reproduce the membrane dipole potential, two layers of charges were

defined as Gaussian distribution functions:

∑

√

where i, oi, and i represent charge per unit area, offset of the charge layer from the membrane

surface, and Gaussian width, respectively. Positive and negative charge layers, separated by 1.0

Å according to experimental data [119], represent the charge distribution in the membrane; i is +

and for the positive and negative charge layers, respectively. The negative and positive charge

layers are localized on and below the plane of the lipid phosphate groups, respectively, to create

a positive dipole potential in the membrane interior. + was set to +1q / A, where A is the area per

lipid within the membrane (68 Å2 for 1,2-dioleylphosphatidylcholine [DOPC] and 1,2-

dioleylphosphatidylglycerol [DOPG] bilayers), and was set to (1 + ZI anfr) q / A, where

33

anfr is the fraction of anionic lipids in the membrane, and ZI is the charge of an anionic lipid

molecule. The hydrocarbon core thickness was set at 26 Å (in accordance with the thickness of

DOPC membranes; He et al. 2013), and anfr of 30% was used, in accordance with the typical

composition of bacterial membranes [239].

The model accounts for the fact that head group density (and therefore charge density) may not

be uniform on curved pore surfaces. It assumes that charge density on the pore rim is equal to

that of a flat membrane (0) and that charge density within the pore changes quadratically with

|z|, or vertical distance from the center of the membrane:

The homogeneity factor h (i.e., the ratio of charge density at the center of the pore to that in the

intact membrane) was 0.6 in this study, according to all-atom simulation results [119].

The system was set up using mBuild, an in-house software package [119]. The Poisson-

Boltzmann equation was solved using the Advanced Poisson-Boltzmann Solver [261], taking

average values in grid volumes after discretizing the space into a finite lattice box. The grid size

was 161 × 161 × 161, with five focusing levels used to improve accuracy; that is, the calculations

were run successively in cubic boxes of edge length 640 Å, 480 Å, 240 Å, 120 Å, and 80 Å (final

resolution: 0.5 Å). For each run, the previous run’s potential was the boundary potential. Each

volume was assigned values of dielectric constant, ion accessibility, and charge density by the

distribution functions above; these simulated membranes were embedded into cubic boxes filled

with 0.1 M aqueous salt ion solution. Multiple Debye-Hückel boundary conditions were used,

and trilinear interpolation was used to obtain the PB values and their derivatives. These are

assumed to be steady state values, not changing throughout the simulation due to ion transport.

Initial Structures

34

The coordinate files for protegrin, θ-defensin, gomesin, polyphemusin, tachyplesin, and

androctonin were downloaded from the Protein Data Bank (PDB; entries 1PG1 [204], 1HVZ

[209], 1KFP [251], 1RKK [250], 1WO0 [Mizuguchi et al., unpublished], and 1CZ6 [252],

respectively). CHARMM version 39a2 [262] was used to import the NMR model of each peptide

monomer’s structure that seemed most conducive to β-barrel formation (i.e., the one in which the

peptide’s structure was closest to a flat, ideal β-hairpin) and assign disulfide bonds between the

appropriate residues. The peptides from the combinatorial library by Rausch et al. [231] were

initially built as β-strands. All charged residues were in their standard ionization states

corresponding to pH ~7.

Then, the proper intramolecular hydrogen bonds for monomers of each peptide were imposed as

distance constraints using a symmetrical potential well. For this, the values of kmin, rmin, kmax,

and rmax within CHARMM’s Nuclear Overhauser Effect (NOE) facility were set to 1.0, 1.8, 5.0,

and 2.3, respectively. Mean miscellaneous field potentials (MMFP) were applied to constrain the

Cα carbons onto a plane, flattening the β-hairpins into conformations more conducive to barrel

formation. After the above constraints were imposed, the energy of the peptides was minimized

using the adopted basis Newton-Raphson algorithm (ABNER; used for all energy minimizations

for 300 steps), followed by 200 ps of MD simulation using the Verlet integrator with a time step

of 2 fs at 298.5 K (the same integrator, time step, and temperature were used in all MD

simulations). Then, energy minimization yielded the final monomeric structures used to

construct the β-barrels or arcs.

Simulations

The monomeric structures were arranged as tetrameric arcs or heptameric, octameric, or

decameric β-barrels around the z-axis by translation of 1114 Å in the x direction followed by

35

rotation around the z-axis. For the β-barrels, the appropriate number of monomers was arranged

in an evenly spaced cylinder around the z-axis in implicit water; for tetrameric arcs, four

monomers were spaced evenly with z-axis rotations of 0°, 45°, 90°, and 135° (effectively

forming half of an octamer barrel). We arranged the barrels and arcs in conformations analogous

to those of protegrin: with the more hydrophobic side facing the membrane, the more hydrophilic

side facing the pore, and the backbone hydrogen atoms both intermolecularly and

intramolecularly H-bonded. Then, without any MMFP or NOE constraints, the β-barrel or arc

underwent minimization in water with backbone constraints. Then, the appropriate intra- and

intermolecular hydrogen bonds were imposed as NOE constraints, and minimization was

performed without backbone constraints. Subsequently, 200 ps of MD simulation was run in

water, followed by minimization.

After the β-barrel or arc underwent brief dynamics in water, the resulting structure was inserted

into an implicit 26-Å-thick membrane and subjected to additional MD simulation. We set out to

select the most realistic possible dimensions to represent the pores generated by the AMPs under

investigation, so we conducted simulations with varying pore radii to find the conditions that

provide optimal binding energies. We selected one value for which good protegrin octamer -

barrel binding results were previously obtained (Ro = 15 Å and k = 15 Å; Lazaridis et al. 2013).

However, Rausch et al. (2007) suggested a pore radius of 10 Å, and initial simulations with

YGKRGF indicated enhanced pore binding of the octamer -barrel with Ro = 12 Å as compared

with Ro = 15 Å. Therefore, for all peptides, we ran 2-ns simulations in pores of Ro = 10 Å, 12 Å,

and 15 Å; we used both 30% anionic and zwitterionic membranes and four oligomeric states:

tetramer arcs and heptamer, octamer, and decamer -barrels. In all cases, k was 15 Å. For the

arcs, shorter simulations were also run with k = 10 or 5 Å, but in no case was the stability in the

36

pore better (and in some cases it was worse) than with k = 15 Å. (For our analysis, we selected

the pore radius for each peptide and membrane charge condition that gave the best results: the

most stable barrel/arc and most favorable binding energies.)

Once the -barrel or arc had been inserted into the center of the pore, NOE and MMFP

constraints were released for the production-length MD simulations. A simulation length of 2 ns

was selected for all conformations. When we performed longer simulations on example peptides,

we obtained results that converged onto those for the 2-ns simulations. In all conditions, the

results seem to have stabilized by the end of a 2-ns MD simulation. The binding energy to the

pore (ΔW) was estimated by averaging the energy of the barrel or arc at its position in the pore

and subtracting the energy of the same conformation in water. In cases where the oligomer

remained bound to the pore throughout the entire simulation, the value of ΔW was calculated by

averaging values obtained every 1 ps throughout the last 1 ns of the simulation; in cases where

the oligomer left the pore within 2 ns of MD simulation, the ΔW values were obtained by similar

averaging during the period of 3‒22 ps. Simulations using different random seeds and longer

durations, run as checks, gave very similar results. At the end of the MD simulation,

minimization provided the final post-MD image of the -barrel or arc.

Results

Structural and Activity Comparison of Peptides

In previous work, protegrin in NCNC parallel topology was observed to form stable β-barrels in

both neutral and anionic membranes, with those in the latter being more stable [224]. In addition,

four separate monomers in an implicit pore were observed to associate, forming a tetrameric arc

of the same topology; the resulting structure formed stable pores in all-atom simulations [100].

In this study, we investigated the behavior of several similar peptides using simulations in

37

implicit membrane pores. Before presenting the simulation results, we qualitatively compare the

sequences (Figure 2.1) and structures of the peptides when configured as β-barrels in NCNC

parallel topology (Figures 2.2–2.4). We also relate these comparisons to the peptides’ reported

activity levels.

Figure 2.1. Sequence alignment of the investigated peptides. Certain conserved residues are

colored. The numbers represent residue positions in protegrin-I. The numbering reflects the

sequence of protegrin-I. Figure created using STRAP [263].

Experimental [205] and computational [221, 223, 224] results indicate protegrin’s ability to form

β-barrels in membrane pores. We thus infer that it has structural properties conducive to that

arrangement. Protegrin’s β-hairpin conformation is constrained by two disulfide bonds, and the

open ends of the hairpin both contain positively charged arginine residues (Figure 2.2a). The turn

region of the hairpin is also highly concentrated in basic residues, containing three consecutive

arginines; the resulting positive electrochemical potential in protegrin’s turn region can be seen

upon solution of the PB equation at the solvent-accessible surface (Figure 2.3a). Further,

protegrin has a relatively clear separation between polar and nonpolar regions. The β-sheet

region between the turn and ends is relatively hydrophobic and nonpolar, with a clear division in

38

hydrophobicity between the two sides of the molecule (Figure 2.4a): no charged or polar residues

face the membrane, increasing its stability in membrane pores, while one positively charged

arginine residue faces the pore in a 26-Å-thick membrane (all discussions of membrane–peptide

structural proximity concern 26-Å-thick membranes; Figure 2.2a). Studies with truncated forms

and disulfide variants of protegrin have shown the important role of the β-sheet and hairpin

regions (especially the three consecutive arginine residues) for its activity against Neisseria

gonorrheae [206]. Protegrin’s minimal inhibitory concentrations (MICs) for Gram-positive and

Gram-negative bacteria in one study were 0.3‒0.8 M and 0.7‒2.8 M, respectively [264].

However, these values vary widely depending on experimental protocol (see Discussion).

Protegrin also causes 50% hemolysis at 11.6 M [265] and about 65% hemolysis at 46.4 M

[266].

39

Figure 2.2. Visual structural comparison of the investigated peptides. Side views of one

monomer from the initial β-barrel/arc conformations of each peptide after 200 ps of molecular

dynamics (MD) simulation in water and 300 minimization steps but before insertion into a

membrane: (a) protegrin-I; (b) θ-defensin; (c) tachyplesin; (d) polyphemusin; (e) gomesin; (f)

androctonin; (g) YGKRGF; (h) AGGKGF. All peptides are oriented with the pore-facing side to

the right and the turn region of the hairpin facing down. The black lines denote where the borders

of a 26-Å-thick membrane region would be if the monomer were at center depth, the side chains

and main chain are represented as sticks, and colors denote atom/side chain properties. Sky blue:

basic side chain; red: acidic side chain or oxygen atom; purple: neutral, polar side chain; green:

40

nonpolar side chain; cyan: glycine H; yellow: cysteine side chain/disulfide bond; gray: main

chain. Figure created using MacPyMOL 1.7 [267].

Figure 2.3. Comparison of the investigated peptides’ electrochemical potential at the solvent-

accessible surface. Red: negative potential; white: middle; blue: positive potential. Potential

denotes charge buildup at the surface. Side views of one monomer from the initial β-barrel/arc

conformations of each peptide after 200 ps of molecular dynamics (MD) simulation in water and

300 minimization steps but before insertion into a membrane: (a) protegrin-I; (b) θ-defensin; (c)

tachyplesin; (d) polyphemusin; (e) gomesin; (f) androctonin; (g) YGKRGF; (h) AGGKGF. All

peptides are oriented with the pore-facing side to the right and the turn region of the hairpin

facing down. The black lines denote where the borders of a 26-Å-thick membrane region would

41

be if the monomer were at center depth, the chains are represented as black sticks, and the color

surface overlay denotes electrochemical potential according to the scale shown. Figure created

by solution of the Poisson-Boltzmann equation using the default parameters of the PyMOL

APBS Tools plugin in MacPyMOL 1.7 [267].

Figure 2.4. Comparison of the investigated peptides’ electrochemical potential at the solvent-

accessible surface. Red: negative potential; white: middle; blue: positive potential. Potential

denotes charge buildup at the surface. Side views of one monomer from the initial β-barrel/arc

conformations of each peptide after 200 ps of molecular dynamics (MD) simulation in water and

300 minimization steps but before insertion into a membrane: (a) protegrin-I; (b) θ-defensin; (c)

tachyplesin; (d) polyphemusin; (e) gomesin; (f) androctonin; (g) YGKRGF; (h) AGGKGF. All

42

peptides are oriented with the pore-facing side to the right and the turn region of the hairpin

facing down. The black lines denote where the borders of a 26-Å-thick membrane region would

be if the monomer were at center depth, the chains are represented as black sticks, and the color

surface overlay denotes electrochemical potential according to the scale shown. Figure created

by solution of the Poisson-Boltzmann equation using the default parameters of the PyMOL

APBS Tools plugin in MacPyMOL 1.7 [267].

θ-defensin has a cyclic backbone and contains three disulfide bonds (compared with two for

protegrin and the other AMPs studied; Figures 1, 2b). In this study, we investigate the open chain

analog of θ-defensin. The cyclic analog is required for antimicrobial activity in the presence of

150 mM sodium chloride and is three times as active as the acyclic analog [268]. MIC values of

1.0 and 2.1 M for Escherichia coli and Staphylococcus aureus, respectively, have been

observed for θ-defensin [266]. This peptide is relatively non-amphiphilic, accounting for its

relatively low antimicrobial activity [208, 209], but it can also prevent HIV entry into cells,

possibly as a competitive inhibitor of the gp120:gp41 membrane binding/fusion process [210]. θ-

defensin is much less hemolytic than protegrin; nevertheless, the cyclic analog caused 3%

hemolysis at 5.5 g/mL [266]. When configured as a β-barrel, three of θ-defensin’s arginine side

chains point towards the membrane rather than the top/bottom edges or pore interior (Figure

2.2b), and one additional polar group (Thr 17) is also oriented towards the membrane; this breaks

the clear division in hydrophobicity between the membrane-facing and pore-facing sides seen in

protegrin (Figure 2.4b). The electrochemical potential surface map (Figure 2.3b) also shows that

θ-defensin has less positive charge concentration in the turn region than does protegrin. These

features make θ-defensin less than ideal for the same type of pore-forming structure as protegrin

43

in bacterial cells. Further, θ-defensin lacks the larger hydrophobic side chains that face the

membrane in protegrin, which may negatively affect its affinity for the membrane.

Tachyplesin also exhibits less amphipathicity than protegrin (Figure 2.4c). One arginine residue

(Arg 15) faces the membrane in embedded tachyplesin β-barrels. Further, in this arrangement,

tachyplesin has two arginine residues (Arg 5 and Arg 14) facing the pore (compared with one for

protegrin), which may cause crowding and electrostatic repulsion within the pore regionand

make β-barrel formation less favorable (Figure 2.2c); the electrochemical potential is also quite

high in this region (Figure 2.3c). These structural differrences may contribute to previous

indications that tachyplesin orients parallel rather than normal to the membrane [212, 213].

Tachyplesin showed about 10% and 25% hemolysis at 100 and 150 g/mL, respectively, but the

hemolytic activity of a cysteine-deleted analog was abolished [269]. Nevertheless, the cysteine-

deleted analog’s antibacterial activity was relatively intact [269]. MICs of 0.8‒12.5, 3.1‒12.5,

and 1.6‒3.1 g/mL for Gram-negative bacteria, Gram-positive bacteria, and fungi, respectively,

have been observed for tachyplesin [270]. Another study observed nearly linear dependence of

hemolysis on tachyplesin’s concentration, finding 5% and 100% hemolysis at 20 and 100M,

respectively [271].

Polyphemusin is extremely similar structurally to tachyplesin (Figure 2.1), but it contains an

additional Arg residue at the N-terminus [270]. The disulfide bridge structure is identical

between polyphemusin and tachyplesin, and each peptide has one charged residue facing the

membrane in β-barrel conformation (Arg 15 and Lys 16 for tachyplesin and polyphemusin,

respectively; Figure 2.2c–2.2d). MIC values of 3.1‒12.5 g/mL for Gram-negative bacteria and

6.3 g/mL for Gram-positive bacteria and fungi have been observed for polyphemusin,

indicating that its activity level is quite similar to tachyplesin’s [270]. Another study of

44

polyphemusin obtained MICs of 0.125‒0.5 g/mL against Gram-negative and Gram-positive

bacteria and 21.3 g/mL against human red blood cells; a study using polyphemusin analogs

indicated that the peptide binds to divalent cation binding sites on target cells’

lipopolysaccharide molecules, displacing divalent cations to penetrate/permeabilize the outer

membrane [214]. Although polyphemusin and tachyplesin have quite similar structures,

polyphemusin’s antimicrobial activity is dependent on disulfide bridges, as a linear analog with

cysteine replaced by serine showed 4‒16-fold less activity than polyphemusin; β-sheet structure

is also required for polyphemusin to translocate past model membranes [250].

Gomesin has a relatively similar structure to protegrin (Figure 2.1) but contains a pyroglutamic

acid residue at the N-terminus. In addition, two arginine residues face the membrane in β-barrel

conformation (Figure 2.2e), which reduces the difference in hydrophobicity between the solvent-

facing and membrane-facing sides of the molecule (Figure 2.4e). Gomesin has less positive

electrochemical potential than protegrin in the turn region (Figure 2.3e). MICs of 0.4‒6.25, 0.2‒

12.5, and 0.2‒25 g/mL for Gram-negative bacteria, Gram-positive bacteria, and fungi,

respectively, have been measured for gomesin; direct comparison with androctonin revealed that

gomesin was more active against most bacteria and fungi [272]. Similarly to some other AMPs

under investigation, gomesin’s disulfide bonds are important to its antimicrobial and hemolytic

activity [251, 273, 274]: activity is markedly decreased upon reduction/alkylation of the disulfide

bridges [272]. Further, while gomesin is hemolytic at low concentrations (16% hemolysis at

1M), hemolytic activity had little dependence on concentration (22% hemolysis at 100M),

making it significantly less hemolytic than protegrin in the high-concentration regime [272]. One

study showed that gomesin made giant unilamellar vesicles burst suddenly; stable pores were not

observed, indicating that gomesin may work by the carpet mechanism [77].

45

Androctonin shows some sequence homology to tachyplesin and polyphemusin [275]; however,

it also has structural features that distinguish it from the other investigated peptides. Whereas

gomesin, tachyplesin, and polyphemusin have three residues in each segment upstream and

downstream of the disulfide bridges, androctonin has three residues in one segment and five in

the other, with Cys 4 and Cys 10 bonded to Cys 20 and Cys 16, respectively (Figure 2.1; see

Figure 5 from [272]). Probably because of this, androctonin’s NMR structure is a highly twisted

antiparallel β-sheet with strands connected by a positively charged turn [252]. This feature might

affect androctonin’s ability to form a β-barrel. In addition, androctonin has one arginine and two

lysine residues facing the membrane in this arrangement, rather than large hydrophobic side

chains (Figure 2.2f); this significantly reduces the hydrophobicity difference between the two

sides of the molecule (Figure 2.4f), although in the conformation we used, the two sides of the

molecule did vary in electrochemical potential (Figure 2.3f). MICs of 1.5‒>30, 0.3‒30, and 2‒50

g/mL for Gram-negative bacteria, Gram-positive bacteria, and fungi, respectively, have been

measured for androctonin [275]; it was significantly less active than gomesin in most conditions

that provided for direct comparison [272]. Androctonin is not hemolytic even at 150 M [275].

Silva et al. [272] attributed the differences in hemolytic activity between androctonin on the one

hand and gomesin and tachyplesin on the other to androctonin’s longer C-terminus and charge

differences throughout the molecule. ATR-FTIR experiments seemed to indicate that

androctonin is localized on the membrane surface and does not destabilize the bilayer structure

[216]. Androctonin binds only to negatively charged lipid vesicles and seems to adopt a -sheet

structure while leaving the acyl chain order unaffected, suggesting a detergent-like mechanism

[216].

46

YGKRGF and AGGKGF have some similarities with the protegrin family, such as the general

locations of the positively charged and polar residues, but they also show several structural

differences (Figure 2.1). These peptides are longer than protegrin (26 residues) and contain no

disulfide linkages. However, the rational combinatorial library from which these peptides were

extracted preserves certain key characteristics of the protegrin family. For example, aromatic

residues are found at the lipid-exposed interfacial positions, and basic residues are found in the

pore-lining region (Figure 2.2g‒2.2h). The general locations of positive charges within the

peptides have some similarity to those in protegrin: there is a pair of polar combinatorial sites in

a position analogous to the pore-facing arginine residue in protegrin. Besides protegrin, these

two peptides are the only ones studied that have no significant interruptions in the

hydrophobicity of the molecule’s membrane-facing side (Figure 2.4g‒2.4h). The turn region of

YGKRGF and AGGKGF differs from the ones found in the AMPs we investigated in that they

lack arginine and include a negative charge; this reduces the turn region’s overall

electrochemical potential (Figure 2.3g‒2.3h). While both YGKRGF and AGGKGF are active

against Escherichia coli and show broad-spectrum antimicrobial activity, only YGKRGF causes

measurable leakage of the contents of lipid vesicles, with the release of molecules as large as 3

kDa signifying a pore diameter of ~10 Å [231]. YGKRGF also had a low MIC against

Staphylococcus aureus (2.1 M; [231]). In contrast, AGGKGF had the highest hemolytic

activity, lysing human red blood cells at 15 M. Relatively small structural differences

differentiate YGKRGF, which forms functional pores, from AGGKGF, which does not. The

presence of two charged side chains facing the pore (instead of one) and the replacement of an

alanine with a tyrosine facing the membrane seem to increase the peptide’s pore-forming ability.

Simulation Results

47

The tetramer arcs and heptamer, octamer, and decamer β-barrels of the peptides were subjected

to 2-ns MD simulations in implicit toroidal pores with Ro = 10 Å, 12 Å, and 15 Å using both

30% anionic and zwitterionic membranes; we observed the peptides’ movement, structure, and

the thermodynamic stability of their arrangement. For each peptide, the pore radius that gave the

best energy in anionic membranes was chosen for further analysis (Table 2.1). The results for the

pore radii not selected for further analysis and further notes on the peptides’ behavior during the

simulations are found in Online Resource 1 from [2]. Not all peptides remained within the pore

for the duration of the simulation; notes on whether or not the peptides left the pore region or

became distorted during the simulations are found in Table 2.1, and top-down and side views of

the post-simulation conformations of the octamer barrels and tetramer arcs in pores of optimal

radii are shown in Figures 2.5–2.6. The binding energies of these β-barrels and arcs to the pores

were estimated by the transfer energy (ΔW) from water to pore (Tables 2.22.5, Figure 2.7).

Negative values indicate favorable binding.

48

Table 2.1. Behavior of selected tetramer arcs and heptamer, octamer, and decamer β-barrels

during 2-ns molecular dynamics (MD) simulations

Peptide Tetramer arc Heptamer barrel Octamer barrel Decamer barrel

Po

re r

adiu

s (Å

)

Pore charge

Po

re r

adiu

s (Å

)

Pore charge

Po

re r

adiu

s (Å

)

Pore charge

Po

re r

adiu

s

(Å)

Pore charge

Neu

tral

30

%

anio

nic

Neu

tral

30

%

anio

nic

Neu

tral

30

%

anio

nic

Neu

tral

30

%

anio

nic

Lea

ves

po

re

Dis

tort

ed

Lea

ves

po

re

Dis

tort

ed

Lea

ves

po

re

Dis

tort

ed

Lea

ves

po

re

Dis

tort

ed

Lea

ves

po

re

Dis

tort

ed

Lea

ves

po

re

Dis

tort

ed

Lea

ves

po

re

Dis

tort

ed

Lea

ves

po

re

Dis

tort

ed

Protegrin-1 10 10 12 15 x

θ-defensin 12 x x 15 x X 15 x x 15 x x

Tachyplesin 12 x x 15 x x x X 15 x x 12 x x

Polyphemusin 12 x x x x 15 x x x X 15 x x x 15 x x x x

Gomesin 10 x x 12 x X 15 x x 15 x x

Androctonin 10 x x 12 x X 15 x x 15 x x x

YGKRGF 10 10 x X 10 12

AGGKGF 10 10 10 10 x x

*This table represents the characteristics of the final minimized conformations of peptide

oligomers after MD simulations in implicit toroidal pores of the radii that gave the most

favorable transfer energies from solvent to membrane. These were the positions and

conformations of the peptides after the water-equilibrated monomers were arranged as octamer

barrels, subject to 200 ps of MD in water, minimized, inserted into pre-formed toroidal pores in

26-Å-thick implicit membranes, and subject to 2 ns of MD followed by minimization. For each

oligomeric state and pore charge condition, whether or not the peptide assembly left the pore

region during the course of the simulation is represented by a checkbox in the “Leaves pore”

column, and the presence of distortion is represented by a checkbox in the “distorted” column.

Table 2.2. Average membrane transfer energies (<ΔW>; kcal/mol) of tetramer arcs of peptides

from water to toroidal pores (k = 15 Å) from 2-ns simulations.

49

Tetramers:

Radius

selected (Å) Neutral pore

30% anionic

pore

Protegrin-1 10 -20.5 ± 2.1 -55.6 ± 3.2

θ-defensin 12 16.7 ± 24.8 a -11.9 ± 17.4

a

Tachyplesin 12 34.0 ± 25.4 a 9.7 ± 27.5

a

Polyphemusin 12 22.4 ± 25.0 a 1.2 ± 24.0

a

Gomesin 10 -5.7 ± 2.9 -23.6 ± 2.8

Androctonin 10 4.2 ± 3.4 -22.6 ± 7.2

YGKRGF 10 -50.6 ± 2.2 -70.2 ± 3.3

AGGKGF 10 -50.0 ± 2.4 -71.8 ± 3.2

a Tetramer left the pore during the course of the simulation; values estimated using the time

window of 3–22 ps. Other values estimated using the window 1001–2000 ps.

Table 2.3. Average membrane transfer energies (<ΔW>; kcal/mol) of heptamer barrels of

peptides from water to toroidal pores (k = 15 Å) from 2-ns simulations.

Heptamers:

Radius

selected (Å) Neutral pore

30% anionic

pore

Protegrin-1 10 -17.1 ± 2.5 -97.3 ± 4.7

θ-defensin 15 3.5 ± 3.4 -30.4 ± 3.6

Tachyplesin 15 17.9 ± 6.1a -19.1 ± 13.8

a

Polyphemusin 15 22.5 ± 18.5a -1.5 ± 21.4

a

Gomesin 12 7.7 ± 5.6 -36.5 ± 4.0

Androctonin 12 36.1 ± 5.5 -35.6 ± 7.0

YGKRGF 10 -77.8 ± 3.1 -127.7 ± 4.9

AGGKGF 10 -73.1 ± 2.8 -116.4 ± 3.5

a Heptamer left the pore during the course of the simulation; values estimated using the time

window of 3–22 ps. Other values estimated using the window 1001–2000 ps.

Table 2.4. Average membrane transfer energies (<ΔW>; kcal/mol) of octamer barrels of peptides

from water to toroidal pores (k = 15 Å) from 2-ns simulations.

Octamers:

Radius

selected (Å) Neutral pore

30% anionic

pore

Protegrin-1 10 -17.1 ± 2.5 -97.3 ± 4.7

50

θ-defensin 15 3.5 ± 3.4 -30.4 ± 3.6

Tachyplesin 15 17.9 ± 6.1a -19.1 ± 13.8

Polyphemusin 15 22.5 ± 18.5a -1.5 ± 21.4

Gomesin 12 7.7 ± 5.6 -36.5 ± 4.0

Androctonin 12 36.1 ± 5.5 -35.6 ± 7.0

YGKRGF 10 -77.8 ± 3.1 -127.7 ± 4.9

AGGKGF 10 -73.1 ± 2.8 -116.4 ± 3.5

a Octamer left the pore during the course of the simulation; values estimated using the time

window of 3–22 ps. Other values estimated using the window 1001–2000 ps.

Table 2.5. Average membrane transfer energies (<ΔW>; kcal/mol) of decamer barrels of

peptides from water to toroidal pores (k = 15 Å) from 2-ns simulations.

Decamers:

Radius

selected (Å) Neutral pore

30% anionic

pore

Protegrin-1 15 -17.2 ± 2.9 -101.8 ± 5.3

θ-defensin 15 137.7 ± 14.2a 62.8 ± 21.5

a

Tachyplesin 12 87.5 ± 48.6a 29.3 ± 75.9

a

Polyphemusin 15 77.7 ± 43.9a 28.8 ± 43.1

a

Gomesin 15 -1.3 ± 3.8 -65.7 ± 6.0

Androctonin 15 189.9 ± 39.1a -70.4 ± 6.4

YGKRGF 12 -106.4 ± 3.7 -177.8 ± 5.0

AGGKGF 10 -102.4 ± 4.6 -150.7 ± 6.5

a Decamer left the pore during the course of the simulation; values estimated using the time

window of 3–22 ps. Other values estimated using the window 1001–2000 ps.

Protegrin is the best studied among the peptides investigated. Throughout the 2-ns simulations,

all studied protegrin oligomers remained bound to both neutral and anionic pores, and transfer

energies to the pore-embedded state were favorable in all conditions (Tables 2.12.5). As

expected, the transfer energies for all protegrin oligomers were significantly more favorable to

anionic than neutral pores. (This trend also held for all other peptides in all conditions.) There

51

was little distortion of the barrels/arcs throughout the simulations at the pore radii that gave

optimum results (Figures 2.5a, 2.6a). The obtained ΔW values for protegrin matched well with

the results from a previous study [224].

The simulations of θ-defensin oligomers resulted in distortion of the peptide assemblies, and in

some conditions, the barrels/arcs of θ-defensin exited the pore (Tables 2.12.5). Throughout the

simulations, the θ-defensin octamer -barrel remained bound to both neutral and anionic pores

with 15 Å radii, but in the neutral case, some monomers moved to the center of the pore instead

of remaining adjacent to the pore interface (Figure 2.5b), and there was an unfavorable transfer

energy from water to pore; in an anionic pore, the octamer barrel distorted only slightly, and the

transfer energy was favorable. The θ-defensin tetramer arcs and heptamer and decamer barrels

displayed the same pattern of binding energies as the corresponding octamer barrels (i.e.,

unfavorable and favorable transfer energies in the neutral and anionic cases, respectively), but

the other oligomeric states of θ-defensin did not show stable behavior during the simulations

(Tables 2.12.5, Figure 2.7). The tetramer arcs migrated outside of both neutral and anionic

pores within 70 ps of simulation onset. During the simulations of heptamer barrels, θ-defensin

remained within the pore throughout the simulation, but the integrity of the barrel was not

maintained: there was barrel shear in a neutral pore, and the ring collapsed in an anionic pore.

The decamer barrels of θ-defensin exited the pore rapidly at the onset of the simulation (Table

2.1).

52

53

Figure 2.5. Top and side views of the minimized final conformations of octamer β-barrels of

peptides in toroidal pores of optimal radius in zwitterionic and 30% anionic membranes, after

molecular dynamics (MD) simulations. (a) protegrin-I; (b) θ-defensin; (c) tachyplesin; (d)

polyphemusin; (e) gomesin; (f) androctonin; (g) YGKRGF; (h) AGGKGF. The barrels of

polyphemusin and tachyplesin exited zwitterionic pores during the simulations, and those images

are omitted. White: nonpolar; blue: basic; red: acidic; green: polar residues. These were the

conformations of the peptides after the water-equilibrated monomers were arranged as octamer

barrels, subject to 200 ps of MD in water and minimized, inserted into pre-formed toroidal pores

in 26-Å-thick implicit membranes, and subject to 2 ns of MD followed by minimization. The

shading and lines represent the boundaries of the toroidal pores in 26-Å-thick membranes. In the

top views, the shading represents the inner and outer boundaries of the toroidal pore region; in

the side views, the shaded volume represents the pore interior, and the lines represent the

membrane edges. Figure created using VMD 1.9 [276].

Although the oligomers of tachyplesin remained relatively coherent throughout the simulations

in most conditions, some conditions resulted in exit from the membrane, even when the transfer

energy was favorable (Tables 2.12.5, Figure 2.7). For heptamer and octamer -barrels of

tachyplesin, transfer energies were favorable in anionic and unfavorable in neutral pores. The

tetramer arcs and decamer -barrels had unfavorable transfer energies to both neutral and anionic

pores. The octamer barrel in an anionic pore was the only condition in which tachyplesin

remained at the pore interface throughout the simulation (Figure 2.5c); the octamer barrel exited

a neutral pore within 50 ps of simulation onset. Tachyplesin tetramer arcs also exited the pore

rapidly, but whereas the tetramer drifted away from a neutral membrane, it remained as a

54

coherent arc with its hydrophobic side adjacent to the anionic membrane’s surface. Similarly, the

heptamer barrel of tachyplesin left a neutral pore rapidly (Table 2.1), whereas it migrated to the

membrane surface of an anionic pore and remained there while the barrel opened. Decamer

barrels of tachyplesin exited the pore region rapidly in all conditions (Table 2.1).

Polyphemusin oligomers generally displayed unstable behavior in pores, with distortions

observed in all conditions (Table 2.1). Polyphemusin’s pattern of favorable vs. unfavorable

binding energies was exactly the same as that for tachyplesin: the octamer and heptamer -

barrels had favorable and unfavorable binding energies for anionic and neutral pores,

respectively, and tetramer arcs and decamer barrels had unfavorable transfer energies in all pores

(Tables 2.22.5, Figure 2.7). Polyphemusin oligomers left the pore in all conditions except for

the octamer in an anionic pore, where the barrel moved toward the surface of the membrane with

only the membrane-facing end of the barrel remaining coherent; the solvent-facing end became

distorted, and the ends of the monomers spread apart (Figure 2.5d). The polyphemusin barrels

did not degrade completely; although there was some distortion, the assemblies remained

somewhat coherent after migrating into the solvent. The tetramer arc in an anionic pore,

however, became highly distorted and remained with the hydrophobic side adjacent to the

membrane surface.

The simulations of gomesin oligomers revealed favorable transfer energies in all conditions

except the heptamer barrel in a neutral pore (Tables 2.22.5, Figure 2.7). The gomesin octamer

-barrel remained bound to both neutral and anionic pore interfaces throughout the simulations,

but some monomers migrated to the center of the pore and away from the pore interface (Figure

2.5e), indicating partial collapse of the octamer barrel. The tetramer arcs of gomesin remained

bound to both neutral and anionic pores throughout the simulation; however, the arcs did not

55

remain coherent, reconfiguring as groups of three and one monomers that remained orthogonal to

the membrane surface (Figure 2.6b). The heptamer and decamer barrels also remained bound to

the pore throughout the 2-ns MD simulations, but barrel collapse and distortion occurred in the

heptameric and decameric conditions, respectively (Table 2.1).

56

57

Figure 2.6. Top and side views of the minimized final conformations of tetramer arcs of peptides

in toroidal pores of optimal radius in zwitterionic and 30% anionic membranes, after molecular

dynamics (MD) simulations. (a) protegrin-I; (b) gomesin; (c) androctonin; (d) YGKRGF; (e)

AGGKGF. The corresponding arcs of polyphemusin, tachyplesin, and θ-defensin exited the

membrane region during the simulation and are omitted. White: nonpolar; blue: basic; red:

acidic; green: polar residues. These were the conformations of the peptides after the water-

equilibrated monomers were arranged as octamer barrels, subject to 200 ps of MD in water and

minimized, inserted into pre-formed toroidal pores in 26-Å-thick implicit membranes, and

subject to 2 ns of MD followed by minimization. The shading and lines represent the boundaries

of the toroidal pores in 26-Å-thick membranes. In the top views, the shading represents the inner

and outer boundaries of the toroidal pore region; in the side views, the shaded volume represents

the pore interior, and the lines represent the membrane edges. Figure created using VMD 1.9

[276].

For all oligomeric states, androctonin showed unfavorable and favorable transfer energies for

neutral and anionic pores, respectively (Tables 2.22.5, Figure 2.7). Although the conformation

of androctonin was altered from its native one to facilitate barrel formation (which may have led

to the high standard deviation in the ΔW values), the androctonin oligomers maintained at least

some coherence throughout the 2 simulations (Figure 2.5f, Figure 2.6c), and they generally

remained bound to the pore throughout the simulation: the only condition in which androctonin

left the pore was the decamer from a neutral membrane. However, distortion of the androctonin

oligomers occurred in all conditions: there was moderate distortion of the octamer barrels, and in

the heptamer and decamer barrel conditions in which androctonin did not leave the pore, the

58

barrels collapsed, indicating a lack of ring stability (Table 2.1). The tetramer arcs of androctonin

reconfigured as barrel-like structures (Figure 2.6c).

Figure 2.7. Average membrane transfer energies (<ΔW>; kcal/mol) of tetramer arcs and

heptamer, octamer, and decamer barrels of peptides from water to toroidal pores (k = 15 Å, pore

radii as described in Tables 2.2–2.5) from 2-ns simulations. * The oligomer left the pore during

the course of the simulation; values were estimated using the time window 3–22 ps. ΔW values

in conditions in which the oligomer remained inside the pore were estimated using the window

1001–2000 ps. Error bars represent ± 1 SD.

YGKRGF and AGGKGF showed remarkably stable behavior in all simulated conditions. They

remained bound to both neutral and anionic pores throughout the 2-ns simulations for all

59

oligomeric states (Table 2.1). In several conditions, there was little distortion of the arc/barrel

conformation: the octamer barrels and tetramer arcs remained intact, with the monomers of the

AGGKGF tetramer tilting in an anionic pore (Figures 2.5gh, 2.6de). Although the heptamer

barrels of YGKRGF and AGGKGF both remained within the pore, the heptamer barrel of

YGKRGF opened even with Ro = 10 Å. The decamer barrel of AGGKGF became distorted in an

anionic pore, but the decamer of YGKRGF remained stable and retained its shape throughout

simulations in both neutral and anionic pores. These peptides’ transfer energies were negative to

both neutral and anionic pores in all conditions (Tables 2.22.5, Figure 2.7); in fact, they had the

most favorable ΔW values of any peptides studied.

Discussion

The results indicate that β-barrels and arcs of θ-defensin, tachyplesin, gomesin, polyphemusin,

and androctonin are not as stable as those of protegrin. In many cases, we observed exit from the

pore, significant distortions of the barrels, and/or unfavorable binding energies. None of them

had transfer energies as favorable as those of protegrin under any conditions. However, two

combinatorial library peptides surpassed protegrin in this measure. We discuss the results in light

of available experimental data.

One reason for the stability of protegrin and the synthetic peptides as β-barrels is that they fit a

pattern of amphipathicity wherein charged/polar residues are predominantly found at the ends or

turn of the hairpin and nonpolar residues in the middle of one face of the hairpin. These peptides

have no polar/charged residues facing the membrane in barrel configuration, whereas ach of the

other studied AMPs have at least one. The desolvation cost of a polar side chain sequestered

among nonpolar membrane lipids likely contributes significantly to the instability of these

peptides in pores. Further, θ-defensin and androctonin lack sufficient large hydrophobic residues

60

facing the membrane for efficient membrane binding in β-barrel conformation. Another factor

could be the amount of charge in the pore: protegrin has one Arg residue facing the pore,

whereas tachyplesin and polyphemusin have two in a more central location, which might create

electrostatic repulsion. There is experimental evidence that tachyplesin [212, 213] and

androctonin [216] orient parallel to the membrane surface instead of adopting a transmembrane

orientation, and a carpet mechanism was suggested for gomesin at high peptide concentrations

[77]. The inability of polyphemusin to cause dye leakage from vesicles led other authors to

propose an internalization mechanism that does not involve pore formation [260].

All peptides considered here show less favorable binding in neutral than 30% anionic pores. This

is not surprising, considering that they are all positively charged. A practical goal in antibiotic

development is to target microbes’ anionic membranes while leaving mammalian cells’

zwitterionic membranes intact. Thus, if the ΔW values in zwitterionic and anionic membranes

reflect antimicrobial and hemolytic activity, respectively, and if the β-barrel mechanism is valid,

one would expect a correlation between these values and the experimental biological activities.

Among the natural AMPs studied, protegrin had the most favorable ΔW values in both anionic

and neutral pores. Thus, the other natural AMPs are expected to be less hemolytic than protegrin.

This seems mostly consistent with available experimental data: θ-defensin is not hemolytic

[266], and gomesin is less hemolytic than protegrin, notably in the high-concentration regime

[272]. Androctonin’s relatively low hemolytic activity levels are in accordance with its relatively

hydrophilic region facing the membrane and moderately unfavorable ΔW in neutral pores. On

the other hand, tachyplesin’s hemolytic activity is comparable to protegrin’s [269], and

polyphemusin is more hemolytic than protegrin [214], so alternative explanations are needed to

61

rationalize these findings, such as toroidal pore stabilization without peptide assembly into a

well-defined structure.

It is also instructive to review the relationship between ΔW in anionic pores and activity against

bacteria [188]. Because there are many species of bacteria against which the activity levels of

several of these peptides have been tested, we select Staphylococcus aureus (SA) and

Escherichia coli (EC) as examples of Gram-positive and Gram-negative bacteria, respectively.

Protegrin has exhibited a range of observed MIC values: one study observed MICs of 30 M

against both EC and SA using a broth dilution technique [254]; however, another study using the

same technique observed an MIC of 4.6 M for EC [277], and another study observed MICs of

2.9 and 5.8 M for EC and SA, respectively [219]. On the low end, a study using a radial

diffusion assay measured MICs of 0.620.68 and 0.820.87 M for EC and SA, respectively

[264]. For θ-defensin, researchers have observed MIC values of 1.0 and 2.1 M for EC and SA,

respectively [266]. For tachyplesin, the results for SA have depended on whether the peptide was

natural or synthetic and the strain of bacteria used; MIC values have ranged 1.45.5 M, and

values for EC ranged 0.71.4 M regardless of whether the peptide was natural or synthetic

[270]. For polyphemusin, the MIC values were 2.6 M for both EC and SA. In the study in

which gomesin was originally isolated, its MIC against EC ranged 0.41.6 M, depending on

strain, and that for SA was 1.63.15 M [272]. The same study measured MIC values for

androctonin of 315 M and 1530 M, respectively, for EC and SA [272]. YGKRGF and

AGGKGF have minimal sterilizing concentrations (MSC) of 2.1 M [231] and 1.0 M [230],

respectively, against SA, and both peptides have MSC values of 0.5 M against EC [230]. If we

adopt the low-end values for protegrin [266], then a correlation is observed between the ΔW

values of the octamer barrels in anionic pores and activity against both types of bacteria, with the

62

same peptides (protegrin, YGKRGF, and AGGKGF) having the most negative ΔW values and

the lowest MIC values. The other peptides, with higher ΔW values of the octamer barrel in

anionic pores, also have higher MIC values.

The binding energy values for YGKRGF and AGGKGF may be misleading, because those

quantities do not contain any conformational, translational, or rotational entropy contributions.

These peptides’ lack of disulfide bonds makes constraining them into hairpin conformations

entropically costly; thus, their pore binding energies are likely significantly less favorable than

those we computed. Nevertheless, the fact that the negative control (AGGKGF) exhibits less

favorable binding energies than the positive control is gratifying. The observed stability of these

peptides’ pore structures contrasts with the experimental observation of graded and incomplete

dye leakage from vesicles [230, 231], which suggested a carpet or “sinking raft” mechanism

(although that could occur as a mechanistic step toward pore formation; [230, 231]). A high

energetic barrier (enthalpic for dissociation and entropic for association) may separate the

barrel/arc states from the rest of the configurational space; this would need to be considered in a

complete computational characterization. It would also be interesting to synthesize disulfide-

bonded versions of the combinatorial library peptides and test their activity.

Mechanisms other than membrane pore formation are possible for many of the peptides

investigated here. For example, polyphemusin might bind to divalent cation binding sites on

target cells’ lipopolysaccharide molecules to penetrate and permeabilize the membrane [214].

Tachyplesin activates annexin labeling and caspase-3 activation [278]. Not only gomesin [279]

but also protegrin itself [278] causes calcium influx through L-type channels and generates

reactive oxygen species. Gomesin’s mechanism may depend on concentration, as lower

concentrations promote apoptosis, whereas higher concentrations result in cell membrane

63

disruption [278]. Thus, higher concentrations of peptide may make pore formation more likely.

There were certain conditions in which non-protegrin AMPs remained within the pore without

becoming distorted, such as the tachyplesin octamer in an anionic membrane; it may be worth

investigating whether pore formation occurs at high concentrations of tachyplesin, with

monomers orienting parallel to the membrane as a first step.

The initial structures in this study had zero tilt angle for the monomers, which implies zero β-

sheet twist in the barrel [280]. Unconstrained simulations did not produce significant systematic

change in tilt, except local distortions. However, many of the tetramer arcs spontaneously

rearranged into configurations with substantial tilt angles. Thus, an energetic barrier might

prevent barrel reconfiguration. It would be useful to consider starting structures with tilted β-

strands in subsequent studies. Membrane thickness was also not varied in this study: all

simulations used a thickness of 26 Å. In addition, we used a generalization regarding the lipid

composition of mammalian and bacterial cells, assuming zwitterionic and 30% anionic lipids in

those respective cases. However, those values are not exact for all cells, so it would be useful to

investigate how changes in membrane charge affect the results. Further, we did not

systematically investigate pore curvature, mainly studying toroidal pores with k = 15 Å, whereas

in the previous study of protegrin, we considered cylindrical pores in addition to toroidal pores

with k = 10, 15, and 20 Å. We did vary the pore radius, but it may be useful to simulate even

smaller radii than 10 Å for arcs. Indeed, tetramer arcs of many of these peptides seemed to curl

naturally into incomplete cylindrical conformations with tilted monomers, some of which had

significantly smaller radii than the corresponding octamer barrels. Additional oligomeric states

could also be considered. These additional model parameter variations could supplement the

results obtained in this study.

64

3. Computational prediction of the optimal oligomeric state for membrane-inserted β-

barrels of protegrin-1 and related mutants

Published as: [3]

Summary

Protegrin-1 is a widely studied 18-residue β-hairpin antimicrobial peptide. Evidence suggests

that it acts via a β-barrel pore formation mechanism, but the exact number of peptides

comprising the pore state is unknown. In this study, we performed molecular dynamics

simulations of β-barrels of protegrin and three related mutants (v14v16l, v14v16a, and r4n) in

NCNC parallel topology in implicit membrane pores of varying radius and curvature for

oligomeric numbers 6–14. We then identified the optimal pore radius and curvature values for all

constructs and determined the total effective energy and the translational and rotational entropic

losses. These, along with an estimate of membrane deformation free energy from experimental

line tension values, provided an estimate of the overall energetics of formation of each pore state.

The results indicated that oligomeric numbers 7–13 are generally stable, allowing the possibility

of a heterogeneous pore state. The optimal oligomeric state for protegrin is the nonamer, shifting

to higher numbers for the mutants. Protegrin, v14v16l, and r4n are stable as membrane-inserted

β-barrels, but v14v16a seems much less so because of its decreased hydrophobicity.

Introduction

Antimicrobial peptides (AMPs) are small, usually cationic peptides that provide innate

immunological defenses against diverse microbial agents [19, 233] and are actively being

explored as the basis for novel antibiotics [236]. Although the identity of the AMP-induced

lethal event is still debated [34, 35], there is strong evidence that these peptides act on

membranes, as they have the ability to permeabilize lipid bilayers in vivo [23-25] and in vitro

65

[26-28] independent of amino acid chirality [29, 30]. AMPs have been proposed to disrupt cell

membranes by a variety of mechanisms, including micellization and disintegration [237] or pore

formation [31]. The pores may vary from cylindrical (lined by peptides [81]) to toroidal (lined by

lipid headgroups [52]). Intermediate forms between prototypical cylindrical and toroidal pores

may also be possible [118].

The 18-residue β-hairpin AMP protegrin-1 is the best-studied member of the β-hairpin AMP

family [204]. Neutron diffraction experiments have indicated that protegrin forms toroidal pores

[69], and its pore-forming activity has been characterized via methods such as oriented CD,

solid-state NMR spectroscopy, and atomic force microscopy [49, 61, 253]. Although protegrin’s

pore state cannot be visualized directly, there is evidence that it forms a -barrel composed of

810 monomers, causing membrane leakage [205]. Nevertheless, its topology in the active state

has been the subject of contradictory evidence: although one solid-state NMR study indicated the

presence of NCCN parallel topology [205], solution NMR of protegrin-1 in detergents has shown

NCCN antiparallel topology [206]. The latter topology has also been found for protegrin-3 in

DPC micelles [207].

Protegrin has also been the subject of several computational studies encompassing various steps

of membrane association and pore formation (for a review, see [203]). Monomers and dimers

have been simulated [220, 257-259], along with β-barrel models of both octamers [221, 223,

224] and decamers [59]. These computational investigations have encompassed simulations

representing the membrane and solvent atoms with varying levels of detail, from all-atom

(explicit solvent; [220]) to coarse-grained [162] to implicit solvent [2, 224] simulations (Chapter

2). All-atom simulations have provided potentials of mean force of putative middle steps in

66

membrane poration, such as insertion of a protegrin monomer into a lipid bilayer [226] and

protegrin dimerization in different environments [96].

In our laboratory’s previous work, we modeled three possible topologies of this -barrel, finding

that the NCNC parallel configuration is most stable [224] because it allows immersion of the

hydrophobic cluster of each peptide into the nonpolar membrane interior. We have also created

barrel models of several other β-hairpin AMPs, finding that none form β-barrels as stable as

those of protegrin, with some being completely unstable [2] (Chapter 2). Implicit and explicit

simulations in our laboratory have shown that protegrin’s NCNC parallel topology may form

stable, tilted arcs in lipid membranes rather than maintaining a strict transmembrane orientation,

especially in anionic membranes [100]. Although our laboratory has only investigated octamers

[224], the actual number of peptides comprising protegrin oligomeric -barrels is unknown, with

at least one study suggesting a larger pore radius (R; [219]). Further, structural similarity to

protegrin was noted when Jang et al. modeled from 12- to 36-mers of an Aβ peptide, finding that

16- to 24-mers were most stable in their 30–50-ns simulations [222].

The goal of the present study is to develop methodology for determining the optimal oligomeric

state of β-barrel forming peptides, starting with protegrin and closely related mutants. A similar

approach for helical peptides was published previously [189]. We use our implicit membrane

approach [108, 112, 186], whereby pores are characterized by their radius (R) and curvature (k).

In this study, we vary those parameters and the oligomeric number (the latter between 6 and 14).

The optimal oligomeric state is selected based on the lowest free energy per monomer, including

contributions from peptide–peptide and peptide–solvent interactions, rotational and translational

entropy (both from a homogeneous solvent environment and association with membrane), and

membrane deformation. This methodology is applied to protegrin, a more hydrophobic mutant

67

(v14v16l) that is more active against several bacterial strains [281], a less hydrophobic variant

(v14v16a) that is expected to be less stable and/or less active, and a mutant in which Arg4 is

replaced by asparagine (r4n), removing the positive charge inside the putative pore lumen. The

results are used to obtain general insights about sequence–structure relationships in AMP pore

formation and the origin of protegrin’s toxicity.

Materials and Methods

Energy Function

The simulations in this chapter were conducted using Implicit Membrane Model 1 (IMM1;

[112]), which is an extension of Effective Energy Function 1 (EEF1) [108] that represents

membrane–water systems using solvation parameters dependent on vertical position. Vertical

dependence of the dielectric is also introduced to account for strengthening of electrostatic

interactions within the membrane:

; – √ (1)

where fi and fj represent

z′ = |z| / (T / 2) (2)

where T is the hydrophobic thickness of the membrane and z = 0 is the membrane midplane.

Switching function f describes the phase transition, and n (equal to 10) controls the transition

steepness. The adjustable parameter a was set to 0.85 to generate membrane binding energies

similar to experimental values [112]. Only neutral (zwitterionic) membranes were considered in

this work.

IMM1 can also accommodate pores [117, 186], whose shape is determined by the dependence of

the radius on vertical position:

R = R0 + k × z′2 (3)

68

where R0 is the pore radius at the membrane center, R is the radius at a given z-level, and k

determines pore curvature. For example, R0 = 15 Å and k = 0 defines a cylindrical pore of radius

15 Å, whereas R0 = 15 Å and k = 20 Å defines a toroidal pore of radii 15 Å and 35 Å at the

center and rims, respectively. The switching function now also depends on horizontal distance

from the z axis:

;

; ; √ (4)

where r is radial distance from the pore center. According to the various pore dimensions used,

we chose the m value to ensure a radial transition width of 6 Å, the same as that in the vertical

direction. The program CHARMM [262] version c41a1 was used for these simulations.

Initial Structures

The solution NMR coordinate file for the protegrin-1 monomer, isolated from porcine leukocytes

[204], was downloaded from the Protein Data Bank (PDB; entry 1PG1). The first model was

used. In addition, we formed several mutants to examine the effects of structural variations on

the free energy components and the optimal oligomeric state. We examined the v14v16l mutant

studied by Gottler et al. [281], the v14v16a mutant, and the r4n mutant. All mutants were

produced by importing the PDB file into MacPyMOL 1.7 [267] and using the mutagenesis

wizard. The sequences of all structures are shown in Table 3.1.

Table 3.1. Sequences of investigated peptides

Name Sequence

Protegrin RGGRLCYCRRRFCVCVGR-NH2

v14v16l RGGRLCYCRRRFCLCLGR-NH2

v14v16a RGGRLCYCRRRFCACAGR-NH2

r4n RGGNLCYCRRRFCVCVGR-NH2

69

Molecular Dynamics Simulations

To equilibrate the monomers, EEF1 was used to set up systems with implicit water solvent at

298.15 K, and then the coordinates of each monomer file were minimized using the adopted

basis Newton–Raphson algorithm (used for all energy minimizations for 300 steps). Then, for

each structure, 200 ps of MD simulation was performed in water using the Verlet integrator with

a time step of 2 fs. Subsequent minimization yielded the final monomeric structures used to

construct the -barrels (Figure 3.1). All molecular graphics were produced using MacPyMOL

1.7 [267].

Figure 3.1. Conformations of monomers after simulations in water, before barrel formation and

pore insertion. When the peptides are arranged inside the pores in parallel NCNC configuration,

the left and right sides face the membrane and pore lumen, respectively. The atoms are

represented as sticks and colored according to amino acid residue. Cysteine: yellow; arginine:

purple; glycine, alanine, tyrosine: green; valine: sky blue; phenylalanine, leucine: blue;

asparagine: red.

70

The final monomeric structures were then arranged as -barrels of oligomeric numbers 614 by

orienting them vertically, rotating them around the z axis to orient the backbones, translating

them by 1120 Å along the x axis, and then arranging them as evenly spaced cylinders by

rotation around the z axis. The more hydrophobic side was oriented to face the membrane, and

the backbones were placed in approximately H-bonded positions. Minimization was then applied

with harmonic constraints on all backbone atoms (k = 5.0), and then the appropriate

intermolecular H-bonds were imposed via energy wells using CHARMM’s NOE constraint

facility, with kmin, rmin, kmax, and rmax values of 1.0, 1.8, 5.0, and 2.3, respectively. Minimization

was applied without backbone constraints, and then 100 ps of MD simulation was run in water to

equilibrate the barrel, followed by another minimization. The NOE constraints were then

released.

After the barrels underwent brief dynamics in water, the resulting structures were each inserted

into the centers of implicit 26-Å-thick IMM1 membranes containing pores with different values

of R and k, and 5-ns production MD simulations were performed to examine the effects of R and

k values on the energetics and kinetic stability of the pre-formed -barrels. To obtain relatively

broad data regarding pore size and shape, we initially used R values from 6 Å to 28 Å in 2-Å

increments and k values of 5, 10, 15, and 20 Å for all oligomeric numbers of protegrin from 6 to

14 (i.e. 12 × 4 5-ns simulations for each oligomeric state). After each production simulation,

minimization provided the final post-MD image of the -barrel. The R value with the most

favorable combination of Wbarrel and ΔW for protegrin was then chosen as the reference pore size

for the mutant simulations. The production MD simulations for mutants were identical to those

for protegrin, but they were only performed at the six R values closest to the reference pore size,

and only at k values of 10, 15, and 20, for each oligomeric number.

71

For each peptide, after the results for R values with increments of 2 Å had been tabulated, we

identified the radius with the most energetically favorable combination of Wbarrel and ΔW as the

putative optimal radius and then ran four additional production MD runs at R = 1 Å above and

below the putative optimal radius and k = 15 and 20 Å. The results from all runs together were

synthesized to make final judgments about the stability of each oligomeric state. Production

simulations of 5 ns were found to be sufficient for convergence. Longer simulations of example

protegrin oligomers gave results within the statistical error. Simulations using different random

seeds, run as checks, also gave very similar results. The total length of all simulations run for

protegrin and the mutants was 5.31 μs.

To estimate the free energy of formation of the oligomeric β-barrels, it was necessary to compare

the energy of the pore state with that of a monomer in water. Therefore, the water simulations

mentioned above were extended to 2 ns, and Wbarrel was calculated for the monomers every 1 ps

throughout the last 1 ns of the simulation (1000 frames).

Calculations of Thermodynamic Stability

The free energy of pore formation can be split into peptide and membrane deformation

contributions:

ΔGpore = ΔGpep + ΔGmem (5)

The contributions to ΔGpep (i.e., the peptide contributions) include the effective energy change

(which comprise peptide–peptide, peptide–water, and peptide–lipid interactions), the loss of

translational (TΔStrans

) and rotational (TΔSrot

) entropy upon barrel formation in solution, and the

loss of translational ( ) and rotational (

) entropy from membrane binding:

ΔGpep = Wbarrel − Wmono − TΔStrans

− TΔSrot

− −

(6)

72

where Wbarrel is the effective energy per monomer in the β-barrel pore state and Wmono that in

water. TΔStrans

and TΔSrot

were calculated as the respective entropic losses of subunit A with

respect to the entire oligomer in solution following [282]. and

were calculated

for an example system, the optimal protegrin octamer, following [183, 283]:

∫

∫ [

]

[ (

) ∫

[

]] ∫ [

]

+

(7)

where zmax and zmin are the maximum and minimum values of the barrel’s center of mass in z,

Ƥ(z) is the probability density of the vertical position of the barrel’s center of mass, and Ƥ(Ƴ) is

the probability density of orientations Ƴ in the membrane simulation. Ƥ0(z) and Ƥ(Ƴ) are the

corresponding theoretical uniform probability distributions. The above orientational distribution

is assumed to be independent of z, so that Ƥ(z,Ƴ) = Ƥ(z)*Ƥ(Ƴ). Here Ƴ represents θ, the tilt

angle of the barrel axis with respect to the bilayer normal, and dƳ = sinθdθ. is split into

two components: the first accounts for the translational restriction from that of a theoretical

particle in a 1-M solution, which would traverse a cubic region with edge length d = 11.84 Å.

The second accounts for the nonuniform probability distribution within the restricted range.

Wbarrel, ΔW, TΔStrans

, and TΔSrot

were calculated by averaging values obtained every 5 ps

throughout the last 2.5 ns of the simulation (500 frames), whereas and

were

calculated by averaging values obtained every 5 ps throughout the last 4.5 ns of the simulation

(900 frames). To calculate and

, we used 20 bins in z and 60 bins in θ.

73

The final contribution to the free energy of pore formation is the membrane deformation free

energy, ΔGmem. An approximate estimate of this quantity can be made using experimental values

of the line tension γ, with ΔGmem = 2πRγ [284]. In this paper, we use two γ values, 0.15 and 0.45

kT/Å, to represent the high and low ends of realistic ΔGmem values. Using these values, the pore

formation free energy ranges 14–42 kcal/mol at R = 15 Å.

An additional quantity calculated was the membrane insertion energy (ΔW), estimated by

averaging Wbarrel at the barrel’s position in the pore and then subtracting the energy of the same

conformation in water. ΔW provides a rough estimate of the favorability of the membrane-

embedded barrel compared with the same barrel in water. In a stable pore state, this quantity is

negative.

Wbarrel and ΔW are calculated from trajectory frames spaced 2500 simulation steps apart for the

oligomers. The variation in these values is expressed in terms of both standard deviation (SD)

and SD / √ , where n is the number of measurements. If the samples were fully

independent, then the standard error of the mean would be SD / √ , but because the frames

may not be adequately spaced, they may not be fully independent, and that number must be

corrected for autocorrelation in the sample. Thus, the sample’s calculated standard error needs to

be multiplied by f, where f = √ , and ρ is the autocorrelation coefficient. To

gain systematic insight into the statistical error, we used a FORTRAN implementation of the

block-averaging method of Flyvbjerg and Petersen [285] on the data values from some of our

simulations. That method samples the overall dataset at various frequencies to form different

block sizes, and the average block variance is graphed according to block size. The results are

expected to plateau at a certain level once the decorrelation time has been reached. At sampling

frequencies approaching that of our trajectory file, we did not observe any significant decline in

74

the average block variance. Therefore, although SD and SD / √ are shown as the maximum

and minimum theoretical sizes of the error bars, respectively, the results from the block-

averaging method indicate that the true standard errors are closer to SD / √ .

Results

Throughout the 5-ns simulations, at the optimal R and k values, the oligomeric β-barrels tended

to remain stable at their positions within the pore. Figure 3.2 illustrates the minimized final

conformations in pores of optimal R and k for all peptides and even oligomeric numbers. The

6mer and 14mer showed distortions for all peptides besides r4n, the only one lacking the bulky,

positively charged Arg inside the pore lumen. All other β-barrels remained in stable

conformations at their location in the pore for the duration of the simulations.

The mean Wbarrel results for the monomers in water were the following (in parentheses: SD, SD /

√ ): protegrin, −385.65 (8.56, 0.27); v14v16l, −387.25 (9.50, 0.30); v14v16a, −394.49

(8.77, 0.28); r4n, −385.47 (8.65, 0.27). The Wbarrel, ΔW, and ΔGpore results are tabulated at the

optimal pore R and k values for each metric in Tables 3.1–3.4 for protegrin, v14v16l, v14v16a,

and r4n, respectively. Figure S1a–d from [3] shows Wbarrel, ΔW, ΔGpep, and ΔGpore at γ = 0.15 for

protegrin, and Figure 3.3 shows ΔGpore at γ = 0.45. Figures S2–S4 from [3] and 3.4–3.6 show the

corresponding information for v14v16l, v14v16a, and r4n, respectively. Figure 3.7a–b shows

ΔGpore per monomer at the optimal k values for each oligomeric number and structure at γ = 0.15

and 0.45, respectively. Figures 3.8–3.9 show interaction energies for protegrin, v14v16l, and r4n.

For the protegrin octamer in its optimal pore state, the total calculated results for and

were 1.13 kcal/mol and 3.75 kcal/mol, respectively. During the membrane simulation,

the translational range of the peptide in the z direction was restricted to 2.81 Å, and θ was

restricted to roughly [0,9°] and [171°,180°], with both distributions nonuniform within the

75

observed range. Additional calculations using other peptides and oligomeric numbers yielded

very similar results, so we extrapolated the protegrin octamer’s and

results to

all systems, dividing according to the number of peptides per barrel. The ranges of TΔStrans

and

TΔSrot

were approximately 3–6.5 kcal/mol and 0.8–3.2 kcal/mol, respectively. TΔStrans

and TΔSrot

per monomer generally increase with oligomeric number, weighing against the formation of

higher oligomeric numbers.

76

Figure 3.2. Configurations of even-numbered oligomeric β-barrels after pore simulations. The

vertical axis labels denote oligomeric number. The upper representations are side views, and the

77

lower views look directly down on the x–y plane from above. The backbones are shown as

cartoons and colored as “chainbows.”

Protegrin

Table 3.2 shows the Wbarrel, ΔW, ΔGmem, and ΔGpore values at the optimal R and k values for

protegrin (depiction of components in Supplementary Material). There is generally good

correspondence between the optimal values of Wbarrel, ΔW, and ΔGpore, but there are some

differences, especially between Wbarrel and ΔW. ΔGmem favors smaller R values but higher

oligomeric numbers. (The same is true for all peptides studied.) The optimal ΔW value was −3 to

−3.5 kcal/mol per monomer across all oligomeric numbers. Its magnitude was larger than that of

ΔGmem for γ=0.15, but smaller for γ=0.45.

ΔGpore of protegrin is shown as a function of R at γ = 0.45 in Figure 3.3. For most oligomeric

numbers, there is a unique R at which the minimum ΔGpore per monomer is found, which

increases with oligomeric number. However, for certain oligomeric numbers, such as 10 and 14,

multiple values of R give a similarly low ΔGpore. Individual energy components are less

discriminatory of the optimal oligomeric state than the total ΔGpore is (see Supplementary

Material from [3]). The ΔGpore values at the optimal R and k values are favorable for all

oligomeric numbers and both investigated γ values. They indicate that oligomeric number 9 is

the most energetically favorable state, although all oligomeric numbers from 7 to 13 seem

plausible. The association between ΔGpore and oligomeric number is shown for γ = 0.15 and 0.45

in Figure 3.7.

78

Table 3.2. Protegrin: Optimal R and k values for each oligomeric number according to three

indicators: total effective energy (Wbarrel), membrane binding energy (ΔW), and total energy of

barrel formation (ΔGpep). Total free energies of pore formation (ΔGpore) with line tension (γ) =

0.15 and 0.45 are also listed. All values per monomer.

Figure 3.3. Protegrin: Variation of pore formation free energy per monomer with pore radius for

each oligomeric number. Line tension γ = 0.45.

v14v16l

Optimal W barrel value Optimal ΔW value Optimal ΔGpep value ΔGmem ΔGmem ΔGpore ΔGpore

# R k W SD SD/√(n-1) R k ΔW SD SD/√(n-1) R k ΔGpep γ = .15 γ = .45 γ = .15 γ = .45

6 9 15 -424.04 4.39 0.20 10 20 -3.10 0.44 0.020 9 15 -30.53 1.41 4.24 -29.11 -26.29

7 12 15 -426.77 3.38 0.15 12 15 -3.12 0.31 0.014 12 15 -32.70 1.62 4.85 -31.09 -27.86

8 12 15 -426.51 3.33 0.15 13 20 -3.40 0.27 0.012 12 15 -32.92 1.41 4.24 -31.51 -28.68

9 13 20 -426.09 3.08 0.14 15 20 -3.15 0.32 0.014 13 20 -34.70 1.36 4.08 -33.34 -30.61

10 17 20 -426.05 2.78 0.12 16 20 -3.59 0.21 0.009 16 20 -32.33 1.51 4.52 -30.82 -27.81

11 17 15 -426.1 2.86 0.13 17 20 -3.51 0.23 0.010 17 15 -32.04 1.46 4.37 -30.58 -27.67

12 19 15 -427.06 2.86 0.13 19 20 -3.37 0.23 0.010 19 15 -32.54 1.49 4.48 -31.05 -28.07

13 20 20 -425.84 2.77 0.12 21 20 -3.19 0.21 0.009 20 20 -32.50 1.45 4.35 -31.05 -28.15

14 20 20 -424.8 2.51 0.11 23 20 -3.26 0.2 0.009 21 20 -33.47 1.41 4.24 -32.06 -29.23

79

Results for the mutant v14v16l are shown in Table 3.3 and Figure 3.4. Although the basic pattern

of results is similar to that for protegrin, as intuitively expected, the increased hydrophobicity of

the membrane-facing region leads to more favorable values of ΔGpore and ΔW, the latter of which

is now competitive with ΔGmem even for the larger line tension value (Table 3.3).

Although oligomeric number 14 showed the optimal ΔGpore value for v14v16l (Table 3.3), that

configuration became distorted over the course of the simulation, with one peptide migrating

inside the barrel to the edge of the pore lumen (Figure 3.2). If we restrict attention to regular

barrels, the optimal oligomeric number is 12. Thus, the v14v16l mutant shows increased

favorability of higher-numbered oligomers compared with protegrin. The origin of this trend is

explored in the Interaction Energies subsection below.

Table 3.3. v14v16l: Optimal R and k values for each oligomeric number according to three

indicators: total effective energy (Wbarrel), membrane binding energy (ΔW), and total energy of

barrel formation (ΔGpep). Total free energies of pore formation (ΔGpore) with line tension (γ) =

0.15 and 0.45 are also listed. All values per monomer.

Optimal W barrel value Optimal ΔW value Optimal ΔGpep value ΔGmem ΔGmem ΔGpore ΔGpore

# R k W SD SD/√(n-1) R k ΔW SD SD/√(n-1) R k ΔGpep γ = .15 γ = .45 γ = .15 γ = .45

6 10 20 -428.17 3.71 0.17 10 20 -4.91 0.36 0.016 10 20 -33.01 1.57 4.71 -31.44 -28.29

7 14 20 -427.04 3.37 0.15 13 20 -4.51 0.39 0.017 14 20 -32.60 1.88 5.65 -30.72 -26.95

8 12 15 -429.23 3.1 0.14 13 20 -3.89 0.34 0.015 12 20 -33.87 1.41 4.24 -32.46 -29.63

9 15 20 -430.72 3.06 0.14 15 20 -4.94 0.21 0.009 15 20 -35.30 1.57 4.71 -33.73 -30.59

10 15 20 -429.37 2.94 0.13 16 15 -4.69 0.28 0.013 15 20 -33.93 1.41 4.24 -32.52 -29.69

11 19 20 -430.03 2.87 0.13 18 20 -4.75 0.24 0.011 19 20 -34.40 1.63 4.88 -32.77 -29.51

12 18 20 -430.16 2.8 0.13 19 20 -4.78 0.22 0.010 18 20 -34.97 1.41 4.24 -33.56 -30.73

13 19 20 -428.25 2.93 0.13 20 20 -4.46 0.2 0.009 16 20 -33.55 1.16 3.48 -32.39 -30.07

14 22 20 -431.58 2.56 0.11 22 20 -4.44 0.21 0.009 22 20 -37.19 1.48 4.44 -35.71 -32.75

80

Figure 3.4. v14v16l: Variation of pore formation free energy per monomer with pore radius for

each oligomeric number. Line tension γ = 0.45.

v14v16a

The corresponding data for v14v16a are shown in Table 3.4 and Figure 3.5. For this peptide, the

ΔW values are uniformly weaker than those for the other peptides investigated (optimal values >

−2 kcal/mol for all oligomeric numbers; Table 3.4). This was expected, as the v → a mutation

decreases the hydrophobicity of the membrane-facing region. Unlike the case with the other

peptides studied, pore formation is predicted to be unfavorable by comparing ΔW with ΔGmem, as

ΔGmem exceeds ΔW for all oligomeric numbers and both line tension values. As a result, the

ΔGpore values for v14v16a are less favorable than those for the other peptides, although they are

favorable overall due to peptide-peptide interactions (see Discussion).

Figure 3.5 lacks a clear relationship between the optimal ΔGpore value and oligomeric number,

but ΔGpore does become more favorable with increasing oligomeric number and is lowest for the

81

13mer (Figure 3.7). However, the patterns in the data are generally not as strong for this mutant

as for the other peptides.

Table 3.4. v14v16a: Optimal R and k values for each oligomeric number according to three

indicators: total effective energy (Wbarrel), membrane binding energy (ΔW), and total energy of

barrel formation (ΔGpep). Total free energies of pore formation (ΔGpore) with line tension (γ) =

0.15 and 0.45 are also listed. All values per monomer.

Optimal W barrel value Optimal ΔW value Optimal ΔGpep value ΔGmem ΔGmem ΔGpore ΔGpore

# R k W SD SD/√(n-1) R k ΔW SD SD/√(n-1) R k ΔGpep γ = .15 γ = .45 γ = .15 γ = .45

6 15 20 -424.75 3.56 0.16 13 20 -0.93 0.3 0.013 10 20 -20.71 1.57 4.71 -19.14 -16.00

7 12 20 -432.17 3.60 0.16 12 20 -1.18 0.29 0.013 10 20 -29.57 1.35 4.04 -28.22 -25.53

8 13 15 -430.90 3.54 0.16 15 15 -1.21 0.28 0.013 13 15 -29.69 1.53 4.59 -28.16 -25.10

9 17 20 -432.67 3.25 0.15 16 20 -1.66 0.24 0.011 17 20 -31.37 1.78 5.34 -29.59 -26.03

10 16 20 -432.14 2.92 0.13 18 15 -1.19 0.28 0.013 16 20 -30.59 1.51 4.52 -29.08 -26.07

11 19 20 -432.71 2.78 0.12 19 20 -1.67 0.18 0.008 19 20 -30.63 1.63 4.88 -29.00 -25.75

12 20 20 -433.15 2.60 0.12 20 20 -1.47 0.22 0.010 20 20 -31.21 1.57 4.71 -29.64 -26.50

13 22 10 -434.91 2.82 0.13 22 20 -1.50 0.17 0.008 21 20 -32.76 1.52 4.57 -31.24 -28.19

14 16 20 -433.24 2.50 0.11 24 20 -1.04 0.15 0.007 22 10 -30.92 1.48 4.44 -29.44 -26.48

82

Figure 3.5. v14v16a: Variation of pore formation free energy per monomer with pore radius for

each oligomeric number. Line tension γ = 0.45.

r4n

The data for r4n are shown in Table 3.5. The optimal ΔW value trends at −3 to −4 kcal/mol,

slightly stronger than the values for wild type protegrin. Like protegrin, the magnitude of ΔW lies

between those of ΔGmem for the two values of line tension. The results, like those of protegrin,

are clarified by factoring in TΔStrans

, TΔSrot

, ,

, Wmono, and ΔGmem (Figure 3.6);

the minimum value of ΔGpore is found at oligomeric number 10. As with v14v16l, this mutation

induces a shift to higher-order oligomers (see Interaction Energies below).

Table 3.5. r4n: Optimal R and k values for each oligomeric number according to three indicators:

total effective energy (Wbarrel), membrane binding energy (ΔW), and total energy of barrel

formation (ΔGpep). Total free energies of pore formation (ΔGpore) with line tension (γ) = 0.15 and

0.45 are also listed. All values per monomer.

Optimal W barrel value Optimal ΔW value Optimal ΔGpep value ΔGmem ΔGmem ΔGpore ΔGpore

# R k W SD SD/√(n-1)R k ΔW SD SD/√(n-1) R k ΔGpep γ = .15 γ = .45 γ = .15 γ = .45

6 12 10 -424.41 3.7 0.17 13 20 -3.96 0.39 0.017 11 20 -30.62 1.73 5.18 -28.89 -25.44

7 12 15 -424.45 3.34 0.15 12 15 -3.49 0.35 0.016 12 15 -31.15 1.62 4.85 -29.53 -26.30

8 14 15 -427.05 3.4 0.15 13 20 -3.7 0.35 0.016 13 15 -32.99 1.53 4.59 -31.46 -28.40

9 15 20 -424.61 2.94 0.13 15 20 -3.36 0.24 0.011 16 20 -32.03 1.68 5.03 -30.35 -27.00

10 17 20 -427.65 2.73 0.12 16 20 -3.73 0.23 0.010 14 20 -34.99 1.32 3.96 -33.67 -31.03

11 18 15 -427.6 2.86 0.13 17 20 -3.55 0.26 0.012 18 15 -33.68 1.54 4.63 -32.14 -29.05

12 18 20 -426.15 2.7 0.12 19 20 -3.65 0.2 0.009 19 20 -33.10 1.49 4.48 -31.61 -28.63

13 21 20 -426.86 2.71 0.12 21 30 -3.43 0.19 0.009 21 20 -33.78 1.52 4.57 -32.26 -29.21

14 22 15 -426.25 2.67 0.12 22 15 -3.22 0.22 0.010 22 15 -32.21 1.48 4.44 -30.73 -27.77

83

Figure 3.6. r4n: Variation of pore formation free energy per monomer with pore radius for each

oligomeric number. Line tension γ = 0.45.

84

Figure 3.7. Total energy of formation per monomer (ΔGpore) by oligomeric number for protegrin,

v14v16l, v14v16a, and r4n. a) line tension γ = 0.15. b) γ = 0.45.

Interaction Energies

On the basis of their structure, r4n and v14v16l might be intuitively expected to exhibit

comparable β-barrel formation tendencies to protegrin, but the mutants show greater relative

favorability of higher-order β-barrel oligomers. (Although v14v16a showed a similar pattern, its

85

pore formation is relatively less favorable overall.) To explore the origin of this shift, we

calculated average interaction energies between several residue pairs selected on the basis of

both structural features and empirical observation for protegrin, v14v16l, and r4n at 500 evenly

spaced time points throughout the last half of the 5-ns production length simulations at the

optimal R and k values for all oligomeric numbers.

The (unfavorable) interaction energies between residues 1 (Arg) and 4 in protegrin and r4n are

illustrated in Figure 3.8. For protegrin, this interaction energy became steadily more unfavorable

with increasing oligomeric number, but for r4n, this interaction energy shows higher overall

variance, with several higher oligomers having the most favorable interactions. Specifically,

from the nonamer to the decamer, a substantially larger drop is observed for r4n than protegrin,

which could partially account for the stabilization of the decamer in the former. The interaction

energies for several other investigated residue pairs showed patterns that were similar between

protegrin and r4n (data not shown).

The corresponding interaction energy comparison for residues 4 and 16 in protegrin and v14v16l

is shown in Figure 3.9. This interaction is less unfavorable for protegrin than v14v16l at

oligomeric numbers 6–10, but that trend disappears at higher oligomeric numbers. Specifically,

from the nonamer to the dodecamer, this interaction energy increases substantially for the wild

type but remains about the same for the mutant. The direct patterns of interaction between

residues 1 and 16 and between residues 14 and 16 did not show convincing patterns (data not

shown).

86

Figure 3.8. Interaction energies between residues 1 and 4 of protegrin and r4n for all oligomeric

numbers. [kcal/mol]

Figure 3.9. Interaction energies between residues 4 and 16 of protegrin and v14v16l for all

oligomeric numbers. [kcal/mol]

87

Discussion

In this work, we have comprehensively accounted for the contributions to the free energy of a

membrane-inserted β-barrel by the AMP protegrin-1 and several mutants thereof, aiming to

predict the optimal oligomeric state. Approximations have been necessary for some of these

components, including the use of the simplified IMM1 and line tensions to obtain membrane

deformation free energies; the latter was assumed to depend only on R and not k, which is likely

untrue.

The ability to determine the optimal R and oligomeric number was greater when the various

components of ΔGpore were combined (Tables 3.1–3.4) than when any single one of them was

examined alone (Supplementary Material from [3]). The results for protegrin indicate that the

nonamer is optimal, although its difference in stability from similar oligomers is small,

suggesting that a heterogeneous ensemble of oligomeric states is most likely. This observation

aligns with previous computational [221, 223, 224] and experimental [205] suggestions of an 8–

10-peptide barrel. Certain studies [219], however, have suggested substantially larger protegrin

pores, which may correspond to more complex, non-barrel states.

For all mutants examined (v14v16l, v14v16a, and r4n), we observed increased favorability of

higher oligomers. This was not intuitively expected in terms of structure and could be partially

explained by analyzing interresidue interactions. Gottler et al. [281] found that the v14v16l

mutant had higher antimicrobial activity, stronger binding to 3:1 PC:PG vesicles, and an

approximately doubled lipid binding stoichiometry of wild type protegrin, which could be

attributed to more extensive oligomerization. This is in agreement with our results, although our

observed shift in oligomeric state seems too small to account for the experimental data fully.

88

For a membrane-inserted barrel to be stable, the free energy of transfer from solution to

membrane needs to be favorable. This free energy includes the (favorable) effective energy

change ΔW , the (unfavorable) membrane deformation free energy ΔGmem, and entropic losses

and

. The latter are roughly 0.4–0.8 kcal/mol per monomer for the systems

considered here. ΔGmem was estimated at either 1.4–1.6 or 4.1–4.9 kcal/mol per monomer at γ =

.15 and .45, respectively. The optimal ΔW per monomer was largely independent of oligomeric

number. The ΔW values per monomer for r4n (−3.2 to −4.0 kcal/mol) were slightly larger those

for protegrin (−3.1 to −3.6 kcal/mol), whereas those for v14v16l and v14v16a had higher (−3.9

to −5.0) and lower (−1 to −1.5 kcal/mol) magnitudes, respectively. Thus, the favorable and

unfavorable contributions were roughly balanced for all peptides except v14v16a, whose

insertion is clearly unfavorable. Membrane insertion for protegrin is marginal in the neutral

membranes studied here, in agreement with its known preference for anionic membranes [281].

Despite the marginal values of membrane insertion free energy, the overall ΔGpore values were

highly negative due to peptide–peptide interactions upon barrel formation. The magnitude of

these interactions seems to be overestimated by the implicit solvent model; otherwise, the barrels

would be stable in water, which does not seem to be the case.

This study provided predictions that can be tested experimentally. The mutant v14v16a is not

predicted to insert into neutral membranes; therefore, it should have no hemolytic activity. The

r4n mutant is predicted to form barrels slightly more favorably—and with a slightly larger

number of monomers—than protegrin. In addition, the absence of Arg 4’s positive charge inside

the pore lumen due to the R → N mutation may alter the pore’s conductance and ion selectivity,

which could be explored by electrophysiology measurements.

89

The present calculations were performed in neutral (zwitterionic) membranes. Additional

computations in anionic membranes would be necessary to evaluate barrel formation in more

bacterial-like membranes. Further, we only considered barrels of parallel NCNC topology,

following the conclusions of previous work [224]. The antiparallel NCCN topology also inserts

favorably into membranes, and its oligomerization properties should also be examined. Finally,

atomistic simulations of different oligomeric states could be performed to test the implicit

membrane approach. The present methodology may also be applied to determine the optimal

pore dimensions and oligomeric state for other putative β-barrel-forming peptides.

90

4. Transmembrane pore structures of β-hairpin antimicrobial peptides by all-atom

simulations

In press at Journal of Physical Chemistry B

Summary

Protegrin-1 is an 18-residue β-hairpin antimicrobial peptide (AMP) that has been suggested to

form transmembrane β-barrels in biological membranes. However, the precise topology and

structure of the β-barrel state is unknown, and alternative structures have also been proposed.

Here, we performed multimicrosecond, all-atom molecular dynamics simulations of various

protegrin-1 oligomers on the membrane surface and in transmembrane topologies. We also

considered an octamer of the β-hairpin AMP tachyplesin. The simulations on the membrane

surface indicated that protegrin dimers are stable, while trimers and tetramers break down

because they assume a bent, twisted β-sheet shape that is unstable on a flat surface. Tetrameric

arcs in membranes of different composition remained stably inserted, but the pore water was

displaced by lipid molecules. Unsheared protegrin β-barrels opened into long, twisted β-sheets

that, nevertheless, surrounded stable aqueous pores, whereas tilted barrels with sheared hydrogen

bonding patterns were stable in most topologies. A third type of observed pore consisted of

multiple small oligomers surrounding a small, partially lipidic pore. Tachyplesin showed less

tendency to oligomerize than protegrin: the octameric bundle resulted in small pores surrounded

by 6 peptides as monomers and dimers, with some peptides returning to the membrane surface.

The results imply that multiple configurations of protegrin oligomers may produce aqueous pores

and illustrate the relationship between topology and putative steps in protegrin-1’s pore

formation. However, the long-term stability of these structures needs to be assessed further.

Introduction

91

Protegrin-1 (hereafter called protegrin [204]) is the best-studied member of the β-hairpin family

of antimicrobial peptides (AMPs), which are small, usually cationic peptides that provide

defenses against several classes of microbial agents [19, 233]. Because AMPs permeabilize lipid

bilayers in vitro [26-28] and in vivo [23-25], the lethal event is thought to be disruption of

bacterial membranes by either detergent-like membrane dissolution (i.e., the carpet mechanism;

[32]) or formation of pores [31], which may vary from cylindrical (lined by peptides [81]) to

toroidal (lined by lipid headgroups [52]) to intermediate forms [118]. AMPs’ cationic charge

imparts selectivity for negatively charged bacterial membranes [33]. Although alternative

mechanisms of AMP action have been proposed [34, 35], including clustering of anionic lipids

[36] and targeting of intracellular molecules, such as DNA [37-39], the overall evidence for

AMP-induced membrane pores is strong (e.g., [67]).

Protegrin’s interaction with biological membranes has been studied with a variety of biophysical

techniques. Neutron diffraction experiments suggested toroidal pores [69], and oriented CD

showed the transition between surface and inserted states [286]. Solid-state NMR provided some

evidence that protegrin may form β-barrels containing 8–10 monomers in NCCN parallel

topology [205] (see Topology below). However, solution NMR in detergents showed NCCN

antiparallel topology for protegrin-1 [206], protegrin-3 [207], and protegrin-5 [287]. The same

solid-state NMR study also showed that 75% of the hairpins have homodimerized N and C

strands in an anionic membrane, implying that the β-barrel state is the dominant component of a

heterogeneous mixture. Polyethylene glycol molecules with hydrodynamic radii up to 9.4 Å

allowed membrane permeabilization, whereas ones with radii of 10.5 Å blocked

permeabilization [205]; therefore, protegrin’s pore diameter was below 21 Å. However, another

92

study that investigated protegrin-induced dextran leakage suggested a pore diameter of at least

3–4 nm at high salt concentrations [219].

An atomic force microscopy study of protegrin-1 and other AMPs in large unilamellar vesicles

and solid-supported phospholipid bilayers showed that protegrin acts as a line-active agent,

lowering interfacial bilayer tensions and promoting changes in membrane morphology [61]. A

more recent study of 13 AMPs found that line activity correlates with an imperfectly

amphipathic secondary structure that positions positively charged arginine sidechains near the

membrane interface [118, 156, 288]. A solid-state NMR study of protegrin-1 in 12-carbon 1,2-

dilauroyl-sn-glycero-3-phosphatidylcholine (DLPC) bilayers observed a tilt angle of 55°, also

noting that positively charged side chains tilted into close proximity to membrane lipid

headgroups [289].

Protegrin has been the subject of numerous computational studies; for reviews, see [1, 203]

(Chapter 1). Simulations have been performed of monomers and dimers [220, 221, 258, 259] and

β-barrel models of octamers [2, 221, 223, 224] (Chapters 2–3) and decamers [3, 59] (Chapter 3).

To illustrate potential mechanistic steps, previous all-atom simulations provided potentials of

mean force of protegrin monomer insertion into a lipid bilayer [226] and dimerization in

different environments [96].

Previous work from our laboratory included both all-atom and implicit membrane simulations.

Our thermodynamic investigation of several octameric protegrin-1 β-barrel topologies in pre-

formed implicit pores indicated maximal favorability of the NCNC parallel topology [224],

which allows the more hydrophobic face of each peptide to contact the membrane. Other

simulations showed that the NCNC parallel tetramer has intrinsic curvature compatible with

tilted arcs [100], which may form or contribute to membrane pores. A 300-ns all-atom simulation

93

of a NCNC parallel tetrameric arc showed a stable aqueous pore [100]. Pre-formed β-barrels of

several similar β-hairpin AMPs in NCNC parallel topology were found to be much less stable

than those of protegrin [2] (Chapter 2). We also studied protegrin NCNC parallel β-barrels of 6–

14 peptides: although the nonamer had the lowest energy, a range of pore sizes 7–13 peptides

had relatively consistent favorability [3] (Chapter 3). Those results were consistent with the

predictions of the solid-state NMR study [205], which suggested an octamer, but inconsistent

with [219], which suggested a larger pore.

Despite the large amount of computational work on protegrin, both the final pore state and the

pathway to that state remain uncertain. This paper describes all-atom molecular dynamics (MD)

simulations of protegrin oligomers performed using the Anton 2 supercomputer. We also check

the results against those for β-hairpin AMP tachyplesin [249], whose β-barrel formation was

assessed as unstable (in contrast to that of protegrin) in a previous implicit membrane

investigation [2] (Chapter 2). To examine whether and how protegrin oligomerizes on membrane

surfaces en route to pore formation, we performed one group of simulations of protegrin

oligomers on 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC):1-palmitoyl-2-oleoyl-

sn-glycero-3-phospho-(1'-rac-glycerol) (POPG) bilayer surfaces. For these, we simulated dimers,

trimers, and tetramers in the NCNC parallel, NCCN antiparallel, and mixed topologies (for a

guide to topology, see the Methods below). To examine how oligomeric multiplicity, topology,

and peptide configuration may be associated with pore formation and stability inside the

membrane, we also studied several protegrin systems inside all-atom membranes: tetrameric and

octameric protegrin bundles (see Topology below), octameric and decameric β-barrels, and one

or two tetrameric arcs. The octameric β-barrel was simulated in NCNC parallel and mixed

topologies; the single tetrameric arcs were in NCNC parallel, NCCN antiparallel, or mixed

94

topologies; and the systems with two tetrameric arcs were NCNC parallel or NCCN antiparallel.

We also generated β-barrels with sheared, tilted peptides (NCNC parallel, NCCN antiparallel,

NCCN parallel, and mixed topologies) and a system with four tilted dimers arranged close

together. The results provide insights into the putative steps of protegrin’s pore formation and

show their relationship with topology, yielding information on the likelihood of possible pore

formation pathways.

Materials and Methods

Topology

Dimers of a β-hairpin can combine in six different topologies, depending on which β-strands (N

or C) associate and the relative positioning of the turns. These topologies are NCNC, NCCN, and

CNNC, each of which can have the peptides’ turn region and ends oriented parallel or

antiparallel to each other. In a closed β-barrel, the NCCN and CNNC topologies are identical. A

characteristic that affects membrane binding ability is whether the topology allows the

hydrophobic sides of all hairpins (i.e., the side opposite the disulfide bridges) to point in the

same direction. The NCNC parallel and NCCN antiparallel topologies satisfy this requirement,

whereas NCCN parallel does not [224]. This study investigates up to decamers in NCNC

parallel, NCCN parallel, NCCN antiparallel, and mixed topologies. The mixed topology was

inspired by a recent crystallization study of a θ-defensin AMP, which found a mixed-topology

trimer wherein one dimer had NCNC parallel topology and the other NCCN antiparallel

topology (Figure 4.1) [211].

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Figure 4.1. Possible topologies of protegrin dimerization. A) NCNC parallel; B) NCCN

antiparallel; C) NCCN parallel. Brackets outline the boundaries of mixed topology trimer and

tetramer. Yellow bridges represent disulfide bonds. Arrows point N→C.

We also distinguish our AMP systems inside lipid bilayers according to their initial hydrogen

bonding pattern. “Transmembrane bundles” are peptide assemblies placed closely together but

without initial hydrogen bonds imposed between peptides (Figure 4.2a). The peptides in those

systems could associate freely during all-atom MD simulations. Second, we simulated

“unsheared” β-barrels (Figure 4.2b), in which the peptides began all-atom MD with hydrogen

bonds imposed in fully transmembrane orientation, flush with one another. In a third type of

system, sheared β-barrels (Figure 4.2c), the initially imposed β-sheet hydrogen bonds between

peptides were shifted by two residues per dimer, tilting the β-barrel’s peptides. A hydrogen

bonding shift of two residues was only employed once per dimer because preliminary implicit

membrane MD simulations indicated that β-barrels with shearing every monomer were highly

unstable. Further, our simulations indicated that units of unsheared dimers were stable, whereas

sheared dimers dissociated rapidly (see Results below).

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Figure 4.2. Initial hydrogen bonding patterns of protegrin octamers. A) Bundle, front half: no

initial hydrogen bonding between peptides; B) Unsheared β-barrel, front half: initial hydrogen

bonding between flush transmembrane peptides; C) Sheared β-barrel, front half: hydrogen

bonding shifted by two residues per pair of peptides, introducing a tilt. Sidechains omitted for

clarity. Where applicable, topology is NCNC parallel. NH atoms, CO atoms, and β-barrel

hydrogen bonds shown in white, red, and magenta, respectively.

Preliminary implicit solvent simulations

Preliminary implicit solvent simulations were conducted using Effective Energy Function 1

(EEF1; [108]) and Implicit Membrane Model 1 (IMM1; [112]) using CHARMM version c41a1

[262]. The membranes with anionic pores were set up using mBuild, an in-house utility that

constructs anionic implicit membranes at 5 different focusing levels with a final resolution of

0.5×0.5×0.5 Å [119]. The lipid bilayer’s dielectric properties were represented so that εmemb,

εhead, and εwater (the dielectric constant inside the membrane, the interfacial region, and water)

were 2, 10, and 80, respectively [119]. Headgroup width D was set to 3.0 Å to place the

boundary around the phosphate group. The ion accessibility factor was set so that the ions, which

were taken as monovalent with radius 2.0 Å, could not penetrate below the phosphate groups.

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The positive and negative charge layers were separated by 1.0 Å, hydrocarbon core thickness

was set to 26 Å, and area per lipid was set to 68 Å2. An anionic fraction of 30% was used,

approximating a typical bacterial membrane [239]. The membranes were embedded in cubic

boxes filled with implicit 0.1-M aqueous salt solution.

A description of the simulated systems is presented in Table 4.1. The protegrin oligomers on the

membrane surface and all of the transmembrane bundles were assembled geometrically from the

coordinate files for protegrin-1 and tachyplesin, which were downloaded from the Protein Data

Bank (PDB) (protegrin: 1PG1 [204], sequence RGGRLCYCRRRFCVCVGR-NH2; tachyplesin:

1WO0, sequence KWCFRVCYRGICYRRCR-NH2 [a tachyplesin sequence without C-terminal

amidation was also investigated]) and imported into CHARMM with all charged residues in

ionization states corresponding with pH ~7 and all disulfide bonds patched. Copies of the

peptides were oriented about the origin and then subjected to translations and rotations until they

reached the appropriate configurations. The sheared dimer and tetramer had the peptides offset

by two residues along the hairpin axis to form an appropriately shifted hydrogen bonding pattern.

The mixed topology for trimers and tetramers both consisted of one dimer in NCNC parallel and

one dimer in NCCN antiparallel topology: NCNCCN(anti) (trimer), NCNCNCCN(anti)

(tetramer). Then, without constraints in water, the peptides’ energy was minimized using the

adopted basis Newton–Raphson algorithm (used for all implicit minimizations for 300 steps), but

no dynamics were applied. The configuration was then imported into the membrane builder

feature of CHARMM-GUI [290] to add lipids, water molecules, and ions for all-atom

simulations, as described below.

For the systems with β-barrels and one or two tetramer arcs, the production runs of which were

run inside explicit membranes, the first step was implicit MD equilibration of a protegrin

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monomer in water. After importing the PDB file for protegrin-1 into CHARMM, the peptide’s

energy was minimized in water, followed by 200 ps of MD simulation with the Verlet integrator

(time step: 2 fs, temperature: 298.5 K; used for all implicit simulations, following [2] [Chapter

2]). Subsequent energy minimization then yielded the monomeric structure used for

oligomerization.

We then constructed a single tetrameric arc or a decameric or octameric β-barrel by geometric

transformation to space the copies approximately 10 Å apart and application of potential wells to

enforce hydrogen bonding, followed by further equilibration MD of the tetramers in water.

During equilibration, we imposed intermolecular β-sheet hydrogen bonds using CHARMM’s

NOE facility, following [2] (Chapter 2). To generate the tilted structure of the sheared β-barrels,

the hydrogen bonding pattern was shifted by two residues only once for each pair of peptides,

and the other half of the hydrogen bonding junctions remained as in an unsheared β-sheet.

Table 4.1. Systems simulated in all-atom studies. All membranes contained 180 lipids unless

noted. Bundle: a tightly packed assembly of peptides with the hydrophobic face outwards but no

imposed hydrogen bonding. Tilted: the dimer’s major axis was reoriented 30° from

transmembrane. POPC: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine. POPE: 1-Palmitoyl-

2-oleoyl-sn-glycero-3-phosphoethanolamine. POPG: 1-palmitoyl-2-oleoyl-sn-glycero-3-

phospho-(1'-rac-glycerol). CL: cardiolipin. Chol: cholesterol. For a guide to topology, see

Methods. Mixed topology: one dimer NCNC parallel and the other dimer NCCN antiparallel.

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After imposition of the β-sheet hydrogen bonds, further equilibration MD was run for 200 ps,

followed by minimization. The NOE constraints were removed, and then the individual tetramers

and octamers were placed with the more hydrophobic side facing an anionic implicit pore with

Peptides Topology Membrane composition Time run

Protegrin oligomers on membrane surface

Dimer NCNC parallel 75% POPC:25% POPG 5 μs

Dimer NCCN antiparallel 75% POPC:25% POPG 5 μs

Dimer (sheared) NCNC parallel 75% POPC:25% POPG 5 μs

Trimer NCNC parallel 75% POPC:25% POPG 5 μs

Trimer NCCN antiparallel 75% POPC:25% POPG 0 μs

Trimer Mixed 75% POPC:25% POPG 5 μs

Tetramer NCNC parallel 75% POPC:25% POPG 1 μs

Tetramer NCCN antiparallel 75% POPC:25% POPG 0 μs

Tetramer Mixed 75% POPC:25% POPG 5 μs

Tetramer (sheared) NCNC parallel 75% POPC:25% POPG 3 μs

Protegrin non-sheared barrels

Octamer NCNC parallel 75% POPC:25% POPG 10 μs

Octamer Mixed 75% POPC:25% POPG 4 μs

Decamer Mixed 75% POPC:25% POPG 3 μs

Protegrin sheared barrels

Octamer NCNC parallel 75% POPC:25% POPG 5 μs

Octamer Mixed 75% POPC:25% POPG 5 μs

Octamer NCCN parallel 75% POPC:25% POPG 5 μs

Octamer NCCN antiparallel 75% POPC:25% POPG 5 μs

Protegrin arcs

Tetramer NCNC parallel 100% POPC (294 lipids) 3 μs

Tetramer NCNC parallel 70% POPE:30% POPG (270 lipids) 2 μs

Tetramer NCNC parallel 70% POPC: 30% Chol (100 lipids) 2 μs

Tetramer NCCN antiparallel 75% POPC:25% POPG 2 μs

Tetramer Mixed 75% POPC:25% POPG 5 μs

Two tetrameric arcs NCNC parallel 75% POPC:25% POPG 8 μs

Two tetrameric arcs NCCN antiparallel 75% POPC:25% POPG 3 μs

Protegrin bundles

Tetramer N/A 100% POPC (72 lipids) 9 μs

Tetramer N/A 70% POPE:22% POPG:8% CL 4 μs

Octamer N/A 75% POPC:25% POPG 5 μs

Octamer (four tilted dimers) NCNC parallel 75% POPC:25% POPG 5 μs

Tachyplesin bundles

Tachyplesin octamer (amidated) N/A 75% POPC:25% POPG 5 μs

Tachyplesin octamer (non-amidated) N/A 75% POPC:25% POPG 5 μs

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radius Ro = 12 Å and curvature k = 15 Å, the optimal pore geometry for protegrin octamers found

in [3] (Chapter 3). The decamer barrel employed the optimal decameric implicit pore geometry

of Ro = 16 Å and k = 20 Å [3] (Chapter 3). Implicit MD simulations were then run for 2 ns. A

final minimization then yielded the tetrameric arc and β-barrel structures imported into the

membrane builder feature of CHARMM-GUI. For the systems containing two tetrameric arcs, a

single tetramer was oriented about the origin, and then two diametrically opposed copies were

translated 10 Å away from each other with both hydrophobic faces outward.

To assemble the system with four tilted protegrin dimers, the final configuration of the 5-μs

production run of the NCNC parallel dimer on the membrane surface was imported into

CHARMM, and we tilted the dimer’s major axis 30° from the vertical axis, translated the entire

dimer 10 Å horizontally so that the more hydrophobic side faced outward, and rotated three

copies by 90°, 180°, and 270° about the vertical axis to distribute all four evenly around the pore

edge. The coordinates were then imported into CHARMM-GUI to add lipids, water molecules,

and ions for all-atom simulations, as described below.

All-atom simulations

We imported the systems generated above into CHARMM-GUI’s membrane builder with the

goal of employing 180 total lipids and approximately 50,000 total atoms, configuring the water

thickness above and below the membrane accordingly (overall system size: approximately

81×81×78 Å), except that during preliminary simulations, the number of lipids varied as noted in

Table 4.1. 0.15 M potassium chloride was added to neutralize excess charges. All-atom

simulations employed the CHARMM C36 force field [291] and the TIP3P water model.

The equilibrations were performed using NAMD 2.11 [292] with an initial time step of 1 fs.

After harmonic constraints (k = 1 kcal/mol/Å2) were applied to the water atoms, ions,

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phosphorous atoms, and peptide backbone atoms, we conducted 20,000 steps of energy

minimization followed by 7 ps of heating to 303 K. The constraints on the lipids were released in

another 100-ps equilibration step, followed by a 500-ps one in which the constraints on waters

and ions were also released. Then, we introduced pressure control using the modified Nosé-

Hoover barostat with Langevin dynamics, and the backbone constraints were scaled down in

increments of 0.2 for 200 ps. Then, we ran a 1-ns unconstrained equilibration with a time step of

1 fs, followed by a final 5-ns initial production step (also in NAMD) with a time step of 2 fs.

The production simulations were carried out on the Anton 2 supercomputer [191] at the

Pittsburgh Supercomputing Center using the Multigrator integration framework [293]. We used

VMD to generate Anton 2 input files from the equilibrated NAMD output and parameter files,

and then we used the viparr program to add the force field information to the Anton input files.

Particle motions, thermostat updates, and the Martyna Tuckerman and Klein (MTK) barostat

were applied using Multigrator every 1, 24, and 240 steps, respectively. Long-range

electrostatics were calculated using the Gaussian Split Ewald method [294], and the cutoff values

for electrostatic interactions were automatically calculated by the Anton setup procedure. We ran

the full production simulations for the lengths indicated in Table 4.1 with a 2 fs time step, saving

coordinates every 1.08 ns.

VMD 1.9.2 [276] was used for trajectory visualization and to wrap the trajectories according to

periodic boundary conditions so that all peptides appeared in the same image. CHARMM [262]

was used to calculate pore radius, number of lipid headgroups near the center of the bilayer,

number of water molecules inside the pore, and interaction energy between peptides over the last

1 μs. The numbers of lipid headgroups and water molecules inside the bilayer were found as

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those in the volumes within 5 and 10 Å of the membrane center, respectively. We used VMD

[276] and PyMol [267] to produce molecular graphics of the resulting configurations.

Results

Protegrin oligomers on the membrane surface

To determine likely early intermediates of protegrin oligomerization, we simulated protegrin

dimers, trimers, and tetramers on the membrane surface. Two types of dimers are distinguished:

flush (completely aligned) and sheared (with the shifted hydrogen bonding pattern). Both of the

flush dimers (NCNC parallel [Figure 4.3a] and NCCN antiparallel topologies) were stable on the

membrane surface for 5 μs. No significant events were recorded in either of the trajectories, and

the peptides did not insert below the level of the membrane surface in any of the dimer (or other

oligomer) simulations. The NCNC parallel sheared dimer system started with the hydrogen

bonds between peptides shifted by two residues from a flush configuration. About 550 ns into the

simulation, the two peptides separated from each other on the membrane surface, not rejoining

for the remainder of the trajectory. Thus, in contrast to the flush dimers, the sheared dimer is

unstable on the membrane surface.

All trimers and tetramers were unstable on the membrane surface. In the NCNC parallel trimer,

one monomer flipped over, leaving the disulfide bonds of two adjacent monomers facing each

other, while the remaining dimer was stable. In the mixed topology trimer on the membrane

surface, one monomer dissociated from the end and separated at about 2.9 μs of simulation time,

whereas the remaining NCNC parallel dimer was stable. The NCNC parallel tetramer simulation

was stopped after 1 μs when the monomers on the ends dissociated within 100 ns, the central

dimer remaining stable. In the mixed topology tetramer on the membrane surface, one monomer

dissociated within 100 ns, whereas the fourth monomer dissociated from the central dimer at

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about 2.2 μs. The central dimer again remained stable throughout the production phase. This

pattern also held for the sheared NCNC parallel tetramer, which broke down in a similar fashion

within 650 ns (Figure 4.3b). These results indicate that surface trimers and tetramers were

unstable because their apparent tendency to curve and twist would have moved the edge

peptides’ surfaces away from the membrane surface.

No production simulation of the NCCN antiparallel trimer and tetramer was performed because

the oligomers broke apart on the membrane surface during equilibration despite repeated

attempts to create a stable structure. In these structures, the N-terminal side of one peptide is

close to the N-terminal side of another, bringing two tyrosine residues together. (In contrast, the

NCCN antiparallel sheared β-barrel, in which this problem may exist but is mitigated by the

shearing, was quite stable.)

Figure 4.3. Snapshots of representative protegrin oligomer systems on the membrane surface at

the end of the production phase of simulation, top views. (A) Dimer, NCNC parallel topology;

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(B) Tetramer, NCNC parallel topology. (Rainbow cartoons) peptides; (Orange spheres) lipid

headgroup phosphates within 5 Å of peptides. Lipid tails omitted for clarity.

Protegrin β-barrels

Unsheared (i.e., untilted, with hydrogen bonds aligned) β-barrels have been the most commonly

proposed final pore structure for protegrin (e.g., [205, 224]) and were investigated first. The

unsheared octameric β-barrel in NCNC parallel topology first tore into an open octameric β-sheet

by breaking apart at a single junction point within 150 ns. The sheet continued to tilt and twist

until the monomers on the edges of the sheet were almost parallel to the membrane surface,

coming into contact with the lipid headgroup region. Then, at about 4.7 μs, a single monomer

separated from the other seven and dissociated from the pore. That monomer had zero interaction

energies with the other seven peptides throughout the last 1 μs of simulation time. However, an

open pore surrounded by seven peptides remained through the end of the 10-μs production phase

(Figure 4.4a).

The mixed-topology octameric β-barrel also broke open into an octameric β-sheet at 2 μs. No

other significant events occurred until the simulation was stopped at 4 μs (Figure 4.4b). The pore

remained open and surrounded by eight peptides. Similarly, the mixed-topology decameric barrel

sheared apart at a single junction point within the first 25 ns. Then, at about 900 ns, the decamer

broke apart into a heptameric sheet and trimeric bundle (Figure 4.5). These two structures

surrounded a large, partially lipidic pore, which remained open until the end of the simulation.

The cause of the unsheared β-barrels’ breakage seems to involve the oligomers’ tendency to bend

and twist, which is not facilitated by the unsheared β-barrel configuration.

Seeing that the unsheared protegrin transmembrane β-barrels all broke apart into twisted β-sheets

during the long production simulations, we designed the sheared octameric β-barrel systems to

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achieve a tilted peptide configuration that would accommodate the β-sheet’s natural tendency to

twist. In preliminary implicit solvent simulations, we attempted to impose four shears by shifting

the hydrogen bonds by two residues once for each pair of peptides, but the NCNC parallel,

mixed, and NCCN antiparallel topologies spontaneously settled with only three total shears,

yielding a configuration of dimer→shear→dimer→shear→tetramer→shear→. The NCCN

parallel topology settled with four shears.

The NCNC parallel sheared β-barrel remained stable with an open pore for 5 μs (Figure 4.6a).

There was no sign of breaking during the simulation and the interaction energies between all

adjacent monomers were ≤ −57.61 ± 6.01 kcal/mol (mean ± SD) over the last 1 μs. The mixed

topology sheared β-barrel showed similar results to the NCNC parallel one, with the pore

remaining open and the barrel intact for 5 μs (Figure 4.6b). The interaction energies between

adjacent monomers were ≤ −47.54 ± 7.18 kcal/mol over the last 1 μs, indicating a stable β-barrel

at the end of the simulation.

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Figure 4.4. Snapshots of protegrin octameric unsheared β-barrel systems at the end of the

production phase of simulation. (A) NCNC parallel topology; (B) Mixed topology. (Rainbow

cartoons) peptides; (Orange spheres) lipid headgroup phosphates within 5 Å of peptides; (Red

and white lines) water. Lipid tails omitted for clarity.

107

The NCCN antiparallel sheared β-barrel also remained intact for 5 μs (Figure 4.6c). The

interaction energies between adjacent monomers were ≤ −62.00 ± 7.83 kcal/mol over the last 1

μs, indicating β-barrel stability. These results indicate that the insertion of shears into the β-barrel

structure satisfies the peptides’ intrinsic tendency to bend and twist in a way that the unsheared

β-barrel structure does not.

Figure 4.5. Snapshots of protegrin mixed topology decameric unsheared β-barrel system at the

end of the production phase of simulation. (Rainbow cartoons) peptides; (Orange spheres) lipid

headgroup phosphates within 5 Å of peptides; (Red and white lines) water. Lipid tails omitted for

clarity.

The octameric NCCN parallel sheared β-barrel, in which the hydrophobic clusters of the β-

hairpins point in alternating directions, was not stable as the other sheared β-barrels in our

simulations. The barrel gradually collapsed and the pore fully closed within 5 μs, with the

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monomers remaining close together in transmembrane orientation (Figure 4.6d). This difference

in results from the other topologies can be attributed to the fact that the peptide’s hydrophobic

side faces the membrane in all topologies except NCCN parallel.

Figure 4.6. Snapshots of protegrin sheared octameric β-barrel systems inside the membrane at

the end of the production phase of simulation. (A) NCNC parallel; (B) Mixed topology; (C)

NCCN antiparallel; (D) NCCN parallel. (Rainbow cartoons) peptides; (Orange spheres) lipid

headgroup phosphates within 5 Å of peptides; (Red and white lines) water. Lipid tails omitted for

clarity.

Protegrin tetramer arcs in the membrane

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Previous studies in our laboratory had indicated that protegrin arcs may form stable pores [100],

but the short length of those simulations did not allow definitive conclusions. The present

simulations of systems containing protegrin NCNC parallel tetramer arcs were conducted in

POPC, POPE/PG, and POPC/cholesterol to determine whether such arcs can surround stable

aqueous pores that are partially lined by lipids. The arcs remained inserted in the membrane, but

the arcs in POPE/PG and POPC/cholesterol deformed slightly, with three peptides forming a β-

sheet and the fourth reorienting to face the other three (Figure 4.7). None of those systems

generated stable, open pores: the simulations ended with lipids occupying space inside the pore

lumen instead of an aqueous channel. We also conducted simulations of NCCN antiparallel and

mixed topology tetramer arcs in POPC/PG, whose configurations remained stable within the

membrane throughout production phases of 2 and 5 μs, respectively, but as above, no aqueous

pore formed for either system. The above results indicate that a single protegrin tetrameric arc is

insufficient to support a stable pore: although the arcs themselves are relatively stable, the

presence of lipids in the pore region prevents stable aqueous conduction.

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Figure 4.7. Snapshots of representative tetramer arc systems inside the membrane at the end of

the production phase of simulation. (A) NCNC parallel, POPC; (B) NCNC parallel, POPE/PG;

(C) NCNC parallel, POPC/cholesterol; (D) NCCN antiparallel, POPC/PG. (Rainbow cartoons)

peptides; (Orange spheres) lipid headgroup phosphates within 5 Å of peptides; (Red and white

lines) water. Lipid tails omitted for clarity.

We then examined the possibility that the arcs are intermediates en route to β-barrel formation.

Therefore, we ran systems containing two transmembrane tetramer arcs (NCNC parallel or

NCCN antiparallel) placed opposite to each other with their centers of mass separated by 20 Å

and water molecules (but no lipids) initially filling the space between them. The arcs diffused in

the membrane throughout the trajectory without forming hydrogen bonds between the two

tetramers. Although very small aqueous channels remained until the simulations ended, no β-

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barrel formation was observed. This indicates that the pairs of protegrin arcs face a kinetic

barrier against combining into a complete β-barrel.

Protegrin bundles

We simulated transmembrane protegrin bundles without imposition of initial hydrogen bonding

to allow the peptides to associate freely and examine the possibility of more classical toroidal

pore structures observed with helical AMPs [52, 67, 68]. This provides a more unbiased look at

oligomerization than the systems beginning with β-barrels or arcs, as the bundle simulations

started farther from the putative final state. The protegrin bundles began as tightly packed

assemblies of monomers rotated with the more hydrophobic faces outward but with no hydrogen

bonding imposed.

We simulated tetrameric protegrin bundles in both pure POPC and POPC/PG membranes. In

POPC, three peptides came together without extensive hydrogen bonding between them, and the

fourth monomer sandwiched behind the third (Figure 4.8a). The peptides’ intermolecular

interaction energies were as strong as −34.00 kcal/mol (SD: 17.5); this indicates that the peptides

interacted moderately strongly despite the absence of a pore. In POPC/PG, the results were

similar: the four peptides rapidly associated into a trimeric arc and a monomer facing the

opposite direction (Figure 4.8b). There was no aqueous pore in either simulation, although the

peptides’ geometries outlined small pores of a few Å in diameter. Therefore, whether the initial

structure was a bundle or arc, four peptides were insufficient to stabilize aqueous channels for

long durations.

The octameric protegrin bundle associated into an NCNC parallel hexameric β-sheet and an

opposing, loosely associated dimer within 300 ns. The hexamer was curved and twisted, and it

and the dimer surrounded a stable, partially lipidic pore (Figure 4.9). The results were in

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accordance with those of the unsheared β-barrels and indicate that eight peptides are sufficient to

stabilize an open pore, whereas four peptides are insufficient.

As reported above, protegrin NCNC parallel dimers were stable on the membrane surface.

However, trimers and tetramers were not and sheared β-barrels were stable, whereas unsheared

ones broke open. Therefore, we arranged four tilted dimers around an aqueous pore to see how

they would associate and whether they would support an open pore. The trajectory showed one

dimer splitting from the other three and returning to the membrane surface at about 2.3 μs. At

about 4.3 μs, one of the three dimers remaining in the pore split up, with one monomer joining

another dimer to form a trimer and the other monomer returning to the membrane surface. A

dimer and a trimer were then left on opposite sides of a small, stable pentameric pore. Although

this situation continued until the end of the simulation (Figure 4.10), a plot of pore radius vs.

simulation time showed the pore continuing to shrink until the end of the production phase,

indicating that the pore may have been in the process of breaking down and destined to close

(see Pore Statistics below; Figure 4.12).

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Figure 4.8. Snapshots of protegrin tetrameric transmembrane bundle systems inside the

membrane at the end of the production phase of simulation. (A) POPC; (B) POPC/PG. (Rainbow

cartoons) peptides; (Orange spheres) lipid headgroup phosphates within 5 Å of peptides; (Red

and white lines) water. Lipid tails omitted for clarity.

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Figure 4.9. Snapshots of protegrin octameric transmembrane bundle inside the membrane at the

end of the production phase of simulation. (Rainbow cartoons) peptides; (Orange spheres) lipid

headgroup phosphates within 5 Å of peptides; (Red and white lines) water. Lipid tails omitted for

clarity.

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Figure 4.10. Snapshot of octameric protegrin system with four tilted dimers inside the membrane

at the end of the production phase of simulation. (Rainbow cartoons) peptides; (Orange spheres)

lipid headgroup phosphates within 5 Å of peptides; (Red and white lines) water. Lipid tails

omitted for clarity.

Tachyplesin bundles

Although tachyplesin has a similar β-hairpin AMP structure to protegrin, our previous implicit

simulations indicated that it is less stable as a β-barrel than protegrin [2] (Chapter 2). We

investigated bundles of tachyplesin for comparison to the data on protegrin. The reference

structure of tachyplesin contains C-terminal amidation, but we also investigated a structure

without C-terminal amidation to determine the effect of this modification on pore formation. The

tachyplesin bundle with C-terminal amidation exhibited some hydrogen bonding between

dimers, but no larger oligomers formed. The peptides’ intramolecular hydrogen bonding

structure remained intact, and at the end of 5 μs, an aqueous pore remained open (Figure 4.11a).

However, three peptides had reoriented to the membrane surface, and four monomers in the pore

all convened in one lipid leaflet, giving the impression that the pore may be en route to breaking

down. (Pore size vs. simulation time for this system is also plotted in Pore Statistics below.) The

dimer in the opposite lipid leaflet remained associated with the pore region but parallel to the

membrane surface.

The tachyplesin bundle without C-terminal amidation showed similar results to the amidated

one. The bundle associated only into monomers and dimers, which only loosely associated with

each other, and multiple peptides reoriented parallel to the membrane surface, possibly indicating

pore breakdown in progress. However, the peptides that remained inside the pore still surrounded

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an aqueous channel at the end of the simulation time (Figure 4.11b). The similarity of these

results indicates that amidation does not significantly affect tachyplesin’s pore formation ability.

Figure 4.11. Snapshots of octameric transmembrane bundle systems of β-hairpin antimicrobial

peptide tachyplesin inside the membrane at the end of the production phase of simulation. (A)

With C-terminal amidation; (B) Without C-terminal amidation. (Rainbow cartoons) peptides;

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(Orange spheres) lipid headgroup phosphates within 5 Å of peptides; (Red and white lines)

water. Lipid tails omitted for clarity.

Pore statistics

The pore radius, number of water molecules in the pore, and number of lipid headgroups

vertically within 5 Å of the membrane center for applicable systems with stable pores are shown

over the last 1 μs of the production phase in Table 4.2.

Table 4.2. Pore radius, number of water molecules in pore, and number of lipid headgroups

within 5 Å of the membrane center for systems with stable pores during the last 1 μs of

simulation time. Bundle: a tightly packed assembly of peptides with the hydrophobic face

outwards but no imposed hydrogen bonding. Tilted: the dimer’s major axis was reoriented 30°

from transmembrane. Pore radius and number of water molecules: determined for the last 1 μs of

simulation, as per the Methods. Lipid headgroups near membrane center: number within 5 Å of

the midline for the last 1 μs. N/A: Certain values not shown for systems without stable aqueous

pores. For a guide to topology, see the Methods. Mixed topology: one dimer NCNC parallel and

the other dimer NCCN antiparallel.

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For the protegrin system with four tilted dimers and the amidated tachyplesin octameric bundle,

which had aqueous channels without the presence of larger oligomers at the end of production,

we plotted pore radius vs. simulation time to visualize their pore stability (Figure 4.12). For both,

pore radius showed a decreasing tendency throughout the simulation, indicating that the pores

may be en route to breaking down. However, the pore radius of the amidated tachyplesin bundle

seems to have stabilized over the last 1.8 μs, and aqueous channels remained in these systems for

the duration of our simulations, so longer simulations are needed to confirm whether this type of

pore is stable.

Peptides Topology Pore radius (Å) Water molecules in pore Lipid headgroups near membrane center

Protegrin non-sheared barrels

Octamer NCNC parallel 7.5 +/- 1.0 130 +/- 20 3 +/- 1

Octamer Mixed 9.4 +/- 0.7 204 +/- 21 0 +/-1

Decamer Mixed 12 +/- 1.0 307 +/- 41 3 +/- 1

Protegrin sheared barrels

Octamer NCNC parallel 8.7 +/- 0.3 159 +/- 10 0

Octamer Mixed 10.0 +/- 0.4 203 +/- 13 0

Octamer NCCN antiparallel 9.0 +/- 0.3 167 +/- 9 0

Protegrin arcs

Tetramer in POPC NCNC parallel 5.0 +/- 1.5 N/A N/A

Tetramer in POPC/Cholesterol NCNC parallel 7.0 +/- 1.0 N/A N/A

Tetramer in POPE/POPG NCNC parallel 4.0 +/- 1.0 N/A N/A

Protegrin bundles

Tetramer N/A 5.5 +/- 0.5 N/A N/A

Octamer N/A 10.5 +/- 1.0 225 +/- 34 3 +/- 1

Octamer (four tilted dimers) NCNC parallel 7.0 +/- 1.0 125 +/- 27 4 +/- 1

Other transmenbrane bundles

Tachyplesin octamer (amidated) N/A 7.0 +/- 1.0 99 +/- 19 5 +/- 1

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Figure 4.12. Pore radius vs. simulation time for selected systems. (A) protegrin system with four

tilted dimers; (B) tachyplesin octameric bundle.

Discussion

In this study, we performed μs-scale all-atom simulations of protegrin oligomers in lipid bilayers

and observed the relationship between oligomeric multiplicity, topology, and pore stability. The

results provide insights regarding the stability of putative pore structures and the feasibility of

certain pore formation pathways but leave important questions unanswered.

We observed three types of pores that are stable on a time scale of 5–10 μs. The first involves

monomers and small oligomers surrounding a partially lipidic pore. These pores tended to shrink

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throughout the simulation and may have closed if the simulation time had been extended.

Nevertheless, even five copies of protegrin (a trimeric arc and an opposing dimer) were

sufficient to support a substantial aqueous channel for 5 μs (Figure 4.10). The bundles of

tachyplesin, which showed lower tendency to aggregate than protegrin, resulted in pores of this

type (Figure 4.11). A second type of stable pore consisted of a twisted β-sheet plus smaller

oligomers surrounding a partially lipidic aqueous channel (Figures 4, 5). The third type observed

was a completely proteinaceous pore comprised by a sheared protegrin β-barrel (Figure 4.6).

Longer simulations are necessary to verify the longer-term stability of these pores.

It is also instructive to examine the systems that did not generate stable pores. The systems with

transmembrane tetrameric arcs did not show stable pores, in contrast to previous shorter

simulations [100]. In addition, tetrameric bundles failed to adopt a configuration that would

support an open pore. The present results indicate that more than four copies of protegrin are

needed to support a stable pore and that a single tetrameric arc is insufficient to maintain a

substantial aqueous channel. Further, two tetrameric arcs placed in proximity to each other failed

to form a β-barrel. Therefore, protegrin β-barrel formation seems to face a substantial kinetic

barrier.

Whereas the sheared β-barrels were stable, the unsheared β-barrels broke open and twisted, in

constrast to our previous shorter simulations [100, 224]. Sheared barrels have not been

previously proposed for protegrin, but they would result in similar NMR signals to those that

have been previously observed (e.g., [205, 289], and result in pore radii within the

experimentally observed range (Table 4.2) [205, 219]. There may be two reasons for the

instability of unsheared barrels: first, β-sheets have a natural tendency to twist, which cannot be

accommodated by unsheared barrels [280]. Indeed, in all known β-barrel membrane proteins, the

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β-strands exhibit a substantial tilt angle [295]. A second possible reason is that tilting may

improve the interaction of the positively charged arginine side chains at the turn region and

termini with the lipid headgroups. The peptide’s overall length, which is larger than the thickness

of the POPC:POPG membranes, necessitates a tilt to optimize these interactions. Large

experimental tilt angles of 48°–55° for 12-carbon DLPC lipids [289] can be compared with

computational results indicating tilt angles of up to 34.9° for 16–18-carbon POPC lipids [259].

Analysis of the last 1 μs of our trajectories using CHARMM showed that, after breaking, the

arginine residues in the unsheared β-barrel systems interacted with approximately the same

number of PG headgroups as those in the sheared β-barrels (data not shown), supporting this

conclusion.

Simulations of oligomers on the membrane surface were performed to determine the stability of

putative early intermediates in the pore formation pathway. Protegrin unsheared dimers on the

membrane surface were stable, but trimers, tetramers, and sheared dimers were not, and none of

the surface oligomer systems resulted in membrane insertion of the peptides. This indicates that a

larger number of protegrin copies must accumulate on the membrane to initiate the poration

event. These results also lead us to propose that the unsheared dimer could function as a basic

building block of larger protegrin oligomers. The sheared β-barrels were comprised by building

block units of unsheared dimers, and most topologies of sheared β-barrels were quite stable.

Sheared β-barrels’ stability when composed of dimeric units matches with unsheared protegrin

dimers’ observed stability on the membrane surface. This is in accordance with previously

obtained potentials of mean force of protegrin dimerization, which showed the favorability of

dimerization in multiple environments [96].

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To test the hypothesis of a dimer as a building block, we performed a simulation starting from

four tilted protegrin dimers. Contrary to expectations, we observed that two NCNC parallel

dimers interacted to form an NCNC parallel trimer and a monomer. After the single peptide split

from its partner and joined the other dimer (as a trimeric β-sheet), the abandoned monomer left

the pore region and returned to the membrane surface. This makes the first type of pore

described above (i.e., one comprised by smaller arcs and oligomers surrounding a partially

lipidic pore) seem like it could be an intermediate towards the formation of other pore states in

the presence of larger numbers of smaller protegrin oligomers. However, in this study, we did

not observe any events of protegrin oligomers coming together to form tilted β-barrels inside the

pore, and even though we witnessed the spontaneous formation of several unsheared β-sheets

during our simulations, unsheared β-barrels always broke down. Further, whereas sheared barrels

are stable in our simulations, we have been unable to observe the formation of such a barrel.

Alternatively, protegrin may form unstructured pores comprised by multiple non-interacting

small oligomers supporting a toroidal channel, analogous to our previous Anton results on

melittin [101]. This could hint at commonalities between the mechanisms of different AMPs.

The present results confirm the importance of topology to protegrin’s pore formation. The

NCCN parallel topology was unstable even as a sheared barrel, in contrast to solid-state NMR

suggestions of a pore with that topology [205], but in accordance with previous computational

studies by our laboratory [224]. The NCCN parallel sheared β-barrel is the only topology with

the peptides’ hydrophobic faces pointing in alternate directions. The other two topologies, in

which all of the peptides’ hydrophobic sides point outward towards the membrane, sustained

aqueous pores as both unsheared and sheared β-barrels, even after the unsheared ones broke open

into β-sheets. In addition, when eight protegrin peptides were placed as a bundle, six associated

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into an NCNC parallel β-sheet. These observations indicate that the hydrophobic faces of all

protegrin monomers must face the membrane to participate in poration.

We also noticed distinctions in pore size between the topologies. Pore radius and number of

water molecules inside the pore were measured for systems that supported stable aqueous pores

(Table 4.2). These measures were both closely associated with the number of peptides

comprising the pore, which ranged from 5 to 10. The observed pore radii for pores comprised by

eight peptides generally agree with previous estimates of protegrin’s pore radius ([205]; but the

pore size is smaller than stated by [219]). Among both sheared and unsheared β-barrels

comprised by eight peptides, the mixed topology resulted in relatively larger pores than NCNC

parallel. This difference is likely due to the increased twist of the NCNC parallel topology. The

protegrin system with four tilted dimers, which formed a pore comprised by five peptides, was

similar in size to the tachyplesin pore (Table 4.2).

Even though all lipid headgroups began the simulations near the plane of the membrane surface,

most systems with stable pores had 3–5 lipid headgroups within 5 Å of the membrane center by

the end of the simulation, whereas all sheared β-barrels had 0 (Table 4.2). This indicates that the

protegrin transmembrane bundles, unsheared β-barrels, and tilted dimers caused the pore to

become more toroidal than the sheared β-barrels did (the sheared β-barrels supported mostly

cylindrical pores). Neutron diffraction experiments have indicated that protegrin forms toroidal

pores [69]. To reconcile this with the presence of sheared barrels, which did not generate toroidal

pores in the current investigation, further studies might assess sheared protegrin β-barrels’ ability

to introduce membrane defects [288].

The tachyplesin octameric bundle simulations yielded similar results with and without C-

terminal amidation. Further, tachyplesin showed lower overall tendency towards mutual

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interaction than protegrin did: larger oligomers than dimers of tachyplesin did not form at all.

This result verifies our previous implicit membrane simulations showing that tachyplesin is

unstable as a β-barrel [2] (Chapter 2). In contrast, protegrin (which had the ability to form stable

β-barrels in [2]) showed the ability to form new associations between peptides within the pore

(i.e., the trimer in Figure 4.10). Further simulations are necessary to determine whether the

observed tachyplesin pore will remain stable or disintegrate in additional time. The tachyplesin

pores were similar in size and constitution to the pore formed by the system beginning with four

tilted protegrin dimers (Table 4.2); longer simulations are necessary to determine whether each

represents a breakdown product (Figure 4.12).

These results can be analyzed in terms of the investigated peptides’ experimentally observed

pore induction. Voltage clamp experiments on protegrin-infused planar lipid bilayers and

liposome studies revealed that protegrin forms weakly anion-selective channels in lipid bilayers

and induces potassium leakage from liposomes [255]. A study of tachyplesin’s interaction with

liposomes and planar lipid bilayers also indicated the formation of anion-selective pores that

allowed peptide translocation across the lipid bilayer [296], in accordance with the movement of

tachyplesin peptides from the present study’s pores back to the membrane surface. A solid-state

NMR study of tachyplesin indicated that the peptide’s orientation was parallel to the membrane

surface, in contrast to that of protegrin [213]. Dye leakage from liposomes has been measured for

both protegrin [255, 297-299] and tachyplesin [269, 300, 301], but a quantitative comparison

between the two peptides’ ability to induce dye leakage has been lacking.

Conclusions

The present all-atom simulations revealed different types of pores induced by β-hairpin AMPs.

First, unsheared β-barrels of protegrin were not stable for long periods, in contrast to previous

125

contentions [205, 224]. Such barrels opened into twisted β-sheets that surrounded stable,

partially lipidic pores. Second, sheared β-barrels of protegrin were stable, and created completely

proteinaceous pores, in all topologies that allow the peptide’s hydrophobic side to face the

membrane. Although these pores represent a relatively ordered state that may face an entropic

barrier to formation, they were stable for the length of our simulations. Third, tachyplesin and the

bundle of protegrin dimers formed small pores that were lined by only a few peptides, with other

peptides seeming to support the pores from the membrane surface. This leads to the overall

conclusion that protegrin can form a diverse set of pore states depending on conditions.

Additional simulations of dimers, trimers, and tetramers on the membrane surface showed only

the unsheared dimers to be viable as early intermediates in pore formation.

This work leaves open several important questions. More simulations are necessary to determine

how various conditions can lead to the formation of these various pore types. Other factors that

could be manipulated more comprehensively include salt concentration, peptide concentration,

and membrane composition. In addition, the present simulations were set up in a biased fashion

that encouraged the formation of the desired final states. Eventually, it would be more

compelling to illustrate the formation of a stable pore from peptides in solution or on a

membrane surface. Sheared β-barrels are stable once formed, but a study showing the formation

of a complete β-barrel from smaller oligomers is highly desirable.

Several of these questions could be straightforwardly addressed by longer conventional MD

simulations. However, we also need to determine the relative favorability of these various states,

for which free energy calculations may also be useful. Our laboratory is also investigating other

computational approaches, such as simulated tempering [302], which may provide additional

information on β-barrel closure with our current computing power. Other simulation methods

126

like reaction path annealing [303] may also provide information about the critical peptide

aggregation steps.

127

5. Conclusions

In conclusion, we summarize the synergy and impact of all these results and future directions.

Collectively, these results provide a more comprehensive and cohesive picture of pore formation

by β-hairpin AMPs than had been available previously. Several β-hairpin AMPs that had not

been previously subjected to MD simulations were studied in Chapter 2. The results indicated

that other naturally occurring β-hairpin AMPs do not form β-barrel pores as efficiently as

protegrin does. To investigate this difference further, tachyplesin was used in both Chapters 2

and 4. The results in Chapter 4 also indicated that tachyplesin is less stable than protegrin as a β-

barrel.

These differences between protegrin and tachyplesin can be understood in terms of structural

distinctions between the peptides. Our previous structural comparison in Chapter 2 indicated the

differences in hydrophobic residue packing between these two peptides’ putative pore structures.

Although both peptides show “imperfect amphipathicity,” the central region of the hairpin

between the two disulfide bonds is longer in tachyplesin than protegrin, and this lengthened

portion in tachyplesin contains two arginine side chains (R5 and R14) that face the same

direction as both disulfide bonds (i.e., into the pore lumen). In contrast, protegrin’s fewer

residues between the two disulfide bonds contain no side chains facing the pore lumen. The

presence of two large arginine side chains per peptide in the center of the pore lumen could

contribute to tachyplesin pores’ lack of observed stability. Because these extra arginine side

chains pack closely together in tachyplesin β-barrel structures, their bulk could cause steric

hindrance that reduces the stability of higher-order oligomers.

The present results emphasize that a variety of related pore types may form an ensemble that

collectively comprises the overall pore state. While Chapter 2 was restricted to tetrameric arcs

128

and β-barrels with 7, 8, and 10 peptides, Chapter 3 investigated β-barrels of protegrin and related

mutants consisting of 6–14 peptides. The latter results indicated that β-barrels of 7–13 peptides

had approximately equal energetic favorability, further supporting that a diverse ensemble of

pore states is formed by protegrin, as proposed by Mani et al. [205]. However, the results in

Chapter 4 suggested that the constituents of this diverse pore state are probably not the ones

previously thought.

Chapter 4’s simulations of protegrin β-barrels and other structures had a longer time scale than

previously reported ones. Whereas previous all-atom simulations of protegrin in our laboratories

had been restricted to a few hundred ns [100, 224], the simulations in Chapter 4 comprised up to

10 µs of simulation time. Therefore, we had time to observe the systems’ evolution more

extensively than had been possible in previous studies. We witnessed that several structures

proposed by previous studies, such as unsheared barrels [2, 3, 224], the NCCN parallel topology

[205], and tetrameric arcs [100], failed to support stable pores when subjected to longer

simulations. Instead, our longer simulations showed the significance of shearing in β-barrel

structure and suggested that regular β-sheets can support partially lipidic pores. This provides a

more diverse view of the β-hairpin AMP pore state than previously available.

Future studies are required to address several questions that arise from this research. First, some

of the pores that seemed marginal in Chapter 4 may have been en route to breaking down, and

therefore, longer simulations are required to verify that they have an extended lifetime. Longer

simulations of tachyplesin may particularly help to determine whether β-hairpin AMPs like

tachyplesin work by different mechanisms than protegrin. However, longer standard MD

simulations may not provide answers to some other questions. For example, the insertion and

aggregation steps of the putative mechanism were not elucidated in any great detail by this

129

research. Illustration of some early and middle steps of pore formation may require

fundamentally different methods than the ones used in the present work. For example, the

relative favorability of the states determined in Chapter 4 needs to be determined, for which free

energy calculations may be useful. Simulated tempering [302] and reaction path annealing [303]

may provide information about the final steps of β-barrel closure and other critical peptide

aggregation steps. These experiments can also be extended to other β-hairpin AMPs to arrive at a

more comprehensive description of structure–function relationships throughout this entire

peptide family. Other factors could also be experimentally manipulated, such as a more detailed

exploration of how peptide concentration affects the formation of oligomeric pores.

130

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