Volumetric Physics of Polypeptide CoilâHelix Transitions

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Volumetric Physics of Polypeptide Coil-Helix Transitions Heinrich Krobath, Tao Chen, and Hue Sun Chan Biochemistry, Just Accepted Manuscript • DOI: 10.1021/acs.biochem.6b00802 • Publication Date (Web): 24 Oct 2016 Downloaded from http://pubs.acs.org on October 31, 2016

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Volumetric Physics of Polypeptide Coil-Helix Transitions

Heinrich Krobath, Tao Chen and Hue Sun Chan*

Departments of Biochemistry and Molecular Genetics, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8 Canada

* Correspondence: Hue Sun Chan, E-Mail: [email protected], Phone: ++1-(416)-978-2697

Funding Statement: This work was funded by the Canadian Institutes of Health Research grant MOP-84281 to HSC.

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List of Abbreviations

FTIR

Fourier transform infrared spectroscopy

MSV

Molecular surface volume

PMV

Partial molar volume

SV

Solvent-excluded volume

SASA

Solvent-accessible surface area

TTET

Triplet-triplet energy transfer

vdW-V

Van der Waals volume


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Abstract

Volumetric properties of proteins bear directly on their biological functions in hyperbaric environments and are useful in general as a biophysical probe. To gain insight into conformation-dependent protein volume, we developed an implicit-solvent atomic chain model that transparently embodies two physical origins of volume. First, a fundamental geometric term capturing the van der Waals volume of the protein and the particulate, finite-size nature of the water molecules, modeled together by the volume encased by the protein's molecular surface. Second, a physico-chemical term for other solvation effects, accounted for by empirical proportionality relationships between experimental partial molar volumes and solvent accessible surface areas of model compounds. We tested this construct by Langevin dynamics simulations of a 16-residue polyalanine. The simulated trajectories indicate an average volume decrease of 1.73 ± 0.1 Å3/residue for coil-helix transition, ~80% of which is caused by a decrease in geometric void/cavity volume, and a robust positive activation volume for helical hydrogen bond formation originating from the transient void created by an approaching donor-acceptor pair and nearby atoms. These findings are consistent with prior experiments on alanine-rich peptides and offer an atomistic analysis of the observed overall volume changes. The results suggest, in general, that hydrostatic pressure likely stabilizes helical conformations of short peptides but slow down the process of helix formation. In contrast, hydrostatic pressure is more likely to destabilize natural globular proteins because of the void volume entrapped in their folded structures. The conceptual framework of our model thus affords a coherent physical rationalization for experiments.


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Introduction

Volumetric properties of proteins—i.e., how they respond to hydrostatic pressure in Nature and in the laboratory à la Le Châtelier's principle—are an important window into the physics of these biomolecules and how they function physiologically or malfunction in diseases1–9. Pressure has long been known to affect the stability of globular proteins, leading to denaturation/unfolding of certain ordered structures10,11. Pressure effects on proteins and peptides have a direct impact on biological adaptation in the deep ocean12 and this environment’s possible role in the origin of life13. While pressure at the deepest reaches of the Earth’s oceans, ≈1,100 atm at the Mariana Trench, is low compared to the 3,000 atm or more that are routinely used to probe proteins in the laboratory, the pressure sustained by subseafloor sedimentary microbes14 could be higher. Closer to home, in our bodies, neuronal excitability is very sensitive to pressures of even a few atm15. Although the biomolecular basis of this medical observation remains to be elucidated, it illustrates the broad relevance of volumetric effects to biomedical sciences8. Pressure—by itself or in conjunction with temperature16 and denaturant17,18 — is a useful but perhaps under-utilized probe in protein biophysics. In principle, pressure can facilitate either protein unfolding or folding, depending on which conformational state has a smaller partial molar volume1–9,19–21. High pressure has also been applied to study folding intermediates22,23 and to dissociate multimeric proteins and protein aggregates to study protein-protein interactions. These include native multiprotein complexes as well as those implicated in amyloidosis and neurodegenerative diseases8,9.

Pressure

conformational dynamics

can 24

induce

other

structural

transitions24–26,

affect

9

and enzymatic activity , and thus can be used to

investigate a wide variety of protein properties and their implications, including structural aspects16 of protein evolution27.

Overall volume changes accompanying unfolding of globular proteins are mostly negative. Although partial molar volume can increase upon unfolding of some proteins at low pressure, it always decreases at high pressure2,28. This trend likely originates from the void volume trapped inside folded structures19,21,29–31. In contrast, 4 ACS Paragon Plus Environment

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spectroscopic experiments indicate that the ordered helical conformations of nonglobular long polylysine (~ 2,000 residues) and short alanine-based peptides of 16 – 21 residues32–34 are stabilized, not destabilized, by pressure20,35–38; i.e., these helices occupy less volume than random-coil-like disordered conformations. This observation need not contradict the void-volume idea because isolated aqueous helices presumably do not form a sequestered core that can harbor appreciable empty space21. In support of this perspective is Kiefhaber and co-workers’ recent experiment on helical hydrogen bond formation20, long been seen as an elementary step in coil-helix transition39–42. They showed that adding a helical segment to an existing helical structure in an alanine-rich peptide entails a negative reaction volume and a positive activation volume that they recognized can involve a steric component20, which is to say that while pressure slows down helix formation kinetically, it favors the helical state thermodynamically. Besides geometric voids, other physico-chemical effects of aqueous solvation3,5,43–46 also factor in the volumetric properties of proteins. Seeking a better delineation of their respective roles and to provide an atomistic description/interpretation which is currently not accessible by experiment, we developed an implicit-water atomic chain model embedded with these two volume contributions to account for the conformation-dependent partial molar volume of polypeptides. Briefly, our formulation uses molecular surface volume47–50 for excluded volume plus water-inaccessible voids; it also uses an empirical volume contribution that is proportional to solvent accessible surface area47,51 and based on model-compound experiments44 to account for the remaining, more “chemical” aspects of solvation volumes. This model is complementary to explicit-water molecular dynamics, which can tackle pressure dependence directly by using NPT simulations52–56 or by combining NVT simulation in different fixed volumes57–60. Several explicit-water simulations posited that the helical state of alanine-rich peptides is destabilized by pressure54,55,57, which is not in accord with experiment20. In contrast, a recent molecular dynamics study reproduced the experimental pressure dependence by using a different water model56. These results indicate that volumetric properties predicted by explicit-water simulations can be highly sensitive to water-model parameterization56. Such sensitivity has indeed been suggested by several investigations of simplified models61–64. In this context, our approach – as a synthesis of intuitive geometric considerations47–51 and empirical 5 ACS Paragon Plus Environment

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volumetric data on model compounds3,5,43–45 – is hereby offered as a tool for conceptual advance. Hydrostatic pressure affects every conformation, not only those belonging to wellpopulated ensembles such as the folded and unfolded states. Activation volumes of sparsely populated transition states dictate how kinetics is affected by pressure. Because our model computes a volume for every conformation, it can address the nature of activation volumes. For globular proteins, experimental activation volume is almost always positive for folding but is often negative for unfolding, though the latter can be positive for some proteins65,66. Experimental activation volumes depend on denaturant concentration, as has been shown for tendamistat67, suggesting a contribution to activation volumes from non-geometric chemical effects. At the same time, explicit-water simulations of small nonpolar solutes21,68 and secondary structure elements52,53 suggested that a part of the volume barrier to folding likely originates geometrically from the transient voids21 caused by imperfect packing and steric dewetting52 in the folding transition state. Transient voids are associated with the desolvation free energy barrier52,53,68 as well as the transition-state heat capacity52,69 and enthalpy52,70. This connection allows pressure-dependent parametrizations of implicit-water potentials with desolvation barriers70–72 to be used to model pressure effects in folding73,74. Our implicit-water approach, which goes beyond this technique by treating volume independently, was inspired by recent direct computation of volume in explicit-water simulations21,52,53,75–77 indicating that molecular surface volume provides a good description of the volume barrier to the association of two methanes21. The present application of our model to (Ala)16 (16-residue polyalanine) produces quantitatively reasonable agreement with experimental negative reaction volume and reproduces the experimental finding of a volume barrier for hydrogen bond formation in short Ala-based peptides20. The approach allows dissecting the observed volume barrier into contributions from various geometric and chemical effects. Within the same modeling framework, volume increase upon folding is deduced to be likely for naturally occurring globular proteins, as would be expected from the void-volume perspective19. These findings and their ramifications are detailed below.


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Model and Methods

Forcefield and Langevin dynamics. Langevin dynamics simulations78 of the 16-residue polyalanine peptide were conducted using a new model modified from that of Knott and Chan79 by replacing its Lennard-Jones sidechain-sidechain hydrophobic potential by one with a desolvation barrier—a physics-based feature21,68,69 demonstrably important for capturing real protein behaviors70–74,80–82. Other terms of the interaction potential follow those of the original simple atomic forcefield introduced by Irbäck and co-workers for Monte Carlo sampling83. Both the original83 and the present modified forcefield can fold selected peptide sequences, based on a three-letter alphabet {G, H, P} of glycine (G), hydrophobic (H), and polar (P) residues, into α-helices and helix-bundles. The polyalanine peptide here is modeled as (H)16, i.e., a homopolymer of 16 hydrophobic residues. Details of the interaction potential and the simulation methodology are provided in Supporting Information (SI) Methods Text with additional references84–89. Although the present study used only three-letter sequences, it is worth noting that the Irbäck et al. forcefield83 has been extended to cover all twenty types of amino acid residues. Notable recent applications of these simple atomic forcefields include studies of mutational effects and conformational switches in protein evolution90–92. Because the primary focus of the present effort is volume, not energetics, the main service provided by the model forcefield to our investigation is as a tool for sampling conformations with different volumes. With this in mind, the conclusions in this work regarding volumetric properties of different polypeptide/protein conformations are expected to be robust against physically reasonable variations of the energy parameters as long as the van der Waals radii in our model are realistic (SI Methods Text). The geometric component of conformational volume. We considered three volumes that are uniquely defined by the geometry of a given protein conformation and the size of a water probe. (i) van der Waals volume (vdWV) does not involve a water probe. It is the volume of the union of overlapping atomic 7 ACS Paragon Plus Environment

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spheres, defined by the center positions {ri} and the vdW radii {ai} of all the atoms in a given conformation, as illustrated by the space-filling diagram in Fig.1A,G93–96. (ii) Molecular surface volume (MSV), as defined by Connolly48, was computed by first analytically constructing49 the molecular surface of the given conformation using a spherical water probe with radius rp = 1.4 Å. MSV is the volume enveloped by this surface and thus is inaccessible to any part of the water probe (Fig.1A). MSV is larger than vdW-V because MSV also accounts for cavity (void) volumes and surface effects arising from the finite size of the probe, including the geometric effect of a volume barrier to solvation/desolvation21. (iii) Solvent-excluded volume (SV) is the volume inaccessible to the center of the water probe due to the presence of the given conformation47,97, defined as the volume of the union of spheres centered at all atomic positions {ri} of the conformation with radii {ai+rp}. (Thus vdW-V is mathematically equivalent to SV with a hypothetical rp = 0.) The surface enveloping SV is the solvent-accessible surface area (SASA, Fig.1A)51. The difference SV ‒ MSV is the envelope volume Venv50. In addition to these volume measures, the Voronoi-Delaunay formalism98 has provided important volumetric insights as well by tracking non-overlapping Voronoi cells of individual atoms in a protein99–101. Depending on the positions of solvent molecules, Voronoi volumes tend to be larger at solvent-exposed than at buried positions102,103, a packing effect that is also captured in part by vdW-V/MSV considerations96,104,105. Because the Voronoi approach accounts for solvent molecules explicitly, it can be used to identify hydration shells. For the same reason, however, it is less useful than MSV for our implicit-water model. Voronoi volumes were not used in the present analysis.

The chemical component and an overall implicit-solvent model of conformational volume. To apply our implicit-water model of conformational volume to experimental helix-coil systems, we first calibrated it against experimental partial molar volumes (PMVs) of model compounds3,5,43–46. The rationale is to partition experimental PMV, in a physically well-motivated manner, into a geometric MSV and a chemical component corresponding to PMV ‒ MSV. PMV and MSV are expected to be different. The 8 ACS Paragon Plus Environment

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reason being that, in addition to the geometric effects captured by MSV, PMV embodies additional structural effects such as void volumes in the solvent caused by thermal fluctuations as well as other physico-chemical effects of solvent-protein interactions such as water ordering near the protein3,106–108. We determined the chemical components of peptide backbone (BB) and alaninesidechain (SC) PMVs by first simulating (Gly)n and (Ala)n oligopeptides using our protein chain representation, yielding MSV(Gly) = MSVBB = 53.32 ± 0.04 Å3 and MSVSC = 31.47 ± 0.1 Å3 (SFig.1). These computed MSVs were then compared with the PMVs obtained using vibrational densimetry by Makhatadze et al.44, viz., PMV(Gly) = 37.6 cm³/mol (62.7 Å3/molecule) and PMV(Ala-SC) = 27.2 cm³/mol (45.3 Å3/molecule) at T = 25°C, as reported in Tables II and V of ref.44. Thus the PMV – MSV volume difference for a backbone unit is PMVBB – MSVBB ≡ δVBB = 9.4 Å3, and that for the alanine sidechain is PMVSC – MSVSC ≡ δVSC = 13.9 Å3. For simplicity, the experimental PMV of the glycine peptide unit (H2CαC’ONH) was used to determine δVBB although Cα hydrogens are not represented in our chain model79,83. The resulting overestimation of δVBB, however, is expected to be small. Based on this analysis, the conformation-dependent PMV of our protein model is defined as

PMV = MSV + δV (1) SASA SASA δV = δV + δV (2) (Θ (Θ < SASA = 0) > < SASA = 0) >

where PMV, MSV, δV, SASAiBB, and SASAiSC are computed for the same protein conformation, and the summation is over the residues (labeled by i) along the protein sequence. SASAiBB and SASAiSC are SASA of the BB and SC, respectively, of residue i. MSV is seen here as the volume intrinsic to a protein conformation plus other associated volume geometrically inaccessible to water, whereas δV is the volumetric effect of protein-solvent contact-like interactions other than simple excluded volume. As such, the δV from a chemical group is intuitively expected to be roughly proportional to the number of water molecules in contact with (i.e., its hydration number108), and thus the SASA of, the group109. Since δVBB and δVSC are 9 ACS Paragon Plus Environment

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δV contributions from a BB and a SC group, respectively, when they are maximally exposed while positioned in the middle of a peptide sequence44, the conformationdependent δV contributions from BB and SC in Eq.(2) are weighted, respectively, by SASAiBB/ and SASAiSC/, where and are the averaged residue-specific SASA of the groups in disordered chains with no helical content. A precise definition of Θ will be given in the Results section below. To assess the merit of the above formulation, as a control we have compared results computed using the PMV defined by Eqs (1) and (2) against those computed using an ad-hoc definition of PMV without the MSV baseline, viz.,

PMV

SASA SASA = PMV + PMV (3) ( < SASA Θ = 0) > < SASA (Θ = 0) >

where PMVBB = 62.7 Å3, PMVSC = 45.3 Å3 as reported by Makhatadze et al.44, and the SASA-dependent weighting factors here are the same as those in Eq. (2). Reaction volumes and volume maxima during hydrogen bond formation and rupture We investigated the volumetric kinetics of hydrogen bond formation and rupture in our model by first identifying all such events in the equilibrated parts of all of our simulated trajectories, in the following manner. Let the beginning time of the equilibrated part of a trajectory be denoted t00. We examined time segments of the trajectory defined by time intervals [t00, t00 + L], [t00 + ∆t, t00 + L + ∆t], [t00 + 2∆t, t00 + L + 2∆t], d, where L is a chosen segment length, ∆t = 250τS is the time interval between two successive volume computations in most of our simulations and τS is the Langevin dynamics time step, until we encountered a time segment with s and s + 1 hydrogen bonds, respectively, at the start and end points of the time segment and s = 4, 5, 6, 7, or 8. We saved such a time segment, which contains a hydrogen bond formation event, for further analysis. We then carried on scanning the trajectory as before, but with a new starting time point equal to the end point of the saved time segment. The process was repeated until all trajectories were scanned. We applied this procedure for L = 1,000τS 1,250τS and 1,500τS, and repeated the entire 10 ACS Paragon Plus Environment

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procedure to study hydrogen bond rupture by identifying and saving time segments with s and s ‒ 1 hydrogen bonds, respectively, at the start and end points of the time segment. For each of the saved time segments, we recorded the starting (S), final (F) and maximum (M) volumes. Volume barriers are defined as the M-volume minus the S-volume. Sharpness of the volume maximum (at t*) may be characterized by ∆V+ ≡ V(t*) ‒ V(t* + ∆t) and ∆V‒ ≡ V(t*) ‒ V(t* ‒ ∆t), as t* was never at the end points of the time segments. We report these quantities using the notation ξ1 = min(∆V+, ∆V‒) and ξ2 = max(∆V+, ∆V‒). Statistics resulting from this analysis is provided in STables 1-6.

Results As outlined above and detailed in SI Methods Text, we adopted a computationally efficient Langevin dynamics model of polypeptides79 in which all backbone atoms except the Cα hydrogens are represented explicitly83 to allow for structural analyses of backbone hydrogen bonds. On this basis, desolvation barriers were added to the sidechain hydrophobic interactions for more physical, real protein-like behaviors68–72. More significantly, a new direct geometric/chemical model of conformation-dependent partial molar volume was incorporated. We now apply this construct primarily to (Ala)16, a model system chosen to provide theoretical insights into recent experimental volumetric data on similar short peptides such as the 16-residue AK1637, 20-residue AK2038, and 21-residue Xan/Nal-containing20 Ala-based peptides. The coil-helix transition of a short model peptide. Starting from random coil-like conformations, our model can reliably access the fully helical state at the simulation temperature T = 0.29T0 (in model units) that corresponds roughly to room temperature (SI Methods Text). Throughout this work, the coil-helix transition is monitored by the progress variable Θ, also termed the reaction coordinate, which is the fractional number of helical hydrogen bonds in a given conformation normalized by the maximum number in the fully helical state. For terminological simplicity, we often refer to the process of achieving Θ = 1 kinetically as “folding”. Equilibrium sampling of our model under different temperatures ranging from strongly helixfavoring (low T) to strongly helix-disfavoring (high T) indicates no free energy barrier along Θ between the coil-like low-Θ state and the fully helical Θ = 1 state. At T = 0.29T0, the (Ala)16 peptide contains an average of 79% ± 20% helical content in 11 ACS Paragon Plus Environment

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equilibrium (SFig.1). This behavior is consistent with the Zimm-Bragg39 and related biophysical pictures40–42 that coil-helix transition is noncooperative, with fraying from ends for example, rather than “all-or-none”. It follows that folding of our model (Ala)16 peptide does not involve a major free energy barrier111 along Θ under strongly folding conditions, such as the T = 0.29T0 condition for our kinetic simulations. Thus, the process is “downhill” as understood in the protein folding literature111, though smaller free energy barriers such as those arising from desolvation and hydrogen bond formation always exist. Folding kinetics of (Ala)16 is approximately single-exponential nonetheless (SFig.2), consistent with the fact that essentially single-exponential relaxation and apparent barrierless folding are not mutually exclusive111. However, because folding kinetics is downhill, the relationship between kinetic and thermodynamic profiles of (Ala)16 is different from that for cooperative protein folding. Unlike the preequilibrium with substantially overlapping profiles in the unfolded basin for cooperative folding112, the kinetic profile for the conformational population sampled during (Ala)16 folding is entirely distinct from the thermodynamic profile at the same T = 0.29T0. Instead, it overlaps significantly with the thermodynamic profile for a much higher T = 0.4T0 (SFig.1). When T is sufficiently low, (Ala)16 is driven to the lowest-energy fully helical state (SFig.3A). Since the Ala sidechains are not in close contact in a helix, there are more hydrophobic contacts in the coil-like disordered state around Θ = 0.25 (SFig.3B) than in the more helical conformations. The decrease in total energy E with increasing Θ is thus a partial trade-off between a decreasing hydrogen bonding energy EHB that is not fully compensated by an increasing hydrophobic energy EHP (SFig.3A). Significant non-helical hydrogen bonding is present in the coil state (SFig.3C). These hydrogen bonds hinder helix folding because they have to be first broken before the full helix can be formed (SFig.3D). A polypeptide volumetric dynamics based on an interplay of Connolly volumes and experimental small-molecule partial molar volumes. Our volumetric model is based on the molecular surface volume (MSV) enveloped by the Connolly molecular surface and the solvent-accessible surface (Fig.1A). As rationalized in Model and Methods and SI Text, we express the partial molar volume of a given polypeptide conformation as PMV = MSV + δV, where MSV and δV are identified, respectively, as the geometric and chemical components of PMV; δV is taken to be a sum of 12 ACS Paragon Plus Environment

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backbone (BB) and sidechain (SC) contributions, each proportional to its respective solvent-accessible surface area (SASA). Parameters for computing δV were deduced from published experimental data44 by subtracting MSV baselines (SFig.4). As the coil-helix transition progresses (Fig.1A-F), the SCs are placed increasingly on the outside, shielding most of the BB from the solvent (Fig.1G). Specifically, as Θ of (Ala)16 increases from 0 to 1, average SASA increases by ≈39% for SC but decreases ≈50% for BB, netting a total average SASA increase of ≈7% (Fig.2). This trend implies that as the helix folds, δV has an increasing contribution from SC relative to BB. In view of the decreasing overall BB SASA with helix formation, a closer examination of the individual SASAs of the carbonyl (C’=O) and amino (N-H) groups is instructive. Helix formation is effectuated by desolvation of hydrogen bond donor (N-H) and acceptor (C’=O) groups. In the coil state, acceptors are more solvent-exposed than donors by a factor of ≈10 in terms of absolute SASA because carbonyl C’ and O are larger than amino N and H, and the C’=O bond is longer than the N-H bond79. For most of the residues except at the chain ends, the coil-helix transition drastically reduces solvent-exposure for both donor and acceptor by up to 90%, whereas the exposure of Cα remains largely unchanged (SFig.5). The present theoretical construct allows for simultaneous tracking of energies and volumes of a folding trajectory (Fig.3). Consistent with a substantial presence of nonhelical hydrogen bonds in the coil state (SFig.3C,D), the example trajectory shows that successful formation of a complete helix often requires rupturing of existing hydrogen bonds and breaking of favorable hydrophobic sidechain contacts, as is indicated in Fig.3A,B by the high EHB and EHP peaks around t/107τS = 7.6 before the complete helix formation at t/107τS ≈ 8.3. Apparently, at least for this trajectory, the kinetic bottleneck in the coil-helix transition is to first access a conformation without non-helical hydrogen bonds to allow for helix propagation; but such conformations are relatively rare in the initial conformations with no or low helical content. For instance, they make up only ≈10% of the conformations at Θ = 0.25 (SFig.3D). Along the volume trajectories in Fig.3C, vdW-V exhibits least fluctuation. This is expected because conformation-dependent variations in atomic overlap, which are quite minimal, are the only source of vdW-V variations. In contrast, MSV accounts also for void-volume and finite-size effects of water. These effects are more sensitive 13 ACS Paragon Plus Environment

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to conformational change. As a result, MSV is approximately 10% larger than vdW-V and has larger fluctuation. With the incorporation of other aspects of solvation beyond simple excluded volume, PMV of (Ala)16 is approximately 28% larger than MSV – meaning that the chemical component δV adds ≈28% volume to PMV on top of the geometric MSV. Because δV entails an extra element of variability by virtue of the proportionalities of its contributions to conformation-dependent SASAs (Fig.3D), PMV exhibits most fluctuation among the three volumes we tracked in Fig.3C. A comparison of Fig.3B and D indicates further that transient hydrophobic contact formation and disruption is a major source of δV variability and hence PMV fluctuation. The geometric-chemical formulation predicts a volume decrease upon formation of an isolated α-helix in water. The trajectory depicted in Fig.3C indicates that MSV is likely lower in the fully helical state than in the coil state, but the PMV trend is less clear because of significant fluctuation. To ascertain the general trend, we computed volumetric properties, averaged over all 122 kinetic trajectories we simulated, to determine their dependence on helicity Θ (Fig.4). Average reaction volumes can be estimated from this dataset since it provides average volumes V(Θ) for individual conformational ensembles with a given Θ. Because the dominant coillike population is centered around Θ = 0.25 (SFig.3B), coil-helix reaction volumes per residue provided below are defined by the quantity V(Θ = 1) – V(Θ = 0.25) divided by the total number of residues (n = 16) unless specified otherwise. Alternatively defined reaction volumes such as [V(Θ = 1) – V(Θ = 0)]/n can also be obtained from the data plotted in Fig.4. For Θ > 0.25, average vdW-V decreases monotonically with increasing Θ. Average vdW-V for fully helical conformations is ≈ 0.4% smaller than coil conformations (Fig.4A). This corresponds to a helix-formation vdW-V reaction volume of ∆vdW-V0 = ‒0.32 ± 0.01 Å3/residue (‒0.19 ± 0.01 cm³/mol/residue) or ‒0.57 ± 0.02 Å3 (‒0.34 ± 0.01 cm³/mol) per helical hydrogen bond, suggesting strongly that a local increase in atomic overlap is associated with the formation of a helical hydrogen bond. Over the same Θ range, MSV also decreases monotonically (Fig.4B), registering a decrease of 3.2% for the entire coil-helix transition, or a MSV reaction volume of ∆MSV0 = ‒ 2.68 ± 0.03 Å3/residue (‒1.61 ± 0.02 cm³/mol/residue) or ‒4.76 ± 0.05 Å3 (‒2.86 ± 0.04 cm³/mol) per hydrogen bond. Indeed, both the mean and standard deviation of 14 ACS Paragon Plus Environment

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MSV distribution decrease with increasing Θ, but there are large overlaps in the distributions for different Θ values (SFig.6), as is expected from the large fluctuations seen in the example folding trajectory (Fig.3C). Because the decrease in MSV is much larger than that in vdW-V, void volume reduction is the dominant contribution to the negative ∆MSV0; only 12% of ∆MSV0 is due to vdW-V reduction. In contrast, the average solvent-excluded volume SV of helical conformation is 1.5% larger than that for coil structures (Fig.4C) because of the increasing envelope volume Venv with increasing Θ (Fig.4D), resulting in a positive reaction volume of ∆SV0 = +2.62 ± 0.3 Å3/residue (+1.57 ± 0.2 cm³/mol/residue). In light of the opposite Θ-dependent trends of MSV and SV, it is worth emphasizing that MSV is a more appropriate baseline for a PMV model than SV because MSV represents a pure, bare-bone geometric effect of excluded volume (Model and Methods). In contrast, the additional Venv part of SV accounts for a volume with significant non-steric solute-solvent interactions; the volumetric effects of which, however, are more desirable to be captured by a separate δV term alone. In other words, we view the PMV = MSV + δV partition of volumes as physically more sensible than some other partitions such as PMV = SV + δVʼ because MSV can be equal to PMV (i.e., δV = 0) for the pure state of a hypothetical solute that allows for 100% packing density at T = 0 (such as a cube); but SV does not share this property. For our model (Ala)16, PMV adds 27–29% to MSV. The δV addition is larger for more helical conformations because of their higher hydrophobic exposure (see above). This Θ-dependent effect reduces the magnitude of the negative reaction volume relative to that of MSV, but only slightly. The average model PMV decreases monotonically with increasing Θ (Fig.4E). This trend is consistent with experiment (see below). Relative to the two dominant coil populations at Θ = 0.167 and 0.25 (SFig.3B), the reaction volumes for helix formation are, respectively, ∆PMV0 = [PMV(Θ = 1) ‒ PMV(Θ = 0.167)]/16 = ‒1.81 ± 0.07 Å3/residue (‒1.09 ± 0.04 cm³/mol/residue) and ∆PMV0 = [PMV(Θ =1) ‒ PMV(Θ = 0.25)]/16 = ‒1.64 ± 0.07 Å3/residue (‒0.98 ± 0.04 cm³/mol/residue). These two values average to a ∆PMV0 = ‒1.73 ± 0.1 Å3/residue (‒1.04 ± 0.06 cm³/mol/residue). Although a volume barrier to the formation of a helical segment was observed experimentally20, the average PMV profile in Fig.4E does not exhibit a barrier along Θ. We will address this apparent mismatch below by examining single-molecule events. The average MSV profile in 15 ACS Paragon Plus Environment

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Fig.4B also lacks a barrier, as has also been observed in a recent explicit-water molecular dynamics study56. Because |∆vdW-V0| < |∆MSV0|, |∆PMV0|, the present coil-helix transition increases packing according to a geometric measure of atomic packing density50, ρ = vdWV/MSV, as well as an apparent packing density ρ* = vdW-V/PMV (Fig.4F), where ρ = 89.3%, 91.8% and ρ* = 70.0%, 71.1% for Θ = 0.25, 1.0, respectively. These measures, related but distinct from other definitions of packing density in mathematical investigations113,114 and studies of globular proteins47,115, are useful for characterizing packing densities of isolated small peptides with relatively large boundary/surface effects. In this context, it is noteworthy that the helix-coil volume differential is grossly overestimated by SV. As a fraction of MSV, experiment-based PMV is 2% larger (Fig.4G), but SV is about 10% larger (Fig.4H) for helices than for coils. The volume barrier to hydrogen bond formation largely originates from transient voids created by the approaching donor-acceptor pair and nearby atoms. To gain a deeper insight into volume barriers and reaction volumes in coilhelix transitions, we now shift attention from averaged volumes of conformational ensembles (Fig.4) to volumetric properties of single-molecule helical hydrogen bond formation and rupture events. As described in Model and Methods, we assembled a collection of these kinetic events from short time segments of the simulated (Ala)16 folding trajectories. General properties were gleaned from the statistics of a total of 148,782 formation and 439,214 rupture events (STables 1–6), in-depth analysis of one helical hydrogen bond formation event is used as illustration (Figs.5, 6). The helical hydrogen bond formation and rupture statistics indicates that PMV and MSV barriers are a very robust feature of these kinetic processes. A PMV and a MSV maximum (M) higher than both the start (S) and final (F) volumes were observed without exception in all formation and rupture events we examined, as illustrated by Fig.5B,C. An MSV peak is expected21 from geometrical consideration (SFig.7A). vdW-V also exhibits a peak in this case (Fig.5A) though it was not expected in general (SFig.7A); only the PMVad-hoc we introduced in Model and Methods as a control does not (Fig.5D). Echoing the general trend for helical hydrogen bond formation (STables 1—3), the reaction volumes in Fig.5 are all negative. (Note that the reaction volumes obtained from Fig.5 and STables 1 – 3 are defined as averages 16 ACS Paragon Plus Environment

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over individual hydrogen bond formation events instead of as differences of ensemble-averaged volumes as in the analysis above for Fig.4.) The PMV/MSV ratio at M is equal to 1.278, which is in line with the aforementioned observation that PMV typically adds 27–29% to MSV, implying that this PMV peak is not caused by an extraordinary high exposure of hydrophobic residues. In fact, the chemical contribution to the PMV peak is negligible in this case because the volume barrier ratio PMV*/MSV* = 1.01. In other words, 99% of the PMV peak in Fig.5 originated from the geometric component of PMV. Since vdW-V*/MSV* = 0.4, roughly 40% and 60% of this PMV peak were caused, respectively, by reduced vdW atomic overlaps and increased desolvated void/cavity volume. We now look into structural details of the S, M and F conformations (Fig.6). In this particular case, the donor (residue 8) and acceptor (residue 4) of the hydrogen bond being formed are in a highly helical environment, with hydrogen bonds between residue pairs 3-7, 5-9, 6-10, 10-14, and 11-15 already established. As the hydrogen bond between residues 4 and 8 materializes, the donor-acceptor distance rDA (Fig.6A) first reduces from 4.7 Å (S) to 4.1 Å (M), then to 1.9 Å (F) (see also SFig.7B). The accompanying helix-enhancing conformational change from S to M entails an increased backbone curvature between residues 4 and 8, contributing more void volume to the peak MSV in addition to the void volume created by the approaching donor-acceptor pair. The existence of an MSV and a PMV peak as observed in Fig.6B,C for the full peptide is a robust feature. When one focuses locally only on residues 3 through 9 of the (Ala)16 peptide and examines the 4-8 hydrogen bond formation process in higher time resolution (SFig.7B-F), MSV increases by 6.3 Å³ from 599.1 Å³ at S to 605.4 Å³ at M (SFig.7D). The corresponding ratio PMV/MSV = 1.265 at M is very similar to the 1.278 value reported above for the entire (Ala)16 peptide, indicating an essentially neutral effect from the chemical component of PMV at M. In contrast, vdW-V of residues 3 to 9 fluctuates widely from S to M (SFig.7C). Unlike MSV, there is no intrinsic vdW-V barrier to hydrogen bond formation (SFig.7A). Thus, vdW-V is not expected to contribute much, if at all, to the volume barrier to hydrogen bonding in general. The vdW-V peak for the full-length peptide in this particular case (Fig.5A) was caused by the rupture of a non-native hydrogen bond between residues 6 and 11 (SFig.8), a chance occurrence not intrinsic to the helical hydrogen bond formation process. The two primary origins of the PMV barrier to hydrogen bond formation are thus (i) the increase in void volume created by local 17 ACS Paragon Plus Environment

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backbone conformation changes between the donor and acceptor positions, and (ii) the void volume created between the approaching donor-acceptor pair itself (Fig.6C). The first effect is seen to be dominant because while the hydrogen bonding partners have to overcome a maximum volumetric desolvation barrier of 2.9 Å³ at d = 3.2 Å (SFig.7A), the PMV barrier for full-length (Ala)16, at more than 9 Å3 on average (STables 1-3), is almost always much higher. The event in Fig.6 is a good illustration, as the increased void volume from decreasing the H-O distance rDA from 4.7 Å at S to 4.1 Å at M here accounts for only 1.25 Å3 (SFig.7A) of the 6.3 Å³ MSV barrier for the residues 3 to 9 peptide fragment. The extensive hydrogen bond formation and rupture statistics in STables 4—6 for full-length (Ala)16 indicates that these processes always entail a sharp PMV barrier that is at least 7 Å³ higher than its preceding or succeeding volume measurement. The PMV barrier always coincides with a MSV barrier of at least 5.5 Å³. Because no donor-acceptor contact exists at the time point of the PMV/MSV barrier, the vdW-V values at M relative to those at S or F, which amounts to at least 2.7 Å³ by the same ξ1/ξ2 sharpness measure, may be used to quantify volumetric noise due to

conformational changes not essential to hydrogen bond formation or rupture. Notably, the observed sharpness of both the PMV and MSV barriers is higher than this level of noise. The picture remains the same if one focuses on the volumetric barrier heights (S to M) of hydrogen bond formation or rupture themselves (STables 1—3): ranges from 11.7 to 16.9 Å³, where ranges from 9.3 to 13.3 Å³, both are significantly larger than the 3.76 to 4.98 Å³ range for . The significant volumetric barrier of hydrogen bond formation and rupture is a major reason for the wide MSV distribution for any given Θ (SFig.6). In all cases, the barrier PMV/MSV ratios suggest no special role of the chemical component of PMV in the PMV barriers. As the chain descends the volume barrier (M) to form the hydrogen bond (F), the MSV of the residues 3–9 peptide fragment decreases from 605.4 Å³ at M to 587.3 Å³ at F (SFig.7D), netting a reaction volume of ‒11.8 Å³ relative to the MSV of 599.1 Å³ at S. About one half of this decrease is contributed by the vdW-V difference 542.7 Å³ ‒ 548.2 Å³ = 5.5 Å³ between F and S (SFig.7C). Negative MSV and vdW-V reaction volumes for helical hydrogen bond formation are expected because of the tight packing of the helical backbone with negligible void volume along the helical axis 18 ACS Paragon Plus Environment

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(Fig.6B,C) as well as the fact that the vdW overlap of the hydrogen bond donor and acceptor itself at rDA ≈ 2 Å contributes ≈ ‒0.78 Å3 (‒0.47 cm³/mol) to the negative reaction volume (SFig.7A). Statistics of hydrogen bond formation and rupture reaction volumes indicates that they depend on the number of helical hydrogen bonds already present (STables 1— 3). With different initial helicities, the F-S partial molar volume difference of individual hydrogen bond formation varies between ∆PMV0 = ‒0.8 Å3 for Θ = 0.33 to ‒2.9 Å3 for Θ = 0.67. In comparison, hydrogen bond rupture can entail a ∆PMV0 of both signs ranging from ‒0.49 Å3 to +0.27 Å3. These subtleties aside, it is clear that helical hydrogen bond formation is the main cause of the overall negative reaction volume of coil-helix transition, averaging to ∆PMV0 = ‒2.31 ± 0.1 Å3 (‒1.39 ± 0.08 cm³/mol) per hydrogen bond formed (Fig.4E). While both the average MSV and PMV reaction volumes for hydrogen bond formation are negative, is always more negative than by 5-25%, indicating that nonpolar exposure is increased by hydrogen bond formation. The average for (Ala)16 is also consistently negative but only amount to ≈20% of the total MSV reaction volume, implying that ≈ 80% of the negative MSV reaction volume for (Ala)16 coil-helix transition is caused by reduced void volume.

Discussion Our MSV/PMV predictions for (Ala)16 are consistent with experiment. The theory developed in this work affords quantitatively reasonable agreements with recent experiments on short alanine-rich peptides. Using Fourier transformed infrared spectroscopy (FTIR), Imamura and Kato38 reported a positive per-residue reaction volume of ∆V0 = +0.45 ± 0.02 Å3 (+0.27 ± 0.01 cm³/mol) or ∆V0 = +1.53 ± 0.05 Å3 (+0.92 ± 0.03 cm³/mol) for the helix to coil unfolding transition of the alanine-rich peptide AK20 at 25.4°C by assuming, respectively, a strictly two-state or a ZimmBragg noncooperative transition38. Since a strictly two-state helix-coil transition is physically unrealistic for polypeptides as noted (SFig.1), we interpret the data in ref.38 as a partial molar volume change of −1.53 ± 0.05 Å3/residue (−0.92 ± 0.03 cm³/mol/residue) for helix formation (hence the sign change). Considering the simplicity of our model, the present computed average ∆PMV0 = ‒1.73 ± 0.1 19 ACS Paragon Plus Environment

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Å3/residue (‒1.04 ± 0.06 cm³/mol/residue) is in good agreement with this experimental measurement. This agreement lends support to the present theoretical approach of extracting δVs from experimental model-compound PMVs using MSV baselines. In contrast, as a control, if MSV baselines were discarded and PMVs assumed to be entirely proportional to SASAs as in the quantity PMVad-hoc (Model and Methods), the predicted ∆PMVad-hoc = ‒10.8 ± 0.3 Å3/residue (SFig.10) would grossly overestimate the coil-helix reaction volume. Consistent with the finding of Imamura and Kato38, a more recent triplet–triplet energy transfer (TTET) study of a 21-residue Xan/Nal-containing Ala-based peptide by Neumaier et al. reported a negative reaction volume for helix formation as well. Their measured reaction volume at 5°C is ‒0.38 Å³ (‒0.23 cm3/mol) per helical segment20. As suggested by the authors, a possible reason for the smaller magnitude of their negative reaction volume vis-à-vis Imamura and Kato’s is that different temperatures were used in the TTET (5°C) and FTIR (25.4°C) experiments20. This consideration may apply to the larger computed magnitudes of negative reaction volumes of −0.8 Å³ (‒0.48 cm3/mol) per helical hydrogen bond from our trajectory analysis (STable 1). Our model result of a positive PMV barrier to helical hydrogen bond formation is consistent with Neumaier et al.’s reported positive activation volume of 3.7 Å³ (2.2 cm3/mol) for a single helical hydrogen bond formation20, although the PMV barriers of at least 11.7 Å³ (7.4 cm3/mol) deduced from our trajectory analysis (Fig.5C, STable 1) is higher. Aside from the difference between experimental and effective simulation temperatures, another possible contributing reason for the higher volume barriers in our simulation is that no term for hydrostatic pressure was applied in the current implementation of our model, whereas activation volumes of atomic associations likely decrease with increasing pressure21. Also of note is that the volume barrier to hydrogen bonding we identified is kinetic in nature and does not manifest as a global PMV/MSV barrier along the progress variable Θ. The volume barrier for the establishment of a helical segment – now confirmed by both experiment and theory – is likely connected with a free energy barrier as is evident by rather slow experimental time constants of ≈ 50 – 60 ns for adding or removing a helical segment116. Helical hydrogen bond formation likely entails an early stage with energetically unfavorable bond angles, which can become a kinetic bottleneck in the formation of a helical segment. 20 ACS Paragon Plus Environment

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The MSV/PMV perspective should also account for volume increases upon folding of naturally occurring globular proteins. Based on our present findings and previous considerations21, we concur with the view that the observed positive reaction volumes for the folding of globular proteins are not caused by the formation of α-helices but rather by the void volumes or packing defects in the proteins’ folded cores19,20. Whether other secondary structure elements such as π-helices that are less tightly packed can contribute positively to the folding reaction volume is an open question that can also be addressed by our formulation in the future. Although a detailed investigation of volumetric properties of globular proteins is beyond the scope of this article, it is instructive to take a first step to extend our formalism to a 54-residue model three-helix bundle (Fig.7, SFig.11) that undergoes reversible folding and unfolding79,83. Despite the structural artificiality of this model, which contains only glycines and one type each of Ala-sized nonpolar and polar residues, its MSV increases upon folding (Fig.7A). This result is in line with our expectation that the volumetric trend of a folding globular protein is opposite to that of coil-helix transition of an isolated α-helix. This MSV-increasing trend is quite robust, as it is observed in a modified version of the model with a larger sidechain vdW radius as well (SFig.11B) even though a larger residue size might be expected to reduce void volume in the sequestered core. However, because of the extraordinary high packing density (ρ > 0.86) of the folded state of this model three-helix bundle, its folding reaction volume is negative when the chemical component of PMV is taken into consideration (black dots in Fig.7B). In other words, the decreasing trend of the δV component upon folding (SFig.11A) overcompensates the increasing MSV trend (Fig.7A). Nonetheless, when the predicted dependence of folding reaction volume on atomic packing density ρ is extrapolated to ρ < 0.82 values that are typical of naturally occurring globular proteins50,117, it is seen to be consistent with positive folding reaction volumes as exemplified by several natural proteins (Fig.7B) for which pertinent data are available2. Two related lessons were learned here. (i) Globular polypeptide structures do not necessarily have a positive reaction volume upon folding, reaction volume can be negative if tight packing comparable to our model three-helix bundle can be achieved. (ii) Natural globular proteins have positive folding reaction volume because of the choice of residues in their sequences, as required by structure and function, that tends to leave relative large cavities in their folded cores and also encode for rough surfaces with significant re-entrant void volumes. 21 ACS Paragon Plus Environment

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Cavities/voids generally destabilize folded state even under constant atmospheric pressure because of loss of favorable van der Waals contacts118. Cavities can be empty (void) or partly filled with water. Consistent with the above perspective, while hydrostatic pressure on the L99A mutant of T4 lysozyme with a large internal cavity119,120 leads to hydration of the cavity and increased conformational fluctuations121, the pressure-induced conformational fluctuation is reduced by filling the empty cavity with a benzene molecule122. Thus one may expect a decreasing trend in pressure-induced destabilizing effect for folded proteins with less and less void volumes. However, because many other effects also contribute to protein stability, the overall effects of void volume changes can be subtle122. In summary, we have presented a coherent theoretical framework for understanding conformation-dependent volumetric effects in peptides and proteins. Aside from the conceptual clarity it provides, the present formulation also sidesteps uncertainties about the applicability of current explicit water models to pressure-related simulations56,57. Because our approach is based in part on experimental PMV measurements, it offers a complementary and practical approach to study pressure effects on polypeptide properties. To achieve this goal more comprehensively, an obvious extension would be to include pressure (P) coupling either as a PV term in Monte Carlo conformational sampling or as a derived P-dependent force in Langevin dynamics simulation. Pressure effects on coil-helix transition paths can be subtle. For instance, the volume barriers observed in our simulation are consistent with a pressure-induced slowdown of coil-helix transition20. However, helix formation time under the present simulation conditions is not correlated with any appreciable biases in PMV-increasing versus PMV-decreasing kinetic transitions (SFig.12), although such biases can be induced when pressure is applied. Another natural extension of our model is the incorporation of all amino acid residue types45. Temperature effects such as expansivity of proteins123 can also be addressed by combining multipletemperature simulations with experimental small-compound PMV data measured at different temperatures44 to address combined pressure-temperature effects100,124. Denaturant effects67 can also be encompassed by additional SASA-dependent terms82. In the foreseeable future, these developments should allow for more systematic theoretical investigations to gain insights into a wide range of pressure effects on protein behaviors7–9. 22 ACS Paragon Plus Environment

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Acknowledgements We thank Cathy Royer for helpful discussion. Part of this work was presented earlier this year by H.K. at the NSF Protein Folding Consortium 2016 Annual Meeting at the Washington University in St. Louis and the 9th International Conference on High Pressure Bioscience and Biotechnology (2016) in Toronto. We thank the interested participants of these conferences for helpful input. This work was supported by the Canadian Institutes of Health Research via grant MOP-84281 to H.S.C. We are grateful for this financial support and also for the generous allotment of computational resources by SciNet of Compute Canada.

Supporting Information Available Supporting Information can be downloaded free of charge at http://pubs.acs.org. SI Methods Text: Details of the model and the simulation procedure. SFigure 1: Thermodynamic and kinetic profiles of (Ala)16. SFigure 2: Approximate singleexponential relaxation of helix formation kinetics. SFigure 3: Properties of the model (Ala)16 coil-helix transition. SFigure 4: Chain length dependence of MSV of (Gly)n and (Ala)n. SFigure 5: Residue-specific SASAs of peptide backbone constituents. SFigure 6: Helicity-dependent MSV distribution. SFigure 7: Detailed analysis of volumetric barrier to hydrogen bond formation. SFigure 8: An example of non-helical hydrogen bond rupture and re-establishment. SFigure 9: S to M change in molecular surface around a hydrogen bond donor and acceptor. SFigure 10: MSV baseline is essential for a viable physical picture in our model formulation. SFigure 11: A model three-helix bundle with a significantly higher atomic packing density than naturally occurring proteins. SFigure 12: Statistics of kinetic PMV changes is nearly invariant with respect to folding time. STable 1-3: Statistics of volumetric three-state analysis of the formation and rupture of a single helical hydrogen bond occurring in different time segments. STable 4-6: Statistics on the sharpness of the volume maximum encountered during hydrogen bond formation and rupture. STable 7: Experimental folding reaction volumes of natural proteins.


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Figure 1: Geometric volumes in coil-helix transition. A. A model (Ala)16 peptide conformation in a space-filling depiction, wherein the vdW surfaces of N, Cα and C’, and O atoms, and SC united atoms are colored differently. A spherical water probe (drawn to scale) rolls over the vdW surfaces, defining direct-contact and re-entrant surfaces, the smoothly connected set of which is the molecular surface (translucent) that envelops MSV. The solvent-accessible surface (black curve) envelops SV. B—F. Ribbon diagrams of snapshots along an example coil-helix transition trajectory at t/107τS = 7.4, 8.0, 8.2, 8.3, and 8.32 respectively. The preceding conformation in (A) was extracted from the same trajectory at t/107τS = 6.8. G. vdW-surface representation of the fully formed helix in (F).


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Figure 2: Solvent exposure in coil-helix transition. Results shown are averages over all simulated (Ala)16 trajectories. A. Total SASA increases with helicity for Θ > 0.5 (top). The residue-specific normalized SASAi averaged over all 16 residues increases monotonically with Θ for SC but decreases monotonically for BB (bottom). B. Residue-specific SASAis for BB (top) and SC (bottom) for Θ = 0 (blue), Θ = 0.5 (green), and Θ = 1 (red) exhibit strong position dependence, especially near the two termini of the peptide when BB shielding is minimal (top). As helicity Θ increases (indicated by small solid arrows), SASAi decreases for BB and increases for SC monotonically (long solid arrows) for most but not all residue positions i. Note that the Θ = 0 blue curves in (B) correspond to the and normalization factors in the present formulation.


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Figure 3: Energetic and volumetric trajectories of a coil-helix transition. Timedependent properties for the final part of the trajectory in Fig.1 show that helix formation correlates with decreased (more favorable) hydrogen bond energy (A) and increased (less favorable) hydrophobic energy (B), and is associated with various degrees of fluctuation in volume measures (C). Variation of chemical component δV of conformational volume (D) is seen to correlate strongly with that of hydrophobic sidechain interactions (B). Shown properties are sliding averages over time windows of 100τS.


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Figure 4: Volume changes induced by coil-helix transition. Mean volumetric quantities averaged over all simulated (Ala)16 trajectories are shown as functions of Θ. Reaction volumes of coil-helix transition were computed as the value of a given volume measure at Θ = 1 minus that at Θ = 0.25, the latter corresponds to the most helical part of the disordered conformational population (SI Fig.3B). Reaction volume is very slightly negative for vdW-V (0.4% decrease) due to increased atomic overlaps upon helix formation (A), more negative for MSV (B), but positive for SV (C) and Venv (D). Following the MSV trend, PMV decreases with increasing Θ (E). Geometry-based and apparent packing densities (ρ and ρ* respectively) both increase with increasing Θ (F). The positive chemical contribution δV to PMV (= MSV + δV) as a fraction of MSV is larger for Θ > 0.5 than for Θ ≤ 0.5 (G). SV exhibits a similar trend but the increase in SV/MSV upon helix formation can be as large as 5 times that of the corresponding increase in PMV/MSV (H). Statistical uncertainties of the plotted mean values are smaller than the size of the plotting symbol except where indicated by error bars.


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Figure 5: Activation volume of single helical hydrogen bond formation. The changes in four volume measures are shown for the formation of an additional helical hydrogen bond in a conformation that already has five such bonds (Θ increases from 0.417 to 0.50). The kinetic event spanning 1,000τS were taken from the trajectory analyzed in Figs.1 and 2. A negative reaction volume is seen for all four volume measures considered here (∆vdW-V0 = ‒ 6.08 Å3, ∆MSV0 = ‒1.39 Å3, ∆PMV0 = ‒4.9 Å3, and ∆PMVad-hoc,0 = ‒47.6 Å3). A volume maximum (indicated by *) with sharpness characterized by ξ1 and ξ2 is observed for vdW-V, MSV and PMV (A-C), but not for the PMVad-hoc (D) that we introduced as a control (Eq.3 in Methods). vdW-V*, MSV*, and PMV* are volume barriers defined as the peak value of the given volume measure minus that at the start (S) conformation.


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Biochemistry

Figure 6: Details of conformational and volumetric changes during the formation of a single helical hydrogen bond. Structural aspects of the event in Fig.5 are analyzed here, with the hydrogen-bond donor (D) and acceptor (A) labeled. A. The S, M, and F conformations are shown, respectively, in green, blue, and yellow. Previously established hydrogen bonds in the vicinity of D and A are shown by thin yellow lines. Local conformational changes during the S-M (left) and M-F (right) transitions are indicated by white arrows. B. Changes in the vdW spherical overlaps between D and A. The vdW surfaces of the carbonyl oxygen (red), amino nitrogen (blue), and donor hydrogen (white) involved in the hydrogen bond being formed are shown with the vdW surface of another carbonyl oxygen (of residue 3, O3) in the vicinity. In this example, the process started (S) with no overlap among these atoms. No overlap developed at the volume-maximum (M) either. The final hydrogen bond formation (F) buried the hydrogen entirely, leading to a substantial vdW overlap between D and A. As a side effect in this particular case, an additional vdW-Vreducing overlap is seen between the two carbonyl oxygens. C. Space-filling representation of the peptide fragment comprising residues 3 to 9, shown in approximately the same orientation as in (B) with the same color code for N, O and H atoms, whereas C atoms are in light brown, and SCs in grey. The re-entrant part of the molecular surface is translucent. The D-A pair yet to be hydrogen bonded is connected by a yellow line (S and M). An increased void volume develops from S to M around the D-A pair because a more curved backbone (A, S-M) deepens the groove and the movement of the sidechain of residue 8 (SC) further enlarges the cavity, as may be visualized by the smaller water probe contact surfaces for A and O3 (bright red patches) and a less curved re-entrant surface (arrows) in M than in S. Close-up images of these structural drawings viewed at different orientations are provided in SFig.9.


Biochemistry

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Figure 7: Larger void/cavity volumes in the folded states of naturally occurring globular proteins lead to larger PMVs relative to their unfolded-state PMVs. A. MSV of our model three-helix bundle increases with fractional number of native contacts Q as packing defects build up toward the hydrophobic core of Q = 1 folded conformations (a snapshot is shown by the ribbon diagram). B. The change in PMV upon folding, ∆PMV, of this model was computed using conformations sampled in the shaded unfolded (uf) and folded (f) regions in (A). Plotted as a function of atomic packing density ρ, each small black dot for ∆PMV in the scatter plot (B) is the PMVf of a folded conformation minus the ensemble average uf = 5478 Å3 of the unfolded region (SFig.11A). Extrapolation of the modelpredicted ρ dependence of ∆PMV for ∆PMV < 0 to smaller ρ values that are typical of natural globular proteins is indicated by the two straight lines. Included for comparison are the published ∆PMV > 0 (ref 2) and ρ values of a selection of natural proteins (larger circles and stars, see STable 7), the volumetric properties of which are seen to be consistent with the present extrapolation. We computed the shown ρ values by MSROLL117 (circles) for CI2 (PDB ID: 2CI2, green), BSCspB (1CSQ, blue), lysozyme (1DPX, cyan), azurin (1AZU, magenta), chymotrypsinogen (1CHG, yellow), thermolysin (1KEI, olive), metmyoglobin (1YMB, dark blue), cytochrome c (1HRC, deep purple), and SNase WT (1EY0, brown), and also by ProteinVolume50 for CI2 and BSCspB (stars).


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Biochemistry

For Table of Contents Use Only

Volumetric Physics of Polypeptide Coil-Helix Transitions Heinrich Krobath, Tao Chen and Hue Sun Chan


Biochemistry

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Fig.1 84x83mm (300 x 300 DPI)

ACS Paragon Plus Environment

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Biochemistry

Fig.2 84x73mm (300 x 300 DPI)


Biochemistry

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Fig.3 73x64mm (600 x 600 DPI)


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Biochemistry

Fig.4 129x197mm (600 x 600 DPI)


Biochemistry

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Fig.5 75x66mm (600 x 600 DPI)


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Biochemistry

Fig.6 84x122mm (300 x 300 DPI)


Biochemistry

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Fig.7 84x42mm (300 x 300 DPI)


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Biochemistry

TOC graphics 32x12mm (300 x 300 DPI)


Volumetric Physics of Polypeptide CoilâHelix Transitions

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Volumetric Physics of Polypeptide CoilâHelix Transitions