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Computational Investigation of the Pore Formation Mechanism of Computational Investigation of the Pore Formation Mechanism of
Beta-Hairpin Antimicrobial Peptides Beta-Hairpin Antimicrobial Peptides
Richard Lipkin The Graduate Center, City University of New York
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COMPUTATIONAL INVESTIGATION OF PORE FORMATION BY BETA-HAIRPIN
ANTIMICROBIAL PEPTIDES
by
RICHARD LIPKIN
A dissertation submitted to the Graduate Faculty in Chemistry in partial fulfillment of the
requirements for the degree of Doctor of Philosophy, The City University of New York
2017
ii
© 2017
RICHARD LIPKIN
All Rights Reserved
iii
Computational Investigation of the Pore Formation Mechanism of Beta-Hairpin Antimicrobial
Peptides
By
Richard Lipkin
This manuscript has been read and accepted for the Graduate Faculty in
Chemistry in satisfaction of the dissertation requirement for the degree of
Doctor of Philosophy.
Date Themis Lazaridis
Chair of Examining Committee
Date Brian Gibney
Executive Officer
Supervisory Committee:
Lei Xie
Marta Filizola
Emilio Gallicchio
THE CITY UNIVERSITY OF NEW YORK
iv
ABSTRACT
Computational Investigation of the Pore Formation Mechanism of Beta-Hairpin Antimicrobial
Peptides
By
Richard Lipkin
Advisor: Themis Lazaridis
β-hairpin antimicrobial peptides (AMPs) are small, usually cationic peptides that provide innate
biological defenses against multiple agents. They have been proposed as the basis for novel
antibiotics, but their pore formation has not been directly observed on a molecular level. We
review previous computational studies of peptide-induced membrane pore formation and report
several new molecular dynamics simulations of β-hairpin AMPs to elucidate their pore formation
mechanism. We simulated β-barrels of various AMPs in anionic implicit membranes, finding
that most of the AMPs’ β-barrels were not as stable as those of protegrin. We also performed an
optimization study of protegrin β-barrels in implicit membranes, finding that nonamers were the
most stable, but that multiplicities 7–13 were almost equally favorable. This indicated the
possibility of a diversity of pore states consisting of various numbers of protegrin peptides.
Finally, we used the Anton 2 supercomputer to perform multimicrosecond, all-atom molecular
dynamics simulations of various protegrin-1 oligomers on the membrane surface and in
v
transmembrane topologies. We also considered an octamer of the β-hairpin AMP tachyplesin.
The simulations on the membrane surface indicated that protegrin dimers are stable, while
trimers and tetramers break down because they assume a bent, twisted β-sheet shape. Tetrameric
arcs remained stably inserted, but the pore water was displaced by lipid molecules. Unsheared
protegrin β-barrels opened into long, twisted β-sheets that surrounded stable aqueous pores,
whereas tilted barrels with sheared hydrogen bonding patterns were stable in most topologies. A
third type of observed pore consisted of multiple small oligomers surrounding a small, partially
lipidic pore. The octameric tachyplesin bundle resulted in small pores surrounded by 6 peptides
as monomers and dimers. The results imply that multiple protegrin configurations may produce
aqueous pores and illustrate the relationship between topology and pore formation steps.
However, these structures’ long-term stability requires further investigation.
vi
ACKNOWLEDGMENTS
Acknowledgments are given for the helpful support and assistance of the following:
Themis Lazaridis
Marta Filizola
Emilio Gallicchio
Lei Xie
Almudena Pino-Angeles
John M. Leveritt III
Yi He
Jorge Ramos
Joel Koplik
Shanan Leeman
Jolinos Vartan Ngilahpong
Maksim Boyko
Brian Gibney
Maria Tamargo
The National Science Foundation
The National Institutes of Health
D.E. Shaw and Associates
Pittsburgh Supercomputing Center (Anton 2 Supercomputer)
Amanda Meyer
Terrance I, Rousey I, Terrance II, and Rousey II (cats)
Satoshi Nakamoto, Vitalik Buterin, and all contributors to the blockchain economy
vii
TABLE OF CONTENTS
1. Introduction 1
2. Implicit membrane investigation of the stability of antimicrobial peptide β-barrels and arcs 27
3. Computational prediction of the optimal oligomeric state for membrane-inserted β-barrels of protegrin-1 and
related mutants 64
4. Transmembrane pore structures of β-hairpin antimicrobial peptides by all-atom simulations 90
5. Conclusions 127
6. Bibliography 130
viii
LISTS OF TABLES, ILLUSTRATIONS, CHARTS, FIGURES, DIAGRAMS
Figure 1.1 4
Figure 1.2 8
Figure 1.3 11
Figure 1.4 19
Figure 1.5 23
Figure 2.1 37
Figure 2.2 39
Figure 2.3 40
Figure 2.4 41
Figure 2.5 52
Figure 2.6 56
Figure 2.7 58
Figure 3.1 69
Figure 3.2 76
Figure 3.3 78
Figure 3.4 81
Figure 3.5 81
Figure 3.6 83
Figure 3.7 84
Figure 3.8 86
Figure 3.9 86
Figure 4.1 95
Figure 4.2 96
Figure 4.3 103
Figure 4.4 106
Figure 4.5 107
ix
Figure 4.6 108
Figure 4.7 110
Figure 4.8 113
Figure 4.9 114
Figure 4.10 114
Figure 4.11 116
Figure 4.12 119
Table 2.1 48
Table 2.2 48
Table 2.3 49
Table 2.4 49
Table 2.5 50
Table 3.1 68
Table 3.2 78
Table 3.3 79
Table 3.4 81
Table 3.5 82
Table 4.1 99
Table 4.2 118
1. Introduction
This dissertation is based on four peer-reviewed publications. Chapter 1 is based partially on the
review paper “Computational studies of peptide-induced membrane pore formation” [1]. In
Chapter 1, we first summarize research and knowledge on the general class of antimicrobial
peptides (AMPs), and then we describe what is known about β-hairpin AMPs and set the goals of
the dissertation in that context. Chapters 2–4, respectively, are identical to three research papers:
“Implicit membrane investigation of the stability of antimicrobial peptide β-barrels and arcs” [2],
“Computational prediction of the optimal oligomeric state for membrane-inserted β-barrels of
protegrin-1 and related mutants” [3], and “Transmembrane pore structures of β-hairpin
antimicrobial peptides by all-atom simulations” [4].
Computational studies of peptide-induced membrane pore formation
A variety of peptides induce pores in biological membranes; the most common ones are naturally
produced AMPs, which are small, usually cationic, and defend diverse organisms against
biological threats. Because it is not possible to observe these pores directly on a molecular scale,
the structure of AMP-induced pores and the exact sequence of steps leading to their formation
remain uncertain. Hence, these questions have been investigated via molecular modelling. In this
chapter, we review computational studies of AMP pore formation using all-atom, coarse-grained,
and implicit solvent models; evaluate the results obtained; and suggest future research directions
to further elucidate the pore formation mechanism of AMPs.
Pore formation in lipid bilayers occurs in important biological processes, such as apoptosis [5-7],
immunity [8, 9], bacterial toxin function [10, 11], viral infection [12], and protein translocation
[13]. In most of these processes, a soluble protein reconfigures and assembles into a membrane-
embedded oligomer. Some available structures [14-16] show a completely proteinaceous pore.
2
However, in other cases, lipids are speculated to participate in the pore’s construction [17]. Pores
can also be induced in pure lipid bilayers by applying electric fields (i.e. electroporation; [18]).
The antibacterial defence mechanisms of a broad range of organisms also seem to involve
membrane pore formation. Antimicrobial peptides (AMPs, or host defense peptides) are usually
small, cationic peptides that provide a diverse array of immunological functions [19-22]. These
amphipathic peptides, which assume various secondary structures, can permeabilize lipid
bilayers in vivo [23-25] and in vitro [26-28]. This, together with the observed lack of dependence
on amino acid chirality [29, 30], led to the suggestion that they target the bacterial membrane,
either by forming pores [31] or by dissolving the membrane in a detergent-like fashion (i.e. the
carpet mechanism; [32]). Their cationic charge is thought to impart selectivity for bacterial
membranes, whose exterior lipid leaflet is negatively charged [33]. Whether membrane
permeabilization is the actual lethal event is still actively debated [34, 35]. Other proposed
mechanisms include clustering of ionic lipids [36] and targeting intracellular components, such
as DNA [37-39]. Nevertheless, the occurrence of AMP-induced membrane poration is
unquestionable, and understanding peptide stabilization of membrane pores has fundamental
value independent of its precise role in AMP action. In this chapter, we will focus on AMPs’
membrane-permeabilizing function.
Extensive experimental effort has been invested in characterizing AMPs’ membrane interactions
and the nature of the pore state. For example, fluorescence measurements have been used to
quantify membrane binding and leakage from vesicles [40, 41]; fluorescence applied to giant
unilamellar vesicles (GUVs) has allowed direct imaging of permeation [42-44]; and fluorescence
imaging of live cells has elucidated the sequence of events [34, 45]. Calorimetry has provided
the thermodynamic properties of membrane binding [46]. Oriented CD has provided information
3
on peptide orientation with respect to the bilayer normal [47, 48]. X-ray diffraction has shown
reduced membrane thickness upon peptide binding [49, 50] and illustrated the shape of peptide-
induced pores [51]. Neutron scattering has provided information on pore size [52].
Electrophysiology studies have described pore ion conductance and its voltage dependence [53-
55]. Solution NMR in detergent micelles has provided structures and sometimes described
oligomerization propensities [56]. Solid-state NMR (ssNMR) has provided structural and
dynamic information in native environments [57, 58]. Atomic force and electron microscopy
have shown AMP-induced membrane damage [59-61]. However, these pores’ lability and
transience have prevented the acquisition of an experimental high-resolution structure of an
AMP-stabilized pore.
A summary of experiments on the dozens of previously investigated AMPs would be beyond the
scope of this review; therefore, we will mostly focus on a few well-studied peptides. Alamethicin
is a 20-residue helical peptide of the peptaibol family with charge 0 or −1 [62]. Melittin is a 26-
residue cytolytic peptide isolated from bee venom that has low target selectivity [63]. Magainin-
2 (hereafter, magainin) is a 23-residue AMP isolated from frog skin that preferentially targets
bacterial membranes [64]. The latter two peptides are cationic, and as expected, they bind more
strongly to membranes containing anionic than zwitterionic lipids [65, 66]. Alamethicin appears
to form cylindrical barrel-stave pores, in which the pore lumen is completely lined by peptides
[67], whereas melittin and magainin appear to form toroidal pores, in which the two membrane
leaflets curve together and the peptides are adjacent to lipid headgroups [52, 68, 69] (Figure 1.1).
Magainin exhibits synergy with another AMP from the same family, PGLa [70], which has also
been the subject of ssNMR studies [71]. Dye leakage from vesicles usually does not proceed to
completion in the presence of AMPs, suggesting that the pores are transient [72]. However,
4
simple mutations to melittin generate peptides that form pores detectable long after equilibration
[73]. Electrochemical impedance spectroscopy has shown the transience of melittin bilayer
permeabilization [74], in sharp contrast to the behavior of its MelP5 mutant [75].
Figure 1.1. Schematics of a) barrel-stave, b) toroidal, and c) semitoroidal pores.
Key questions
Despite valuable information provided by over four decades of experimental investigations, our
understanding of membrane pore formation, and therefore our predictive abilities, are severely
limited. Presently, it is not possible to predict a peptide’s pore-forming ability given its sequence.
To generate such predictions, we would need to resolve the following key questions:
1. Pore vs. carpet mechanisms. Do well-defined pores form [31], or is the membrane dissolved in
a detergent-like fashion [32]? There is evidence supporting both models. In favour of the pore
mechanism, many experiments using GUVs show permeation without membrane dissolution [44,
76]. However, in other cases, the GUV bursts, supporting the carpet model [77]. Also in favour
of the carpet model, some peptides seem unable to adopt transmembrane orientations [78],
although, whether such orientations are necessary for pore formation remains to be determined.
The carpet model implies quite high peptide concentrations in the membrane, and membrane
partitioning measurements suggest that such concentrations are attainable at typical solution
concentrations [79, 80].
5
2. Pore structure. When well-defined pores are formed, what is their detailed structure? The most
common proposed models are the classical barrel-stave pore—where the pore is cylindrical and
lined by peptides [81]—and the toroidal pore, where the two membrane leaflets bend and join
together [52, 82]. Although toroidal pores’ overall lipidic shape has been visualized [31], the
number, position, and orientation of the peptide constituents with respect to the pore is unknown.
Some computational studies have suggested highly disordered pores [83, 84] (see below).
3. Pore lifetime. Are the pores long-lived or transient, and what determines their lifetime? What
peptide features lead to pore stability or transience? Electrophysiological techniques are the
primary sources of direct information on pore lifetime; however, AMP-induced membrane pores
seem to change dynamically. For example, time-lapse AFM has shown lateral pore expansion
with time [85].
4. Aggregation. Do the peptides need to aggregate (i.e. directly contact each other) during the
pore formation process? Numerous biophysical studies over the past decades have looked for
signs of such aggregation (e.g. [86-89]. Direct contact is implied in the barrel-stave model but is
not necessary in the toroidal model; indeed, most toroidal-pore-forming peptides’ high charge
levels would discourage direct peptide–peptide contact [90]. However, dimerization has been
detected for magainin [91] and other AMPs in detergent micelles.
5. Pore formation pathway. Do the peptides adsorb to the membrane surface as monomers and
then oligomerize? Is the reverse possible? At what point does pore opening occur? The exact
sequence of steps and the factors that influence their interaction have not been completely
elucidated for any peptide.
6. Selectivity and toxicity. What is the origin of most AMPs’ selectivity toward bacterial
membranes and other AMPs’ toxicity towards mammalian cells? The prevalent explanation is
6
that most AMPs’ positive charge directs them towards negatively charged bacterial membranes
as opposed to the largely neutral outer leaflet of mammalian membranes. However, the situation
is somewhat more complex. For example, both melittin and magainin are positively charged and
bind anionic membranes more strongly than zwitterionic ones. However, melittin
preferenentially permeabilizes zwitterionic membranes [92], whereas magainin does so for
anionic membranes [93]. This shows that there is no simple correlation between membrane
affinity and permeabilization. Other contributions to selectivity include the effects of cholesterol
(which is present in mammalian but not bacterial membranes) and the magnitude of the
transmembrane voltage [33]. The dominant determinant of toxicity seems to be hydrophobicity,
which is usually positively related to binding strength to neutral membranes and hemolysis; e.g.
[94].
Computational investigations
The lack of an experimental atomic-level picture of peptide-stabilized pores has prompted
numerous molecular modelling studies. The standard computational technique in molecular
biophysics is classical molecular dynamics (MD) simulations: all peptide, lipid, and water atoms
are represented by particles interacting according to an empirical energy function, and Newton’s
equations of motion are solved to provide an atomic-level view of the system on a timescale
dependent on the available resources, currently limited to the microsecond range. Because pore
formation typically occurs on much longer timescales, a single MD trajectory normally cannot
show the entire sequence of events from water-soluble (usually unfolded) peptides to folded,
membrane-inserted oligomeric pore. Hence, researchers have resorted to the following courses of
action:
7
a) Study putative initial steps of the pore formation process, such as monomer binding to a lipid
bilayer [95] or association between two peptides in water or on the membrane surface [96].
b) Use free energy calculation techniques, such as umbrella sampling [97] or adaptive biasing
force [98], to compute the free energy profiles (or potentials of mean force, PMFs) for these
elementary steps. These calculations are time-consuming and expensive, with slow convergence
reported [99].
c) Start the simulation closer to the putative final pore state (e.g. with preformed pores [100] or
several inserted transmembrane peptides [101]). Sufficiently long simulations should remove the
initial bias and allow the system to relax to a local free energy minimum, which hopefully will be
the desired pore state.
An alternative way to address the limitations of atomistic simulations is to simplify the model.
One popular direction is to employ coarse-grained (CG) simulations, which represent the lipids,
water, and often the peptide itself with particles corresponding to more than one atom [102-104].
Several procedures to devise CG representations have been implemented: interactions between
CG ‘beads’ can be calibrated to reproduce forces between corresponding groups of atoms in
atomistic simulations [105], or the CG system’s density, phase transitions, or structure can be
adjusted to match the physical system’s characteristics [106]. CG modelling speeds up the
computations considerably, but the added approximations can cause problems. For example, the
representation of groups of four water molecules by one particle may not be appropriate for
small pores [107], and peptide secondary structure is usually fixed, preventing conformational
adaptation.
Even greater simplification is attained by implicit solvent simulations, which represent water and
lipids implicitly through extra terms in the energy function. Implicit solvent models were first
8
created for water-soluble proteins [108-110] and were extended to membranes soon afterwards
[111-114]. Such models can easily account for surface charge using Gouy–Chapman theory
[115]. Implicit membrane models typically describe intact membranes, but one model permits
dynamic changes in membrane thickness [116], and Implicit Membrane Model 1 (IMM1),
developed in our lab, has been extended to pores [117, 118]. In IMM1, pore shape is specified by
making the radius R dependent on vertical position within the membrane, z′, according to a
desired curvature k [2, 118, 119] (Figure 1.2). Transmembrane voltage [120], membrane dipole
potential [121], and lateral pressure effects [122] can also be included in IMM1. Because Gouy–
Chapman theory is restricted to modelling flat anionic membranes, the electrostatic potential in
anionic membrane pores is found by numerical solution of the Poisson–Boltzmann equation,
with the bilayer’s dielectric properties represented by a five-slab model accounting for solvent,
lipid headgroup, and lipid tail regions [2, 119]. The work published as [2] is included as Chapter
2 below.
Figure 1.2. Dependence of solvation parameters on internal pore radius (R0), vertical position
(z′), and pore curvature (R = R0 + k × z′2). a) k = 0 in cylindrical pores. b) k > 0 in toroidal pores.
9
Below, we review the available computational results on AMP pore formation obtained by all-
atom, CG, and implicit modelling. Earlier general reviews of this topic can be found in [123-
127].
All-atom modelling
In addition to AMP studies, atomistic simulations have been used to study pore formation in pure
lipid bilayers. Because this is not a spontaneous process, it has to be induced, either by
application of an electric field (as in the experimental electroporation process; [128-131]) or by
constraining collective variables [132-134]. However, many of the latter approaches suffer from
slow convergence and hysteresis [135]. In addition, pronounced force field dependence has been
noted in the calculated free energy of pore formation [136], which impacts interpretation of the
AMP simulations mentioned below. Strong force field dependence of results has also been
reported in another study [137].
The simplest objective of AMP simulation research has been to examine monomer binding,
usually parallel to the membrane surface but also in a transmembrane orientation. This has been
done for numerous peptides, such as melittin [138-141], alamethicin [142], magainin [143], and
others [144-147]. The peptide is usually placed on the membrane interface with the more
hydrophobic side towards the membrane, but it can also be placed a small distance from the
membrane, in which case it usually binds rapidly, e.g. [148]. Simulations have also been
performed in micelles [149, 150], because they are the standard medium in solution NMR.
Simulations like these reveal details of AMPs’ orientation, depth of membrane insertion, and
lipid interactions but give no information about the permeabilization mechanism.
Spontaneous pore formation starting from peptides dissolved in the water phase has rarely been
observed in simulations. The only reported examples in AMPs are a study of a magainin
10
derivative [83] and a similar subsequent study of melittin [84], which inspired the ‘disordered
toroidal pore’ model. The exceedingly fast insertion observed in those studies may have been
caused by the systems’ lack of counterions. A similar issue was noted in a simulation of
spontaneous translocation of an arginine-rich peptide [151]. Recent microsecond-scale atomistic
MD simulations of multiple melittin–membrane systems showed bent U-shaped conformations
of melittin without any transmembrane insertion or pore formation [152].
The difficulty of observing spontaneous pore formation has led to efforts to circumvent the
timescale problem by starting from preformed pores or preinserted peptides. An early example is
simulations of transmembrane helical alamethicin bundles [153, 154]. Similar studies have been
done on other peptides; for example, a transmembrane melittin tetramer was found to decay to a
trimer and generate a toroidal pore in 5.8 ns [155]. Increases in available computational power
have gradually allowed much longer simulations. Work in our laboratory compared alamethicin
with melittin in preformed pores and confirmed their preference for cylindrical and semitoroidal
pores, respectively [118]. Further work examined the influence of intrapeptide charge position
and imperfect amphipathicity (i.e. the presence of polar or charged sidechains within a peptide’s
hydrophobic part) on pore character [156].
Other groups have studied melittin tetramers, either half-inserted [157] or fully inserted [158] in
preformed pores. The latter study found that antiparallel arrangement and reduced peptide
folding yielded stable toroidal pores. Another group studied various oligomers on the surface or
in transmembrane orientation [159]. Our group’s much longer atomistic simulations of a melittin
tetramer conducted on the Anton supercomputer revealed a classical toroidal pore characterized
by dynamic orientation change of one or two peptides (Figure 1.3a) [101]. Similar simulations of
magainin and PGLa in lipid membranes showed a different picture: highly tilted peptides around
11
a very small pore, with tilt angles in agreement with ssNMR experiments (Figure 1.3b) [160].
This work also provided insights into the synergy between these two magainin-family peptides:
more transmembrane orientations, stronger interactions, and a larger and more ordered pore were
seen in the 1:1 heterotetramer with antiparallel helix arrangement than in homogeneous peptide
mixtures [160]. Starkly different results were obtained for another AMP called piscidin: a 26-μs
Anton simulation starting from 20 peptides in 4 barrel-stave pores resulted in almost all peptides
moving to a surface-bound state, suggesting a non-pore mechanism for this peptide [145].
Figure 1.3. Snapshots from all-atom simulations of α-helical antimicrobial peptides. a) Melittin
tetramer at 8.3 µs [101]. b) Magainin–PGLa heterotetramer at 9 µs [160].
In addition to standard MD simulations, attempts have been made to obtain thermodynamic
information for putative steps in the pore formation pathway via free energy calculations. The
free energy of melittin binding and reorientation in phospholipid bilayers has also been
calculated [95, 161, 162], as well as the free energy of membrane binding of a lipopeptide at the
CG level [163] (see next section).
Coarse-grained modelling
12
CG modelling of AMP pore formation can offer unique insights, as it allows longer simulation
times and larger systems than all-atom modelling. Most CG studies so far have used the
MARTINI model [103, 107], but models that employ coarser graining have also appeared [164].
MARTINI-based studies have included: a study of PAMAM dendrimers that showed
unacetylated molecules forming pores ; a study of alamethicin that showed aggregation and some
transitions to an interfacial state [165]; a study of the synthetic LS3 peptide that showed the
spontaneous formation of mostly hexameric barrel-stave pores [166]; a study showing
spontaneous pore formation by a hydrophobic magainin derivative [167]; a study of magainin
and melittin that found U-shaped conformations for melittin and disordered toroidal pores for
magainin [168, 169]; studies of antimicrobial lipopeptides that found clustering of anionic lipids
but no pore formation [170, 171]; a dissipative particle dynamics study of eight AMPs
employing a MARTINI-like model showing pore formation and translocation [172]; and a study
of the AMP maculatin that found that an increased peptide-to-lipid ratio caused an interfacial–
transmembrane orientation change and cooperative membrane insertion of peptide aggregates
without a well-defined central pore lumen [173]. The last authors also observed maculatin-
induced spontaneous membrane curvature and used that evidence to suggest that pore formation
may not be responsible for maculatin’s activity. In a larger-scale setting, beyond the practical
limits of all-atom simulations, up to 1600 magainin peptides added to only one side of the bilayer
induced spontaneous buckling and vesicle budding of the lipid bilayer [174].
While these results sound very promising, some issues interfere with their applicability. The
pores observed in CG simulations often contain no water [123, 165, 168], and coarse graining the
water to a spherically symmetric particle corresponding to four water molecules limits
reproduction of the pore’s structural details. A detailed comparison of CG with atomistic
13
simulations revealed deficiencies in the CG pore structures [175]. Models that employ
polarizable CG water models provide improvements [107, 176], although they still have
difficulties forming aqueous pores under standard parameterization. Coarse graining of the
abundant water molecules is generally a quite important factor in the computational efficiency
gains offered by CG: one study estimated a speedup factor of 50 from coarse graining the water
molecules [177].
Implicit solvent modelling
In the 1980s and 1990s, when atomistic simulation of peptides in membranes was out of reach,
researchers were forced to develop simple ways to account for the membrane environment [178-
182]. The newer generation of implicit membrane models [111, 112, 114] are extensions of
implicit aqueous solvation models [108-110] and thus account for the energetics of both
membrane insertion and conformational changes. The Poisson-Boltzmann continuum model can
also be used to study peptide–membrane interactions [183, 184], but usually for static peptide
configurations. Even with modern computational power, implicit membrane modelling allows
studies that are impossible with all-atom and CG methods and facilitates unique insights because
of its fast convergence and simple energetic interpretation.
Modern implicit membrane models are routinely and trivially used to determine the
configurations and membrane binding energetics of AMP monomers (e.g. [185, 186]). More
sophisticated approaches have included the effects of transmembrane voltage, dipole potential,
and lateral pressure profile [120-122]. For example, using such simulations we showed that
voltage induces the interfacial–transmembrane orientation change in alamethicin [120] and the
addition of a membrane dipole potential term reduced the membrane binding affinity of
magainin [121]. Negative lateral pressure at the water–lipid interface stabilized interfacial
14
binding and yielded an interfacial–transmembrane orientation shift with an increased
peptide:lipid ratio, in accord with experiment. Further, with the inclusion of a lateral pressure
term, an increased DOPE mole fraction in mixed DOPC:DOPE bilayers stabilized interfacial as
opposed to transmembrane orientations [122].
Additional results of interest have been produced by implicit pore modelling [115, 119, 186].
When we compared peptide binding to pores of different shapes, we found that most AMPs bind
more favourably to both zwitterionic and anionic toroidal pores than to flat membranes [119,
186]. Alamethicin exhibited similar transfer energy to cylindrical and toroidal pores, whereas
toroidal pore-forming peptides, such as melittin, exhibited a preference for toroidal pores. One
factor driving these favourable transfer energies appears to be imperfect amphipathicity, which
reduces binding strength to flat membranes but does not affect binding to membranes with
positive curvature. Melittin and protegrin are examples of this type of amphipathic structure.
(Note that the term ‘imperfect amphipathicity’ has a broader meaning in Wimley’s independently
developed interfacial activity model [187].)
A large-scale computational study using IMM1 analysed activity determinants of 53 α-helical
AMPs [188], testing the hypothesis that antimicrobial and haemolytic activity correlate with
binding affinity to anionic and zwitterionic membranes, respectively. Antibacterial and
haemolytic activity were found to correlate best with transfer energy to membranes with anionic
lipid fractions of >30% and 10%, respectively. Surface area occupation, insertion depth, and
structural fluctuation were significantly correlated with antibacterial, haemolytic, and both
activity levels, respectively. Peptides active at low membrane surface coverage ratios tended to
be those identified in the literature as pore-forming. Further, the transfer energy to toroidal pores
was negative in almost all cases, while that to cylindrical pores was more favourable in neutral
15
than anionic pores, and pore transfer energy correlated with deviation from the predictions of the
carpet model. There were significant correlations of hydrophobic quadrupole moment (a
biophysical descriptor related to imperfect amphipathicity) with lethality against both E. coli and
red blood cells.
Implicit simulations in our laboratory that accounted for the free energy cost of acyl chain
exposure showed that certain antiparallel alamethicin bundles have lower free energy than
parallel ones and could be present under experimental conditions [189]. Multiple combinations
of radius and oligomeric number were investigated, with all oligomeric numbers 5–9 forming
open pores at their optimal radii. All oligomers 6–9 had comparable energies, consistent with
multiple experimentally observed conductance levels [190] and the barrel-stave model. The N-
terminal part was less tilted than the C-terminal part, resulting in hybrid funnel/hourglass pore
shapes; this shape was not affected by transmembrane voltage, but pore stability was. The
presence of a pore raised the total effective energy, suggesting that alamethicin pores may
correspond to excited states stabilized by voltage and ion flux.
Conclusions and Future Directions
Computational studies have provided a wealth of insights on pore-forming peptides, some of
which have been listed above. However, the limitations and uncertainties of the calculations have
not allowed definitive conclusions. Moreover, many studies focus on certain stages of the pore-
forming process, such as early membrane binding and dimerization or the final pore state. Thus,
a picture of the entire process is still lacking. In some cases, modelling results seem to conflict
with each other: in the example case of melittin, one study found disordered pores with half-
folded peptides [84], and another found mostly helical peptides around a classical-type toroidal
pore [101]. The origin of these discrepancies—whether the force field or other technical
16
details—needs to be clarified, and convergence needs to be achieved. As always, experimental
validation will be necessary for reliable conclusions.
The ‘to-do’ list in this field is long and exciting. The ability to perform multi-microsecond MD
simulations on Anton or other powerful computers has started to provide better-equilibrated pore
structures and detailed views of peptide–lipid interactions. Extending the timescale to a
millisecond, which is now conceivable with Anton II [191], may bring into view processes like
spontaneous aggregation, pore formation, expansion, contraction, and annihilation. This will start
to provide information on not only on pore structure but also dynamics. Additional PMF
calculations of higher-order oligomer insertion into lipid membranes, similar to those available
for monomers and dimers, are also needed to obtain the complete energetic landscape for pore
formation. It would also be useful to increase the diversity of lipid membrane compositions
simulated, because activity and toxicity are clearly dependent on membrane lipid composition.
CG simulations face some challenges to reproduce the details of peptide-stabilized pores. One
possible way forward could be mixed-resolution models that represent system components at
different resolution levels according to importance (e.g. [192-194]) or adaptive resolution models
whose resolution depends on location [195]. However, application to membrane pores will not
be trivial. An additional challenge is that peptide conformation is usually restrained in CG
simulations, which is not ideal, as considerable evidence indicates that conformational changes
in AMPs are possible during the poration process [196]. A challenging solution to this problem
could come from the development of CG peptide models that correctly reproduce the
environment-dependent conformational distribution. Because of the above-mentioned
difficulties, the investigation of large-scale membrane remodelling effects (e.g. membrane
bilayer buckling and vesicular budding [174]) may be a more fruitful application of CG models.
17
Significant work remains to be done, e.g. to understand the effects of the dependence of area per
lipid on the peptide:lipid ratio and how this determines the properties of both quasispherical
vesicular buds and their narrow necks.
Implicit membrane models could also be further developed. Extensions to curved membranes
would allow a more systematic exploration of the effects of curvature, especially Gaussian
curvature [197], on peptide binding. One significant limitation of most implicit models is the
assumption that the membrane is fixed. Large-scale changes, like bilayer buckling or vesicular
budding, are very difficult—and perhaps counterproductive—to pursue via implicit solvent
methods. However, making pore radius or shape dynamic simulation variables is feasible. Some
of these developments are in progress in our laboratory.
Eventually, to enable quantitative predictions, we need to develop a detailed molecular
thermodynamic model of peptide-induced pore formation. That would require quantitative
characterization of contributions to the pore state’s free energy from peptide–peptide, peptide–
lipid, and lipid–lipid interactions. Implicit solvent models are best positioned to provide the first
two terms; however, their quantitative accuracy needs to be ascertained by comparison with
atomistic PMF calculations. Although we have previously done this by computing PMFs
between ionisable side chains in solution [198] and at the bilayer–water interface [198], it is also
necessary to consider free energy profiles for entire peptides, as has been done for glycophorin A
[199] and model peptides [43]. A critical ingredient in this energetic landscape is the free energy
of opening a pore in a pure bilayer (i.e. lipid–lipid interactions in the above scheme). This
contribution has previously been estimated roughly from line tension measurements [200], but
such values suffer from large experimental uncertainty and correspond to the lowest free energy
state of a pore in a pure bilayer. Although we need to know the free energy of lipidic pore
18
formation as a function of radius, shape, and lipid headgroup distribution, existing approaches do
not provide this level of detail [132-134].
Beyond thermodynamics, dynamic models of pore creation, growth, and annihilation would also
be useful. For example, the pore could represent a dynamic state constituted by a growing
number of peptides: AMP pores may be able to expand laterally, even to the micrometre scale,
until the membrane disintegrates [85]. Future multiscale approaches could integrate atomistic
MD simulations, mesoscale models of single-pore electrodiffusion, and models of transient
bacterial cell ion transport [201].
Integrated multiscale computational models could not only provide a general understanding of
AMPs’ pore formation mechanism but facilitate the development of efficient antimicrobial
pharmaceutical products. In addition to ones based on protegrin (discussed below), several
AMPs are in clinical development as drugs, such as thanatin and heliomycin [202], but the lack
of detailed understanding of AMPs’ mechanisms of action has limited the rational design of
AMP-based therapeutics. A bottleneck has been most AMPs’ high toxicity levels at therapeutic
doses [203]. Future insights from computational studies could facilitate efficient drug design by
identifying peptides with the desired pharmacological properties.
Protegrin and the β-hairpin AMP family
Protegrin-1 (hereafter, protegrin) is an 18-residue β-hairpin derived from porcine leukocytes that
is stabilized by two disulfide bonds [204]. It is the most-studied member of the larger family of
β-hairpin AMPs. In this section, we summarize the experimental and computational techniques
that have been applied to protegrin and the rest of the β-hairpin AMP family, their results, and
their shortcomings.
19
Several experimental studies have measured the minimal inhibitory concentrations (MICs)
against Gram-positive and Gram-negative bacteria for both protegrin and other β-hairpin AMPs,
and other studies have verified biological effects on other types of cells. Both MIC and other
biological activity results are listed in detail in Chapter 2. Although a detailed experimental
review would be beyond the scope of this dissertation, a few previous experimental results
specifically guided the present research on protegrin, and many other experimental studies of
protegrin are also mentioned in Chapters 2–4. A crystallization study of protegrin pores in
membranes suggested that protegrin forms toroidal pores [69], and ssNMR evidence indicates
that protegrin oligomerizes into a closed β-barrel composed of 4–5 dimers in anionic bacterial
membrane mimetics [205]. Dimerization of protegrin has also been detected in detergent
micelles [206]. Protegrin-1 dimers have been suggested to assume NCCN parallel topology on
the basis of NMR evidence [205] (Figure 1.4a), although solution NMR in detergents yielded
NCCN antiparallel topology (Figure 1.4b) [206]. Further, protegrin-3 adopts NCCN antiparallel
topology in DPC micelles [207]. These studies have provided a rudimentary picture of
protegrin’s pore state, even though such pores are impossible to observe directly on an atomic
scale. Those experiments also provided useful information on topology from which we can draw
comparisons with our results.
20
Figure 1.4. Three possible topologies of protegrin-1 dimerization. a) NCNC parallel; b) NCCN
parallel; c) NCCN antiparallel. Yellow bridges represent disulphide bonds, which point inward
only on the right side of b). Arrows point N→C.
Other β-hairpin AMPs besides protegrin have not been experimentally studied as extensively as
protegrin has. However, there have been some experimental investigations of several other
peptides in this family, and those have revealed some structural and mechanistic insights.
Although a detailed experimental review would be beyond the scope of this section, the
subsections for each AMP studied in Chapter 2 contain additional notes on experimental
research. Here, we mention some experimental results that are interesting or relevant to the
investigations in the present dissertation. The β-hairpin AMP θ-defensin has relatively low
antimicrobial activity [208, 209], but it can prevent the entry of HIV into cells, possibly by
inhibiting the gp120:gp41 membrane binding/fusion process [210]. A crystallization study of a θ-
defensin AMP found a mixed-topology trimer wherein one dimer had NCNC parallel and the
other NCCN antiparallel topology [211]. Tachyplesin is structurally similar to protegrin, but
solid-state NMR results have indicated that tachyplesin orients in a surface rather than
transmembrane orientation [212, 213], leading to doubt that it could function by the same pore
formation mechanism as protegrin. Experimental studies of β-hairpin AMPs have shown
targeting of not only the bacterial inner membrane, but also components of the outer membrane:
a study using polyphemusin analogs indicated binding to divalent cation binding sites on
lipopolysaccharide (LPS) molecules [214]. Tachyplesin has also been shown to interact with
LPS micelles via NMR [215]. A study using giant unilamellar vesicles (GUVs) showed that
gomesin made the GUVs burst suddenly; stable pores were not observed, indicating that gomesin
21
may affect GUVs by the carpet mechanism [77]. Androctonin is a β-hairpin AMP that has a
structural twist in its backbone; ATR-FTIR experiments indicated that androctonin stays on the
membrane surface without destabilizing the bilayer structure [216]. Androctonin binds only to
negatively charged lipid vesicles and adopts a -sheet structure but leaves the acyl chain order
unaffected, suggesting a detergent-like mechanism [216].
Experimental results obtained using the β-hairpin family have not only provided the fundamental
knowledge listed above, but also led to their identification as a possible basis for the
development of novel antimicrobial therapeutics. Iseganan IB-367, a protegrin AMP designed
for activity against microflora associated with oral mucositis [217], was granted fast-track status
in both the United States and European Union for a Phase-II/III trial for prevention of
nosocomial pneumonia [218]. However, those trials were discontinued in 2004, as they failed to
show improvements over existing treatments, and no AMP-based drugs have ultimately been
given final approval, despite these compounds’ promisingly low in vitro minimum inhibitory
concentrations.
Besides the lack of progress in therapeutic development, the experimental work on β-hairpin
AMPs has limitations. For example, deconvolution of NMR signals does not always produce
definitive information about pore structure and topology, and NMR signal processing would
make it difficult to distinguish the characteristics of a diverse population of pores. Although the
previous NMR study of a protegrin pore yielded reasonable conclusions about the number of
peptides in the pore (8–10 peptides), it came to a suspect conclusion about the topology of the
peptides within the pore (NCCN parallel; [205]). That study could not definitively determine
whether the peptides formed a closed β-barrel or were arranged as a β-sheet. In addition, the
numerous experimental studies of protegrin have sometimes resulted in contradictory evidence.
22
While NCCN parallel topology was favored by the previously mentioned NMR study, other
studies have revealed a mixed or NCCN antiparallel topology (see above). There has also been
contradictory evidence regarding protegrin’s pore size: despite numerous predictions of a pore
diameter of approximately 20 Å, one experiment suggested a much larger pore of diameter 30–
40 Å [219]. Finally, experimental techniques generally do a poor job of revealing detailed
information about intricate processes such as the pore formation pathway, which tend to occur on
short timescales.
Because of those experimental shortcomings, protegrin has also been the subject of many
computational studies. Although a comprehensive review of protegrin simulations would be
beyond the scope of this section, we briefly mention a few of the most relevant results here;
further, a previous review of computational studies of protegrin is available [203]. Monomers of
protegrin have been subject to all-atom simulations in both surface and transmembrane
orientations [220]. In addition, complete β-barrel models of protegrin-1 based on the
experimentally suggested NCCN parallel β-barrel structure have been subjected to all-atom
simulations [59, 221-223]. Our laboratory observed that the intrinsic tilt and twist values of
NCNC parallel tetramers formed protegrin-1 into an arc shape, which formed stable pores on a
timescale of 300 ns [100] (Figure 1.5). However, those explicit simulations showed that a lipid
entered the pore lumen, displacing water; this implies that a single NCNC parallel tetrameric arc
may be insufficient for a stable conductive pore. Our laboratory has also investigated complete
NCNC parallel protegrin β-barrel models [100, 224], which concluded that the barrels were
stable in simulations shorter than the present dissertation’s all-atom investigations.
23
Figure 1.5. Snapshot from simulation of single NCNC parallel protegrin-1 tetrameric arc [100].
Our laboratory has also proposed implicit models of protegrin β-barrels, which show the highest
octameric β-barrel stability in NCNC parallel topology [224]. Although ssNMR results had
suggested NCCN parallel topology [205], in that topology, the barrels were much less stable in
implicit pores than those in NCNC parallel or NCCN antiparallel topologies, because the latter
two topologies allow all monomers’ hydrophobic sides to face the membrane [224]. Explicit
simulations also showed the NCNC parallel topology to be more stable. Therefore, simulation
studies have provided information regarding topology that has been difficult to generate using
experimental methods.
Protegrin has also been the subject of free energy calculations to determine the favorability of
dimerization, insertion, and tilting within the membrane. PMFs have been calculated for
protegrin dimerization [96], adsorption of monomers and dimers to membrane bilayer interfaces
[225], and insertion into a lipid bilayer [226] in an effort to clarify the major steps in protegrin
pore formation. Another study also calculated PMFs for protegrin’s orientation within membrane
bilayers, finding a significant tilt angle at the optimal orientation [227]. This is information that
has been difficult to obtain experimentally.
24
The rest of the β-hairpin AMP family has not been studied computationally as thoroughly as
protegrin has. Some peptides from the β-hairpin family, such as androctonin, had not been
simulated at all until the investigations reported in Chapter 2. However, some computational
investigations of β-hairpin AMPs besides protegrin have been performed. For example, the sum
frequency generation spectroscopy results used to assert that tachyplesin orients parallel to the
membrane surface were also backed by MD studies verifying the results [212]. An MD study of
three C-terminal analogues of human β-defensin 3 indicated the accretion of well-defined
structures that compacted positive charges together within peptide oligomers, which was
correlated with antimicrobial activity [228]. That study offered a picture of aggregation leading
to toxicity, which is attractive in light of the present dissertation’s goals. Zhou et al. performed
equilibrium and restrained MD simulations of bovine lactoferrin, which should show a transition
from a mixed α-helical β-strand region in the protein to a twisted antiparallel β-sheet in the
peptide [229]. Although the peptide as released from the protein was relatively unstable, a
directional force had to be exerted on the peptide for the change to a β-strand to be observed in
60 ns. Rausch et al. formed a combinatorial library of β-sheet-forming peptides [230, 231],
arriving at insights regarding structure–function relationships. That information could be useful
when designing future β-hairpin AMP-based therapeutics. Although some of the peptides from
their combinatorial library are studied in Chapter 2, those peptides differ from the rest of the β-
hairpin family in their larger size and absence of disulfide bonds. The absence of disulfide bonds
may make the formation of those combinatorial library peptides entropically unfavorable.
Although previous computational studies of β-hairpin AMPs have yielded some promising
results, those results also have limitations. For example, some previous authors may have
assumed that their results applied uniformly or generally when such assumptions were not
25
warranted: one study estimated that 100 total protegrin pores are necessary to kill an E. coli cell
[232], but this estimate was made using a rough, static estimate of pore size. Other studies have
also made analogous assumptions about the uniformity of protegrin pores. For example, although
previous computational studies of protegrin β-barrels have employed only 8 or 10 peptides, it is
not clear that protegrin pores comprise a uniform population, and some have speculated that the
pore population is nonuniform [205]. Further, there has been a lack of β-hairpin AMP
simulations at time scales that could determine the pores’ lifetime or long-term stability. For
example, our laboratory’s previous all-atom simulations of protegrin β-barrels [224] and arcs
[100] have been limited by computational resources to a few hundred ns. Therefore, we have
been unable to make any definitive determinations about the stability of the previously simulated
pore structures. Such simulations by our laboratory have also been limited by computational
resources to only a few initial configurations and oligomeric multiplicities, and we have not been
able to run any simulations using a tilt angle from vertical. The PMF calculations run on
protegrin have investigated only limited situations, such as dimerization on the membrane
surface and membrane insertion of a monomer, and no PMF calculations have been run on other
β-hairpin AMPs. The simulations necessary for PMF calculations are expensive and complicated
to run, contributing to this lack of information about these peptides’ energetic landscape of pore
formation.
Aims of Dissertation
In view of the lack of authoritative knowledge about the pore state of β-hairpin AMPs, in this
dissertation, we performed MD simulations to clarify both the final pore state and its formation
pathway. In addition to exploring various possibilities for the protegrin pore state, we aimed to
compare the results with analogous ones found using different β-hairpin AMPs. We did this
26
using both implicit membrane and all-atom simulations; the all-atom simulations reported here,
to the author’s knowledge, are the longest ones yet reported on β-hairpin AMPs.
In Chapter 2, we report simulations of β-barrels and arcs of several β-hairpin AMPs in anionic
implicit membranes. The goal was to determine the relative favorability of β-barrels, which have
been proposed as the basis of protegrin pores, for the rest of the β-hairpin AMP family.
In Chapter 3, we perform an optimization study of protegrin β-barrels in implicit membranes and
compare the results with those for various mutants. The goal was to determine the range of the
number of monomers per pore that would result in the most stable β-barrels. This was predicted
to indicate whether the β-barrel pore state may consist of a diverse population of sizes.
In Chapter 4, we report all-atom simulations of various protegrin-1 oligomers on the membrane
surface and in transmembrane topologies, which were executed on the Anton 2 supercomputer.
We also compared the results with those for the β-hairpin AMP tachyplesin. The goal was to
illustrate β-hairpin AMP pores using longer all-atom simulations than had been available
previously, which was predicted to show the feasibility of putative pore structures. In this
chapter, we varied the peptides’ initial topology and configuration to gain insights about peptide
aggregation and how it affects the final pore state. The overall aim of the dissertation was to
elucidate the pore state and formation pathway of β-hairpin AMPs.
27
2. Implicit membrane investigation of the stability of antimicrobial peptide β-barrels and
arcs
Published as: [2]
Summary
Previous simulations showed that the β-hairpin antimicrobial peptide (AMP) protegrin-I can
form stable octameric β-barrels and tetrameric arcs (half barrels) in both implicit and explicit
membranes. Here, we extend this investigation to several AMPs of similar structure: tachyplesin,
androctonin, polyphemusin, gomesin, and the retrocyclin θ-defensin. These peptides form short
β-hairpins stabilized by 2‒3 disulfide bonds. We also examine synthetic β-sheet peptides selected
from a combinatorial library for their ability or inability to form pores in lipid membranes. When
heptameric, octameric, and decameric β-barrels and tetrameric arcs of these peptides were
embedded in preformed neutral or anionic lipid pores (i.e., pores in neutral or anionic
membranes, respectively), a variety of behaviors and membrane binding energies were observed.
Due to the cationic charge of the peptides, more favorable transfer energies and more stable
binding were observed in anionic than neutral pores. The synthetic peptides bound very strongly
and formed stable barrels and arcs in both neutral and anionic pores. The natural AMPs exhibited
unfavorable or marginally favorable binding energy and kinetic stability in neutral pores,
consistent with the lower hemolytic activity of some of them compared with protegrin-I. Binding
to anionic pores was more favorable, but significant distortions of the barrel or arc structures
were sometimes noted. These results are discussed in light of the available experimental data.
The diversity of behaviors obtained makes it unlikely that the barrel and arc mechanisms are
valid for the entire family of β-hairpin AMPs.
Introduction
28
Antimicrobial peptides (AMPs) are small (12‒50-amino-acid), usually cationic peptides that
provide immunological defenses [19, 196, 233] against bacteria, fungi, parasites, the HIV virus,
and even cancer cells [19, 21, 78, 82, 233-235]. They could serve as the basis of novel antibiotics
[236]. Their mechanism of action is not known precisely, but there is considerable evidence that
they target cell membranes [70, 237].
The positive charge of AMPs offers an explanation for their selectivity for prokaryotic over
eukaryotic cells [33, 238]. Bacterial membranes tend to be anionic, (i.e., rich in acidic
phospholipids like phosphatidylglycerol [PG] and cardiolipin [239]). In mammalian cells, acidic
phospholipids are usually sequestered in the inner plasma membrane leaflet, whereas the outer
leaflet is usually comprised of zwitterionic phosphatidylcholine and sphingomyelin molecules
[200]. Although the anionic composition of bacterial inner membranes varies widely, 30%
anionic content is typical [239]. For example, the composition of Escherichia coli inner
membrane was found to be 70%‒75% phosphatidylethanolamine (PE), 18%‒22% PG, and 6%‒
8% cardiolipin [240], depending on temperature. Bilayers of PE and PG at a 7:3 ratio are
commonly used to mimic bacterial cell membranes [241].
AMPs may micellize and/or disintegrate the membrane (i.e., the carpet mechanism; [237]) or
aggregate to form pores that cause fatal ion leakage [31, 242]. The pores may be cylindrical,
lined by peptides (i.e., the barrel-stave model) or toroidal, stabilized by peptides and lined
partially by lipids. There is evidence that alamethicin forms barrel-stave pores, whereas melittin
and magainin form toroidal pores [52, 68]. Both cylindrical and toroidal pores were classically
viewed as ordered structures, but molecular dynamics (MD) simulations have suggested that
some AMPs may form disordered pores [83, 84, 165].
29
Most AMPs are helical when membrane-bound. However, some are disordered, and some form
β-hairpins. The best-studied of the latter family are the protegrins, small β-hairpins stabilized by
2 disulfide bonds; the face with the disulfide bonds contains charged or polar residues, and the
opposite face has a hydrophobic cluster flanked by charged residues. They are active against
Gram-positive and Gram-negative bacteria and fungi in vitro [243, 244]. A large number of
variants [245, 246] and synthetic analogs [247] have been synthesized. Other β-hairpin AMPs
include the retrocyclin θ-defensin [248], tachyplesin [249], polyphemusin [250], gomesin [251],
and androctonin [252].
Protegrin-1 (hereafter called protegrin) is the best-studied AMP of this family, both
experimentally [49, 61, 253] and computationally [203]. It forms ion channels in membranes
[254, 255]. MD simulations have been performed of protegrin monomers in micelles (e.g., [256])
and of monomers and dimers in bilayers with transmembrane and interfacial orientations [149,
220, 257-259]. Tilting within the membrane [227] and association with and insertion into an
anionic membrane [226] have also been calculated. The evidence that it oligomerizes into a
closed β-barrel [205] inspired simulations of β-barrel models [59, 221-224].
Previous computational studies from this laboratory in implicit and explicit membranes
examined the interaction of protegrin monomers with membranes and pores and the relative
stability of different β-barrel topologies [224]. The NCNC parallel topology was most stable,
because it allows immersion of the hydrophobic cluster of each peptide into the nonpolar
membrane interior. Further, incomplete barrels (arcs) formed kinetically stable pores for 300 ns
[100]. Thus, the barrel or arc structures seem to constitute viable pore formation mechanisms for
protegrin.
30
We presently ask whether the other β-hairpin AMPs could work by the same mechanism. While
that would be an attractive proposal, experimental studies have suggested the carpet mechanism
for gomesin [77], non-pore-forming internalization for polyphemusin [260], and an orientation
parallel to the membrane plane for tachyplesin [213]. It would be interesting to rationalize these
differences through molecular modeling; we do this here using an implicit membrane approach
[117, 186]. We construct tetrameric arcs and heptameric, octameric, and decameric β-barrels of
θ-defensin, tachyplesin, polyphemusin, gomesin, and androctonin, insert them into implicit
toroidal pores of varying radii, and subject them to MD simulations. We observe their kinetic
stability and estimate their thermodynamic stability by computing their transfer energies from the
pores to bulk water. Our goal is to determine how structural differences are associated with
differences in pore-forming ability.
In addition to the AMPs, we studied two 26-residue peptides selected from a combinatorial
library based on known structures of membrane-spanning β-sheet peptides [231]. The first is a
good pore former and contains the residues YGKRGF in the combinatorial sites; it has sterilizing
antimicrobial activity and low activity against mammalian cell membranes [230]. The second
peptide lacks pore-forming ability and contains AGGKGF in the combinatorial sites. Rausch et
al. [231] noted that the interfacial, hydrophobic sites in the library peptides support a membrane-
spanning mechanism. However, fluorescence spectroscopy showed that the peptides were
partially exposed to water on the bilayer surface rather than being in a membrane spanning-state,
which suggested a carpet mechanism [230]. The authors also speculated that carpet model pores
might be formed on a mechanistic pathway toward more structured β-barrel pores [231].
Methods
Energy Functions
31
The simulations in this study employed Implicit Membrane Model 1 (IMM1; [112]), which is an
extension of Effective Energy Function 1 (EEF1) for soluble proteins [108]. IMM1 extends
EEF1 to heterogeneous membrane-water systems by making the solvation parameters dependent
on vertical position. These are modeled as linear combinations of the values for water and
cyclohexane; further, the dielectric’s dependence on vertical position accounts for strengthening
of electrostatic interactions within the membrane. IMM1 has been extended to account for
surface charge due to anionic lipids using Gouy-Chapman theory [115], transmembrane voltage
[120], membrane dipole potential (Zhan and Lazaridis 2012), and lateral pressure effects [122].
IMM1 can also accommodate pores [117, 118], whose shape can be adjusted by making the
radius dependent on vertical position:
R = Ro + kz2; z = |z| / (T / 2)
where Ro is the pore radius at the membrane center, R is the radius at a given z-level, T
represents the hydrophobic thickness of the membrane, and k (curvature) determines pore shape.
For example, Ro = 15 Å and k = 0 defines a cylindrical pore of radius 15 Å, whereas Ro = 15 Å
and k = 20 Å defines a toroidal pore with radii of 15 and 35 Å at its center and rims, respectively.
Because Gouy-Chapman theory can no longer be used in pore geometries, the electrostatic
potential in anionic pores (i.e., ones comprised of anionic lipids) is obtained by solution of the
Poisson-Boltzmann (PB) equation [119]; those potential values are applied as a static field in
MD simulations. We solve the PB equation and use it similarly to the analytical Gouy-Chapman
equations by adding an extra term to the effective energy function representing the interaction
between solute charges and the electrostatic potential ⃑ :
∑ ⃑
32
This simple approximation gives acceptable results compared with the full nonlinear PB
treatment [183]. The bilayer’s dielectric properties are represented by a five-slab model (see
Figure 2 from [119]), whereby ε(d) depends on distance (d) to the hydrophobic core’s surface:
{
where εmemb (the dielectric constant inside the membrane), εhead (that inside the interfacial
region), and εwater (that in water) are 2, 10, and 80, respectively [119]. Width D was set to 3.0 Å,
localizing the boundary around the phosphate group. The ion accessibility factor is assigned
values of
{
so that ions cannot penetrate below the phosphate groups; the ions were taken as monovalent
with radius 2.0 Å. To reproduce the membrane dipole potential, two layers of charges were
defined as Gaussian distribution functions:
∑
√
where i, oi, and i represent charge per unit area, offset of the charge layer from the membrane
surface, and Gaussian width, respectively. Positive and negative charge layers, separated by 1.0
Å according to experimental data [119], represent the charge distribution in the membrane; i is +
and for the positive and negative charge layers, respectively. The negative and positive charge
layers are localized on and below the plane of the lipid phosphate groups, respectively, to create
a positive dipole potential in the membrane interior. + was set to +1q / A, where A is the area per
lipid within the membrane (68 Å2 for 1,2-dioleylphosphatidylcholine [DOPC] and 1,2-
dioleylphosphatidylglycerol [DOPG] bilayers), and was set to (1 + ZI anfr) q / A, where
33
anfr is the fraction of anionic lipids in the membrane, and ZI is the charge of an anionic lipid
molecule. The hydrocarbon core thickness was set at 26 Å (in accordance with the thickness of
DOPC membranes; He et al. 2013), and anfr of 30% was used, in accordance with the typical
composition of bacterial membranes [239].
The model accounts for the fact that head group density (and therefore charge density) may not
be uniform on curved pore surfaces. It assumes that charge density on the pore rim is equal to
that of a flat membrane (0) and that charge density within the pore changes quadratically with
|z|, or vertical distance from the center of the membrane:
The homogeneity factor h (i.e., the ratio of charge density at the center of the pore to that in the
intact membrane) was 0.6 in this study, according to all-atom simulation results [119].
The system was set up using mBuild, an in-house software package [119]. The Poisson-
Boltzmann equation was solved using the Advanced Poisson-Boltzmann Solver [261], taking
average values in grid volumes after discretizing the space into a finite lattice box. The grid size
was 161 × 161 × 161, with five focusing levels used to improve accuracy; that is, the calculations
were run successively in cubic boxes of edge length 640 Å, 480 Å, 240 Å, 120 Å, and 80 Å (final
resolution: 0.5 Å). For each run, the previous run’s potential was the boundary potential. Each
volume was assigned values of dielectric constant, ion accessibility, and charge density by the
distribution functions above; these simulated membranes were embedded into cubic boxes filled
with 0.1 M aqueous salt ion solution. Multiple Debye-Hückel boundary conditions were used,
and trilinear interpolation was used to obtain the PB values and their derivatives. These are
assumed to be steady state values, not changing throughout the simulation due to ion transport.
Initial Structures
34
The coordinate files for protegrin, θ-defensin, gomesin, polyphemusin, tachyplesin, and
androctonin were downloaded from the Protein Data Bank (PDB; entries 1PG1 [204], 1HVZ
[209], 1KFP [251], 1RKK [250], 1WO0 [Mizuguchi et al., unpublished], and 1CZ6 [252],
respectively). CHARMM version 39a2 [262] was used to import the NMR model of each peptide
monomer’s structure that seemed most conducive to β-barrel formation (i.e., the one in which the
peptide’s structure was closest to a flat, ideal β-hairpin) and assign disulfide bonds between the
appropriate residues. The peptides from the combinatorial library by Rausch et al. [231] were
initially built as β-strands. All charged residues were in their standard ionization states
corresponding to pH ~7.
Then, the proper intramolecular hydrogen bonds for monomers of each peptide were imposed as
distance constraints using a symmetrical potential well. For this, the values of kmin, rmin, kmax,
and rmax within CHARMM’s Nuclear Overhauser Effect (NOE) facility were set to 1.0, 1.8, 5.0,
and 2.3, respectively. Mean miscellaneous field potentials (MMFP) were applied to constrain the
Cα carbons onto a plane, flattening the β-hairpins into conformations more conducive to barrel
formation. After the above constraints were imposed, the energy of the peptides was minimized
using the adopted basis Newton-Raphson algorithm (ABNER; used for all energy minimizations
for 300 steps), followed by 200 ps of MD simulation using the Verlet integrator with a time step
of 2 fs at 298.5 K (the same integrator, time step, and temperature were used in all MD
simulations). Then, energy minimization yielded the final monomeric structures used to
construct the β-barrels or arcs.
Simulations
The monomeric structures were arranged as tetrameric arcs or heptameric, octameric, or
decameric β-barrels around the z-axis by translation of 1114 Å in the x direction followed by
35
rotation around the z-axis. For the β-barrels, the appropriate number of monomers was arranged
in an evenly spaced cylinder around the z-axis in implicit water; for tetrameric arcs, four
monomers were spaced evenly with z-axis rotations of 0°, 45°, 90°, and 135° (effectively
forming half of an octamer barrel). We arranged the barrels and arcs in conformations analogous
to those of protegrin: with the more hydrophobic side facing the membrane, the more hydrophilic
side facing the pore, and the backbone hydrogen atoms both intermolecularly and
intramolecularly H-bonded. Then, without any MMFP or NOE constraints, the β-barrel or arc
underwent minimization in water with backbone constraints. Then, the appropriate intra- and
intermolecular hydrogen bonds were imposed as NOE constraints, and minimization was
performed without backbone constraints. Subsequently, 200 ps of MD simulation was run in
water, followed by minimization.
After the β-barrel or arc underwent brief dynamics in water, the resulting structure was inserted
into an implicit 26-Å-thick membrane and subjected to additional MD simulation. We set out to
select the most realistic possible dimensions to represent the pores generated by the AMPs under
investigation, so we conducted simulations with varying pore radii to find the conditions that
provide optimal binding energies. We selected one value for which good protegrin octamer -
barrel binding results were previously obtained (Ro = 15 Å and k = 15 Å; Lazaridis et al. 2013).
However, Rausch et al. (2007) suggested a pore radius of 10 Å, and initial simulations with
YGKRGF indicated enhanced pore binding of the octamer -barrel with Ro = 12 Å as compared
with Ro = 15 Å. Therefore, for all peptides, we ran 2-ns simulations in pores of Ro = 10 Å, 12 Å,
and 15 Å; we used both 30% anionic and zwitterionic membranes and four oligomeric states:
tetramer arcs and heptamer, octamer, and decamer -barrels. In all cases, k was 15 Å. For the
arcs, shorter simulations were also run with k = 10 or 5 Å, but in no case was the stability in the
36
pore better (and in some cases it was worse) than with k = 15 Å. (For our analysis, we selected
the pore radius for each peptide and membrane charge condition that gave the best results: the
most stable barrel/arc and most favorable binding energies.)
Once the -barrel or arc had been inserted into the center of the pore, NOE and MMFP
constraints were released for the production-length MD simulations. A simulation length of 2 ns
was selected for all conformations. When we performed longer simulations on example peptides,
we obtained results that converged onto those for the 2-ns simulations. In all conditions, the
results seem to have stabilized by the end of a 2-ns MD simulation. The binding energy to the
pore (ΔW) was estimated by averaging the energy of the barrel or arc at its position in the pore
and subtracting the energy of the same conformation in water. In cases where the oligomer
remained bound to the pore throughout the entire simulation, the value of ΔW was calculated by
averaging values obtained every 1 ps throughout the last 1 ns of the simulation; in cases where
the oligomer left the pore within 2 ns of MD simulation, the ΔW values were obtained by similar
averaging during the period of 3‒22 ps. Simulations using different random seeds and longer
durations, run as checks, gave very similar results. At the end of the MD simulation,
minimization provided the final post-MD image of the -barrel or arc.
Results
Structural and Activity Comparison of Peptides
In previous work, protegrin in NCNC parallel topology was observed to form stable β-barrels in
both neutral and anionic membranes, with those in the latter being more stable [224]. In addition,
four separate monomers in an implicit pore were observed to associate, forming a tetrameric arc
of the same topology; the resulting structure formed stable pores in all-atom simulations [100].
In this study, we investigated the behavior of several similar peptides using simulations in
37
implicit membrane pores. Before presenting the simulation results, we qualitatively compare the
sequences (Figure 2.1) and structures of the peptides when configured as β-barrels in NCNC
parallel topology (Figures 2.2–2.4). We also relate these comparisons to the peptides’ reported
activity levels.
Figure 2.1. Sequence alignment of the investigated peptides. Certain conserved residues are
colored. The numbers represent residue positions in protegrin-I. The numbering reflects the
sequence of protegrin-I. Figure created using STRAP [263].
Experimental [205] and computational [221, 223, 224] results indicate protegrin’s ability to form
β-barrels in membrane pores. We thus infer that it has structural properties conducive to that
arrangement. Protegrin’s β-hairpin conformation is constrained by two disulfide bonds, and the
open ends of the hairpin both contain positively charged arginine residues (Figure 2.2a). The turn
region of the hairpin is also highly concentrated in basic residues, containing three consecutive
arginines; the resulting positive electrochemical potential in protegrin’s turn region can be seen
upon solution of the PB equation at the solvent-accessible surface (Figure 2.3a). Further,
protegrin has a relatively clear separation between polar and nonpolar regions. The β-sheet
region between the turn and ends is relatively hydrophobic and nonpolar, with a clear division in
38
hydrophobicity between the two sides of the molecule (Figure 2.4a): no charged or polar residues
face the membrane, increasing its stability in membrane pores, while one positively charged
arginine residue faces the pore in a 26-Å-thick membrane (all discussions of membrane–peptide
structural proximity concern 26-Å-thick membranes; Figure 2.2a). Studies with truncated forms
and disulfide variants of protegrin have shown the important role of the β-sheet and hairpin
regions (especially the three consecutive arginine residues) for its activity against Neisseria
gonorrheae [206]. Protegrin’s minimal inhibitory concentrations (MICs) for Gram-positive and
Gram-negative bacteria in one study were 0.3‒0.8 M and 0.7‒2.8 M, respectively [264].
However, these values vary widely depending on experimental protocol (see Discussion).
Protegrin also causes 50% hemolysis at 11.6 M [265] and about 65% hemolysis at 46.4 M
[266].
39
Figure 2.2. Visual structural comparison of the investigated peptides. Side views of one
monomer from the initial β-barrel/arc conformations of each peptide after 200 ps of molecular
dynamics (MD) simulation in water and 300 minimization steps but before insertion into a
membrane: (a) protegrin-I; (b) θ-defensin; (c) tachyplesin; (d) polyphemusin; (e) gomesin; (f)
androctonin; (g) YGKRGF; (h) AGGKGF. All peptides are oriented with the pore-facing side to
the right and the turn region of the hairpin facing down. The black lines denote where the borders
of a 26-Å-thick membrane region would be if the monomer were at center depth, the side chains
and main chain are represented as sticks, and colors denote atom/side chain properties. Sky blue:
basic side chain; red: acidic side chain or oxygen atom; purple: neutral, polar side chain; green:
40
nonpolar side chain; cyan: glycine H; yellow: cysteine side chain/disulfide bond; gray: main
chain. Figure created using MacPyMOL 1.7 [267].
Figure 2.3. Comparison of the investigated peptides’ electrochemical potential at the solvent-
accessible surface. Red: negative potential; white: middle; blue: positive potential. Potential
denotes charge buildup at the surface. Side views of one monomer from the initial β-barrel/arc
conformations of each peptide after 200 ps of molecular dynamics (MD) simulation in water and
300 minimization steps but before insertion into a membrane: (a) protegrin-I; (b) θ-defensin; (c)
tachyplesin; (d) polyphemusin; (e) gomesin; (f) androctonin; (g) YGKRGF; (h) AGGKGF. All
peptides are oriented with the pore-facing side to the right and the turn region of the hairpin
facing down. The black lines denote where the borders of a 26-Å-thick membrane region would
41
be if the monomer were at center depth, the chains are represented as black sticks, and the color
surface overlay denotes electrochemical potential according to the scale shown. Figure created
by solution of the Poisson-Boltzmann equation using the default parameters of the PyMOL
APBS Tools plugin in MacPyMOL 1.7 [267].
Figure 2.4. Comparison of the investigated peptides’ electrochemical potential at the solvent-
accessible surface. Red: negative potential; white: middle; blue: positive potential. Potential
denotes charge buildup at the surface. Side views of one monomer from the initial β-barrel/arc
conformations of each peptide after 200 ps of molecular dynamics (MD) simulation in water and
300 minimization steps but before insertion into a membrane: (a) protegrin-I; (b) θ-defensin; (c)
tachyplesin; (d) polyphemusin; (e) gomesin; (f) androctonin; (g) YGKRGF; (h) AGGKGF. All
42
peptides are oriented with the pore-facing side to the right and the turn region of the hairpin
facing down. The black lines denote where the borders of a 26-Å-thick membrane region would
be if the monomer were at center depth, the chains are represented as black sticks, and the color
surface overlay denotes electrochemical potential according to the scale shown. Figure created
by solution of the Poisson-Boltzmann equation using the default parameters of the PyMOL
APBS Tools plugin in MacPyMOL 1.7 [267].
θ-defensin has a cyclic backbone and contains three disulfide bonds (compared with two for
protegrin and the other AMPs studied; Figures 1, 2b). In this study, we investigate the open chain
analog of θ-defensin. The cyclic analog is required for antimicrobial activity in the presence of
150 mM sodium chloride and is three times as active as the acyclic analog [268]. MIC values of
1.0 and 2.1 M for Escherichia coli and Staphylococcus aureus, respectively, have been
observed for θ-defensin [266]. This peptide is relatively non-amphiphilic, accounting for its
relatively low antimicrobial activity [208, 209], but it can also prevent HIV entry into cells,
possibly as a competitive inhibitor of the gp120:gp41 membrane binding/fusion process [210]. θ-
defensin is much less hemolytic than protegrin; nevertheless, the cyclic analog caused 3%
hemolysis at 5.5 g/mL [266]. When configured as a β-barrel, three of θ-defensin’s arginine side
chains point towards the membrane rather than the top/bottom edges or pore interior (Figure
2.2b), and one additional polar group (Thr 17) is also oriented towards the membrane; this breaks
the clear division in hydrophobicity between the membrane-facing and pore-facing sides seen in
protegrin (Figure 2.4b). The electrochemical potential surface map (Figure 2.3b) also shows that
θ-defensin has less positive charge concentration in the turn region than does protegrin. These
features make θ-defensin less than ideal for the same type of pore-forming structure as protegrin
43
in bacterial cells. Further, θ-defensin lacks the larger hydrophobic side chains that face the
membrane in protegrin, which may negatively affect its affinity for the membrane.
Tachyplesin also exhibits less amphipathicity than protegrin (Figure 2.4c). One arginine residue
(Arg 15) faces the membrane in embedded tachyplesin β-barrels. Further, in this arrangement,
tachyplesin has two arginine residues (Arg 5 and Arg 14) facing the pore (compared with one for
protegrin), which may cause crowding and electrostatic repulsion within the pore regionand
make β-barrel formation less favorable (Figure 2.2c); the electrochemical potential is also quite
high in this region (Figure 2.3c). These structural differrences may contribute to previous
indications that tachyplesin orients parallel rather than normal to the membrane [212, 213].
Tachyplesin showed about 10% and 25% hemolysis at 100 and 150 g/mL, respectively, but the
hemolytic activity of a cysteine-deleted analog was abolished [269]. Nevertheless, the cysteine-
deleted analog’s antibacterial activity was relatively intact [269]. MICs of 0.8‒12.5, 3.1‒12.5,
and 1.6‒3.1 g/mL for Gram-negative bacteria, Gram-positive bacteria, and fungi, respectively,
have been observed for tachyplesin [270]. Another study observed nearly linear dependence of
hemolysis on tachyplesin’s concentration, finding 5% and 100% hemolysis at 20 and 100M,
respectively [271].
Polyphemusin is extremely similar structurally to tachyplesin (Figure 2.1), but it contains an
additional Arg residue at the N-terminus [270]. The disulfide bridge structure is identical
between polyphemusin and tachyplesin, and each peptide has one charged residue facing the
membrane in β-barrel conformation (Arg 15 and Lys 16 for tachyplesin and polyphemusin,
respectively; Figure 2.2c–2.2d). MIC values of 3.1‒12.5 g/mL for Gram-negative bacteria and
6.3 g/mL for Gram-positive bacteria and fungi have been observed for polyphemusin,
indicating that its activity level is quite similar to tachyplesin’s [270]. Another study of
44
polyphemusin obtained MICs of 0.125‒0.5 g/mL against Gram-negative and Gram-positive
bacteria and 21.3 g/mL against human red blood cells; a study using polyphemusin analogs
indicated that the peptide binds to divalent cation binding sites on target cells’
lipopolysaccharide molecules, displacing divalent cations to penetrate/permeabilize the outer
membrane [214]. Although polyphemusin and tachyplesin have quite similar structures,
polyphemusin’s antimicrobial activity is dependent on disulfide bridges, as a linear analog with
cysteine replaced by serine showed 4‒16-fold less activity than polyphemusin; β-sheet structure
is also required for polyphemusin to translocate past model membranes [250].
Gomesin has a relatively similar structure to protegrin (Figure 2.1) but contains a pyroglutamic
acid residue at the N-terminus. In addition, two arginine residues face the membrane in β-barrel
conformation (Figure 2.2e), which reduces the difference in hydrophobicity between the solvent-
facing and membrane-facing sides of the molecule (Figure 2.4e). Gomesin has less positive
electrochemical potential than protegrin in the turn region (Figure 2.3e). MICs of 0.4‒6.25, 0.2‒
12.5, and 0.2‒25 g/mL for Gram-negative bacteria, Gram-positive bacteria, and fungi,
respectively, have been measured for gomesin; direct comparison with androctonin revealed that
gomesin was more active against most bacteria and fungi [272]. Similarly to some other AMPs
under investigation, gomesin’s disulfide bonds are important to its antimicrobial and hemolytic
activity [251, 273, 274]: activity is markedly decreased upon reduction/alkylation of the disulfide
bridges [272]. Further, while gomesin is hemolytic at low concentrations (16% hemolysis at
1M), hemolytic activity had little dependence on concentration (22% hemolysis at 100M),
making it significantly less hemolytic than protegrin in the high-concentration regime [272]. One
study showed that gomesin made giant unilamellar vesicles burst suddenly; stable pores were not
observed, indicating that gomesin may work by the carpet mechanism [77].
45
Androctonin shows some sequence homology to tachyplesin and polyphemusin [275]; however,
it also has structural features that distinguish it from the other investigated peptides. Whereas
gomesin, tachyplesin, and polyphemusin have three residues in each segment upstream and
downstream of the disulfide bridges, androctonin has three residues in one segment and five in
the other, with Cys 4 and Cys 10 bonded to Cys 20 and Cys 16, respectively (Figure 2.1; see
Figure 5 from [272]). Probably because of this, androctonin’s NMR structure is a highly twisted
antiparallel β-sheet with strands connected by a positively charged turn [252]. This feature might
affect androctonin’s ability to form a β-barrel. In addition, androctonin has one arginine and two
lysine residues facing the membrane in this arrangement, rather than large hydrophobic side
chains (Figure 2.2f); this significantly reduces the hydrophobicity difference between the two
sides of the molecule (Figure 2.4f), although in the conformation we used, the two sides of the
molecule did vary in electrochemical potential (Figure 2.3f). MICs of 1.5‒>30, 0.3‒30, and 2‒50
g/mL for Gram-negative bacteria, Gram-positive bacteria, and fungi, respectively, have been
measured for androctonin [275]; it was significantly less active than gomesin in most conditions
that provided for direct comparison [272]. Androctonin is not hemolytic even at 150 M [275].
Silva et al. [272] attributed the differences in hemolytic activity between androctonin on the one
hand and gomesin and tachyplesin on the other to androctonin’s longer C-terminus and charge
differences throughout the molecule. ATR-FTIR experiments seemed to indicate that
androctonin is localized on the membrane surface and does not destabilize the bilayer structure
[216]. Androctonin binds only to negatively charged lipid vesicles and seems to adopt a -sheet
structure while leaving the acyl chain order unaffected, suggesting a detergent-like mechanism
[216].
46
YGKRGF and AGGKGF have some similarities with the protegrin family, such as the general
locations of the positively charged and polar residues, but they also show several structural
differences (Figure 2.1). These peptides are longer than protegrin (26 residues) and contain no
disulfide linkages. However, the rational combinatorial library from which these peptides were
extracted preserves certain key characteristics of the protegrin family. For example, aromatic
residues are found at the lipid-exposed interfacial positions, and basic residues are found in the
pore-lining region (Figure 2.2g‒2.2h). The general locations of positive charges within the
peptides have some similarity to those in protegrin: there is a pair of polar combinatorial sites in
a position analogous to the pore-facing arginine residue in protegrin. Besides protegrin, these
two peptides are the only ones studied that have no significant interruptions in the
hydrophobicity of the molecule’s membrane-facing side (Figure 2.4g‒2.4h). The turn region of
YGKRGF and AGGKGF differs from the ones found in the AMPs we investigated in that they
lack arginine and include a negative charge; this reduces the turn region’s overall
electrochemical potential (Figure 2.3g‒2.3h). While both YGKRGF and AGGKGF are active
against Escherichia coli and show broad-spectrum antimicrobial activity, only YGKRGF causes
measurable leakage of the contents of lipid vesicles, with the release of molecules as large as 3
kDa signifying a pore diameter of ~10 Å [231]. YGKRGF also had a low MIC against
Staphylococcus aureus (2.1 M; [231]). In contrast, AGGKGF had the highest hemolytic
activity, lysing human red blood cells at 15 M. Relatively small structural differences
differentiate YGKRGF, which forms functional pores, from AGGKGF, which does not. The
presence of two charged side chains facing the pore (instead of one) and the replacement of an
alanine with a tyrosine facing the membrane seem to increase the peptide’s pore-forming ability.
Simulation Results
47
The tetramer arcs and heptamer, octamer, and decamer β-barrels of the peptides were subjected
to 2-ns MD simulations in implicit toroidal pores with Ro = 10 Å, 12 Å, and 15 Å using both
30% anionic and zwitterionic membranes; we observed the peptides’ movement, structure, and
the thermodynamic stability of their arrangement. For each peptide, the pore radius that gave the
best energy in anionic membranes was chosen for further analysis (Table 2.1). The results for the
pore radii not selected for further analysis and further notes on the peptides’ behavior during the
simulations are found in Online Resource 1 from [2]. Not all peptides remained within the pore
for the duration of the simulation; notes on whether or not the peptides left the pore region or
became distorted during the simulations are found in Table 2.1, and top-down and side views of
the post-simulation conformations of the octamer barrels and tetramer arcs in pores of optimal
radii are shown in Figures 2.5–2.6. The binding energies of these β-barrels and arcs to the pores
were estimated by the transfer energy (ΔW) from water to pore (Tables 2.22.5, Figure 2.7).
Negative values indicate favorable binding.
48
Table 2.1. Behavior of selected tetramer arcs and heptamer, octamer, and decamer β-barrels
during 2-ns molecular dynamics (MD) simulations
Peptide Tetramer arc Heptamer barrel Octamer barrel Decamer barrel
Po
re r
adiu
s (Å
)
Pore charge
Po
re r
adiu
s (Å
)
Pore charge
Po
re r
adiu
s (Å
)
Pore charge
Po
re r
adiu
s
(Å)
Pore charge
Neu
tral
30
%
anio
nic
Neu
tral
30
%
anio
nic
Neu
tral
30
%
anio
nic
Neu
tral
30
%
anio
nic
Lea
ves
po
re
Dis
tort
ed
Lea
ves
po
re
Dis
tort
ed
Lea
ves
po
re
Dis
tort
ed
Lea
ves
po
re
Dis
tort
ed
Lea
ves
po
re
Dis
tort
ed
Lea
ves
po
re
Dis
tort
ed
Lea
ves
po
re
Dis
tort
ed
Lea
ves
po
re
Dis
tort
ed
Protegrin-1 10 10 12 15 x
θ-defensin 12 x x 15 x X 15 x x 15 x x
Tachyplesin 12 x x 15 x x x X 15 x x 12 x x
Polyphemusin 12 x x x x 15 x x x X 15 x x x 15 x x x x
Gomesin 10 x x 12 x X 15 x x 15 x x
Androctonin 10 x x 12 x X 15 x x 15 x x x
YGKRGF 10 10 x X 10 12
AGGKGF 10 10 10 10 x x
*This table represents the characteristics of the final minimized conformations of peptide
oligomers after MD simulations in implicit toroidal pores of the radii that gave the most
favorable transfer energies from solvent to membrane. These were the positions and
conformations of the peptides after the water-equilibrated monomers were arranged as octamer
barrels, subject to 200 ps of MD in water, minimized, inserted into pre-formed toroidal pores in
26-Å-thick implicit membranes, and subject to 2 ns of MD followed by minimization. For each
oligomeric state and pore charge condition, whether or not the peptide assembly left the pore
region during the course of the simulation is represented by a checkbox in the “Leaves pore”
column, and the presence of distortion is represented by a checkbox in the “distorted” column.
Table 2.2. Average membrane transfer energies (<ΔW>; kcal/mol) of tetramer arcs of peptides
from water to toroidal pores (k = 15 Å) from 2-ns simulations.
49
Tetramers:
Radius
selected (Å) Neutral pore
30% anionic
pore
Protegrin-1 10 -20.5 ± 2.1 -55.6 ± 3.2
θ-defensin 12 16.7 ± 24.8 a -11.9 ± 17.4
a
Tachyplesin 12 34.0 ± 25.4 a 9.7 ± 27.5
a
Polyphemusin 12 22.4 ± 25.0 a 1.2 ± 24.0
a
Gomesin 10 -5.7 ± 2.9 -23.6 ± 2.8
Androctonin 10 4.2 ± 3.4 -22.6 ± 7.2
YGKRGF 10 -50.6 ± 2.2 -70.2 ± 3.3
AGGKGF 10 -50.0 ± 2.4 -71.8 ± 3.2
a Tetramer left the pore during the course of the simulation; values estimated using the time
window of 3–22 ps. Other values estimated using the window 1001–2000 ps.
Table 2.3. Average membrane transfer energies (<ΔW>; kcal/mol) of heptamer barrels of
peptides from water to toroidal pores (k = 15 Å) from 2-ns simulations.
Heptamers:
Radius
selected (Å) Neutral pore
30% anionic
pore
Protegrin-1 10 -17.1 ± 2.5 -97.3 ± 4.7
θ-defensin 15 3.5 ± 3.4 -30.4 ± 3.6
Tachyplesin 15 17.9 ± 6.1a -19.1 ± 13.8
a
Polyphemusin 15 22.5 ± 18.5a -1.5 ± 21.4
a
Gomesin 12 7.7 ± 5.6 -36.5 ± 4.0
Androctonin 12 36.1 ± 5.5 -35.6 ± 7.0
YGKRGF 10 -77.8 ± 3.1 -127.7 ± 4.9
AGGKGF 10 -73.1 ± 2.8 -116.4 ± 3.5
a Heptamer left the pore during the course of the simulation; values estimated using the time
window of 3–22 ps. Other values estimated using the window 1001–2000 ps.
Table 2.4. Average membrane transfer energies (<ΔW>; kcal/mol) of octamer barrels of peptides
from water to toroidal pores (k = 15 Å) from 2-ns simulations.
Octamers:
Radius
selected (Å) Neutral pore
30% anionic
pore
Protegrin-1 10 -17.1 ± 2.5 -97.3 ± 4.7
50
θ-defensin 15 3.5 ± 3.4 -30.4 ± 3.6
Tachyplesin 15 17.9 ± 6.1a -19.1 ± 13.8
Polyphemusin 15 22.5 ± 18.5a -1.5 ± 21.4
Gomesin 12 7.7 ± 5.6 -36.5 ± 4.0
Androctonin 12 36.1 ± 5.5 -35.6 ± 7.0
YGKRGF 10 -77.8 ± 3.1 -127.7 ± 4.9
AGGKGF 10 -73.1 ± 2.8 -116.4 ± 3.5
a Octamer left the pore during the course of the simulation; values estimated using the time
window of 3–22 ps. Other values estimated using the window 1001–2000 ps.
Table 2.5. Average membrane transfer energies (<ΔW>; kcal/mol) of decamer barrels of
peptides from water to toroidal pores (k = 15 Å) from 2-ns simulations.
Decamers:
Radius
selected (Å) Neutral pore
30% anionic
pore
Protegrin-1 15 -17.2 ± 2.9 -101.8 ± 5.3
θ-defensin 15 137.7 ± 14.2a 62.8 ± 21.5
a
Tachyplesin 12 87.5 ± 48.6a 29.3 ± 75.9
a
Polyphemusin 15 77.7 ± 43.9a 28.8 ± 43.1
a
Gomesin 15 -1.3 ± 3.8 -65.7 ± 6.0
Androctonin 15 189.9 ± 39.1a -70.4 ± 6.4
YGKRGF 12 -106.4 ± 3.7 -177.8 ± 5.0
AGGKGF 10 -102.4 ± 4.6 -150.7 ± 6.5
a Decamer left the pore during the course of the simulation; values estimated using the time
window of 3–22 ps. Other values estimated using the window 1001–2000 ps.
Protegrin is the best studied among the peptides investigated. Throughout the 2-ns simulations,
all studied protegrin oligomers remained bound to both neutral and anionic pores, and transfer
energies to the pore-embedded state were favorable in all conditions (Tables 2.12.5). As
expected, the transfer energies for all protegrin oligomers were significantly more favorable to
anionic than neutral pores. (This trend also held for all other peptides in all conditions.) There
51
was little distortion of the barrels/arcs throughout the simulations at the pore radii that gave
optimum results (Figures 2.5a, 2.6a). The obtained ΔW values for protegrin matched well with
the results from a previous study [224].
The simulations of θ-defensin oligomers resulted in distortion of the peptide assemblies, and in
some conditions, the barrels/arcs of θ-defensin exited the pore (Tables 2.12.5). Throughout the
simulations, the θ-defensin octamer -barrel remained bound to both neutral and anionic pores
with 15 Å radii, but in the neutral case, some monomers moved to the center of the pore instead
of remaining adjacent to the pore interface (Figure 2.5b), and there was an unfavorable transfer
energy from water to pore; in an anionic pore, the octamer barrel distorted only slightly, and the
transfer energy was favorable. The θ-defensin tetramer arcs and heptamer and decamer barrels
displayed the same pattern of binding energies as the corresponding octamer barrels (i.e.,
unfavorable and favorable transfer energies in the neutral and anionic cases, respectively), but
the other oligomeric states of θ-defensin did not show stable behavior during the simulations
(Tables 2.12.5, Figure 2.7). The tetramer arcs migrated outside of both neutral and anionic
pores within 70 ps of simulation onset. During the simulations of heptamer barrels, θ-defensin
remained within the pore throughout the simulation, but the integrity of the barrel was not
maintained: there was barrel shear in a neutral pore, and the ring collapsed in an anionic pore.
The decamer barrels of θ-defensin exited the pore rapidly at the onset of the simulation (Table
2.1).
52
53
Figure 2.5. Top and side views of the minimized final conformations of octamer β-barrels of
peptides in toroidal pores of optimal radius in zwitterionic and 30% anionic membranes, after
molecular dynamics (MD) simulations. (a) protegrin-I; (b) θ-defensin; (c) tachyplesin; (d)
polyphemusin; (e) gomesin; (f) androctonin; (g) YGKRGF; (h) AGGKGF. The barrels of
polyphemusin and tachyplesin exited zwitterionic pores during the simulations, and those images
are omitted. White: nonpolar; blue: basic; red: acidic; green: polar residues. These were the
conformations of the peptides after the water-equilibrated monomers were arranged as octamer
barrels, subject to 200 ps of MD in water and minimized, inserted into pre-formed toroidal pores
in 26-Å-thick implicit membranes, and subject to 2 ns of MD followed by minimization. The
shading and lines represent the boundaries of the toroidal pores in 26-Å-thick membranes. In the
top views, the shading represents the inner and outer boundaries of the toroidal pore region; in
the side views, the shaded volume represents the pore interior, and the lines represent the
membrane edges. Figure created using VMD 1.9 [276].
Although the oligomers of tachyplesin remained relatively coherent throughout the simulations
in most conditions, some conditions resulted in exit from the membrane, even when the transfer
energy was favorable (Tables 2.12.5, Figure 2.7). For heptamer and octamer -barrels of
tachyplesin, transfer energies were favorable in anionic and unfavorable in neutral pores. The
tetramer arcs and decamer -barrels had unfavorable transfer energies to both neutral and anionic
pores. The octamer barrel in an anionic pore was the only condition in which tachyplesin
remained at the pore interface throughout the simulation (Figure 2.5c); the octamer barrel exited
a neutral pore within 50 ps of simulation onset. Tachyplesin tetramer arcs also exited the pore
rapidly, but whereas the tetramer drifted away from a neutral membrane, it remained as a
54
coherent arc with its hydrophobic side adjacent to the anionic membrane’s surface. Similarly, the
heptamer barrel of tachyplesin left a neutral pore rapidly (Table 2.1), whereas it migrated to the
membrane surface of an anionic pore and remained there while the barrel opened. Decamer
barrels of tachyplesin exited the pore region rapidly in all conditions (Table 2.1).
Polyphemusin oligomers generally displayed unstable behavior in pores, with distortions
observed in all conditions (Table 2.1). Polyphemusin’s pattern of favorable vs. unfavorable
binding energies was exactly the same as that for tachyplesin: the octamer and heptamer -
barrels had favorable and unfavorable binding energies for anionic and neutral pores,
respectively, and tetramer arcs and decamer barrels had unfavorable transfer energies in all pores
(Tables 2.22.5, Figure 2.7). Polyphemusin oligomers left the pore in all conditions except for
the octamer in an anionic pore, where the barrel moved toward the surface of the membrane with
only the membrane-facing end of the barrel remaining coherent; the solvent-facing end became
distorted, and the ends of the monomers spread apart (Figure 2.5d). The polyphemusin barrels
did not degrade completely; although there was some distortion, the assemblies remained
somewhat coherent after migrating into the solvent. The tetramer arc in an anionic pore,
however, became highly distorted and remained with the hydrophobic side adjacent to the
membrane surface.
The simulations of gomesin oligomers revealed favorable transfer energies in all conditions
except the heptamer barrel in a neutral pore (Tables 2.22.5, Figure 2.7). The gomesin octamer
-barrel remained bound to both neutral and anionic pore interfaces throughout the simulations,
but some monomers migrated to the center of the pore and away from the pore interface (Figure
2.5e), indicating partial collapse of the octamer barrel. The tetramer arcs of gomesin remained
bound to both neutral and anionic pores throughout the simulation; however, the arcs did not
55
remain coherent, reconfiguring as groups of three and one monomers that remained orthogonal to
the membrane surface (Figure 2.6b). The heptamer and decamer barrels also remained bound to
the pore throughout the 2-ns MD simulations, but barrel collapse and distortion occurred in the
heptameric and decameric conditions, respectively (Table 2.1).
56
57
Figure 2.6. Top and side views of the minimized final conformations of tetramer arcs of peptides
in toroidal pores of optimal radius in zwitterionic and 30% anionic membranes, after molecular
dynamics (MD) simulations. (a) protegrin-I; (b) gomesin; (c) androctonin; (d) YGKRGF; (e)
AGGKGF. The corresponding arcs of polyphemusin, tachyplesin, and θ-defensin exited the
membrane region during the simulation and are omitted. White: nonpolar; blue: basic; red:
acidic; green: polar residues. These were the conformations of the peptides after the water-
equilibrated monomers were arranged as octamer barrels, subject to 200 ps of MD in water and
minimized, inserted into pre-formed toroidal pores in 26-Å-thick implicit membranes, and
subject to 2 ns of MD followed by minimization. The shading and lines represent the boundaries
of the toroidal pores in 26-Å-thick membranes. In the top views, the shading represents the inner
and outer boundaries of the toroidal pore region; in the side views, the shaded volume represents
the pore interior, and the lines represent the membrane edges. Figure created using VMD 1.9
[276].
For all oligomeric states, androctonin showed unfavorable and favorable transfer energies for
neutral and anionic pores, respectively (Tables 2.22.5, Figure 2.7). Although the conformation
of androctonin was altered from its native one to facilitate barrel formation (which may have led
to the high standard deviation in the ΔW values), the androctonin oligomers maintained at least
some coherence throughout the 2 simulations (Figure 2.5f, Figure 2.6c), and they generally
remained bound to the pore throughout the simulation: the only condition in which androctonin
left the pore was the decamer from a neutral membrane. However, distortion of the androctonin
oligomers occurred in all conditions: there was moderate distortion of the octamer barrels, and in
the heptamer and decamer barrel conditions in which androctonin did not leave the pore, the
58
barrels collapsed, indicating a lack of ring stability (Table 2.1). The tetramer arcs of androctonin
reconfigured as barrel-like structures (Figure 2.6c).
Figure 2.7. Average membrane transfer energies (<ΔW>; kcal/mol) of tetramer arcs and
heptamer, octamer, and decamer barrels of peptides from water to toroidal pores (k = 15 Å, pore
radii as described in Tables 2.2–2.5) from 2-ns simulations. * The oligomer left the pore during
the course of the simulation; values were estimated using the time window 3–22 ps. ΔW values
in conditions in which the oligomer remained inside the pore were estimated using the window
1001–2000 ps. Error bars represent ± 1 SD.
YGKRGF and AGGKGF showed remarkably stable behavior in all simulated conditions. They
remained bound to both neutral and anionic pores throughout the 2-ns simulations for all
59
oligomeric states (Table 2.1). In several conditions, there was little distortion of the arc/barrel
conformation: the octamer barrels and tetramer arcs remained intact, with the monomers of the
AGGKGF tetramer tilting in an anionic pore (Figures 2.5gh, 2.6de). Although the heptamer
barrels of YGKRGF and AGGKGF both remained within the pore, the heptamer barrel of
YGKRGF opened even with Ro = 10 Å. The decamer barrel of AGGKGF became distorted in an
anionic pore, but the decamer of YGKRGF remained stable and retained its shape throughout
simulations in both neutral and anionic pores. These peptides’ transfer energies were negative to
both neutral and anionic pores in all conditions (Tables 2.22.5, Figure 2.7); in fact, they had the
most favorable ΔW values of any peptides studied.
Discussion
The results indicate that β-barrels and arcs of θ-defensin, tachyplesin, gomesin, polyphemusin,
and androctonin are not as stable as those of protegrin. In many cases, we observed exit from the
pore, significant distortions of the barrels, and/or unfavorable binding energies. None of them
had transfer energies as favorable as those of protegrin under any conditions. However, two
combinatorial library peptides surpassed protegrin in this measure. We discuss the results in light
of available experimental data.
One reason for the stability of protegrin and the synthetic peptides as β-barrels is that they fit a
pattern of amphipathicity wherein charged/polar residues are predominantly found at the ends or
turn of the hairpin and nonpolar residues in the middle of one face of the hairpin. These peptides
have no polar/charged residues facing the membrane in barrel configuration, whereas ach of the
other studied AMPs have at least one. The desolvation cost of a polar side chain sequestered
among nonpolar membrane lipids likely contributes significantly to the instability of these
peptides in pores. Further, θ-defensin and androctonin lack sufficient large hydrophobic residues
60
facing the membrane for efficient membrane binding in β-barrel conformation. Another factor
could be the amount of charge in the pore: protegrin has one Arg residue facing the pore,
whereas tachyplesin and polyphemusin have two in a more central location, which might create
electrostatic repulsion. There is experimental evidence that tachyplesin [212, 213] and
androctonin [216] orient parallel to the membrane surface instead of adopting a transmembrane
orientation, and a carpet mechanism was suggested for gomesin at high peptide concentrations
[77]. The inability of polyphemusin to cause dye leakage from vesicles led other authors to
propose an internalization mechanism that does not involve pore formation [260].
All peptides considered here show less favorable binding in neutral than 30% anionic pores. This
is not surprising, considering that they are all positively charged. A practical goal in antibiotic
development is to target microbes’ anionic membranes while leaving mammalian cells’
zwitterionic membranes intact. Thus, if the ΔW values in zwitterionic and anionic membranes
reflect antimicrobial and hemolytic activity, respectively, and if the β-barrel mechanism is valid,
one would expect a correlation between these values and the experimental biological activities.
Among the natural AMPs studied, protegrin had the most favorable ΔW values in both anionic
and neutral pores. Thus, the other natural AMPs are expected to be less hemolytic than protegrin.
This seems mostly consistent with available experimental data: θ-defensin is not hemolytic
[266], and gomesin is less hemolytic than protegrin, notably in the high-concentration regime
[272]. Androctonin’s relatively low hemolytic activity levels are in accordance with its relatively
hydrophilic region facing the membrane and moderately unfavorable ΔW in neutral pores. On
the other hand, tachyplesin’s hemolytic activity is comparable to protegrin’s [269], and
polyphemusin is more hemolytic than protegrin [214], so alternative explanations are needed to
61
rationalize these findings, such as toroidal pore stabilization without peptide assembly into a
well-defined structure.
It is also instructive to review the relationship between ΔW in anionic pores and activity against
bacteria [188]. Because there are many species of bacteria against which the activity levels of
several of these peptides have been tested, we select Staphylococcus aureus (SA) and
Escherichia coli (EC) as examples of Gram-positive and Gram-negative bacteria, respectively.
Protegrin has exhibited a range of observed MIC values: one study observed MICs of 30 M
against both EC and SA using a broth dilution technique [254]; however, another study using the
same technique observed an MIC of 4.6 M for EC [277], and another study observed MICs of
2.9 and 5.8 M for EC and SA, respectively [219]. On the low end, a study using a radial
diffusion assay measured MICs of 0.620.68 and 0.820.87 M for EC and SA, respectively
[264]. For θ-defensin, researchers have observed MIC values of 1.0 and 2.1 M for EC and SA,
respectively [266]. For tachyplesin, the results for SA have depended on whether the peptide was
natural or synthetic and the strain of bacteria used; MIC values have ranged 1.45.5 M, and
values for EC ranged 0.71.4 M regardless of whether the peptide was natural or synthetic
[270]. For polyphemusin, the MIC values were 2.6 M for both EC and SA. In the study in
which gomesin was originally isolated, its MIC against EC ranged 0.41.6 M, depending on
strain, and that for SA was 1.63.15 M [272]. The same study measured MIC values for
androctonin of 315 M and 1530 M, respectively, for EC and SA [272]. YGKRGF and
AGGKGF have minimal sterilizing concentrations (MSC) of 2.1 M [231] and 1.0 M [230],
respectively, against SA, and both peptides have MSC values of 0.5 M against EC [230]. If we
adopt the low-end values for protegrin [266], then a correlation is observed between the ΔW
values of the octamer barrels in anionic pores and activity against both types of bacteria, with the
62
same peptides (protegrin, YGKRGF, and AGGKGF) having the most negative ΔW values and
the lowest MIC values. The other peptides, with higher ΔW values of the octamer barrel in
anionic pores, also have higher MIC values.
The binding energy values for YGKRGF and AGGKGF may be misleading, because those
quantities do not contain any conformational, translational, or rotational entropy contributions.
These peptides’ lack of disulfide bonds makes constraining them into hairpin conformations
entropically costly; thus, their pore binding energies are likely significantly less favorable than
those we computed. Nevertheless, the fact that the negative control (AGGKGF) exhibits less
favorable binding energies than the positive control is gratifying. The observed stability of these
peptides’ pore structures contrasts with the experimental observation of graded and incomplete
dye leakage from vesicles [230, 231], which suggested a carpet or “sinking raft” mechanism
(although that could occur as a mechanistic step toward pore formation; [230, 231]). A high
energetic barrier (enthalpic for dissociation and entropic for association) may separate the
barrel/arc states from the rest of the configurational space; this would need to be considered in a
complete computational characterization. It would also be interesting to synthesize disulfide-
bonded versions of the combinatorial library peptides and test their activity.
Mechanisms other than membrane pore formation are possible for many of the peptides
investigated here. For example, polyphemusin might bind to divalent cation binding sites on
target cells’ lipopolysaccharide molecules to penetrate and permeabilize the membrane [214].
Tachyplesin activates annexin labeling and caspase-3 activation [278]. Not only gomesin [279]
but also protegrin itself [278] causes calcium influx through L-type channels and generates
reactive oxygen species. Gomesin’s mechanism may depend on concentration, as lower
concentrations promote apoptosis, whereas higher concentrations result in cell membrane
63
disruption [278]. Thus, higher concentrations of peptide may make pore formation more likely.
There were certain conditions in which non-protegrin AMPs remained within the pore without
becoming distorted, such as the tachyplesin octamer in an anionic membrane; it may be worth
investigating whether pore formation occurs at high concentrations of tachyplesin, with
monomers orienting parallel to the membrane as a first step.
The initial structures in this study had zero tilt angle for the monomers, which implies zero β-
sheet twist in the barrel [280]. Unconstrained simulations did not produce significant systematic
change in tilt, except local distortions. However, many of the tetramer arcs spontaneously
rearranged into configurations with substantial tilt angles. Thus, an energetic barrier might
prevent barrel reconfiguration. It would be useful to consider starting structures with tilted β-
strands in subsequent studies. Membrane thickness was also not varied in this study: all
simulations used a thickness of 26 Å. In addition, we used a generalization regarding the lipid
composition of mammalian and bacterial cells, assuming zwitterionic and 30% anionic lipids in
those respective cases. However, those values are not exact for all cells, so it would be useful to
investigate how changes in membrane charge affect the results. Further, we did not
systematically investigate pore curvature, mainly studying toroidal pores with k = 15 Å, whereas
in the previous study of protegrin, we considered cylindrical pores in addition to toroidal pores
with k = 10, 15, and 20 Å. We did vary the pore radius, but it may be useful to simulate even
smaller radii than 10 Å for arcs. Indeed, tetramer arcs of many of these peptides seemed to curl
naturally into incomplete cylindrical conformations with tilted monomers, some of which had
significantly smaller radii than the corresponding octamer barrels. Additional oligomeric states
could also be considered. These additional model parameter variations could supplement the
results obtained in this study.
64
3. Computational prediction of the optimal oligomeric state for membrane-inserted β-
barrels of protegrin-1 and related mutants
Published as: [3]
Summary
Protegrin-1 is a widely studied 18-residue β-hairpin antimicrobial peptide. Evidence suggests
that it acts via a β-barrel pore formation mechanism, but the exact number of peptides
comprising the pore state is unknown. In this study, we performed molecular dynamics
simulations of β-barrels of protegrin and three related mutants (v14v16l, v14v16a, and r4n) in
NCNC parallel topology in implicit membrane pores of varying radius and curvature for
oligomeric numbers 6–14. We then identified the optimal pore radius and curvature values for all
constructs and determined the total effective energy and the translational and rotational entropic
losses. These, along with an estimate of membrane deformation free energy from experimental
line tension values, provided an estimate of the overall energetics of formation of each pore state.
The results indicated that oligomeric numbers 7–13 are generally stable, allowing the possibility
of a heterogeneous pore state. The optimal oligomeric state for protegrin is the nonamer, shifting
to higher numbers for the mutants. Protegrin, v14v16l, and r4n are stable as membrane-inserted
β-barrels, but v14v16a seems much less so because of its decreased hydrophobicity.
Introduction
Antimicrobial peptides (AMPs) are small, usually cationic peptides that provide innate
immunological defenses against diverse microbial agents [19, 233] and are actively being
explored as the basis for novel antibiotics [236]. Although the identity of the AMP-induced
lethal event is still debated [34, 35], there is strong evidence that these peptides act on
membranes, as they have the ability to permeabilize lipid bilayers in vivo [23-25] and in vitro
65
[26-28] independent of amino acid chirality [29, 30]. AMPs have been proposed to disrupt cell
membranes by a variety of mechanisms, including micellization and disintegration [237] or pore
formation [31]. The pores may vary from cylindrical (lined by peptides [81]) to toroidal (lined by
lipid headgroups [52]). Intermediate forms between prototypical cylindrical and toroidal pores
may also be possible [118].
The 18-residue β-hairpin AMP protegrin-1 is the best-studied member of the β-hairpin AMP
family [204]. Neutron diffraction experiments have indicated that protegrin forms toroidal pores
[69], and its pore-forming activity has been characterized via methods such as oriented CD,
solid-state NMR spectroscopy, and atomic force microscopy [49, 61, 253]. Although protegrin’s
pore state cannot be visualized directly, there is evidence that it forms a -barrel composed of
810 monomers, causing membrane leakage [205]. Nevertheless, its topology in the active state
has been the subject of contradictory evidence: although one solid-state NMR study indicated the
presence of NCCN parallel topology [205], solution NMR of protegrin-1 in detergents has shown
NCCN antiparallel topology [206]. The latter topology has also been found for protegrin-3 in
DPC micelles [207].
Protegrin has also been the subject of several computational studies encompassing various steps
of membrane association and pore formation (for a review, see [203]). Monomers and dimers
have been simulated [220, 257-259], along with β-barrel models of both octamers [221, 223,
224] and decamers [59]. These computational investigations have encompassed simulations
representing the membrane and solvent atoms with varying levels of detail, from all-atom
(explicit solvent; [220]) to coarse-grained [162] to implicit solvent [2, 224] simulations (Chapter
2). All-atom simulations have provided potentials of mean force of putative middle steps in
66
membrane poration, such as insertion of a protegrin monomer into a lipid bilayer [226] and
protegrin dimerization in different environments [96].
In our laboratory’s previous work, we modeled three possible topologies of this -barrel, finding
that the NCNC parallel configuration is most stable [224] because it allows immersion of the
hydrophobic cluster of each peptide into the nonpolar membrane interior. We have also created
barrel models of several other β-hairpin AMPs, finding that none form β-barrels as stable as
those of protegrin, with some being completely unstable [2] (Chapter 2). Implicit and explicit
simulations in our laboratory have shown that protegrin’s NCNC parallel topology may form
stable, tilted arcs in lipid membranes rather than maintaining a strict transmembrane orientation,
especially in anionic membranes [100]. Although our laboratory has only investigated octamers
[224], the actual number of peptides comprising protegrin oligomeric -barrels is unknown, with
at least one study suggesting a larger pore radius (R; [219]). Further, structural similarity to
protegrin was noted when Jang et al. modeled from 12- to 36-mers of an Aβ peptide, finding that
16- to 24-mers were most stable in their 30–50-ns simulations [222].
The goal of the present study is to develop methodology for determining the optimal oligomeric
state of β-barrel forming peptides, starting with protegrin and closely related mutants. A similar
approach for helical peptides was published previously [189]. We use our implicit membrane
approach [108, 112, 186], whereby pores are characterized by their radius (R) and curvature (k).
In this study, we vary those parameters and the oligomeric number (the latter between 6 and 14).
The optimal oligomeric state is selected based on the lowest free energy per monomer, including
contributions from peptide–peptide and peptide–solvent interactions, rotational and translational
entropy (both from a homogeneous solvent environment and association with membrane), and
membrane deformation. This methodology is applied to protegrin, a more hydrophobic mutant
67
(v14v16l) that is more active against several bacterial strains [281], a less hydrophobic variant
(v14v16a) that is expected to be less stable and/or less active, and a mutant in which Arg4 is
replaced by asparagine (r4n), removing the positive charge inside the putative pore lumen. The
results are used to obtain general insights about sequence–structure relationships in AMP pore
formation and the origin of protegrin’s toxicity.
Materials and Methods
Energy Function
The simulations in this chapter were conducted using Implicit Membrane Model 1 (IMM1;
[112]), which is an extension of Effective Energy Function 1 (EEF1) [108] that represents
membrane–water systems using solvation parameters dependent on vertical position. Vertical
dependence of the dielectric is also introduced to account for strengthening of electrostatic
interactions within the membrane:
; – √ (1)
where fi and fj represent
z′ = |z| / (T / 2) (2)
where T is the hydrophobic thickness of the membrane and z = 0 is the membrane midplane.
Switching function f describes the phase transition, and n (equal to 10) controls the transition
steepness. The adjustable parameter a was set to 0.85 to generate membrane binding energies
similar to experimental values [112]. Only neutral (zwitterionic) membranes were considered in
this work.
IMM1 can also accommodate pores [117, 186], whose shape is determined by the dependence of
the radius on vertical position:
R = R0 + k × z′2 (3)
68
where R0 is the pore radius at the membrane center, R is the radius at a given z-level, and k
determines pore curvature. For example, R0 = 15 Å and k = 0 defines a cylindrical pore of radius
15 Å, whereas R0 = 15 Å and k = 20 Å defines a toroidal pore of radii 15 Å and 35 Å at the
center and rims, respectively. The switching function now also depends on horizontal distance
from the z axis:
;
; ; √ (4)
where r is radial distance from the pore center. According to the various pore dimensions used,
we chose the m value to ensure a radial transition width of 6 Å, the same as that in the vertical
direction. The program CHARMM [262] version c41a1 was used for these simulations.
Initial Structures
The solution NMR coordinate file for the protegrin-1 monomer, isolated from porcine leukocytes
[204], was downloaded from the Protein Data Bank (PDB; entry 1PG1). The first model was
used. In addition, we formed several mutants to examine the effects of structural variations on
the free energy components and the optimal oligomeric state. We examined the v14v16l mutant
studied by Gottler et al. [281], the v14v16a mutant, and the r4n mutant. All mutants were
produced by importing the PDB file into MacPyMOL 1.7 [267] and using the mutagenesis
wizard. The sequences of all structures are shown in Table 3.1.
Table 3.1. Sequences of investigated peptides
Name Sequence
Protegrin RGGRLCYCRRRFCVCVGR-NH2
v14v16l RGGRLCYCRRRFCLCLGR-NH2
v14v16a RGGRLCYCRRRFCACAGR-NH2
r4n RGGNLCYCRRRFCVCVGR-NH2
69
Molecular Dynamics Simulations
To equilibrate the monomers, EEF1 was used to set up systems with implicit water solvent at
298.15 K, and then the coordinates of each monomer file were minimized using the adopted
basis Newton–Raphson algorithm (used for all energy minimizations for 300 steps). Then, for
each structure, 200 ps of MD simulation was performed in water using the Verlet integrator with
a time step of 2 fs. Subsequent minimization yielded the final monomeric structures used to
construct the -barrels (Figure 3.1). All molecular graphics were produced using MacPyMOL
1.7 [267].
Figure 3.1. Conformations of monomers after simulations in water, before barrel formation and
pore insertion. When the peptides are arranged inside the pores in parallel NCNC configuration,
the left and right sides face the membrane and pore lumen, respectively. The atoms are
represented as sticks and colored according to amino acid residue. Cysteine: yellow; arginine:
purple; glycine, alanine, tyrosine: green; valine: sky blue; phenylalanine, leucine: blue;
asparagine: red.
70
The final monomeric structures were then arranged as -barrels of oligomeric numbers 614 by
orienting them vertically, rotating them around the z axis to orient the backbones, translating
them by 1120 Å along the x axis, and then arranging them as evenly spaced cylinders by
rotation around the z axis. The more hydrophobic side was oriented to face the membrane, and
the backbones were placed in approximately H-bonded positions. Minimization was then applied
with harmonic constraints on all backbone atoms (k = 5.0), and then the appropriate
intermolecular H-bonds were imposed via energy wells using CHARMM’s NOE constraint
facility, with kmin, rmin, kmax, and rmax values of 1.0, 1.8, 5.0, and 2.3, respectively. Minimization
was applied without backbone constraints, and then 100 ps of MD simulation was run in water to
equilibrate the barrel, followed by another minimization. The NOE constraints were then
released.
After the barrels underwent brief dynamics in water, the resulting structures were each inserted
into the centers of implicit 26-Å-thick IMM1 membranes containing pores with different values
of R and k, and 5-ns production MD simulations were performed to examine the effects of R and
k values on the energetics and kinetic stability of the pre-formed -barrels. To obtain relatively
broad data regarding pore size and shape, we initially used R values from 6 Å to 28 Å in 2-Å
increments and k values of 5, 10, 15, and 20 Å for all oligomeric numbers of protegrin from 6 to
14 (i.e. 12 × 4 5-ns simulations for each oligomeric state). After each production simulation,
minimization provided the final post-MD image of the -barrel. The R value with the most
favorable combination of Wbarrel and ΔW for protegrin was then chosen as the reference pore size
for the mutant simulations. The production MD simulations for mutants were identical to those
for protegrin, but they were only performed at the six R values closest to the reference pore size,
and only at k values of 10, 15, and 20, for each oligomeric number.
71
For each peptide, after the results for R values with increments of 2 Å had been tabulated, we
identified the radius with the most energetically favorable combination of Wbarrel and ΔW as the
putative optimal radius and then ran four additional production MD runs at R = 1 Å above and
below the putative optimal radius and k = 15 and 20 Å. The results from all runs together were
synthesized to make final judgments about the stability of each oligomeric state. Production
simulations of 5 ns were found to be sufficient for convergence. Longer simulations of example
protegrin oligomers gave results within the statistical error. Simulations using different random
seeds, run as checks, also gave very similar results. The total length of all simulations run for
protegrin and the mutants was 5.31 μs.
To estimate the free energy of formation of the oligomeric β-barrels, it was necessary to compare
the energy of the pore state with that of a monomer in water. Therefore, the water simulations
mentioned above were extended to 2 ns, and Wbarrel was calculated for the monomers every 1 ps
throughout the last 1 ns of the simulation (1000 frames).
Calculations of Thermodynamic Stability
The free energy of pore formation can be split into peptide and membrane deformation
contributions:
ΔGpore = ΔGpep + ΔGmem (5)
The contributions to ΔGpep (i.e., the peptide contributions) include the effective energy change
(which comprise peptide–peptide, peptide–water, and peptide–lipid interactions), the loss of
translational (TΔStrans
) and rotational (TΔSrot
) entropy upon barrel formation in solution, and the
loss of translational ( ) and rotational (
) entropy from membrane binding:
ΔGpep = Wbarrel − Wmono − TΔStrans
− TΔSrot
− −
(6)
72
where Wbarrel is the effective energy per monomer in the β-barrel pore state and Wmono that in
water. TΔStrans
and TΔSrot
were calculated as the respective entropic losses of subunit A with
respect to the entire oligomer in solution following [282]. and
were calculated
for an example system, the optimal protegrin octamer, following [183, 283]:
∫
∫ [
]
[ (
) ∫
[
]] ∫ [
]
+
(7)
where zmax and zmin are the maximum and minimum values of the barrel’s center of mass in z,
Ƥ(z) is the probability density of the vertical position of the barrel’s center of mass, and Ƥ(Ƴ) is
the probability density of orientations Ƴ in the membrane simulation. Ƥ0(z) and Ƥ(Ƴ) are the
corresponding theoretical uniform probability distributions. The above orientational distribution
is assumed to be independent of z, so that Ƥ(z,Ƴ) = Ƥ(z)*Ƥ(Ƴ). Here Ƴ represents θ, the tilt
angle of the barrel axis with respect to the bilayer normal, and dƳ = sinθdθ. is split into
two components: the first accounts for the translational restriction from that of a theoretical
particle in a 1-M solution, which would traverse a cubic region with edge length d = 11.84 Å.
The second accounts for the nonuniform probability distribution within the restricted range.
Wbarrel, ΔW, TΔStrans
, and TΔSrot
were calculated by averaging values obtained every 5 ps
throughout the last 2.5 ns of the simulation (500 frames), whereas and
were
calculated by averaging values obtained every 5 ps throughout the last 4.5 ns of the simulation
(900 frames). To calculate and
, we used 20 bins in z and 60 bins in θ.
73
The final contribution to the free energy of pore formation is the membrane deformation free
energy, ΔGmem. An approximate estimate of this quantity can be made using experimental values
of the line tension γ, with ΔGmem = 2πRγ [284]. In this paper, we use two γ values, 0.15 and 0.45
kT/Å, to represent the high and low ends of realistic ΔGmem values. Using these values, the pore
formation free energy ranges 14–42 kcal/mol at R = 15 Å.
An additional quantity calculated was the membrane insertion energy (ΔW), estimated by
averaging Wbarrel at the barrel’s position in the pore and then subtracting the energy of the same
conformation in water. ΔW provides a rough estimate of the favorability of the membrane-
embedded barrel compared with the same barrel in water. In a stable pore state, this quantity is
negative.
Wbarrel and ΔW are calculated from trajectory frames spaced 2500 simulation steps apart for the
oligomers. The variation in these values is expressed in terms of both standard deviation (SD)
and SD / √ , where n is the number of measurements. If the samples were fully
independent, then the standard error of the mean would be SD / √ , but because the frames
may not be adequately spaced, they may not be fully independent, and that number must be
corrected for autocorrelation in the sample. Thus, the sample’s calculated standard error needs to
be multiplied by f, where f = √ , and ρ is the autocorrelation coefficient. To
gain systematic insight into the statistical error, we used a FORTRAN implementation of the
block-averaging method of Flyvbjerg and Petersen [285] on the data values from some of our
simulations. That method samples the overall dataset at various frequencies to form different
block sizes, and the average block variance is graphed according to block size. The results are
expected to plateau at a certain level once the decorrelation time has been reached. At sampling
frequencies approaching that of our trajectory file, we did not observe any significant decline in
74
the average block variance. Therefore, although SD and SD / √ are shown as the maximum
and minimum theoretical sizes of the error bars, respectively, the results from the block-
averaging method indicate that the true standard errors are closer to SD / √ .
Results
Throughout the 5-ns simulations, at the optimal R and k values, the oligomeric β-barrels tended
to remain stable at their positions within the pore. Figure 3.2 illustrates the minimized final
conformations in pores of optimal R and k for all peptides and even oligomeric numbers. The
6mer and 14mer showed distortions for all peptides besides r4n, the only one lacking the bulky,
positively charged Arg inside the pore lumen. All other β-barrels remained in stable
conformations at their location in the pore for the duration of the simulations.
The mean Wbarrel results for the monomers in water were the following (in parentheses: SD, SD /
√ ): protegrin, −385.65 (8.56, 0.27); v14v16l, −387.25 (9.50, 0.30); v14v16a, −394.49
(8.77, 0.28); r4n, −385.47 (8.65, 0.27). The Wbarrel, ΔW, and ΔGpore results are tabulated at the
optimal pore R and k values for each metric in Tables 3.1–3.4 for protegrin, v14v16l, v14v16a,
and r4n, respectively. Figure S1a–d from [3] shows Wbarrel, ΔW, ΔGpep, and ΔGpore at γ = 0.15 for
protegrin, and Figure 3.3 shows ΔGpore at γ = 0.45. Figures S2–S4 from [3] and 3.4–3.6 show the
corresponding information for v14v16l, v14v16a, and r4n, respectively. Figure 3.7a–b shows
ΔGpore per monomer at the optimal k values for each oligomeric number and structure at γ = 0.15
and 0.45, respectively. Figures 3.8–3.9 show interaction energies for protegrin, v14v16l, and r4n.
For the protegrin octamer in its optimal pore state, the total calculated results for and
were 1.13 kcal/mol and 3.75 kcal/mol, respectively. During the membrane simulation,
the translational range of the peptide in the z direction was restricted to 2.81 Å, and θ was
restricted to roughly [0,9°] and [171°,180°], with both distributions nonuniform within the
75
observed range. Additional calculations using other peptides and oligomeric numbers yielded
very similar results, so we extrapolated the protegrin octamer’s and
results to
all systems, dividing according to the number of peptides per barrel. The ranges of TΔStrans
and
TΔSrot
were approximately 3–6.5 kcal/mol and 0.8–3.2 kcal/mol, respectively. TΔStrans
and TΔSrot
per monomer generally increase with oligomeric number, weighing against the formation of
higher oligomeric numbers.
76
Figure 3.2. Configurations of even-numbered oligomeric β-barrels after pore simulations. The
vertical axis labels denote oligomeric number. The upper representations are side views, and the
77
lower views look directly down on the x–y plane from above. The backbones are shown as
cartoons and colored as “chainbows.”
Protegrin
Table 3.2 shows the Wbarrel, ΔW, ΔGmem, and ΔGpore values at the optimal R and k values for
protegrin (depiction of components in Supplementary Material). There is generally good
correspondence between the optimal values of Wbarrel, ΔW, and ΔGpore, but there are some
differences, especially between Wbarrel and ΔW. ΔGmem favors smaller R values but higher
oligomeric numbers. (The same is true for all peptides studied.) The optimal ΔW value was −3 to
−3.5 kcal/mol per monomer across all oligomeric numbers. Its magnitude was larger than that of
ΔGmem for γ=0.15, but smaller for γ=0.45.
ΔGpore of protegrin is shown as a function of R at γ = 0.45 in Figure 3.3. For most oligomeric
numbers, there is a unique R at which the minimum ΔGpore per monomer is found, which
increases with oligomeric number. However, for certain oligomeric numbers, such as 10 and 14,
multiple values of R give a similarly low ΔGpore. Individual energy components are less
discriminatory of the optimal oligomeric state than the total ΔGpore is (see Supplementary
Material from [3]). The ΔGpore values at the optimal R and k values are favorable for all
oligomeric numbers and both investigated γ values. They indicate that oligomeric number 9 is
the most energetically favorable state, although all oligomeric numbers from 7 to 13 seem
plausible. The association between ΔGpore and oligomeric number is shown for γ = 0.15 and 0.45
in Figure 3.7.
78
Table 3.2. Protegrin: Optimal R and k values for each oligomeric number according to three
indicators: total effective energy (Wbarrel), membrane binding energy (ΔW), and total energy of
barrel formation (ΔGpep). Total free energies of pore formation (ΔGpore) with line tension (γ) =
0.15 and 0.45 are also listed. All values per monomer.
Figure 3.3. Protegrin: Variation of pore formation free energy per monomer with pore radius for
each oligomeric number. Line tension γ = 0.45.
v14v16l
Optimal W barrel value Optimal ΔW value Optimal ΔGpep value ΔGmem ΔGmem ΔGpore ΔGpore
# R k W SD SD/√(n-1) R k ΔW SD SD/√(n-1) R k ΔGpep γ = .15 γ = .45 γ = .15 γ = .45
6 9 15 -424.04 4.39 0.20 10 20 -3.10 0.44 0.020 9 15 -30.53 1.41 4.24 -29.11 -26.29
7 12 15 -426.77 3.38 0.15 12 15 -3.12 0.31 0.014 12 15 -32.70 1.62 4.85 -31.09 -27.86
8 12 15 -426.51 3.33 0.15 13 20 -3.40 0.27 0.012 12 15 -32.92 1.41 4.24 -31.51 -28.68
9 13 20 -426.09 3.08 0.14 15 20 -3.15 0.32 0.014 13 20 -34.70 1.36 4.08 -33.34 -30.61
10 17 20 -426.05 2.78 0.12 16 20 -3.59 0.21 0.009 16 20 -32.33 1.51 4.52 -30.82 -27.81
11 17 15 -426.1 2.86 0.13 17 20 -3.51 0.23 0.010 17 15 -32.04 1.46 4.37 -30.58 -27.67
12 19 15 -427.06 2.86 0.13 19 20 -3.37 0.23 0.010 19 15 -32.54 1.49 4.48 -31.05 -28.07
13 20 20 -425.84 2.77 0.12 21 20 -3.19 0.21 0.009 20 20 -32.50 1.45 4.35 -31.05 -28.15
14 20 20 -424.8 2.51 0.11 23 20 -3.26 0.2 0.009 21 20 -33.47 1.41 4.24 -32.06 -29.23
79
Results for the mutant v14v16l are shown in Table 3.3 and Figure 3.4. Although the basic pattern
of results is similar to that for protegrin, as intuitively expected, the increased hydrophobicity of
the membrane-facing region leads to more favorable values of ΔGpore and ΔW, the latter of which
is now competitive with ΔGmem even for the larger line tension value (Table 3.3).
Although oligomeric number 14 showed the optimal ΔGpore value for v14v16l (Table 3.3), that
configuration became distorted over the course of the simulation, with one peptide migrating
inside the barrel to the edge of the pore lumen (Figure 3.2). If we restrict attention to regular
barrels, the optimal oligomeric number is 12. Thus, the v14v16l mutant shows increased
favorability of higher-numbered oligomers compared with protegrin. The origin of this trend is
explored in the Interaction Energies subsection below.
Table 3.3. v14v16l: Optimal R and k values for each oligomeric number according to three
indicators: total effective energy (Wbarrel), membrane binding energy (ΔW), and total energy of
barrel formation (ΔGpep). Total free energies of pore formation (ΔGpore) with line tension (γ) =
0.15 and 0.45 are also listed. All values per monomer.
Optimal W barrel value Optimal ΔW value Optimal ΔGpep value ΔGmem ΔGmem ΔGpore ΔGpore
# R k W SD SD/√(n-1) R k ΔW SD SD/√(n-1) R k ΔGpep γ = .15 γ = .45 γ = .15 γ = .45
6 10 20 -428.17 3.71 0.17 10 20 -4.91 0.36 0.016 10 20 -33.01 1.57 4.71 -31.44 -28.29
7 14 20 -427.04 3.37 0.15 13 20 -4.51 0.39 0.017 14 20 -32.60 1.88 5.65 -30.72 -26.95
8 12 15 -429.23 3.1 0.14 13 20 -3.89 0.34 0.015 12 20 -33.87 1.41 4.24 -32.46 -29.63
9 15 20 -430.72 3.06 0.14 15 20 -4.94 0.21 0.009 15 20 -35.30 1.57 4.71 -33.73 -30.59
10 15 20 -429.37 2.94 0.13 16 15 -4.69 0.28 0.013 15 20 -33.93 1.41 4.24 -32.52 -29.69
11 19 20 -430.03 2.87 0.13 18 20 -4.75 0.24 0.011 19 20 -34.40 1.63 4.88 -32.77 -29.51
12 18 20 -430.16 2.8 0.13 19 20 -4.78 0.22 0.010 18 20 -34.97 1.41 4.24 -33.56 -30.73
13 19 20 -428.25 2.93 0.13 20 20 -4.46 0.2 0.009 16 20 -33.55 1.16 3.48 -32.39 -30.07
14 22 20 -431.58 2.56 0.11 22 20 -4.44 0.21 0.009 22 20 -37.19 1.48 4.44 -35.71 -32.75
80
Figure 3.4. v14v16l: Variation of pore formation free energy per monomer with pore radius for
each oligomeric number. Line tension γ = 0.45.
v14v16a
The corresponding data for v14v16a are shown in Table 3.4 and Figure 3.5. For this peptide, the
ΔW values are uniformly weaker than those for the other peptides investigated (optimal values >
−2 kcal/mol for all oligomeric numbers; Table 3.4). This was expected, as the v → a mutation
decreases the hydrophobicity of the membrane-facing region. Unlike the case with the other
peptides studied, pore formation is predicted to be unfavorable by comparing ΔW with ΔGmem, as
ΔGmem exceeds ΔW for all oligomeric numbers and both line tension values. As a result, the
ΔGpore values for v14v16a are less favorable than those for the other peptides, although they are
favorable overall due to peptide-peptide interactions (see Discussion).
Figure 3.5 lacks a clear relationship between the optimal ΔGpore value and oligomeric number,
but ΔGpore does become more favorable with increasing oligomeric number and is lowest for the
81
13mer (Figure 3.7). However, the patterns in the data are generally not as strong for this mutant
as for the other peptides.
Table 3.4. v14v16a: Optimal R and k values for each oligomeric number according to three
indicators: total effective energy (Wbarrel), membrane binding energy (ΔW), and total energy of
barrel formation (ΔGpep). Total free energies of pore formation (ΔGpore) with line tension (γ) =
0.15 and 0.45 are also listed. All values per monomer.
Optimal W barrel value Optimal ΔW value Optimal ΔGpep value ΔGmem ΔGmem ΔGpore ΔGpore
# R k W SD SD/√(n-1) R k ΔW SD SD/√(n-1) R k ΔGpep γ = .15 γ = .45 γ = .15 γ = .45
6 15 20 -424.75 3.56 0.16 13 20 -0.93 0.3 0.013 10 20 -20.71 1.57 4.71 -19.14 -16.00
7 12 20 -432.17 3.60 0.16 12 20 -1.18 0.29 0.013 10 20 -29.57 1.35 4.04 -28.22 -25.53
8 13 15 -430.90 3.54 0.16 15 15 -1.21 0.28 0.013 13 15 -29.69 1.53 4.59 -28.16 -25.10
9 17 20 -432.67 3.25 0.15 16 20 -1.66 0.24 0.011 17 20 -31.37 1.78 5.34 -29.59 -26.03
10 16 20 -432.14 2.92 0.13 18 15 -1.19 0.28 0.013 16 20 -30.59 1.51 4.52 -29.08 -26.07
11 19 20 -432.71 2.78 0.12 19 20 -1.67 0.18 0.008 19 20 -30.63 1.63 4.88 -29.00 -25.75
12 20 20 -433.15 2.60 0.12 20 20 -1.47 0.22 0.010 20 20 -31.21 1.57 4.71 -29.64 -26.50
13 22 10 -434.91 2.82 0.13 22 20 -1.50 0.17 0.008 21 20 -32.76 1.52 4.57 -31.24 -28.19
14 16 20 -433.24 2.50 0.11 24 20 -1.04 0.15 0.007 22 10 -30.92 1.48 4.44 -29.44 -26.48
82
Figure 3.5. v14v16a: Variation of pore formation free energy per monomer with pore radius for
each oligomeric number. Line tension γ = 0.45.
r4n
The data for r4n are shown in Table 3.5. The optimal ΔW value trends at −3 to −4 kcal/mol,
slightly stronger than the values for wild type protegrin. Like protegrin, the magnitude of ΔW lies
between those of ΔGmem for the two values of line tension. The results, like those of protegrin,
are clarified by factoring in TΔStrans
, TΔSrot
, ,
, Wmono, and ΔGmem (Figure 3.6);
the minimum value of ΔGpore is found at oligomeric number 10. As with v14v16l, this mutation
induces a shift to higher-order oligomers (see Interaction Energies below).
Table 3.5. r4n: Optimal R and k values for each oligomeric number according to three indicators:
total effective energy (Wbarrel), membrane binding energy (ΔW), and total energy of barrel
formation (ΔGpep). Total free energies of pore formation (ΔGpore) with line tension (γ) = 0.15 and
0.45 are also listed. All values per monomer.
Optimal W barrel value Optimal ΔW value Optimal ΔGpep value ΔGmem ΔGmem ΔGpore ΔGpore
# R k W SD SD/√(n-1)R k ΔW SD SD/√(n-1) R k ΔGpep γ = .15 γ = .45 γ = .15 γ = .45
6 12 10 -424.41 3.7 0.17 13 20 -3.96 0.39 0.017 11 20 -30.62 1.73 5.18 -28.89 -25.44
7 12 15 -424.45 3.34 0.15 12 15 -3.49 0.35 0.016 12 15 -31.15 1.62 4.85 -29.53 -26.30
8 14 15 -427.05 3.4 0.15 13 20 -3.7 0.35 0.016 13 15 -32.99 1.53 4.59 -31.46 -28.40
9 15 20 -424.61 2.94 0.13 15 20 -3.36 0.24 0.011 16 20 -32.03 1.68 5.03 -30.35 -27.00
10 17 20 -427.65 2.73 0.12 16 20 -3.73 0.23 0.010 14 20 -34.99 1.32 3.96 -33.67 -31.03
11 18 15 -427.6 2.86 0.13 17 20 -3.55 0.26 0.012 18 15 -33.68 1.54 4.63 -32.14 -29.05
12 18 20 -426.15 2.7 0.12 19 20 -3.65 0.2 0.009 19 20 -33.10 1.49 4.48 -31.61 -28.63
13 21 20 -426.86 2.71 0.12 21 30 -3.43 0.19 0.009 21 20 -33.78 1.52 4.57 -32.26 -29.21
14 22 15 -426.25 2.67 0.12 22 15 -3.22 0.22 0.010 22 15 -32.21 1.48 4.44 -30.73 -27.77
83
Figure 3.6. r4n: Variation of pore formation free energy per monomer with pore radius for each
oligomeric number. Line tension γ = 0.45.
84
Figure 3.7. Total energy of formation per monomer (ΔGpore) by oligomeric number for protegrin,
v14v16l, v14v16a, and r4n. a) line tension γ = 0.15. b) γ = 0.45.
Interaction Energies
On the basis of their structure, r4n and v14v16l might be intuitively expected to exhibit
comparable β-barrel formation tendencies to protegrin, but the mutants show greater relative
favorability of higher-order β-barrel oligomers. (Although v14v16a showed a similar pattern, its
85
pore formation is relatively less favorable overall.) To explore the origin of this shift, we
calculated average interaction energies between several residue pairs selected on the basis of
both structural features and empirical observation for protegrin, v14v16l, and r4n at 500 evenly
spaced time points throughout the last half of the 5-ns production length simulations at the
optimal R and k values for all oligomeric numbers.
The (unfavorable) interaction energies between residues 1 (Arg) and 4 in protegrin and r4n are
illustrated in Figure 3.8. For protegrin, this interaction energy became steadily more unfavorable
with increasing oligomeric number, but for r4n, this interaction energy shows higher overall
variance, with several higher oligomers having the most favorable interactions. Specifically,
from the nonamer to the decamer, a substantially larger drop is observed for r4n than protegrin,
which could partially account for the stabilization of the decamer in the former. The interaction
energies for several other investigated residue pairs showed patterns that were similar between
protegrin and r4n (data not shown).
The corresponding interaction energy comparison for residues 4 and 16 in protegrin and v14v16l
is shown in Figure 3.9. This interaction is less unfavorable for protegrin than v14v16l at
oligomeric numbers 6–10, but that trend disappears at higher oligomeric numbers. Specifically,
from the nonamer to the dodecamer, this interaction energy increases substantially for the wild
type but remains about the same for the mutant. The direct patterns of interaction between
residues 1 and 16 and between residues 14 and 16 did not show convincing patterns (data not
shown).
86
Figure 3.8. Interaction energies between residues 1 and 4 of protegrin and r4n for all oligomeric
numbers. [kcal/mol]
Figure 3.9. Interaction energies between residues 4 and 16 of protegrin and v14v16l for all
oligomeric numbers. [kcal/mol]
87
Discussion
In this work, we have comprehensively accounted for the contributions to the free energy of a
membrane-inserted β-barrel by the AMP protegrin-1 and several mutants thereof, aiming to
predict the optimal oligomeric state. Approximations have been necessary for some of these
components, including the use of the simplified IMM1 and line tensions to obtain membrane
deformation free energies; the latter was assumed to depend only on R and not k, which is likely
untrue.
The ability to determine the optimal R and oligomeric number was greater when the various
components of ΔGpore were combined (Tables 3.1–3.4) than when any single one of them was
examined alone (Supplementary Material from [3]). The results for protegrin indicate that the
nonamer is optimal, although its difference in stability from similar oligomers is small,
suggesting that a heterogeneous ensemble of oligomeric states is most likely. This observation
aligns with previous computational [221, 223, 224] and experimental [205] suggestions of an 8–
10-peptide barrel. Certain studies [219], however, have suggested substantially larger protegrin
pores, which may correspond to more complex, non-barrel states.
For all mutants examined (v14v16l, v14v16a, and r4n), we observed increased favorability of
higher oligomers. This was not intuitively expected in terms of structure and could be partially
explained by analyzing interresidue interactions. Gottler et al. [281] found that the v14v16l
mutant had higher antimicrobial activity, stronger binding to 3:1 PC:PG vesicles, and an
approximately doubled lipid binding stoichiometry of wild type protegrin, which could be
attributed to more extensive oligomerization. This is in agreement with our results, although our
observed shift in oligomeric state seems too small to account for the experimental data fully.
88
For a membrane-inserted barrel to be stable, the free energy of transfer from solution to
membrane needs to be favorable. This free energy includes the (favorable) effective energy
change ΔW , the (unfavorable) membrane deformation free energy ΔGmem, and entropic losses
and
. The latter are roughly 0.4–0.8 kcal/mol per monomer for the systems
considered here. ΔGmem was estimated at either 1.4–1.6 or 4.1–4.9 kcal/mol per monomer at γ =
.15 and .45, respectively. The optimal ΔW per monomer was largely independent of oligomeric
number. The ΔW values per monomer for r4n (−3.2 to −4.0 kcal/mol) were slightly larger those
for protegrin (−3.1 to −3.6 kcal/mol), whereas those for v14v16l and v14v16a had higher (−3.9
to −5.0) and lower (−1 to −1.5 kcal/mol) magnitudes, respectively. Thus, the favorable and
unfavorable contributions were roughly balanced for all peptides except v14v16a, whose
insertion is clearly unfavorable. Membrane insertion for protegrin is marginal in the neutral
membranes studied here, in agreement with its known preference for anionic membranes [281].
Despite the marginal values of membrane insertion free energy, the overall ΔGpore values were
highly negative due to peptide–peptide interactions upon barrel formation. The magnitude of
these interactions seems to be overestimated by the implicit solvent model; otherwise, the barrels
would be stable in water, which does not seem to be the case.
This study provided predictions that can be tested experimentally. The mutant v14v16a is not
predicted to insert into neutral membranes; therefore, it should have no hemolytic activity. The
r4n mutant is predicted to form barrels slightly more favorably—and with a slightly larger
number of monomers—than protegrin. In addition, the absence of Arg 4’s positive charge inside
the pore lumen due to the R → N mutation may alter the pore’s conductance and ion selectivity,
which could be explored by electrophysiology measurements.
89
The present calculations were performed in neutral (zwitterionic) membranes. Additional
computations in anionic membranes would be necessary to evaluate barrel formation in more
bacterial-like membranes. Further, we only considered barrels of parallel NCNC topology,
following the conclusions of previous work [224]. The antiparallel NCCN topology also inserts
favorably into membranes, and its oligomerization properties should also be examined. Finally,
atomistic simulations of different oligomeric states could be performed to test the implicit
membrane approach. The present methodology may also be applied to determine the optimal
pore dimensions and oligomeric state for other putative β-barrel-forming peptides.
90
4. Transmembrane pore structures of β-hairpin antimicrobial peptides by all-atom
simulations
In press at Journal of Physical Chemistry B
Summary
Protegrin-1 is an 18-residue β-hairpin antimicrobial peptide (AMP) that has been suggested to
form transmembrane β-barrels in biological membranes. However, the precise topology and
structure of the β-barrel state is unknown, and alternative structures have also been proposed.
Here, we performed multimicrosecond, all-atom molecular dynamics simulations of various
protegrin-1 oligomers on the membrane surface and in transmembrane topologies. We also
considered an octamer of the β-hairpin AMP tachyplesin. The simulations on the membrane
surface indicated that protegrin dimers are stable, while trimers and tetramers break down
because they assume a bent, twisted β-sheet shape that is unstable on a flat surface. Tetrameric
arcs in membranes of different composition remained stably inserted, but the pore water was
displaced by lipid molecules. Unsheared protegrin β-barrels opened into long, twisted β-sheets
that, nevertheless, surrounded stable aqueous pores, whereas tilted barrels with sheared hydrogen
bonding patterns were stable in most topologies. A third type of observed pore consisted of
multiple small oligomers surrounding a small, partially lipidic pore. Tachyplesin showed less
tendency to oligomerize than protegrin: the octameric bundle resulted in small pores surrounded
by 6 peptides as monomers and dimers, with some peptides returning to the membrane surface.
The results imply that multiple configurations of protegrin oligomers may produce aqueous pores
and illustrate the relationship between topology and putative steps in protegrin-1’s pore
formation. However, the long-term stability of these structures needs to be assessed further.
Introduction
91
Protegrin-1 (hereafter called protegrin [204]) is the best-studied member of the β-hairpin family
of antimicrobial peptides (AMPs), which are small, usually cationic peptides that provide
defenses against several classes of microbial agents [19, 233]. Because AMPs permeabilize lipid
bilayers in vitro [26-28] and in vivo [23-25], the lethal event is thought to be disruption of
bacterial membranes by either detergent-like membrane dissolution (i.e., the carpet mechanism;
[32]) or formation of pores [31], which may vary from cylindrical (lined by peptides [81]) to
toroidal (lined by lipid headgroups [52]) to intermediate forms [118]. AMPs’ cationic charge
imparts selectivity for negatively charged bacterial membranes [33]. Although alternative
mechanisms of AMP action have been proposed [34, 35], including clustering of anionic lipids
[36] and targeting of intracellular molecules, such as DNA [37-39], the overall evidence for
AMP-induced membrane pores is strong (e.g., [67]).
Protegrin’s interaction with biological membranes has been studied with a variety of biophysical
techniques. Neutron diffraction experiments suggested toroidal pores [69], and oriented CD
showed the transition between surface and inserted states [286]. Solid-state NMR provided some
evidence that protegrin may form β-barrels containing 8–10 monomers in NCCN parallel
topology [205] (see Topology below). However, solution NMR in detergents showed NCCN
antiparallel topology for protegrin-1 [206], protegrin-3 [207], and protegrin-5 [287]. The same
solid-state NMR study also showed that 75% of the hairpins have homodimerized N and C
strands in an anionic membrane, implying that the β-barrel state is the dominant component of a
heterogeneous mixture. Polyethylene glycol molecules with hydrodynamic radii up to 9.4 Å
allowed membrane permeabilization, whereas ones with radii of 10.5 Å blocked
permeabilization [205]; therefore, protegrin’s pore diameter was below 21 Å. However, another
92
study that investigated protegrin-induced dextran leakage suggested a pore diameter of at least
3–4 nm at high salt concentrations [219].
An atomic force microscopy study of protegrin-1 and other AMPs in large unilamellar vesicles
and solid-supported phospholipid bilayers showed that protegrin acts as a line-active agent,
lowering interfacial bilayer tensions and promoting changes in membrane morphology [61]. A
more recent study of 13 AMPs found that line activity correlates with an imperfectly
amphipathic secondary structure that positions positively charged arginine sidechains near the
membrane interface [118, 156, 288]. A solid-state NMR study of protegrin-1 in 12-carbon 1,2-
dilauroyl-sn-glycero-3-phosphatidylcholine (DLPC) bilayers observed a tilt angle of 55°, also
noting that positively charged side chains tilted into close proximity to membrane lipid
headgroups [289].
Protegrin has been the subject of numerous computational studies; for reviews, see [1, 203]
(Chapter 1). Simulations have been performed of monomers and dimers [220, 221, 258, 259] and
β-barrel models of octamers [2, 221, 223, 224] (Chapters 2–3) and decamers [3, 59] (Chapter 3).
To illustrate potential mechanistic steps, previous all-atom simulations provided potentials of
mean force of protegrin monomer insertion into a lipid bilayer [226] and dimerization in
different environments [96].
Previous work from our laboratory included both all-atom and implicit membrane simulations.
Our thermodynamic investigation of several octameric protegrin-1 β-barrel topologies in pre-
formed implicit pores indicated maximal favorability of the NCNC parallel topology [224],
which allows the more hydrophobic face of each peptide to contact the membrane. Other
simulations showed that the NCNC parallel tetramer has intrinsic curvature compatible with
tilted arcs [100], which may form or contribute to membrane pores. A 300-ns all-atom simulation
93
of a NCNC parallel tetrameric arc showed a stable aqueous pore [100]. Pre-formed β-barrels of
several similar β-hairpin AMPs in NCNC parallel topology were found to be much less stable
than those of protegrin [2] (Chapter 2). We also studied protegrin NCNC parallel β-barrels of 6–
14 peptides: although the nonamer had the lowest energy, a range of pore sizes 7–13 peptides
had relatively consistent favorability [3] (Chapter 3). Those results were consistent with the
predictions of the solid-state NMR study [205], which suggested an octamer, but inconsistent
with [219], which suggested a larger pore.
Despite the large amount of computational work on protegrin, both the final pore state and the
pathway to that state remain uncertain. This paper describes all-atom molecular dynamics (MD)
simulations of protegrin oligomers performed using the Anton 2 supercomputer. We also check
the results against those for β-hairpin AMP tachyplesin [249], whose β-barrel formation was
assessed as unstable (in contrast to that of protegrin) in a previous implicit membrane
investigation [2] (Chapter 2). To examine whether and how protegrin oligomerizes on membrane
surfaces en route to pore formation, we performed one group of simulations of protegrin
oligomers on 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC):1-palmitoyl-2-oleoyl-
sn-glycero-3-phospho-(1'-rac-glycerol) (POPG) bilayer surfaces. For these, we simulated dimers,
trimers, and tetramers in the NCNC parallel, NCCN antiparallel, and mixed topologies (for a
guide to topology, see the Methods below). To examine how oligomeric multiplicity, topology,
and peptide configuration may be associated with pore formation and stability inside the
membrane, we also studied several protegrin systems inside all-atom membranes: tetrameric and
octameric protegrin bundles (see Topology below), octameric and decameric β-barrels, and one
or two tetrameric arcs. The octameric β-barrel was simulated in NCNC parallel and mixed
topologies; the single tetrameric arcs were in NCNC parallel, NCCN antiparallel, or mixed
94
topologies; and the systems with two tetrameric arcs were NCNC parallel or NCCN antiparallel.
We also generated β-barrels with sheared, tilted peptides (NCNC parallel, NCCN antiparallel,
NCCN parallel, and mixed topologies) and a system with four tilted dimers arranged close
together. The results provide insights into the putative steps of protegrin’s pore formation and
show their relationship with topology, yielding information on the likelihood of possible pore
formation pathways.
Materials and Methods
Topology
Dimers of a β-hairpin can combine in six different topologies, depending on which β-strands (N
or C) associate and the relative positioning of the turns. These topologies are NCNC, NCCN, and
CNNC, each of which can have the peptides’ turn region and ends oriented parallel or
antiparallel to each other. In a closed β-barrel, the NCCN and CNNC topologies are identical. A
characteristic that affects membrane binding ability is whether the topology allows the
hydrophobic sides of all hairpins (i.e., the side opposite the disulfide bridges) to point in the
same direction. The NCNC parallel and NCCN antiparallel topologies satisfy this requirement,
whereas NCCN parallel does not [224]. This study investigates up to decamers in NCNC
parallel, NCCN parallel, NCCN antiparallel, and mixed topologies. The mixed topology was
inspired by a recent crystallization study of a θ-defensin AMP, which found a mixed-topology
trimer wherein one dimer had NCNC parallel topology and the other NCCN antiparallel
topology (Figure 4.1) [211].
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Figure 4.1. Possible topologies of protegrin dimerization. A) NCNC parallel; B) NCCN
antiparallel; C) NCCN parallel. Brackets outline the boundaries of mixed topology trimer and
tetramer. Yellow bridges represent disulfide bonds. Arrows point N→C.
We also distinguish our AMP systems inside lipid bilayers according to their initial hydrogen
bonding pattern. “Transmembrane bundles” are peptide assemblies placed closely together but
without initial hydrogen bonds imposed between peptides (Figure 4.2a). The peptides in those
systems could associate freely during all-atom MD simulations. Second, we simulated
“unsheared” β-barrels (Figure 4.2b), in which the peptides began all-atom MD with hydrogen
bonds imposed in fully transmembrane orientation, flush with one another. In a third type of
system, sheared β-barrels (Figure 4.2c), the initially imposed β-sheet hydrogen bonds between
peptides were shifted by two residues per dimer, tilting the β-barrel’s peptides. A hydrogen
bonding shift of two residues was only employed once per dimer because preliminary implicit
membrane MD simulations indicated that β-barrels with shearing every monomer were highly
unstable. Further, our simulations indicated that units of unsheared dimers were stable, whereas
sheared dimers dissociated rapidly (see Results below).
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Figure 4.2. Initial hydrogen bonding patterns of protegrin octamers. A) Bundle, front half: no
initial hydrogen bonding between peptides; B) Unsheared β-barrel, front half: initial hydrogen
bonding between flush transmembrane peptides; C) Sheared β-barrel, front half: hydrogen
bonding shifted by two residues per pair of peptides, introducing a tilt. Sidechains omitted for
clarity. Where applicable, topology is NCNC parallel. NH atoms, CO atoms, and β-barrel
hydrogen bonds shown in white, red, and magenta, respectively.
Preliminary implicit solvent simulations
Preliminary implicit solvent simulations were conducted using Effective Energy Function 1
(EEF1; [108]) and Implicit Membrane Model 1 (IMM1; [112]) using CHARMM version c41a1
[262]. The membranes with anionic pores were set up using mBuild, an in-house utility that
constructs anionic implicit membranes at 5 different focusing levels with a final resolution of
0.5×0.5×0.5 Å [119]. The lipid bilayer’s dielectric properties were represented so that εmemb,
εhead, and εwater (the dielectric constant inside the membrane, the interfacial region, and water)
were 2, 10, and 80, respectively [119]. Headgroup width D was set to 3.0 Å to place the
boundary around the phosphate group. The ion accessibility factor was set so that the ions, which
were taken as monovalent with radius 2.0 Å, could not penetrate below the phosphate groups.
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The positive and negative charge layers were separated by 1.0 Å, hydrocarbon core thickness
was set to 26 Å, and area per lipid was set to 68 Å2. An anionic fraction of 30% was used,
approximating a typical bacterial membrane [239]. The membranes were embedded in cubic
boxes filled with implicit 0.1-M aqueous salt solution.
A description of the simulated systems is presented in Table 4.1. The protegrin oligomers on the
membrane surface and all of the transmembrane bundles were assembled geometrically from the
coordinate files for protegrin-1 and tachyplesin, which were downloaded from the Protein Data
Bank (PDB) (protegrin: 1PG1 [204], sequence RGGRLCYCRRRFCVCVGR-NH2; tachyplesin:
1WO0, sequence KWCFRVCYRGICYRRCR-NH2 [a tachyplesin sequence without C-terminal
amidation was also investigated]) and imported into CHARMM with all charged residues in
ionization states corresponding with pH ~7 and all disulfide bonds patched. Copies of the
peptides were oriented about the origin and then subjected to translations and rotations until they
reached the appropriate configurations. The sheared dimer and tetramer had the peptides offset
by two residues along the hairpin axis to form an appropriately shifted hydrogen bonding pattern.
The mixed topology for trimers and tetramers both consisted of one dimer in NCNC parallel and
one dimer in NCCN antiparallel topology: NCNCCN(anti) (trimer), NCNCNCCN(anti)
(tetramer). Then, without constraints in water, the peptides’ energy was minimized using the
adopted basis Newton–Raphson algorithm (used for all implicit minimizations for 300 steps), but
no dynamics were applied. The configuration was then imported into the membrane builder
feature of CHARMM-GUI [290] to add lipids, water molecules, and ions for all-atom
simulations, as described below.
For the systems with β-barrels and one or two tetramer arcs, the production runs of which were
run inside explicit membranes, the first step was implicit MD equilibration of a protegrin
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monomer in water. After importing the PDB file for protegrin-1 into CHARMM, the peptide’s
energy was minimized in water, followed by 200 ps of MD simulation with the Verlet integrator
(time step: 2 fs, temperature: 298.5 K; used for all implicit simulations, following [2] [Chapter
2]). Subsequent energy minimization then yielded the monomeric structure used for
oligomerization.
We then constructed a single tetrameric arc or a decameric or octameric β-barrel by geometric
transformation to space the copies approximately 10 Å apart and application of potential wells to
enforce hydrogen bonding, followed by further equilibration MD of the tetramers in water.
During equilibration, we imposed intermolecular β-sheet hydrogen bonds using CHARMM’s
NOE facility, following [2] (Chapter 2). To generate the tilted structure of the sheared β-barrels,
the hydrogen bonding pattern was shifted by two residues only once for each pair of peptides,
and the other half of the hydrogen bonding junctions remained as in an unsheared β-sheet.
Table 4.1. Systems simulated in all-atom studies. All membranes contained 180 lipids unless
noted. Bundle: a tightly packed assembly of peptides with the hydrophobic face outwards but no
imposed hydrogen bonding. Tilted: the dimer’s major axis was reoriented 30° from
transmembrane. POPC: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine. POPE: 1-Palmitoyl-
2-oleoyl-sn-glycero-3-phosphoethanolamine. POPG: 1-palmitoyl-2-oleoyl-sn-glycero-3-
phospho-(1'-rac-glycerol). CL: cardiolipin. Chol: cholesterol. For a guide to topology, see
Methods. Mixed topology: one dimer NCNC parallel and the other dimer NCCN antiparallel.
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After imposition of the β-sheet hydrogen bonds, further equilibration MD was run for 200 ps,
followed by minimization. The NOE constraints were removed, and then the individual tetramers
and octamers were placed with the more hydrophobic side facing an anionic implicit pore with
Peptides Topology Membrane composition Time run
Protegrin oligomers on membrane surface
Dimer NCNC parallel 75% POPC:25% POPG 5 μs
Dimer NCCN antiparallel 75% POPC:25% POPG 5 μs
Dimer (sheared) NCNC parallel 75% POPC:25% POPG 5 μs
Trimer NCNC parallel 75% POPC:25% POPG 5 μs
Trimer NCCN antiparallel 75% POPC:25% POPG 0 μs
Trimer Mixed 75% POPC:25% POPG 5 μs
Tetramer NCNC parallel 75% POPC:25% POPG 1 μs
Tetramer NCCN antiparallel 75% POPC:25% POPG 0 μs
Tetramer Mixed 75% POPC:25% POPG 5 μs
Tetramer (sheared) NCNC parallel 75% POPC:25% POPG 3 μs
Protegrin non-sheared barrels
Octamer NCNC parallel 75% POPC:25% POPG 10 μs
Octamer Mixed 75% POPC:25% POPG 4 μs
Decamer Mixed 75% POPC:25% POPG 3 μs
Protegrin sheared barrels
Octamer NCNC parallel 75% POPC:25% POPG 5 μs
Octamer Mixed 75% POPC:25% POPG 5 μs
Octamer NCCN parallel 75% POPC:25% POPG 5 μs
Octamer NCCN antiparallel 75% POPC:25% POPG 5 μs
Protegrin arcs
Tetramer NCNC parallel 100% POPC (294 lipids) 3 μs
Tetramer NCNC parallel 70% POPE:30% POPG (270 lipids) 2 μs
Tetramer NCNC parallel 70% POPC: 30% Chol (100 lipids) 2 μs
Tetramer NCCN antiparallel 75% POPC:25% POPG 2 μs
Tetramer Mixed 75% POPC:25% POPG 5 μs
Two tetrameric arcs NCNC parallel 75% POPC:25% POPG 8 μs
Two tetrameric arcs NCCN antiparallel 75% POPC:25% POPG 3 μs
Protegrin bundles
Tetramer N/A 100% POPC (72 lipids) 9 μs
Tetramer N/A 70% POPE:22% POPG:8% CL 4 μs
Octamer N/A 75% POPC:25% POPG 5 μs
Octamer (four tilted dimers) NCNC parallel 75% POPC:25% POPG 5 μs
Tachyplesin bundles
Tachyplesin octamer (amidated) N/A 75% POPC:25% POPG 5 μs
Tachyplesin octamer (non-amidated) N/A 75% POPC:25% POPG 5 μs
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radius Ro = 12 Å and curvature k = 15 Å, the optimal pore geometry for protegrin octamers found
in [3] (Chapter 3). The decamer barrel employed the optimal decameric implicit pore geometry
of Ro = 16 Å and k = 20 Å [3] (Chapter 3). Implicit MD simulations were then run for 2 ns. A
final minimization then yielded the tetrameric arc and β-barrel structures imported into the
membrane builder feature of CHARMM-GUI. For the systems containing two tetrameric arcs, a
single tetramer was oriented about the origin, and then two diametrically opposed copies were
translated 10 Å away from each other with both hydrophobic faces outward.
To assemble the system with four tilted protegrin dimers, the final configuration of the 5-μs
production run of the NCNC parallel dimer on the membrane surface was imported into
CHARMM, and we tilted the dimer’s major axis 30° from the vertical axis, translated the entire
dimer 10 Å horizontally so that the more hydrophobic side faced outward, and rotated three
copies by 90°, 180°, and 270° about the vertical axis to distribute all four evenly around the pore
edge. The coordinates were then imported into CHARMM-GUI to add lipids, water molecules,
and ions for all-atom simulations, as described below.
All-atom simulations
We imported the systems generated above into CHARMM-GUI’s membrane builder with the
goal of employing 180 total lipids and approximately 50,000 total atoms, configuring the water
thickness above and below the membrane accordingly (overall system size: approximately
81×81×78 Å), except that during preliminary simulations, the number of lipids varied as noted in
Table 4.1. 0.15 M potassium chloride was added to neutralize excess charges. All-atom
simulations employed the CHARMM C36 force field [291] and the TIP3P water model.
The equilibrations were performed using NAMD 2.11 [292] with an initial time step of 1 fs.
After harmonic constraints (k = 1 kcal/mol/Å2) were applied to the water atoms, ions,
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phosphorous atoms, and peptide backbone atoms, we conducted 20,000 steps of energy
minimization followed by 7 ps of heating to 303 K. The constraints on the lipids were released in
another 100-ps equilibration step, followed by a 500-ps one in which the constraints on waters
and ions were also released. Then, we introduced pressure control using the modified Nosé-
Hoover barostat with Langevin dynamics, and the backbone constraints were scaled down in
increments of 0.2 for 200 ps. Then, we ran a 1-ns unconstrained equilibration with a time step of
1 fs, followed by a final 5-ns initial production step (also in NAMD) with a time step of 2 fs.
The production simulations were carried out on the Anton 2 supercomputer [191] at the
Pittsburgh Supercomputing Center using the Multigrator integration framework [293]. We used
VMD to generate Anton 2 input files from the equilibrated NAMD output and parameter files,
and then we used the viparr program to add the force field information to the Anton input files.
Particle motions, thermostat updates, and the Martyna Tuckerman and Klein (MTK) barostat
were applied using Multigrator every 1, 24, and 240 steps, respectively. Long-range
electrostatics were calculated using the Gaussian Split Ewald method [294], and the cutoff values
for electrostatic interactions were automatically calculated by the Anton setup procedure. We ran
the full production simulations for the lengths indicated in Table 4.1 with a 2 fs time step, saving
coordinates every 1.08 ns.
VMD 1.9.2 [276] was used for trajectory visualization and to wrap the trajectories according to
periodic boundary conditions so that all peptides appeared in the same image. CHARMM [262]
was used to calculate pore radius, number of lipid headgroups near the center of the bilayer,
number of water molecules inside the pore, and interaction energy between peptides over the last
1 μs. The numbers of lipid headgroups and water molecules inside the bilayer were found as
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those in the volumes within 5 and 10 Å of the membrane center, respectively. We used VMD
[276] and PyMol [267] to produce molecular graphics of the resulting configurations.
Results
Protegrin oligomers on the membrane surface
To determine likely early intermediates of protegrin oligomerization, we simulated protegrin
dimers, trimers, and tetramers on the membrane surface. Two types of dimers are distinguished:
flush (completely aligned) and sheared (with the shifted hydrogen bonding pattern). Both of the
flush dimers (NCNC parallel [Figure 4.3a] and NCCN antiparallel topologies) were stable on the
membrane surface for 5 μs. No significant events were recorded in either of the trajectories, and
the peptides did not insert below the level of the membrane surface in any of the dimer (or other
oligomer) simulations. The NCNC parallel sheared dimer system started with the hydrogen
bonds between peptides shifted by two residues from a flush configuration. About 550 ns into the
simulation, the two peptides separated from each other on the membrane surface, not rejoining
for the remainder of the trajectory. Thus, in contrast to the flush dimers, the sheared dimer is
unstable on the membrane surface.
All trimers and tetramers were unstable on the membrane surface. In the NCNC parallel trimer,
one monomer flipped over, leaving the disulfide bonds of two adjacent monomers facing each
other, while the remaining dimer was stable. In the mixed topology trimer on the membrane
surface, one monomer dissociated from the end and separated at about 2.9 μs of simulation time,
whereas the remaining NCNC parallel dimer was stable. The NCNC parallel tetramer simulation
was stopped after 1 μs when the monomers on the ends dissociated within 100 ns, the central
dimer remaining stable. In the mixed topology tetramer on the membrane surface, one monomer
dissociated within 100 ns, whereas the fourth monomer dissociated from the central dimer at
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about 2.2 μs. The central dimer again remained stable throughout the production phase. This
pattern also held for the sheared NCNC parallel tetramer, which broke down in a similar fashion
within 650 ns (Figure 4.3b). These results indicate that surface trimers and tetramers were
unstable because their apparent tendency to curve and twist would have moved the edge
peptides’ surfaces away from the membrane surface.
No production simulation of the NCCN antiparallel trimer and tetramer was performed because
the oligomers broke apart on the membrane surface during equilibration despite repeated
attempts to create a stable structure. In these structures, the N-terminal side of one peptide is
close to the N-terminal side of another, bringing two tyrosine residues together. (In contrast, the
NCCN antiparallel sheared β-barrel, in which this problem may exist but is mitigated by the
shearing, was quite stable.)
Figure 4.3. Snapshots of representative protegrin oligomer systems on the membrane surface at
the end of the production phase of simulation, top views. (A) Dimer, NCNC parallel topology;
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(B) Tetramer, NCNC parallel topology. (Rainbow cartoons) peptides; (Orange spheres) lipid
headgroup phosphates within 5 Å of peptides. Lipid tails omitted for clarity.
Protegrin β-barrels
Unsheared (i.e., untilted, with hydrogen bonds aligned) β-barrels have been the most commonly
proposed final pore structure for protegrin (e.g., [205, 224]) and were investigated first. The
unsheared octameric β-barrel in NCNC parallel topology first tore into an open octameric β-sheet
by breaking apart at a single junction point within 150 ns. The sheet continued to tilt and twist
until the monomers on the edges of the sheet were almost parallel to the membrane surface,
coming into contact with the lipid headgroup region. Then, at about 4.7 μs, a single monomer
separated from the other seven and dissociated from the pore. That monomer had zero interaction
energies with the other seven peptides throughout the last 1 μs of simulation time. However, an
open pore surrounded by seven peptides remained through the end of the 10-μs production phase
(Figure 4.4a).
The mixed-topology octameric β-barrel also broke open into an octameric β-sheet at 2 μs. No
other significant events occurred until the simulation was stopped at 4 μs (Figure 4.4b). The pore
remained open and surrounded by eight peptides. Similarly, the mixed-topology decameric barrel
sheared apart at a single junction point within the first 25 ns. Then, at about 900 ns, the decamer
broke apart into a heptameric sheet and trimeric bundle (Figure 4.5). These two structures
surrounded a large, partially lipidic pore, which remained open until the end of the simulation.
The cause of the unsheared β-barrels’ breakage seems to involve the oligomers’ tendency to bend
and twist, which is not facilitated by the unsheared β-barrel configuration.
Seeing that the unsheared protegrin transmembrane β-barrels all broke apart into twisted β-sheets
during the long production simulations, we designed the sheared octameric β-barrel systems to
105
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.
106
Figure 4.4. Snapshots of protegrin octameric unsheared β-barrel systems at the end of the
production phase of simulation. (A) NCNC parallel topology; (B) Mixed topology. (Rainbow
cartoons) peptides; (Orange spheres) lipid headgroup phosphates within 5 Å of peptides; (Red
and white lines) water. Lipid tails omitted for clarity.
107
The NCCN antiparallel sheared β-barrel also remained intact for 5 μs (Figure 4.6c). The
interaction energies between adjacent monomers were ≤ −62.00 ± 7.83 kcal/mol over the last 1
μs, indicating β-barrel stability. These results indicate that the insertion of shears into the β-barrel
structure satisfies the peptides’ intrinsic tendency to bend and twist in a way that the unsheared
β-barrel structure does not.
Figure 4.5. Snapshots of protegrin mixed topology decameric unsheared β-barrel system at the
end of the production phase of simulation. (Rainbow cartoons) peptides; (Orange spheres) lipid
headgroup phosphates within 5 Å of peptides; (Red and white lines) water. Lipid tails omitted for
clarity.
The octameric NCCN parallel sheared β-barrel, in which the hydrophobic clusters of the β-
hairpins point in alternating directions, was not stable as the other sheared β-barrels in our
simulations. The barrel gradually collapsed and the pore fully closed within 5 μs, with the
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monomers remaining close together in transmembrane orientation (Figure 4.6d). This difference
in results from the other topologies can be attributed to the fact that the peptide’s hydrophobic
side faces the membrane in all topologies except NCCN parallel.
Figure 4.6. Snapshots of protegrin sheared octameric β-barrel systems inside the membrane at
the end of the production phase of simulation. (A) NCNC parallel; (B) Mixed topology; (C)
NCCN antiparallel; (D) NCCN parallel. (Rainbow cartoons) peptides; (Orange spheres) lipid
headgroup phosphates within 5 Å of peptides; (Red and white lines) water. Lipid tails omitted for
clarity.
Protegrin tetramer arcs in the membrane
109
Previous studies in our laboratory had indicated that protegrin arcs may form stable pores [100],
but the short length of those simulations did not allow definitive conclusions. The present
simulations of systems containing protegrin NCNC parallel tetramer arcs were conducted in
POPC, POPE/PG, and POPC/cholesterol to determine whether such arcs can surround stable
aqueous pores that are partially lined by lipids. The arcs remained inserted in the membrane, but
the arcs in POPE/PG and POPC/cholesterol deformed slightly, with three peptides forming a β-
sheet and the fourth reorienting to face the other three (Figure 4.7). None of those systems
generated stable, open pores: the simulations ended with lipids occupying space inside the pore
lumen instead of an aqueous channel. We also conducted simulations of NCCN antiparallel and
mixed topology tetramer arcs in POPC/PG, whose configurations remained stable within the
membrane throughout production phases of 2 and 5 μs, respectively, but as above, no aqueous
pore formed for either system. The above results indicate that a single protegrin tetrameric arc is
insufficient to support a stable pore: although the arcs themselves are relatively stable, the
presence of lipids in the pore region prevents stable aqueous conduction.
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Figure 4.7. Snapshots of representative tetramer arc systems inside the membrane at the end of
the production phase of simulation. (A) NCNC parallel, POPC; (B) NCNC parallel, POPE/PG;
(C) NCNC parallel, POPC/cholesterol; (D) NCCN antiparallel, POPC/PG. (Rainbow cartoons)
peptides; (Orange spheres) lipid headgroup phosphates within 5 Å of peptides; (Red and white
lines) water. Lipid tails omitted for clarity.
We then examined the possibility that the arcs are intermediates en route to β-barrel formation.
Therefore, we ran systems containing two transmembrane tetramer arcs (NCNC parallel or
NCCN antiparallel) placed opposite to each other with their centers of mass separated by 20 Å
and water molecules (but no lipids) initially filling the space between them. The arcs diffused in
the membrane throughout the trajectory without forming hydrogen bonds between the two
tetramers. Although very small aqueous channels remained until the simulations ended, no β-
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barrel formation was observed. This indicates that the pairs of protegrin arcs face a kinetic
barrier against combining into a complete β-barrel.
Protegrin bundles
We simulated transmembrane protegrin bundles without imposition of initial hydrogen bonding
to allow the peptides to associate freely and examine the possibility of more classical toroidal
pore structures observed with helical AMPs [52, 67, 68]. This provides a more unbiased look at
oligomerization than the systems beginning with β-barrels or arcs, as the bundle simulations
started farther from the putative final state. The protegrin bundles began as tightly packed
assemblies of monomers rotated with the more hydrophobic faces outward but with no hydrogen
bonding imposed.
We simulated tetrameric protegrin bundles in both pure POPC and POPC/PG membranes. In
POPC, three peptides came together without extensive hydrogen bonding between them, and the
fourth monomer sandwiched behind the third (Figure 4.8a). The peptides’ intermolecular
interaction energies were as strong as −34.00 kcal/mol (SD: 17.5); this indicates that the peptides
interacted moderately strongly despite the absence of a pore. In POPC/PG, the results were
similar: the four peptides rapidly associated into a trimeric arc and a monomer facing the
opposite direction (Figure 4.8b). There was no aqueous pore in either simulation, although the
peptides’ geometries outlined small pores of a few Å in diameter. Therefore, whether the initial
structure was a bundle or arc, four peptides were insufficient to stabilize aqueous channels for
long durations.
The octameric protegrin bundle associated into an NCNC parallel hexameric β-sheet and an
opposing, loosely associated dimer within 300 ns. The hexamer was curved and twisted, and it
and the dimer surrounded a stable, partially lipidic pore (Figure 4.9). The results were in
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accordance with those of the unsheared β-barrels and indicate that eight peptides are sufficient to
stabilize an open pore, whereas four peptides are insufficient.
As reported above, protegrin NCNC parallel dimers were stable on the membrane surface.
However, trimers and tetramers were not and sheared β-barrels were stable, whereas unsheared
ones broke open. Therefore, we arranged four tilted dimers around an aqueous pore to see how
they would associate and whether they would support an open pore. The trajectory showed one
dimer splitting from the other three and returning to the membrane surface at about 2.3 μs. At
about 4.3 μs, one of the three dimers remaining in the pore split up, with one monomer joining
another dimer to form a trimer and the other monomer returning to the membrane surface. A
dimer and a trimer were then left on opposite sides of a small, stable pentameric pore. Although
this situation continued until the end of the simulation (Figure 4.10), a plot of pore radius vs.
simulation time showed the pore continuing to shrink until the end of the production phase,
indicating that the pore may have been in the process of breaking down and destined to close
(see Pore Statistics below; Figure 4.12).
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Figure 4.8. Snapshots of protegrin tetrameric transmembrane bundle systems inside the
membrane at the end of the production phase of simulation. (A) POPC; (B) POPC/PG. (Rainbow
cartoons) peptides; (Orange spheres) lipid headgroup phosphates within 5 Å of peptides; (Red
and white lines) water. Lipid tails omitted for clarity.
114
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.
115
Figure 4.10. Snapshot of octameric protegrin system with four tilted dimers inside the membrane
at the end of the production phase of simulation. (Rainbow cartoons) peptides; (Orange spheres)
lipid headgroup phosphates within 5 Å of peptides; (Red and white lines) water. Lipid tails
omitted for clarity.
Tachyplesin bundles
Although tachyplesin has a similar β-hairpin AMP structure to protegrin, our previous implicit
simulations indicated that it is less stable as a β-barrel than protegrin [2] (Chapter 2). We
investigated bundles of tachyplesin for comparison to the data on protegrin. The reference
structure of tachyplesin contains C-terminal amidation, but we also investigated a structure
without C-terminal amidation to determine the effect of this modification on pore formation. The
tachyplesin bundle with C-terminal amidation exhibited some hydrogen bonding between
dimers, but no larger oligomers formed. The peptides’ intramolecular hydrogen bonding
structure remained intact, and at the end of 5 μs, an aqueous pore remained open (Figure 4.11a).
However, three peptides had reoriented to the membrane surface, and four monomers in the pore
all convened in one lipid leaflet, giving the impression that the pore may be en route to breaking
down. (Pore size vs. simulation time for this system is also plotted in Pore Statistics below.) The
dimer in the opposite lipid leaflet remained associated with the pore region but parallel to the
membrane surface.
The tachyplesin bundle without C-terminal amidation showed similar results to the amidated
one. The bundle associated only into monomers and dimers, which only loosely associated with
each other, and multiple peptides reoriented parallel to the membrane surface, possibly indicating
pore breakdown in progress. However, the peptides that remained inside the pore still surrounded
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an aqueous channel at the end of the simulation time (Figure 4.11b). The similarity of these
results indicates that amidation does not significantly affect tachyplesin’s pore formation ability.
Figure 4.11. Snapshots of octameric transmembrane bundle systems of β-hairpin antimicrobial
peptide tachyplesin inside the membrane at the end of the production phase of simulation. (A)
With C-terminal amidation; (B) Without C-terminal amidation. (Rainbow cartoons) peptides;
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(Orange spheres) lipid headgroup phosphates within 5 Å of peptides; (Red and white lines)
water. Lipid tails omitted for clarity.
Pore statistics
The pore radius, number of water molecules in the pore, and number of lipid headgroups
vertically within 5 Å of the membrane center for applicable systems with stable pores are shown
over the last 1 μs of the production phase in Table 4.2.
Table 4.2. Pore radius, number of water molecules in pore, and number of lipid headgroups
within 5 Å of the membrane center for systems with stable pores during the last 1 μs of
simulation time. Bundle: a tightly packed assembly of peptides with the hydrophobic face
outwards but no imposed hydrogen bonding. Tilted: the dimer’s major axis was reoriented 30°
from transmembrane. Pore radius and number of water molecules: determined for the last 1 μs of
simulation, as per the Methods. Lipid headgroups near membrane center: number within 5 Å of
the midline for the last 1 μs. N/A: Certain values not shown for systems without stable aqueous
pores. For a guide to topology, see the Methods. Mixed topology: one dimer NCNC parallel and
the other dimer NCCN antiparallel.
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For the protegrin system with four tilted dimers and the amidated tachyplesin octameric bundle,
which had aqueous channels without the presence of larger oligomers at the end of production,
we plotted pore radius vs. simulation time to visualize their pore stability (Figure 4.12). For both,
pore radius showed a decreasing tendency throughout the simulation, indicating that the pores
may be en route to breaking down. However, the pore radius of the amidated tachyplesin bundle
seems to have stabilized over the last 1.8 μs, and aqueous channels remained in these systems for
the duration of our simulations, so longer simulations are needed to confirm whether this type of
pore is stable.
Peptides Topology Pore radius (Å) Water molecules in pore Lipid headgroups near membrane center
Protegrin non-sheared barrels
Octamer NCNC parallel 7.5 +/- 1.0 130 +/- 20 3 +/- 1
Octamer Mixed 9.4 +/- 0.7 204 +/- 21 0 +/-1
Decamer Mixed 12 +/- 1.0 307 +/- 41 3 +/- 1
Protegrin sheared barrels
Octamer NCNC parallel 8.7 +/- 0.3 159 +/- 10 0
Octamer Mixed 10.0 +/- 0.4 203 +/- 13 0
Octamer NCCN antiparallel 9.0 +/- 0.3 167 +/- 9 0
Protegrin arcs
Tetramer in POPC NCNC parallel 5.0 +/- 1.5 N/A N/A
Tetramer in POPC/Cholesterol NCNC parallel 7.0 +/- 1.0 N/A N/A
Tetramer in POPE/POPG NCNC parallel 4.0 +/- 1.0 N/A N/A
Protegrin bundles
Tetramer N/A 5.5 +/- 0.5 N/A N/A
Octamer N/A 10.5 +/- 1.0 225 +/- 34 3 +/- 1
Octamer (four tilted dimers) NCNC parallel 7.0 +/- 1.0 125 +/- 27 4 +/- 1
Other transmenbrane bundles
Tachyplesin octamer (amidated) N/A 7.0 +/- 1.0 99 +/- 19 5 +/- 1
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Figure 4.12. Pore radius vs. simulation time for selected systems. (A) protegrin system with four
tilted dimers; (B) tachyplesin octameric bundle.
Discussion
In this study, we performed μs-scale all-atom simulations of protegrin oligomers in lipid bilayers
and observed the relationship between oligomeric multiplicity, topology, and pore stability. The
results provide insights regarding the stability of putative pore structures and the feasibility of
certain pore formation pathways but leave important questions unanswered.
We observed three types of pores that are stable on a time scale of 5–10 μs. The first involves
monomers and small oligomers surrounding a partially lipidic pore. These pores tended to shrink
120
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
123
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
124
interaction than protegrin did: larger oligomers than dimers of tachyplesin did not form at all.
This result verifies our previous implicit membrane simulations showing that tachyplesin is
unstable as a β-barrel [2] (Chapter 2). In contrast, protegrin (which had the ability to form stable
β-barrels in [2]) showed the ability to form new associations between peptides within the pore
(i.e., the trimer in Figure 4.10). Further simulations are necessary to determine whether the
observed tachyplesin pore will remain stable or disintegrate in additional time. The tachyplesin
pores were similar in size and constitution to the pore formed by the system beginning with four
tilted protegrin dimers (Table 4.2); longer simulations are necessary to determine whether each
represents a breakdown product (Figure 4.12).
These results can be analyzed in terms of the investigated peptides’ experimentally observed
pore induction. Voltage clamp experiments on protegrin-infused planar lipid bilayers and
liposome studies revealed that protegrin forms weakly anion-selective channels in lipid bilayers
and induces potassium leakage from liposomes [255]. A study of tachyplesin’s interaction with
liposomes and planar lipid bilayers also indicated the formation of anion-selective pores that
allowed peptide translocation across the lipid bilayer [296], in accordance with the movement of
tachyplesin peptides from the present study’s pores back to the membrane surface. A solid-state
NMR study of tachyplesin indicated that the peptide’s orientation was parallel to the membrane
surface, in contrast to that of protegrin [213]. Dye leakage from liposomes has been measured for
both protegrin [255, 297-299] and tachyplesin [269, 300, 301], but a quantitative comparison
between the two peptides’ ability to induce dye leakage has been lacking.
Conclusions
The present all-atom simulations revealed different types of pores induced by β-hairpin AMPs.
First, unsheared β-barrels of protegrin were not stable for long periods, in contrast to previous
125
contentions [205, 224]. Such barrels opened into twisted β-sheets that surrounded stable,
partially lipidic pores. Second, sheared β-barrels of protegrin were stable, and created completely
proteinaceous pores, in all topologies that allow the peptide’s hydrophobic side to face the
membrane. Although these pores represent a relatively ordered state that may face an entropic
barrier to formation, they were stable for the length of our simulations. Third, tachyplesin and the
bundle of protegrin dimers formed small pores that were lined by only a few peptides, with other
peptides seeming to support the pores from the membrane surface. This leads to the overall
conclusion that protegrin can form a diverse set of pore states depending on conditions.
Additional simulations of dimers, trimers, and tetramers on the membrane surface showed only
the unsheared dimers to be viable as early intermediates in pore formation.
This work leaves open several important questions. More simulations are necessary to determine
how various conditions can lead to the formation of these various pore types. Other factors that
could be manipulated more comprehensively include salt concentration, peptide concentration,
and membrane composition. In addition, the present simulations were set up in a biased fashion
that encouraged the formation of the desired final states. Eventually, it would be more
compelling to illustrate the formation of a stable pore from peptides in solution or on a
membrane surface. Sheared β-barrels are stable once formed, but a study showing the formation
of a complete β-barrel from smaller oligomers is highly desirable.
Several of these questions could be straightforwardly addressed by longer conventional MD
simulations. However, we also need to determine the relative favorability of these various states,
for which free energy calculations may also be useful. Our laboratory is also investigating other
computational approaches, such as simulated tempering [302], which may provide additional
information on β-barrel closure with our current computing power. Other simulation methods
126
like reaction path annealing [303] may also provide information about the critical peptide
aggregation steps.
127
5. Conclusions
In conclusion, we summarize the synergy and impact of all these results and future directions.
Collectively, these results provide a more comprehensive and cohesive picture of pore formation
by β-hairpin AMPs than had been available previously. Several β-hairpin AMPs that had not
been previously subjected to MD simulations were studied in Chapter 2. The results indicated
that other naturally occurring β-hairpin AMPs do not form β-barrel pores as efficiently as
protegrin does. To investigate this difference further, tachyplesin was used in both Chapters 2
and 4. The results in Chapter 4 also indicated that tachyplesin is less stable than protegrin as a β-
barrel.
These differences between protegrin and tachyplesin can be understood in terms of structural
distinctions between the peptides. Our previous structural comparison in Chapter 2 indicated the
differences in hydrophobic residue packing between these two peptides’ putative pore structures.
Although both peptides show “imperfect amphipathicity,” the central region of the hairpin
between the two disulfide bonds is longer in tachyplesin than protegrin, and this lengthened
portion in tachyplesin contains two arginine side chains (R5 and R14) that face the same
direction as both disulfide bonds (i.e., into the pore lumen). In contrast, protegrin’s fewer
residues between the two disulfide bonds contain no side chains facing the pore lumen. The
presence of two large arginine side chains per peptide in the center of the pore lumen could
contribute to tachyplesin pores’ lack of observed stability. Because these extra arginine side
chains pack closely together in tachyplesin β-barrel structures, their bulk could cause steric
hindrance that reduces the stability of higher-order oligomers.
The present results emphasize that a variety of related pore types may form an ensemble that
collectively comprises the overall pore state. While Chapter 2 was restricted to tetrameric arcs
128
and β-barrels with 7, 8, and 10 peptides, Chapter 3 investigated β-barrels of protegrin and related
mutants consisting of 6–14 peptides. The latter results indicated that β-barrels of 7–13 peptides
had approximately equal energetic favorability, further supporting that a diverse ensemble of
pore states is formed by protegrin, as proposed by Mani et al. [205]. However, the results in
Chapter 4 suggested that the constituents of this diverse pore state are probably not the ones
previously thought.
Chapter 4’s simulations of protegrin β-barrels and other structures had a longer time scale than
previously reported ones. Whereas previous all-atom simulations of protegrin in our laboratories
had been restricted to a few hundred ns [100, 224], the simulations in Chapter 4 comprised up to
10 µs of simulation time. Therefore, we had time to observe the systems’ evolution more
extensively than had been possible in previous studies. We witnessed that several structures
proposed by previous studies, such as unsheared barrels [2, 3, 224], the NCCN parallel topology
[205], and tetrameric arcs [100], failed to support stable pores when subjected to longer
simulations. Instead, our longer simulations showed the significance of shearing in β-barrel
structure and suggested that regular β-sheets can support partially lipidic pores. This provides a
more diverse view of the β-hairpin AMP pore state than previously available.
Future studies are required to address several questions that arise from this research. First, some
of the pores that seemed marginal in Chapter 4 may have been en route to breaking down, and
therefore, longer simulations are required to verify that they have an extended lifetime. Longer
simulations of tachyplesin may particularly help to determine whether β-hairpin AMPs like
tachyplesin work by different mechanisms than protegrin. However, longer standard MD
simulations may not provide answers to some other questions. For example, the insertion and
aggregation steps of the putative mechanism were not elucidated in any great detail by this
129
research. Illustration of some early and middle steps of pore formation may require
fundamentally different methods than the ones used in the present work. For example, the
relative favorability of the states determined in Chapter 4 needs to be determined, for which free
energy calculations may be useful. Simulated tempering [302] and reaction path annealing [303]
may provide information about the final steps of β-barrel closure and other critical peptide
aggregation steps. These experiments can also be extended to other β-hairpin AMPs to arrive at a
more comprehensive description of structure–function relationships throughout this entire
peptide family. Other factors could also be experimentally manipulated, such as a more detailed
exploration of how peptide concentration affects the formation of oligomeric pores.
130
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