Exploring the helix-coil transition via all-atom equilibrium ensemble simulations

The helix-coil transition revisited

In this article, we perform a dynamic Monte Carlo simulation study of the helix-coil transition by using a bond-fluctuation lattice model. The results of the simulations are compared with those predicted by the Zimm-Bragg statistical thermodynamic theory with propagation and nucleation parameters determined from simulation data. The Zimm-Bragg theory provides a satisfactory description of the helix-coil transition of a homopolypeptide chain of 32 residues (N = 32). For such a medium-length chain, however, the analytical equation based on a widely-used large-N approximation to the Zimm-Bragg theory is not suitable to predict the average length of helical blocks at low temperatures when helicity is high. We propose an analytical large-eigenvalue (lambda) approximation. The new equation yields a significantly improved agreement on the average helix-block length with the original Zimm-Bragg theory for both medium and long chain lengths in the entire temperature range. Nevertheless, even the original Zimm-Bragg theory does not provide an accurate description of helix-coil transition for longer chains. We assume that the single-residue nucleation of helix formation as suggested in the original Zimm-Bragg model might be responsible for this deviation. A mechanism of nucleation by a short helical block is proposed by us and provides a significantly improved agreement with our simulation data.

Parameters of Monovalent Ions in the AMBER-99 Forcefield: Assessment of Inaccuracies and Proposed Improvements

The monovalent ion parameters used by the AMBER-99 forcefield are shown to exhibit physically inaccurate behavior in molecular dynamics simulations of strong 1:1 electrolytes. These errors arise from an ad hoc adaptation of Aqvist's cation parameters. The result is the rapid formation of large, unphysical clusters at concentrations that are well below solubility limits. The observed unphysical behavior poses a serious challenge for simulating ions around highly charged polymers such as nucleic acids. In this communication, we explain the source of this unphysical behavior. To facilitate the continued use of the popular AMBER parameters, we prescribe a simple fix whereby Aqvist's cations and anions are used in conjunction with the AMBER forcefield for nucleic acids. A preliminary test of this strategy suggests that the proposed fix is reasonable and is likely to be generalizable for simulating diffuse and specific ion binding to nucleic acids.

Water penetration in the low and high pressure native states of ubiquitin

Theoretical studies on the solvation of methane molecules in water have shown that the effect of increased pressure is to stabilize solvent separated contacts relative to direct contacts. This suggests that high pressure stabilizes waters that have penetrated into a protein's core, indicating a mechanism for the high pressure denaturation of proteins. We test this theory on a folded protein by studying the penetration of water into the native state of ubiquitin at low and high pressures, using molecular dynamics. An ensemble of conformations sampled in the folded state of ubiquitin has been determined by NMR at two pressures below the protein's denaturation pressure, 30 atm and 3000 atm. We find that 1-5 more waters penetrate the high pressure conformations than the low pressure conformations. Low volume configurations of the system are favored at high pressures, but different components of the system may experience increases or decreases in their specific volumes. We find that penetrating waters have a higher volume per water than bulk waters, but that the volume per protein residue may be lowered by solvation. Furthermore, we find that penetration of the protein by water at high pressures is driven by the difference in the pressure dependence of the probability of cavity opening in the protein and pressure dependence of the probability of cavity opening in the bulk solvent. The volume changes associated with cavity opening and closing indicate that each penetrating water reduces the volume of the system by about 12 mL/mol. The experimental volume change going from the low pressure to the high pressure native state of ubiquitin is 24 mL/mol. Our results indicate that this volume change can be explained by penetration of the protein by two water molecules.

The effect of charge-charge interactions on the kinetics of alpha-helix formation

The formation of the monomeric alpha-helix represents one of the simplest scenarios in protein folding; however, our current understanding of the folding dynamics of the alpha-helix motif is mainly based on studies of alanine-rich model peptides. To examine the effect of peptide sequence on the folding kinetics of alpha-helices, we studied the relaxation kinetics of a 21-residue helical peptide, Conantokin-T (Con-T), using time-resolved infrared spectroscopy in conjunction with a laser-induced temperature jump technique. Con-T is a neuroactive peptide containing a large number of charged residues that is found in the venom of the piscivorous cone snail Conus tulipa . The temperature-jump relaxation kinetics of Con-T is distinctly slower than that of previously studied alanine-based peptides, suggesting that the folding time of alpha-helices is sequence-dependent. Furthermore, it appears that the slower folding of Con-T can be attributed to the fact that its helical conformation is stabilized by charge-charge interactions or salt bridges. Although this finding contradicts an earlier molecular dynamics simulation, it also has implications for existing models of protein folding.

Modeling of folding and unfolding mechanisms in alanine-based alpha-helical polypeptides

alpha-Helix formation is known to be opposed by the entropy loss due to the folding and favored by the energy of molecular interactions. However, the underlying mechanism of these factors is still being discussed. Here we have used the experimental and calculation data for short alanine-based peptides embedded in water to model the mechanism of helix folding and unfolding and to calculate microscopically the free energy factors of alanine in the frame of helix coil conformational integrals. Classical helix-coil transition theories take into account the interactions in a peptide chain only if the i, i + 3 peptide bond participates in hydrogen bonding. But quantum mechanical calculations showed that interactions of the i, i + 2 peptide bond play an important role in helix folding too. We also included the short-range repulsive interactions due to molecular steric clashes and the end effects due to polar/hydrogen-bonding interactions at the N and C termini. The helix and coil regions of peptide conformational space were defined using an experimental steric criterion for hydrogen bonding. Arginine helix propensity was discussed and estimated. Monte Carlo numerical simulations of thermodynamics and kinetics for the 21 amino acid alpha-helical polypeptide Ac-A5(AAARA)3A-NMe were carried out and found to be in an agreement with the experimental results.

Hierarchical analysis of conformational dynamics in biomolecules: transition networks of metastable states

Molecular dynamics simulation generates large quantities of data that must be interpreted using physically meaningful analysis. A common approach is to describe the system dynamics in terms of transitions between coarse partitions of conformational space. In contrast to previous work that partitions the space according to geometric proximity, the authors examine here clustering based on kinetics, merging configurational microstates together so as to identify long-lived, i.e., dynamically metastable, states. As test systems microsecond molecular dynamics simulations of the polyalanines Ala(8) and Ala(12) are analyzed. Both systems clearly exhibit metastability, with some kinetically distinct metastable states being geometrically very similar. Using the backbone torsion rotamer pattern to define the microstates, a definition is obtained of metastable states whose lifetimes considerably exceed the memory associated with interstate dynamics, thus allowing the kinetics to be described by a Markov model. This model is shown to be valid by comparison of its predictions with the kinetics obtained directly from the molecular dynamics simulations. In contrast, clustering based on the hydrogen-bonding pattern fails to identify long-lived metastable states or a reliable Markov model. Finally, an approach is proposed to generate a hierarchical model of networks, each having a different number of metastable states. The model hierarchy yields a qualitative understanding of the multiple time and length scales in the dynamics of biomolecules.

Structural characterization of alpha-helices of implicitly solvated poly-alanine

The structural characteristics of alpha-helices in poly-alanine-based peptides have been investigated via molecular dynamics simulation with the goal of understanding the basic features of peptide simulations within the context of a model system, classical molecular dynamics with generalized Born (GB) solvation, and to shed insight into the formation and stabilization of alpha-helices in short peptides. The effects of peptide length, terminal charges, proline substitution, and temperature on the alpha-helical secondary structure have been studied. The simulations have shown that distinct secondary structure begins to develop in peptides with lengths approaching 10 residues while ambiguous structures occur in shorter peptides. The helical content of peptides with lengths > or =10 amino acids is observed to be nearly constant up to (Ala)(40). Interestingly, terminal charges and proline in the second position from the N-terminus alter the secondary structure locally with little effect on the overall alpha-helical content of the peptide. The free energy profile of helix formation was also investigated. A large increase in free energy accompanying the formation of helices with more than two consecutive hydrogen bonds in the (i, i + 4) pattern was observed while the free energy increases linearly with additional hydrogen bonds. Values for the change in enthalpy and entropy of helix nucleation and propagation are reported. Additionally the results obtained from the GB model are compared to explicit solvent simulations of two synthetic alanine-based peptides.

Predicting absolute ligand binding free energies to a simple model site

A central challenge in structure-based ligand design is the accurate prediction of binding free energies. Here we apply alchemical free energy calculations in explicit solvent to predict ligand binding in a model cavity in T4 lysozyme. Even in this simple site, there are challenges. We made systematic improvements, beginning with single poses from docking, then including multiple poses, additional protein conformational changes, and using an improved charge model. Computed absolute binding free energies had an RMS error of 1.9 kcal/mol relative to previously determined experimental values. In blind prospective tests, the methods correctly discriminated between several true ligands and decoys in a set of putative binders identified by docking. In these prospective tests, the RMS error in predicted binding free energies relative to those subsequently determined experimentally was only 0.6 kcal/mol. X-ray crystal structures of the new ligands bound in the cavity corresponded closely to predictions from the free energy calculations, but sometimes differed from those predicted by docking. Finally, we examined the impact of holding the protein rigid, as in docking, with a view to learning how approximations made in docking affect accuracy and how they may be improved.

Quantitative characterization of intrinsic disorder in polyglutamine: insights from analysis based on polymer theories

Intrinsically disordered proteins (IDPs) are unfolded under physiological conditions. Here we ask if archetypal IDPs in aqueous milieus are best described as swollen disordered coils in a good solvent or collapsed disordered globules in a poor solvent. To answer this question, we analyzed data from molecular simulations for a 20-residue polyglutamine peptide and concluded, in accord with experimental results, that water is a poor solvent for this system. The relevance of monomeric polyglutamine is twofold: It is an archetypal IDP sequence and its aggregation is associated with nine neurodegenerative diseases. The main advance in this work lies in our ability to make accurate assessments of solvent quality from analysis of simulations for a single, rather than multiple chain lengths. We achieved this through the proper design of simulations and analysis of order parameters that are used to describe conformational equilibria in polymer physics theories. Despite the preference for collapsed structures, we find that polyglutamine is disordered because a heterogeneous ensemble of conformations of equivalent compactness is populated at equilibrium. It is surprising that water is a poor solvent for polar polyglutamine and the question is: why? Our preliminary analysis suggests that intrabackbone interactions provide at least part of the driving force for the collapse of polyglutamine in water. We also show that dynamics for conversion between distinct conformations resemble structural relaxation in disordered, glassy systems, i.e., the energy landscape for monomeric polyglutamine is rugged. We end by discussing generalizations of our methods to quantitative studies of conformational equilibria of other low-complexity IDP sequences.

How sensitive are nanosecond molecular dynamics simulations of proteins to changes in the force field?

The sensitivity of molecular dynamics simulations to variations in the force field has been examined in relation to a set of 36 structures corresponding to 31 proteins simulated by using different versions of the GROMOS force field. The three parameter sets used (43a1, 53a5, and 53a6) differ significantly in regard to the nonbonded parameters for polar functional groups and their ability to reproduce the correct solvation and partitioning behavior of small molecular analogues of the amino acid side chains. Despite the differences in the force field parameters no major differences could be detected in a wide range of structural properties such as the root-mean-square deviation from the experimental structure, radii of gyration, solvent accessible surface, secondary structure, or hydrogen bond propensities on a 5 to 10 ns time scale. The small differences that were observed correlated primarily with the presence of charged residues as opposed to residues that differed most between the parameter sets. The work highlights the variation that can be observed in nanosecond simulations of protein systems and implications of this for force field validation, as well as for the analysis of protein simulations in general.

Protein-Folding Dynamics: Overview of Molecular Simulation Techniques

Molecular dynamics (MD) is an invaluable tool with which to study protein folding in silico. Although just a few years ago the dynamic behavior of a protein molecule could be simulated only in the neighborhood of the experimental conformation (or protein unfolding could be simulated at high temperature), the advent of distributed computing, new techniques such as replica-exchange MD, new approaches (based on, e.g., the stochastic difference equation), and physics-based reduced models of proteins now make it possible to study protein-folding pathways from completely unfolded structures. In this review, we present algorithms for MD and their extensions and applications to protein-folding studies, using all-atom models with explicit and implicit solvent as well as reduced models of polypeptide chains.

Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics

To meet the challenge of modeling the conformational dynamics of biological macromolecules over long time scales, much recent effort has been devoted to constructing stochastic kinetic models, often in the form of discrete-state Markov models, from short molecular dynamics simulations. To construct useful models that faithfully represent dynamics at the time scales of interest, it is necessary to decompose configuration space into a set of kinetically metastable states. Previous attempts to define these states have relied upon either prior knowledge of the slow degrees of freedom or on the application of conformational clustering techniques which assume that conformationally distinct clusters are also kinetically distinct. Here, we present a first version of an automatic algorithm for the discovery of kinetically metastable states that is generally applicable to solvated macromolecules. Given molecular dynamics trajectories initiated from a well-defined starting distribution, the algorithm discovers long lived, kinetically metastable states through successive iterations of partitioning and aggregating conformation space into kinetically related regions. The authors apply this method to three peptides in explicit solvent-terminally blocked alanine, the 21-residue helical F(s) peptide, and the engineered 12-residue beta-hairpin trpzip2-to assess its ability to generate physically meaningful states and faithful kinetic models.

UV Raman spatially resolved melting dynamics of isotopically labeled polyalanyl peptide: slow alpha-helix melting follows 3(10)-helices and pi-bulges premelting

We used UV resonance Raman (UVRR) to examine the spatial dependence of the T-jump secondary structure relaxation of an isotopically labeled 21-residue mainly Ala peptide, AdP. The AdP penultimate Ala residues were perdeuterated, leaving the central residues hydrogenated, to allow separate monitoring of melting of the middle versus the end peptide bonds. For 5 to 30 degrees C T-jumps, the central peptide bonds show a approximately 2-fold slower relaxation time (189 +/- 31 ns) than do the exterior peptide bonds (97 +/- 15 ns). In contrast, for a 20 to 40 degrees C T-jump, the central peptide bond relaxation appears to be faster (56 +/- 6 ns) than that of the penultimate peptide bonds (131 +/- 46 ns). We show that, if the data are modeled as a two-state transition, we find that only exterior peptide bonds show anti-Arrhenius folding behavior; the middle peptide bonds show both normal Arrhenius-like folding and unfolding. This anti-Arrhenius behavior results from the involvement of pi-bulges/helices and 3(10)-helix states in the melting. The unusual temperature dependence of the (un)folding rates of the interior and exterior peptide bonds is due to the different relative (un)folding rates of 3(10)-helices, alpha-helices, and pi-bulges/helices. Pure alpha-helix unfolding rates are approximately 12-fold slower (approximately 1 micros) than that of pi-bulges and 3(10)-helices. In addition, we also find that the alpha-helix is most stable at the AdP N-terminus where eight consecutive Ala occur, whereas the three hydrophilic Arg located in the middle and at the C-terminus destabilize the alpha-helix in these regions and induce defects such as pi-bulges and 3(10)-helices.

Both the N-terminal Loop and Wing W2 of the Forkhead Domain of Transcription Factor Foxo4 Are Important for DNA Binding

FoxO4 belongs to the "O" subset of forkhead transcription factors, which participate in various cellular processes. The forkhead DNA binding domain (DBD) consists of three-helix bundle resting on a small antiparallel beta-sheet from which two extended loops protrude and create two wing-like structures. The wing W2 of FoxO factors contains a 14-3-3 protein-binding motif that is phosphorylated by protein kinase B in response to insulin or growth factors. In this report, we investigated the role of the N-terminal loop (portion located upstream of first helix H1) and the C-terminal region (loop known as wing W2) of the forkhead domain of transcription factor FoxO4 in DNA binding. Although the deletion of either portion partly reduces the FoxO4-DBD binding to the DNA, the simultaneous deletion of both regions inhibits DNA binding significantly. Förster resonance energy transfer measurements and molecular dynamics simulations suggest that both studied N- and C-terminal regions of FoxO4-DBD directly interact with DNA. In the presence of the N-terminal loop the protein kinase B-induced phosphorylation of wing W2 by itself has negligible effect on DNA binding. On the other hand, in the absence of this loop the phosphorylation of wing W2 significantly inhibits the FoxO4-DBD binding to the DNA. The binding of the 14-3-3 protein efficiently reduces DNA-binding potential of phosphorylated FoxO4-DBD regardless of the presence of the N-terminal loop. Our results show that both N- and C-terminal regions of forkhead domain are important for stability of the FoxO4-DBD.DNA complex.

Near-native structure refinement using in vacuo energy minimization

One of the greatest shortcomings of macromolecular energy minimization and molecular dynamics techniques is that they generally do not preserve the native structure of proteins as observed by x-ray crystallography. This deformation of the native structure means that these methods are not generally used to refine structures produced by homology-modeling techniques. Here, we use a database of 75 proteins to test the ability of a variety of popular molecular mechanics force fields to maintain the native structure. Minimization from the native structure is a weak test of potential energy functions: It is complemented by a much stronger test in which the same methods are compared for their ability to attract a near-native decoy protein structure toward the native structure. We use a powerfully convergent energy-minimization method and show that, of the traditional molecular mechanics potentials tested, only one showed a modest net improvement over a large data set of structurally diverse proteins. A smooth, differentiable knowledge-based pairwise atomic potential performs better on this test than traditional potential functions. This work is expected to have important implications for protein structure refinement, homology modeling, and structure prediction.

Comparison of multiple Amber force fields and development of improved protein backbone parameters

The ff94 force field that is commonly associated with the Amber simulation package is one of the most widely used parameter sets for biomolecular simulation. After a decade of extensive use and testing, limitations in this force field, such as over-stabilization of alpha-helices, were reported by us and other researchers. This led to a number of attempts to improve these parameters, resulting in a variety of "Amber" force fields and significant difficulty in determining which should be used for a particular application. We show that several of these continue to suffer from inadequate balance between different secondary structure elements. In addition, the approach used in most of these studies neglected to account for the existence in Amber of two sets of backbone phi/psi dihedral terms. This led to parameter sets that provide unreasonable conformational preferences for glycine. We report here an effort to improve the phi/psi dihedral terms in the ff99 energy function. Dihedral term parameters are based on fitting the energies of multiple conformations of glycine and alanine tetrapeptides from high level ab initio quantum mechanical calculations. The new parameters for backbone dihedrals replace those in the existing ff99 force field. This parameter set, which we denote ff99SB, achieves a better balance of secondary structure elements as judged by improved distribution of backbone dihedrals for glycine and alanine with respect to PDB survey data. It also accomplishes improved agreement with published experimental data for conformational preferences of short alanine peptides and better accord with experimental NMR relaxation data of test protein systems.

Effect of different treatments of long-range interactions and sampling conditions in molecular dynamic simulations of rhodopsin embedded in a dipalmitoyl phosphatidylcholine bilayer

The present study analyzes the effect of the simulation conditions on the results of molecular dynamics simulations of G-protein coupled receptors (GPCRs) performed with an explicit lipid bilayer. Accordingly, the present work reports the analysis of different simulations of bovine rhodopsin embedded in a dipalmitoyl phosphatidylcholine (DPPC) lipid bilayer using two different sampling conditions and two different approaches for the treatment of long-range electrostatic interactions. Specifically, sampling was carried out either by using the statistical ensembles NVT or NPT (constant number of atoms, a pressure of 1 atm in all directions and fixed temperature), and the electrostatic interactions were treated either by using a twin-cutoff, or the particle mesh Ewald summation method (PME). The results of the present study suggest that the use of the NPT ensemble in combination with the PME method provide more realistic simulations. The use of NPT during the equilibration avoids the need of an a priori estimation of the box dimensions, giving the correct area per lipid. However, once the system is equilibrated, the simulations are irrespective of the sampling conditions used. The use of an electrostatic cutoff induces artifacts on both lipid thickness and the ion distribution, but has no direct effect on the protein and water molecules.

Understanding the molecular basis for differential binding of integrins to collagen and gelatin

Integrin-mediated cell adhesion plays a central role in cell migration and signaling. Overexpression of integrins is also associated with cancer invasion and metastasis. Although a number of problems in integrin-matrix interactions have been studied in detail, the molecular specificity, which increases integrin adhesion to native collagen but results in poor integrin-gelatin interaction, is not understood. In this report, we study the role of individual amino acids in integrin-collagen and integrin-gelatin interactions using long-term (>100 ns) molecular simulations. The results, which are force-field independent, show that denatured collagen induces helical conformations in integrin amino acids and significantly reduces the poly-proline II content, which stabilizes the integrin-collagen interactions. Our simulations provide a possible explanation of the molecular specificity in integrin binding and suggest new targets for regulating integrin-mediated invasion and metastasis.

Glass transition in biomolecules and the liquid-liquid critical point of water

Using molecular dynamics simulations, we investigate the relation between the dynamic transitions of biomolecules (lysozyme and DNA) and the dynamic and thermodynamic properties of hydration water. We find that the dynamic transition of the macromolecules, sometimes called a "protein glass transition," occurs at the temperature of dynamic crossover in the diffusivity of hydration water and also coincides with the maxima of the isobaric specific heat C_{P} and the temperature derivative of the orientational order parameter. We relate these findings to the hypothesis of a liquid-liquid critical point in water. Our simulations are consistent with the possibility that the protein glass transition results from crossing the Widom line, which is defined as the locus of correlation length maxima emanating from the hypothesized second critical point of water.

The planar conformation of a strained proline ring: a QM/MM study

QM and QM/MM energy calculations have been carried out on an atomic resolution structure of liganded triosephosphate isomerase (TIM) that has an active site proline (Pro168) in a planar conformation. The origin of the planarity of this proline has been identified. Steric interactions between the atoms of the proline ring and a tyrosine ring (Tyr166) on one side of the proline prevent the ring from adopting the up pucker (chi1 is approximately -30 degrees), while the side chain of a nearby alanine (Ala171) forbids the down pucker (chi1 is approximately +30 degrees). To obtain a proline conformation that is in agreement with the experimentally observed planar state, a quantum system of sufficient size is required and should at least include the nearby side chains of Tyr166, Ala171, and Glu129 to provide enough stabilization. It is argued that the current force fields for structure optimization do not describe strained protein fragments correctly. The proline is part of a catalytic loop that closes upon ligand binding. Comparison of the proline conformation in different TIM X-ray structures, indicates that in the closed conformation of TIM the proline is planar or nearly planar, while in the open conformation it is down puckered. This suggests that the planarity possibly plays a role in the overall catalytic cycle of TIM, presumable acting as a reservoir of energy that becomes available upon loop opening.

On the use of orientational restraints and symmetry corrections in alchemical free energy calculations

Alchemical free energy calculations are becoming a useful tool for calculating absolute binding free energies of small molecule ligands to proteins. Here, we find that the presence of multiple metastable ligand orientations can cause convergence problems when distance restraints alone are used. We demonstrate that the use of orientational restraints can greatly accelerate the convergence of these calculations. However, even with this acceleration, we find that sufficient sampling requires substantially longer simulations than are used in many published protocols. To further accelerate convergence, we introduce a new method of configuration space decomposition by orientation which reduces required simulation lengths by at least a factor of 5 in the cases examined. Our method is easily parallelizable, well suited for cases where a ligand cocrystal structure is not available, and can utilize initial orientations generated by docking packages.

Using massively parallel simulation and Markovian models to study protein folding: Examining the dynamics of the villin headpiece

We report on the use of large-scale distributed computing simulation and novel analysis techniques for examining the dynamics of a small protein. Matters addressed include folding rate, very long time scale kinetics, ensemble properties, and interaction with water. The target system for the study, the villin headpiece, has been of great interest to experimentalists and theorists both. Sampling totaled nearly 500 mus-the most extensive published to date for a system of villin's size in explicit solvent with all atom detail-and was in the form of tens of thousands of independent molecular dynamics trajectories, each several tens of nanoseconds in length. We report on kinetics sensitivity analyses that, using a set of short simulations, probed the role of water in villin's folding and sensitivity to the simulation's electrostatics treatment. By constructing Markovian state models (MSMs) from the collected data, we were able to propagate dynamics to times far beyond those directly simulated and to rapidly compute mean first passage times, long time kinetics (tens of microseconds), and evolution of ensemble property distributions over long times, otherwise currently impossible. We also tested our MSM by using it to predict the structure of villin de novo.

ARTIST: An activated method in internal coordinate space for sampling protein energy landscapes

We present the first applications of an activated method in internal coordinate space for sampling all-atom protein conformations, the activation-relaxation technique for internal coordinate space trajectories (ARTIST). This method differs from all previous internal coordinate-based studies aimed at folding or refining protein structures in that conformational changes result from identifying and crossing well-defined saddle points connecting energy minima. Our simulations of four model proteins containing between 4 and 47 amino acids indicate that this method is efficient for exploring conformational space in both sparsely and densely packed environments, and offers new perspectives for applications ranging from computer-aided drug design to supramolecular assembly.

Removal of kinetic traps and enhanced protein folding by strategic substitution of amino acids in a model α-helical hairpin peptide

The presence of non-native kinetic traps in the free energy landscape of a protein may significantly lengthen the overall folding time so that the folding process becomes unreliable. We use a computational model alpha-helical hairpin peptide to calculate structural free energy landscapes and relate them to the kinetics of folding. We show how protein engineering through strategic changes in only a few amino acid residues along the primary sequence can greatly increase the speed and reliability of the folding process, as seen experimentally. These strategic substitutions also prevent the formation of long-lived misfolded configurations that can cause unwanted aggregations of peptides. These results support arguments that removal of kinetic traps, obligatory or nonobligatory, is crucial for fast folding.

The solvation interface is a determining factor in peptide conformational preferences

The 21 residue polyalanine-based F(s) peptide was studied using thousands of long, explicit solvent, atomistic molecular dynamics simulations that reached equilibrium at the ensemble level. Peptide conformational preference as a function of hydrophobicity was examined using a spectrum of explicit solvent models, and the peptide length-dependence of the hydrophilic and hydrophobic components of solvent-accessible surface area for several ideal conformational types was considered. Our results demonstrate how the character of the solvation interface induces several conformational preferences, including a decrease in mean helical content with increased hydrophilicity, which occurs predominantly through reduced nucleation tendency and, to a lesser extent, destabilization of helical propagation. Interestingly, an opposing effect occurs through increased propensity for 3(10)-helix conformations, as well as increased polyproline structure. Our observations provide a framework for understanding previous reports of conformational preferences in polyalanine-based peptides including (i) terminal 3(10)-helix prominence, (ii) low pi-helix propensity, (iii) increased polyproline conformations in short and unfolded peptides, and (iv) membrane helix stability in the presence and absence of water. These observations provide physical insight into the role of water in peptide conformational equilibria at the atomic level, and expand our view of the complexity of even the most "simple" of biopolymers. Whereas previous studies have focused predominantly on hydrophobic effects with respect to tertiary structure, this work highlights the need for consideration of such effects at the secondary structural level.

How large is an alpha-helix? Studies of the radii of gyration of helical peptides by small-angle X-ray scattering and molecular dynamics

Using synchrotron radiation and the small-angle X-ray scattering technique we have measured the radii of gyration of a series of alanine-based alpha-helix-forming peptides of the composition Ace-(AAKAA)(n)-GY-NH(2), n=2-7, in aqueous solvent at 10(+/-1) degrees C. In contrast to other techniques typically used to study alpha-helices in isolation (such as nuclear magnetic resonance and circular dichroism), small-angle X-ray scattering reports on the global structure of a molecule and, as such, provides complementary information to these other, more sequence-local measuring techniques. The radii of gyration that we measure are, except for the 12-mer, lower than the radii of gyration of ideal alpha-helices or helices with frayed ends of the equivalent sequence-length. For example, the measured radius of gyration of the 37-mer is 14.2(+/-0.6)A, which is to be compared with the radius of gyration of an ideal 37-mer alpha-helix of 17.6A. Attempts are made to analyze the origin of this discrepancy in terms of the analytical Zimm-Bragg-Nagai (ZBN) theory, as well as distributed computing explicit solvent molecular dynamics simulations using two variants of the AMBER force-field. The ZBN theory, which treats helices as cylinders connected by random walk segments, predicts markedly larger radii of gyration than those measured. This is true even when the persistence length of the random walk parts is taken to be extremely short (about one residue). Similarly, the molecular dynamics simulations, at the level of sampling available to us, give inaccurate values of the radii of gyration of the molecules (by overestimating them by around 25% for longer peptides) and/or their helical content. We conclude that even at the short sequences examined here (< or =37 amino acid residues), these alpha-helical peptides behave as fluctuating semi-broken rods rather than straight cylinders with frayed ends.

Protein folding by distributed computing and the denatured state ensemble

The distributed computing (DC) paradigm in conjunction with the folding@home (FH) client server has been used to study the folding kinetics of small peptides and proteins, giving excellent agreement with experimentally measured folding rates, although pathways sampled in these simulations are not always consistent with the folding mechanism. In this study, we use a coarse-grain model of protein L, whose two-state kinetics have been characterized in detail by using long-time equilibrium simulations, to rigorously test a FH protocol using approximately 10,000 short-time, uncoupled folding simulations starting from an extended state of the protein. We show that the FH results give non-Poisson distributions and early folding events that are unphysical, whereas longer folding events experience a correct barrier to folding but are not representative of the equilibrium folding ensemble. Using short-time, uncoupled folding simulations started from an equilibrated denatured state ensemble (DSE), we also do not get agreement with the equilibrium two-state kinetics because of overrepresented folding events arising from higher energy subpopulations in the DSE. The DC approach using uncoupled short trajectories can make contact with traditionally measured experimental rates and folding mechanism when starting from an equilibrated DSE, when the simulation time is long enough to sample the lowest energy states of the unfolded basin and the simulated free-energy surface is correct. However, the DC paradigm, together with faster time-resolved and single-molecule experiments, can also reveal the breakdown in the two-state approximation due to observation of folding events from higher energy subpopulations in the DSE.

Mechanism of Helix Nucleation and Propagation: Microscopic View from Microsecond Time Scale MD Simulations

Microsecond time scale molecular dynamics simulations of the 13-residue peptide RN24 were carried out to investigate the mechanism of helix nucleation and propagation. An extended and an ideal alpha-helical conformation were used as starting structures. NOE-derived interatomic distances were compared with distances calculated from the simulations, showing good agreement between experimental and simulation results. Based on almost 200 helix nucleation events observed, beta-turn and 3(10)-helix play an important role in helix nucleation; in most cases, helix nucleation is preceded by the formation of a short-lived beta-turn (60% probability) or 3(10)-helix (20% probability), and the conversion from beta-turn to alpha-turn involves bifurcated hydrogen bonds. Helix propagation in RN24 appears to occur preferentially from the N-terminus to the C-terminus, and helix unfolding preferentially in the opposite direction.

Foldamer dynamics expressed via Markov state models. II. State space decomposition

The structural landscape of poly-phenylacetylene (pPA), otherwise known as m-phenylene ethynylene oligomers, has been shown to consist of a very diverse set of conformations, including helices, turns, and knots. Defining a state space decomposition to classify these conformations into easily identifiable states is an important step in understanding the dynamics in relation to Markov state models. We define the state decomposition of pPA oligomers in terms of the sequence of discretized dihedral angles between adjacent phenyl rings along the oligomer backbone. Furthermore, we derive in mathematical detail an approach to further reduce the number of states by grouping symmetrically equivalent states into a single parent state. A more challenging problem requires a formal definition for knotted states in the structural landscape. Assuming that the oligomer chain can only cross the ideal helix path once, we propose a technique to define a knotted state derived from a helical state determined by the position along the helical nucleus where the chain crosses the ideal helix path. Several examples of helical states and knotted states from the pPA 12-mer illustrate the principles outlined in this article.

Unusual compactness of a polyproline type II structure

Polyproline type II (PPII) helix has emerged recently as the dominant paradigm for describing the conformation of unfolded polypeptides. However, most experimental observables used to characterize unfolded proteins typically provide only short-range, sequence-local structural information that is both time- and ensemble-averaged, giving limited detail about the long-range structure of the chain. Here, we report a study of a long-range property: the radius of gyration of an alanine-based peptide, Ace-(diaminobutyric acid)2-(Ala)7-(ornithine)2-NH2. This molecule has previously been studied as a model for the unfolded state of proteins under folding conditions and is believed to adopt a PPII fold based on short-range techniques such as NMR and CD. By using synchrotron radiation and small-angle x-ray scattering, we have determined the radius of gyration of this peptide to be 7.4 +/- 0.5 angstroms, which is significantly less than the value expected from an ideal PPII helix in solution (13.1 angstroms). To further study this contradiction, we have used molecular dynamics simulations using six variants of the AMBER force field and the GROMOS 53A6 force field. However, in all cases, the simulated ensembles underestimate the PPII content while overestimating the experimental radius of gyration. The conformational model that we propose, based on our small angle x-ray scattering results and what is known about this molecule from before, is that of a very flexible, fluctuating structure that on the level of individual residues explores a wide basin around the ideal PPII geometry but is never, or only rarely, in the ideal extended PPII helical conformation.

How well can simulation predict protein folding kinetics and thermodynamics?

Simulation of protein folding has come a long way in five years. Notably, new quantitative comparisons with experiments for small, rapidly folding proteins have become possible. As the only way to validate simulation methodology, this achievement marks a significant advance. Here, we detail these recent achievements and ask whether simulations have indeed rendered quantitative predictions in several areas, including protein folding kinetics, thermodynamics, and physics-based methods for structure prediction. We conclude by looking to the future of such comparisons between simulations and experiments.

Thermodynamics Of α‐Helix Formation

The alpha-helix was the first proposed and experimentally confirmed secondary structure. The elegant simplicity of the alpha-helical structure, stabilized by hydrogen bonding between the backbone carbonyl oxygen and the peptide amide four residues away, has captivated the scientific community. In proteins, alpha-helices are also stabilized by the so-called capping interactions that occur at both the C- and the N-termini of the helix. This chapter provides a brief historical overview of the thermodynamic studies of the energetics of helix formation, and reviews recent progress in our understanding of the thermodynamics of helix formation.