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

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COMPUTATIONAL INVESTIGATION OF PORE FORMATION BY BETA-HAIRPIN

ANTIMICROBIAL PEPTIDES

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

RICHARD LIPKIN

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

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

iii

ABSTRACT

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

Peptides

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

iv 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.

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

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

vii

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

viii

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.

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

2 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,

3 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].

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

5 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:

6 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

7 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

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

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

9 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

10 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

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

12 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

13 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

14 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

15 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.

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

17 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.

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.

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

20 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.

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.

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.

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

24 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

25 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.

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

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].

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.

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

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:

2 R = Ro + kz ; 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 ⃑ :

∑ ⃑

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

32 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

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 1114 Å in the x direction followed by

34 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

35 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

36 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

37 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].

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:

39 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

40 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

41 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

42 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 100M, 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

43 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

1M), hemolytic activity had little dependence on concentration (22% hemolysis at 100M), 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].

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].

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

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 2.22.5, Figure 2.7).

Negative values indicate favorable binding.

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

Pore charge Pore charge Pore charge Pore charge

(Å)

30% 30% 30% 30%

anionic anionic anionic anionic

Neutral Neutral Neutral Neutral

Pore radius

istorted istorted istorted istorted istorted istorted istorted istorted

vespore

Pore radius (Å) Pore radius (Å) Pore radius (Å)

D D D D D D D

Lea Leavespore Leavespore Leavespore Leavespore Leavespore Leavespore Leavespore

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.

Radius 30% anionic Tetramers: selected (Å) Neutral pore 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.

Radius 30% anionic Heptamers: selected (Å) Neutral pore 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 ± 13.8a Polyphemusin 15 22.5 ± 18.5a -1.5 ± 21.4a 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.

Radius 30% anionic Octamers: selected (Å) Neutral pore 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 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.

Radius 30% anionic Decamers: selected (Å) Neutral pore pore Protegrin-1 15 -17.2 ± 2.9 -101.8 ± 5.3 θ-defensin 15 137.7 ± 14.2a 62.8 ± 21.5a Tachyplesin 12 87.5 ± 48.6a 29.3 ± 75.9a Polyphemusin 15 77.7 ± 43.9a 28.8 ± 43.1a 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 2.12.5). 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

50 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 2.12.5). 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 2.12.5, 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).

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 2.12.5, 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

53 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 2.22.5, 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 2.22.5, 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

54 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).

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 2.22.5, 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

57 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

58 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 2.5gh, 2.6de). 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 2.22.5, 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

59 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

60 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 0.620.68 and 0.820.87 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 1.45.5 M, and values for EC ranged 0.71.4 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 0.41.6 M, depending on strain, and that for SA was 1.63.15 M [272]. The same study measured MIC values for androctonin of 315 M and 1530 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

61 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

62 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.

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

[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

810 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

65 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

(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:

2 R = R0 + k × z′ (3)

67 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

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.

The final monomeric structures were then arranged as -barrels of oligomeric numbers 614 by orienting them vertically, rotating them around the z axis to orient the backbones, translating them by 1120 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.

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:

trans rot ΔGpep = Wbarrel − Wmono − TΔS − TΔS − − (6)

71 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.

trans rot Wbarrel, ΔW, TΔS , and TΔS 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.

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

73 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

74 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.

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

76 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.

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

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

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.

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

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.

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

13mer (Figure 3.7). However, the patterns in the data are generally not as strong for this mutant as for the other peptides.

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

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.

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,

trans rot are clarified by factoring in TΔS , TΔS , , , 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).

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

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.

Figure 3.6. r4n: Variation of pore formation free energy per monomer with pore radius for each oligomeric number. Line tension γ = 0.45.

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

84 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).

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]

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.

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.

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.

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

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

91 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 preformed 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

92 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

93 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].

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).

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.

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

97 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.

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

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

99 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,

100 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

101 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

102 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

104 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.

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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

107 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-

110 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

111 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

115 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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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

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.

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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

119 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

122 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

123 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

124 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

125 like reaction path annealing [303] may also provide information about the critical peptide aggregation steps.

126

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

127 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

128 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.

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