Insights into Peptoid Helix Folding Cooperativity from an Improved

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Insights Into Peptoid Helix Folding Cooperativity From an Improved Backbone Potential Sudipto Mukherjee, Guangfeng Zhou, Chris Michel, and Vincent Alvin Voelz J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b09625 • Publication Date (Web): 19 Nov 2015 Downloaded from http://pubs.acs.org on November 26, 2015

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The Journal of Physical Chemistry

Insights Into Peptoid Helix Folding Cooperativity From an Improved Backbone Potential Sudipto Mukherjee, Guangfeng Zhou, Chris Michel† and Vincent A. Voelz* Department of Chemistry, Temple University, Philadelphia PA

ABSTRACT

Peptoids (N-substituted oligoglycines) are biomimetic polymers that can fold into a variety of unique structural scaffolds. Peptoid helices, which result from the incorporation of bulky chiral side chains, are a key peptoid structural motif whose formation has not yet been accurately modeled in molecular simulations. Here, we report that a simple modification of the backbone φ-angle potential in GAFF is able to produce well-folded cis-amide helices of (S)-N-(1phenylethyl) glycine (Nspe), consistent with experiment.

We validate our results against both

QM calculations and NMR experiments. For this latter task, we make quantitative comparisons to sparse NOE data (Armand et al., PNAS 1997) using the Bayesian Inference of Conformational Populations (BICePs) algorithm (Voelz et al. JCC 2014), a method we have recently developed for this purpose. We then performed extensive REMD simulations of Nspe oligomers as a function of chain length and temperature to probe the molecular forces driving cooperative helix formation. Analysis of simulation data by Lifson-Roig helix-coil theory show that the modified

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potential predicts much more cooperative folding for Nspe helices. Unlike peptides, per-residue entropy changes for helix nucleation and extension are mostly positive, suggesting that steric bulk provides the main driving force for folding. We expect these results to inform future work aimed at predicting and designing peptoid peptidomimetics and tertiary assemblies of peptoid helices.

INTRODUCTION Peptoids (N-substituted oligoglycines) are a class of sequence-specific polymers1 whose favorable peptide mimic properties have found numerous applications as antimicrobials,2-4 drug delivery vehicles,5 biotherapeutics,6-14 catalysis15 and nanomaterials.16-19 Peptoids are easily synthesized,20 and resistant to proteolysis.21 Peptoids are also foldamers, capable of self-assembling into unique three-dimensional structures, a property which has been exploited to design peptidomimetic scaffolds for molecular recognition.4, 22-23 Unlike peptides, the tertiary amines of peptoids allow both cis- and transamide bond conformations. While this additional degree of conformational freedom and the absence of backbone hydrogen-bonding confer a great deal of backbone flexibility, secondary structure can be controlled through specific side chain substitutions. For instance, peptoids with bulky chiral substituents such as (R)- or (S)-N-(1-phenylethyl)glycine (Nspe), and (R)- or (S)-N(1-napthyl ethyl)glycine (Ns1npe), induce cis-amide helical structures, with (R)- and (S)stereochemistry forming left- and right-handed helices, respectively,24-27 while N-aryl substitutions induce primarily trans-amide configurations.28 Sequences with alternative cis- and trans-amide propensities form so-called peptoid ribbon structures.29


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The cis-amide peptoid helix scaffold, exemplified by poly-Nspe, has been the focus of much previous work. The structure of Nspe helices had been predicted computationally,30 and experimentally confirmed using 2D NMR spectroscopy.24 An X-ray crystal structure was obtained of a similar sequence, (Nrch)5, a pentamer of (R)-N-(1-cyclohexyl)glycine).31 Like peptide helices, peptoid helices exhibit a characteristic circular dichroism spectrum, and lengthdependent structuring indicative of a helix-coil transition.26, 32-33 Due to the lack of backbone hydrogen bonds, however, the molecular forces that drive peptoid helix formation are thought to be very different from peptides. Two complementary mechanisms have been put forth to explain the folding mechanism and stability of peptoid helices. The first is excluded volume effects, whereby the chiral bulk of side chain groups creates significant steric clashes that can be avoided most effectively when the backbone assumes a single-handed cis-amide helix conformation. The second is n→π* interactions, which have been established by experimental and theoretical studies as playing a stabilizing role for peptoid helices.34-36 Consistent with these mechanisms, peptoid helices are extremely stable under high temperatures and high denaturant concentrations.26, 37 Despite the discovery of peptoid monomers with bulky chiral sidechains that strongly promote helical secondary structural propensities,27, 31, 37-38 designing scaffolds with well-defined tertiary structure has been challenging.23, 39 Crystal structures of linear peptoids have only been characterized for sequences of six residues or less.24, 29, 31, 37, 40-43 Based in part on the success of computational protein design algorithms,44 it has long been thought that more accurate modeling of peptoid folding could enable the computational design of sequences with highly stable and specific folds, and/or stable tertiary assemblies. For this reason, and to obtain insight into the fundamental molecular mechanisms of peptoid folding, several groups have performed


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molecular simulation studies of linear and cyclic peptoids using all-atom and/or coarse-grained potentials.45-51 A common conclusion of all-atom molecular simulation studies of peptoids and other foldamers is the need to better parameterize existing potentials, a prudent strategy when simulating any non-peptide polymer.52-53 Mirajinan et al. reparameterized backbone partial charges and van der Waals parameters of the CHARMM potential to achieve a more accurate description of achiral peptoids that has enabled further work in simulating peptoid nanostructures.50 In earlier work, we found that REMD simulations of model peptoid systems using the General Amber Force Field (GAFF)54 along with the GBSA implicit solvation model55 worked well in predicting a range of experimental structures.45, 48 A key aspect of this approach was the use of replica exchange molecular dynamics (REMD) to sample all possible backbone cis/trans-amide isomers. One key exception was that GAFF failed to correctly model the conformational landscape of Nspe oligomers, the canonical helix-forming peptoid. Simulations using GAFF failed to form helices or display the correct torsional preferences, as known from experiment and QM studies,56 which predict negative backbone φ-angles should be more stable than positive angles. Given the widespread use of Nspe residues in helix-forming peptoids, and the wealth of existing experimental data, it is surprising that previous simulation studies have not been performed to accurately model the folding of poly-(Nspe).

Here, we present a simple re-

parameterization of the GAFF backbone torsion potential to better match the conformational landscape predicted by QM studies, which we validate against solution NMR experiments. Using the improved potential, which we call GAFF-φ, we perform REMD simulations of poly-(Nspe) to gain insight into peptoid helix formation as a function of chain length and temperature.


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analysis of the resulting data using Lifson-Roig helix-coil theory suggests that unlike peptides, entropic driving forces play a large role in peptoid helix formation, due to side chain steric effects.

METHODS Peptoid oligomer modeling and parameterization. To construct a custom peptoid residue topology for Nspe, a capped structure (acetylated at the N-terminus and N-dimethylated at the Cterminus) was built using UCSF Chimera,57 and AM1-BCC partial charges were assigned using antechamber and sqm from the AMBER12 suite of tools.58 An AMBER residue topology unit was constructed using a custom python script and the tleap program to remove the caps, redistribute the excess partial charge over the remaining atoms to maintain a net neutral charge, and assign GAFF atom types. Finally, the GAFF-φ force field modification (described below) was applied with the AMBER12 parmed tool.

In this way, molecular topologies for Ac-

(Nspe)n-NH2 were constructed, for chain lengths n=3 to n=15, in an all-trans amide configuration. The ACPYPE program59 was used to convert AMBER molecular topologies for use with the GROMACS simulation package. Replica Exchange Molecular Dynamics (REMD) simulations. Temperature replica-exchange molecular dynamics simulation was performed using GROMACS 4.5.460 on the Owlsnest highperformance computing cluster at Temple University, for all chain lengths n=3 to n=15, in both GAFF-φ and GAFF potentials. Stochastic dynamics was performed using Langevin integration with a water-like viscosity of 91 ps-1, and 2 fs time step. The OBC GBSA implicit solvation model,55 which has previously shown to perform well in modeling peptoid structure and


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dynamics,45 was used in all simulations. Twenty-four log-spaced temperature replicas, ranging from 300 K to 800 K, with exchanges performed every 10 ps, were used for production runs. Overlapping potential energy distributions for nearby replicas (Figure S1) ensured acceptance ratios ranging from 0.5 to 0.8. For parameterization runs (see below), eight replicas were used in the same temperature range. The high maximum temperature of 800K is required to efficiently sample across cis/trans isomerization barriers, a key feature of peptoids not present in peptides. The minimum GAFF-φ simulation length was 3.5 µs, although many trajectories were longer, with an average simulation length of 4.3 µs (Table S1). The average GAFF trajectory length was 3.7 µs. The aggregate simulation time across all chain lengths, replicas and potentials totaled over 103.9 µs × 24 replicas = 2.4 ms. Free energy estimation and calculation of structural observables. The multi-state Bennett acceptance ratio (MBAR) algorithm,61 as implemented in the pymbar python package (http://github.com/choderalab/pymbar), was used to estimate conformational free energies, expectation values of structural observables, and associated uncertainties. Per-residue structural observables computed using MBAR include cis vs. trans backbone amide populations, and helical populations (see Lifson-Roig helix-coil theory, below). Importantly, our MBAR analysis utilizes a preliminary step to subsample the simulation data according to a time series analysis that determines the statistical inefficiency, g, which is the number of samples between effectively uncorrelated data points.62

In this calculation,

temperature replicas are ordered by replica index (i.e. 24 parallel replicas undergoing a random walk in temperature space) to determine autocorrelation times. The value of g is set to 1 + 2τ, where τ is the largest autocorrelation time calculated across the ω, φ and ψ backbone angle time series for all residues.

The most correlated of these observables are the ω angles, due to the


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large cis/trans isomerization barriers.

For structural observables that involve ω angles (which

include cis vs. trans amide populations and helix populations), the longest ω-angle autocorrelation times are consistently around 100 ns for all chain lengths (Table S2), resulting in about 500 uncorrelated samples across all temperatures from which to estimate values of structural observables. Based on this autocorrelation time, we also discarded all trajectory snapshots in the first 100 ns of each replica trajectory (i.e. the so-called “burn-in” time).62 Bayesian Inference of Conformational Populations (BICePs). The BICePs algorithm63 was used to infer conformational populations of (Nspe)5 using a combination the REMD simulation data and experimental NOE distance restraints from Armand et. al.24 Full details on the BICePs algorithm are available elsewhere.63 Briefly, BICePs uses a Bayesian approach to infer a distribution of conformational populations, by sampling a posterior probability function P(X|D) ∝ P(D|X)P(X) where X is one of a set of molecular conformations, and D represents the experimental data. P(X) is a prior probability function, calculated from the results of molecular simulation. P(D|X) is a likelihood function representing experimental restraints. To obtain a set of molecular conformations and their equilibrium populations, we used the MSMBuilder2 software64 to perform k-centers clustering in dihedral angle space (ω, φ, ψ and χ of all residues) on the lowest-temperature (300 K) replica of the 4 µs REMD simulation of (Nspe)5 (3.5 µs for GAFF-φ). This procedure produced 1000 cluster generators with welldefined dihedral states to be used as exemplar structures, along with estimates of cluster populations P(X).

To enforce experimental restraints, Gaussian distributions of inter-proton

distances rj were used, centered on the upper distance bounds rjexp used by Armand et al.,


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parameterized by standard deviation σ, and distance scaling factor γ′ = γ-1/6, according to a likelihood function P(D|X,σ,γ′). The σ and γ′values are treated as nuisance parameters included in the posterior sampling. Groups of n equivalent protons were given equal weights of 1/n. Absent distance restraints were not used. BICePs Bayes factors. To select between two competing models M1 and M2, Bayes factors KBF are computed as

The Bayes factor represents the strength of evidence in support of model M1 over M2, and is analogous to the likelihood ratio test used in classical hypothesis testing. Computing this ratio is equivalent to computing a free energy difference,

where Ei = -ln P(σ, X|D,M1), which we estimate using the MBAR algorithm.61 Lifson-Roig theory of the helix-coil transition. Several well established theoretical models such as the Zimm-Bragg model65 and the Lifson-Roig (LR) model66 have been used to successfully model the cooperative helix-coil transition of peptides.67 In particular, LR theory has been a very useful tool for quantitatively comparing molecular simulations to experiments, by way of the model parameters fit to each kind of data. In LR theory, each residue of a polypeptide can be in one of two discrete states: a helix (‘h’) state, or a coil (‘c’) state. Conformations of peptide residues sampled in molecular simulations are assigned to one of these states based on the backbone (φ,ψ) angles, with the ‘h’ state assigned when the backbone angles


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are sufficiently close to the αR ~(-60°, -45°) minima in the dihedral Ramachandran plot, and ‘c’ assigned otherwise. To model the helix-coil transition for peptoids, we similarly define the helix ‘h’ state based on backbone dihedral angles. In order to correctly form a right-handed Nspe helix, the peptoid backbone must have a cis ω angle (|ω| < 90˚) and a negative ϕ angle, which we call the “cis minus” (c-) conformation. Thus, a peptoid residue in the c- conformation is assigned to be a helical residue (‘h’), and coil (‘c’) otherwise. In LR theory, two key parameters model the driving forces for helix formation: v, a nucleation parameter, and w, an elongation parameter.

For peptides, nucleation of a helical

residue is initially unfavorable due to conformational entropy loss, while elongation (the formation of a sequence of multiple helical residues) is favorable due to the cooperative effects of desolvation and forming backbone hydrogen bonds. LR theory is a statistical mechanical model in which each residue a statistical weight according to its conformational state, and that of its adjacent residues. The reference state for these weights is the coil (‘c’) state, so any residue in the coil state receives a weight of 1. A residue with sequence index i in a helical (‘h’) conformation is assigned one of two weights: if either adjacent residue i-1 or i+1 is in a coil conformation, it receives a weight of v; if both adjacent residues are in a helical conformation, it receives a weight of w. Cooperative helix formation occurs when v < 1 and w > 1. Formation of a single helical residue is unfavorable, while elongated helical sequences are highly favorable, resulting in cooperative, “all-or-nothing” folding behavior. If so desired, per-residue weights vi and wi can be used for individual residues in a sequence. Weights assigned to each residue are assumed to be statistically independent; thus, the statistical weight of a particular sequence of residues can be calculated as the product of weights


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for each residue.

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The partition function—the sum of the weights of all possible sequences—

can be calculated in the compact matrix form:

where N is the total number of residues in the sequence, and the weight matrix Mi is defined as

With the partition function in this form, many ensemble average properties can be calculated, such as

where

hi

is the ensemble average of the probability that residue i has weight wi. For peptides,

the physical meaning of hi is associated with the formation of a hydrogen bond. For peptoids, there are no backbone hydrogen bonds, and hi represents the probability that residue i is a helical residue within a helical segment with at least three consecutive helical residues (i.e. the shortest helical segment is ‘chhhc’). The average (non-terminal) residue helicity fh

is calculated using

the following equation:68

To estimate the LR parameters from molecular simulation data, we used a Bayesian inference approach. By Bayes Theorem, we can express the probability of parameters λ = (v1,...,vN,w1,...,wN), given the data, as P(λ | data) ∝ P(data | λ) P(λ)


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where P(data | λ) is the likelihood function, and P(λ) is a prior distribution of the parameters. The likelihood function can be expressed as

where Nk is the total number of conformations observed in the simulation and pk = Z-1 Πi xik is the probability of observing chain conformation k, where xik is the statistical weight of residue i in conformation k. For the prior, we choose a uniform distribution P(λ) =1. In this way, the most probable (best-fit) value of the v and w parameters are found by maximizing the likelihood function P(data | λ). In practice, we maximize the negative logarithm of the likelihood function, which can be expressed as

where Nw,i (Nv,i) is the number of times that residue i has a weight wi (vi) out of a total of Nk conformations. In all of the analysis reported below, we use a single v and w parameter to model all residues. The model parameters and their posterior distributions were inferred by Monte Carlo Metropolis sampling in parameter space. Random moves are made in w and v, and accepted with probability min(1, Ltrial/L), where Ltrial is the trial likelihood. Values are collected after the sampling reaches equilibrium.

The best-fit values of v and w, along with their

uncertainties, are estimated from the mode and standard deviations of their posterior distributions, respectively. Estimation of thermodynamic parameters. In addition to fitting LR parameters to the simulation data at a fixed temperature, we also fit the entire set of temperature data to a thermodynamic model to extract enthalpies and entropies of helix nucleation and elongation, parameters which give great insight into the physical mechanisms that drive peptoid helix


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formation. In this model, the per-residue statistical weights arise from a temperature-dependent Gibbs free energy of helix formation, –β∆Gv = ln v and -β∆Gw = ln w, where β = 1/kBT, and

∆Gv = ∆Hv – T∆Sv + ∆Cp,v (T-300K) – T∆Cp,v ln (T/300K) ∆Gw = ∆Hw – T∆Sw + ∆Cp,w (T-300K) – T∆Cp,w ln (T/300K)

Here, ∆Hv and ∆Hw are the per-residue enthalpies of helix nucleation and elongation, respectively, and ∆Sv and ∆Sw are the per-residue entropies of helix nucleation and elongation. The additional heat capacity parameters ∆Cp,w are needed to model the temperature dependence of ∆Gv and ∆Gw. We use the same posterior sampling method to fit the simulation data, but using a likelihood function that considers all the temperature data, and making Monte Carlo moves in the values of ∆H, ∆S, and ∆Cp.

Monte Carlo sampling was performed for

approximately 1 million steps, with step sizes of 0.001 for v and w, and 0.01 for all thermodynamic parameters. Converged results are obtained typically within 30,000 steps. Ab initio QM calculations. Ab initio QM energies of Ac-Nspe-N(CH3)2 were computed as a function of backbone φ and ψ angles (scans in 15 ̊ intervals) using Gaussian09.69 Conformations were first optimized at the HF/6-31G* level, followed by single-point calculations at the B3LYP/6-311+G(2d,p) level, with initial ω angle set to either 0 ̊ (cis) or 180 ̊ (trans). 

RESULTS


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Parameterization of the GAFF backbone φ-angle potential. To determine the backbone conformational preferences of monomeric Nspe, we calculated ab initio QM energy landscapes of cis- and trans-amide Ac-Nspe-N(CH3)2 as a function of backbone φ and ψ angles (scanned in 15 ̊ intervals), as described in Methods. The results (Figure 1) are similar to results obtained by Butterfoss et al. using the same level of theory:56 both cis (ω=0˚) and trans (ω=180˚) amide conformations show a preference for negative φ-angles ~(-90˚) versus positive φ-angles ~(+90˚) for the αD minima near ψ=180˚; trans-amide conformations display an additional C7β minima near φ, ψ = (-130°, 80°) seen in tight turns.70-71 The cis-amide state is slightly more preferred, with the energy difference of the cis-amide minimum 0.20 kcal/mol lower than the trans-amide minimum. For the cis-amide energy minima, the negative φ-angle αD minimum is 1.01 kcal/mol lower in energy than the positive φ-angle αD minimum. For the trans-amide energy minima, the negative φ-angle αD minimum is 1.42 kcal/mol lower in energy than the positive φ-angle αD minimum. Previously, we showed that molecular simulations of Nspe monomers and trimers using the GAFF force field with GBSA implicit solvent were inconsistent with QM studies of Nspe, incorrectly showing a preference for positive φ-angles by about ~1 kcal/mol,45 and proposed an ad hoc harmonic biasing potential to reproduce the correct preferences.

Here, to more

systematically parameterize GAFF using the functional form of AMBER-style dihedral potentials, we introduce an additional term, kφ cos(φ – π/2), to the cosine series that defines the c-n-c3-c dihedral potential in GAFF. We call this modified force field GAFF-φ. To optimize the value of kφ, we performed a series of 100 ns REMD simulations at various values of kφ, for a capped Nspe monomer Ac-Nspe-N(CH3)2 and trimer Ac-Nspe3-N(CH3)2. Eight temperature replicas were used (300K, 345K, 396K, 456K, 524K, 603K, 695K, 800K) for


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independent REMD production runs using kφ = 0.0, 0.7, 1.0, 1.5, 2.0, and 2.5 kcal/mol. The best calibration between simulated and experimental free energy differences between negative φangle and positive φ-angle states, occurs for kφ =1.0 kcal/mol, which we choose for GAFF-φ (Figure 2).

GAFF-φ correctly predicts cis-amide right-handed Nspe helices. REMD simulations using GAFF-φ, but not GAFF, consistently form right-handed helices with cis-amide backbones (Figure 3). Conformational free energy plots as a function of φ and ψ dihedral angles, averaged across all residues, show that GAFF-φ landscapes are in much closer alignment with the QM results than GAFF, which displays an incorrect φ-angle preference, and tends to favor C7β over αD minima (Figure 4). REMD simulations of ~4 µs, performed using GAFF-φ for chain lengths n=3 through n=15 (see Methods) show an initial increase in the residue-averaged populations of backbone cis-amide bonds, from about 0.6 to 0.85, followed by a decrease for n > 9 (Figure 5, top panel). The length-dependent increase we observe is consistent with previous circular dichroism studies of (Nspe)n performed in acetonitrile.33 We conjecture that the decrease is due to non-local intrachain interactions that become prevalent as the chain length increases. We expect to observe such features to some extent because while our simulations model the aqueous solution-phase, Nspe is not especially water-soluble.

Interestingly, residue-averaged populations of cis-amide

bonds are larger for GAFF-φ than GAFF, in some cases by more than 10%, indicating that ωangle and φ-angle are coupled and not statistically independent, suggesting a role in cooperative folding.


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A comparison with experimentally measured Kcis/trans ratios is made possible by estimating predicted ratios from residue-averaged populations pcis as Kcis/trans = pcis/(1-pcis) (Figure 5, bottom panel). The Kcis/trans values computed from the simulations range from about 2 to 5, in general agreement with various published values ranging from 1.5 to 3.3 (Table 1).

Validation of GAFF-φ against experimental NMR observables using BICePs. The above comparisons of GAFF-φ predictions with experimental observables are largely qualitative. For a more quantitative validation of the modified potential, we must compare the predictions of molecular simulations using GAFF and GAFF-φ to experimental structural observables in the solution-phase. Unfortunately, there is a paucity of such experimental data for peptoids, which has hampered previous efforts to parameterize and validate molecular force fields. In particular, only a handful of 2D NMR structural studies exist for folded peptoids24, 29, 42 due to the lack of NH hydrogen groups and poor peak dispersion, which has been overcome in some cases by judicious substitution of side-chain analogs. Although several X-ray crystal structures of helical peptoids exist,31, 37 only a single NMR structural refinement, for a peptoid pentamer of (S)-N-(1phenylethyl)glycine, (Nspe)5, has been published showing helical conformations of peptoids in the solution phase.24 To leverage this sparse experimental NMR data, we apply a new Bayesian inference method, Bayesian Inference of Conformational Populations (BICePs),63 to infer conformational populations of molecules from both computational models and sparse experimental observables. BICePs has several unique aspects, including (1) posterior sampling of over nuisance parameters


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(e.g. the uncertainty of experimental measurements), (2) proper use of reference potentials, and (3) the ability to compute Bayes factors for model selection. Armand et al. used the observed NOE cross-peaks to derive a sparse set of fifteen shortand medium-range distance restraints to refine the conformational ensemble of (Nspe)5-NH2 in methanol.24 The major solution structure was found to be a right-handed cis-amide helix. To achieve good dispersion, F-, Cl- and NO2 para-substitutions on the phenyl groups were used, but it is assumed that the molecule is otherwise directly comparable to (Nspe)5. We note that the original NMR refinement also used several simplifying assumptions: all amides were constrained to the cis form, and absent distance restraints were also enforced. Our BICePs calculations do not restrain ω angles nor use absent distance restraints. BICePs was performed as described in Methods. In addition to enforcing NOE distance restraints as described in Voelz et al.63 we additionally restrained cis-amide populations to a given experimentally measured cis/trans ratio, Kct.. This was achieved using an additional binomial term in the likelihood function, L(k|p) = n!/[(n-k)!k!] pk(1-p)n-k where k is the number of amides in the cis configuration for a given conformation, n is the total number of residues (n=5 in this case), and p = Kct../(1+ Kct.) is the experimentally measured probability that the amide is in the cis configuration. Experimental estimates of Kct for Nspe oligomers depend upon solvent conditions and oligomer length,33 so we performed calculations using a range of plausible values of Kct (1.5 to 3.2); all give similar results (Table S3). Ten million steps of Markov Chain Monte Carlo were used to sample over conformations and nuisance parameters σ and γ′ (see Methods). Proper reference potentials are used as described in Voelz et al.63 BICePs population estimates, and Bayes factors P(M1)/P(M2) comparing two different models M1 and M2 of conformational populations, were calculated using the MBAR algorithm.61


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Figure 6 shows the results of the BICePs algorithm (with Kct set to 2.5) applied to simulations of (Nspe)5 performed in GAFF and GAFF-φ.

Both simulations are highly

compatible with the experimental distance restraints, with posterior distributions of σ and γ′ centered around 1.5 Å and 1.16, respectively (Figure S3). For GAFF-φ, 60% of the population can be described by two conformational clusters (46% and 14%), differing only by the sidechain χ angle of the C-terminal residue. Both conformations are right-handed helices having all negative φ angles and all cis-amides, with the exception of the C-terminal residue, which has a trans-amide configuration, thus facilitating a backbone hydrogen bond between the terminal NH2 group and the preceding carbonyl oxygen. This trans isomer of the C-terminal residue was clearly observed and described in the original NMR studies by Armand et al.24 The ten largest conformational populations computed by BICePs all share the same c-c-c-c-t- backbone state, differing only in backbone φ and χ angles (Table S4). Conformational populations computed using the GAFF simulations are more heterogeneous (Table S4): 38% of the total population is described by two conformations (24% and 14%) differing by only the ψ angle of the C-terminal capping group, with a pattern of backbone ω and φ angles c-c+t+c-t+. The next most populated state comprises 11% of the total population, and has a backbone conformation of c-c-c-c+t+. We performed additional simulations using GAFF for the para-substituted phenylethyl groups used in the Armand et al. peptoid pentamer, and found similarly heterogeneous conformational distributions (data not shown). Bayes factors comparing models using a combination of simulation data and experimental data (e.g. GAFF-φ + exp), versus experimental data only (exp only), are positive and significant (Table 2), 2.68 and 1.75, for GAFF-φ + exp and GAFF + exp respectively. These results indicate that the simulations are highly compatible with the experimental data, and furthermore that using


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simulation-weighted populations results in even better agreement with experiment. Assuming Kct = 2.5, the computed Bayes factors for comparing models GAFF-φ + exp and GAFF + exp is 1.53, which means that GAFF-φ is at least 1.5 times more likely to be a correct model of the experimental data compared to GAFF. Bayes factors for other values of Kct are shown in Table S3. Insights into peptoid helix folding cooperativity from GAFF-φ. The MBAR algorithm was used to estimate per-residue helix populations as a function of temperature from REMD simulations performed using GAFF and GAFF-φ, as described in Methods. A peptoid residue is assumed to be in a helical conformation if |ω| < 90˚ and φ is negative, i.e. the ‘c-’ state. Average helix populations versus temperature, pcis(T), for chain lengths n=3 to n=15 are shown in Figure 7. Similar to the estimated cis-amide populations versus chain length, helical populations at 300 K for GAFF-φ show an initial increase from about 0.6 to 0.85 as chain length increases, and a slight decrease in helix populations thereafter, likely due to non-local interactions. Helix populations decrease with increasing temperature in a sigmoid-like fashion, espeically for longer chain lengths, resulting in helix populations of around 0.45 at 800 K. Consistent with experimental studies,25-26 peptoid helices are robustly temperature-stable: extrapolated melting temperatures in GAFF-φ range from about 450 K to 550 K, with persistent residual helical structure even at high temperatures. In contrast, the GAFF simulations do not exhibit strong helix formation, with helix populations increasing with temperature and chain length, from values of 0.1 to 0.3, for all chain lengths simulated. The REMD simulation data generated using both GAFF and GAFF-φ were used to derive bestfit Lifson-Roig nucleation and elongation parameters v and w, as a function of temperature and chain length, using the posterior sampling technique described in Methods. Example results for


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the single-temperature fits and thermodynamic fits are shown in Figure 8. Both kinds of LR fits show excellent aggrement between the observed helicity in simulations. Per-residue thermodynamic parameters ∆Hv (nucleation enthalpy), ∆Hw (elongation enthalpy), ∆Sv (nucleation entropy), and ∆Sw (elongation entropy) were determined as a function of chain length, using helix-coil theory fits to the entire set of temperature replica data, as described in Methods (Figure 9). Similar to the computed cis-amide and helix populations as a function of chain lengths, nucleation enthalpies and entropies for helix formation tend to initially increase as chain length increases, and decrease for longer chain lengths. In contrast, contributions of elongation enthalpies and entropies tend to increase monotonically with chain length, indicating increased cooperativity (one exception is the n=3 outlier, which is too short for Lifson-Roig theory to properly address). Comparison of GAFF and GAFF-φ results show that both ∆Hv and ∆Hw are lower in GAFF-φ compared to GAFF by about 1 to 1.5 kcal/mol. This is easily rationalized by our modification of the φ-angle torsion potential, which is designed to provide an enthalpic reward for helical states (i.e. negative φ-angles). Entropic parameters ∆Sv and ∆Sw are more similar between GAFF and GAFF-φ, which is expected given that both models are being applied to the same molecular system, and there should be a similar distribution of conformational states. Peptoid helix formation is entropically favorable. A great deal of insight into peptoid folding mechanisms can be gained by comparing our thermodynamic parameters to those determined for peptides, both from simulations and experiments (Table 3). Previous circular dichroism (CD) and differential scanning calorimetry (DSC) experiments72-74 have measured perresidue enthalpies of helix formation to be around -1 kcal/mol, due to favorable backbone hydrogen bonding. DSC measurements of a water-soluble acid-denatured peptoid have provided


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similar estimates of per-residue calorimetic enthapies ∆Hcal (comparable to ∆Hw) of -1.1 kcal/mol. Molecular simulations of both peptides and peptoids agree well with these values, and are similar to each other. LR parameters derived from peptide simulation data typically yield ∆Hw values from -0.4 to -1.25 kcal/mol, depending on the potential used,68, 75 and our GAFF-φ simulations yield ∆Hw values for peptoids that increase with chain length from -0.9 to 0.5 kcal/mol. Per-residue nucleation enthlapies ∆Hv derived from peptide simulations are typically positive, ranging from +0.4 to +0.9 kcal/mol, depending on the potential used, while values of ∆Hv extracted from our GAFF-φ simulations of peptoids are a bit lower, ranging from about -0.5 to +0.5 kcal/mol. Overall, these comparisons suggest that enthalpic stabilization plays a weaker role for peptoids in helix formation than it does for peptides. This makes sense in light of the fact that peptides, unlike peptoids, have the ability to make enthalpically favorable backbone hydrogen-bonds. More striking is the comparison between the calculated per-residue entropies of helix formation for peptoids versus peptides.

Whereas ∆Sv and ∆Sw extracted from peptide

simulations are unformly negative, reflecting the loss of conformational entropy of helix formation, values of ∆Sv and ∆Sw extracted from our GAFF-φ simulations are mostly positive, with ∆Sw increasing with chain length to values as large as +3.0 cal/mol/K. This suggests that peptoid helix formation is driven by favorable gains in conformational entropy, which is quite different from peptides. What is the source of this favorable per-residue entropy gain? Steric interactions have long been thought to drive the conformational preference of polypeptoids,30 with bulky non-chiral sidechains like tert-butyl37, 76 and triazolium38 able to promote high populations cis-amide bonds, and chiral sidechains with increasing steric bulk promote proportionally larger helix populations


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(for example, helicity increases as Nsce < Nspe < N1npe, for 1-carboxyethyl, 1-phenylethyl and 1-napthylethyl sidechains, respectively).

Alternatively, another explanation for favorable per-

residue entropy changes might be increased sidechain flexibility when the peptoid backbone is in the helical ‘c-’ state. To test this idea, we examined the distributions of χ and ψ angles in all four helical states of the backbone, ‘c-’, ‘c+’, ‘t-’ and ‘t+’ (Figure S4). The results, which show a great deal more flexibility for states with a trans-amide backbone, do not support this model. Thus we believe this favorable entropy gain arises mainly from steric interactions; helical peptoid formation minimizes potential steric clashes, and facilitates an overall greater conformational volume of allowed conformations.

Discussion The finding that, unlike peptides, peptoid helix formation is entropically favorable has repercussions for peptoid design, specifically in helping to computational predict peptoid tertiary assemblies as new structural scaffolds.

To date, only a handful of water-soluble bundles of

amphipathic peptoid helices have been designed,23, 39 and these have been not been amenable to structural characterization by x-ray crystallography or solution-phase NMR.

Statistical

mechanical models fitted to peptoid helix bundle folding data predict that their tertiary assembly is anti-cooperative,77 suggesting room for improved designs.

One problem has been the

necessary trade-off between residues known to promote helix formation, which are largely hydrophobic, and residues needed to achieve solubility, which have mostly been achiral. Interestingly, both the successful helix bundle designs of Lee et al.,23, 39 as well as recently published water-soluble peptoid sequence that self-associates,78 incorporate deliberate patterns of acidic and basic residues. Similar charge-patterning is used in the design of peptoid nanosheets.1,


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Such charge-charge interactions likely help to introduce enthalpically favorable interactions

which promote helix formation, although the specificity of these interactions could likely be improved.

Preliminary simulations of peptoid designs from Fuller et al. suggest that indeed

non-specific salt-bridge formation can be quite prevalent (data not shown). The incorporation of diverse non-canonical backbones in Rosetta,79-81 including peptoids,82 now opens up the possibility of engineering highly specific enthalpic interactions, which can be further virtually-screened for favorable folding properties using molecular simulation models of the kind we present here.

We believe that this, and the experimental identification of bulky

chiral peptoid sidechains that also promote solubility, could be used to design improved peptidomimetics that can disrupt protein interfaces, as well as form improved tertiary assembles amenable to structural characterization, and further optimization as non-natural bio-inspired scaffolds for molecular design.

Conclusion By introducing a term that biases backbone conformations toward negative φ-angles, we have parameterized an improved potential for the simulation of Nspe peptoid helices, called GAFF- φ, that accurately models peptoid helix folding when used with GBSA implicit solvent. To validate this model, we have applied a new Bayesian inference approach, BICePs, to reconcile molecular simulation data with sparse NOE distance restraints for a peptoid pentamer.

Our results

quantitatively estimate conformational populations, and give Bayes factors that unambiguously show GAFF-φ to be more accurate than GAFF.

Extensive REMD simulations of Nspe

polypeptoids using GAFF-φ for chain lengths ranging from n=3 to n=15 were performed and


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analysed using Lifson-Roig helix coil theory.

The results show that, unlike peptides, peptoid

helix formation is entropically favorable, implicating steric interactions as a key driving force for folding. These findings should enable continued efforts towards the computational design of peptoid folding and assembly.

ASSOCIATED CONTENT Supporting Information. Tables S1-S4 and Figures S1-S4. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Email: [email protected] Present Addresses †Current address: School of Medicine, Temple University Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT This work was supported by National Science Foundation through NSF MCB-1412508 and major research instrumentation grant CNS-09-58854.


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Tables

Table 1. Published experimental Kcis/trans values for various Nspe polypeptoid systems.

sequence

Kcis/trans solvent

Ac-(Nspe)5-CONH2

1.5

reference

acetonitrile Gorske et al. 200936

Ac-(Nspe)5-COOtBu 3.3

acetonitrile Stringer et al. 201137

(Nspe)15

acetonitrile Wu et al. 200331

3.2


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Table 2. Bayes factors P(M1)/P(M2) comparing two different models M1 and M2 of conformational populations, assuming an experimental cis/trans amide equilibrium constant of Kct = 2.5. Model 1

Model 2

GAFF-φ + exp exp only GAFF + exp

Bayes Factor 2.68

exp only

GAFF-φ + exp GAFF+ exp

1.75 1.53

Table 3. A comparsion of thermodynamic helix-coil parameters extrapolated from experimental and simulation data. ∆Hv

∆Hw

(kcal/mol) experiment simulation (LR)

∆Sv

∆Sw

reference

(cal/mol/K)

peptide a

-1.2

-3.7

Rohl and Baldwin 199772

peptoid b

-1.1

n/a

Kirshenbaum et al. 199825 Best and Hummer 200968

peptide c

+0.7

-0.6

-0.9

-1.8

peptoid d

+0.7

-0.5

+1.5

+2

a

Ac-AAKAAGY-NH2, with ∆Hw and ∆Sw estimated from LR fits to temperature-dependent CD and NH exchange studies. b

(NsceNsceNspe)10, Nsce = (S)-N-(1-carboxyethyl)glycine. ∆Hw estimated from DSC in aciddenaturing conditions. c

Ac-(AAQAA)3-NH2, with values from LR fits to simulations using AMBER ff03* + TIP3P water. d

Ac-(Nspe)8-NH2, this work.


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Figures

O χ N ω

C C ψ φ α

NH 2 5

10.0 8.0 6.0 4.0 3.0 2.0 1.0 0.5 0.0 kcal/mol

O

Figure 1.

(top) Structure of Ac-(Nspe)5-NH2, a peptoid pentamer of (S)-N-(1-

phenylethyl)glycine studied by Armand et al.24 Shown are backbone dihedral angles ω (Cα’-C’N-Cα-C), φ (C’-N-Cα-C), ψ (N-Cα-C–N’), and sidechain χ angle. (bottom) Ab initio backbone dihedral energies of Ac-Nspe-N(CH3)2 show a ~1 kcal/mol preference for negative (ca. -90˚) φ angles in both cis (ω=0˚) and trans (ω=180˚) amide states. Dihedral plots are shown in the range of 0-360˚ for ease of viewing (negative φ appearing as values greater than 180˚).


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Figure 2. Estimated free energy differences of negative vs. positive φ-angle populations, shown for REMD simulations of Nspe monomers and trimers performed using various force constants kφ used to parameterize the GAFF c-n-c3-c amide bond potential. The dotted line denotes the value shown for GAFF-φ.


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Figure 3. Ac-(Nspe)5-NH2 forms right-handed cis-amide peptoid helices in GAFF-φ. Shown is an (left) axial view and (right) longitudinal view of a representative frame selected from the lowest-temperature replica (300 K).


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cis amide

trans amide

cis amide

trans amide

Page 30 of 53

kcal/mol

Figure 4. Distributions of φ and ψ backbone dihedral angles for GAFF-φ and GAFF simulations of (Nspe)6. Shown are averages over all residues, estimated from REMD simulation data using the MBAR algorithm.


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Figure 5. Estimated cis amide populations (top) and cis/trans equilibrium constants (bottom) as a function of chain length, using the GAFF-φ and GAFF potentials. Shaded region denotes the uncertainty of these quantities estimated using MBAR.


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GAFF-φ

46% 14%

24% 14% 11%

GAFF

Figure 6.

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Results of BICePs calculations for (Nspe)5. Scatter plots show a comparison of

BICePs-computed probabilities for each of the 1000 conformations used in the sampling. On the x-axis are probabilities computed when only NMR experimental distance constraints are used to refine the ensemble, and the y-axis shows the resulting populations with the combined use of information from simulation and experiment. Points above the diagonal line indicate that simulations predict a higher conformational population than experimental restraints alone. Results using the GAFF-φ potential are shown at top, and results using GAFF are shown below. Circled on the scatterplot and shown on the right are (rmsd-aligned) structures predicted to comprise 50% or more of the conformational ensemble. Red points on the scatter plot show the ten largest conformational populations.


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Figure 7.

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Estimated average helix populations as a function of temperature, pcis(T), for chain

lengths n=3 to n=15, for the GAFF-φ and GAFF potentials. Shaded region denotes the uncertainty of these quantities estimated using MBAR.


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Figure 8. An example of Lifson-Roig (LR) helix-coil parameters fit to peptoid molecular simulation data, shown here for (Nspe)10. (a) The average fraction of (non-terminal) helical


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residues, ⟨fh⟩, shown as a function of temperature. Values computed from single-temperature LR fits (green) and thermodynamic LR fits using all temperature replicas (red, dashed) agree well with values computed directly from the REMD simulations. (b) Values of the nucleation parameter v derived from single-temperature and thermodynamic LR fits to GAFF-φ and GAFF REMD simulations of (Nspe)10. (c) Values of the elongation parameter w derived from singletemperature and thermodynamic LR fits to GAFF-φ and GAFF REMD simulations of (Nspe)10.


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Figure 9.

Thermodynamic parameters (a) ∆Hv (b) ∆Hw (c) ∆Sv (d) ∆Sw, as a function of chain

length, extracted from Lifson-Roig helix-coil theory fits to the molecular simulation data. Shaded region denotes the uncertainty of these quantities estimated using posterior sampling. REFERENCES

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χ N ω

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NH 2 5

O


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cis amide The Journal of Physical Chemistry trans amide

cis amide

trans amide

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Kcis/trans

pcis

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Page 48 of 53 0.9The Journal of Physical Chemistry 0.8 0.7 0.6 GAFF-φ 0.5 0.4 GAFF 0.3 3 5 7 9 11 13 15 6 GAFF-φ 5 GAFF 4 3 2 1 ACS 3 Paragon 5 7Plus Environment 9 11 13 15 chain length

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4 3 2 1 0 1 2 3

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∆Hw (kcal/mol)

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∆Sw (cal/mol/K)

∆Sv (cal/mol/K)

∆Hv (kcal/mol)

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TOC Figure 50x21mm (300 x 300 DPI)


Insights into Peptoid Helix Folding Cooperativity from an Improved

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