Folding cooperativity in a three-stranded beta-sheet model

Online Optimization of Total Acceptance in Hamiltonian Replica Exchange Simulations

Replica exchange is a widely used sampling strategy in molecular simulation. While a variety of methods exist to optimize parameters for temperature replica exchange, less is known about how to optimize parameters for more general Hamiltonian replica exchange simulations. We present an algorithm for the online optimization of total acceptance for both temperature and Hamiltonian replica exchange simulations using stochastic gradient descent. We optimize the total acceptance, a heuristic objective function capturing the efficiency of replica exchange. Our approach is general and has several desirable properties, including: (1) it makes few assumptions about the system of interest, (2) optimization occurs online without the requirement of presimulation, and (3) most importantly, it readily generalizes to systems where there are multiple control parameters (e.g., temperatures, force constants, etc.) that determine the Hamiltonian of each replica. We explore some general properties of the algorithm on a simple harmonic oscillator system, and demonstrate its effectiveness on a more complex data-guided protein folding simulation.

Structure of focal adhesion kinase in healthy heart versus pathological cardiac hypertrophy: A modeling and simulation study

Focal adhesion kinase (FAK) is required for signaling in the heart. S910 phosphorylated FAK is known to cause pathological cardiac hypertrophy. The switching of FAK between its inactive (-i), activated (-a) and hyperactive (-h) state is controlled by phosphorylation. FAK consists of three domains, namely: FERM, Kinase, and FAT joined by linkers L1 and L2. The structural basis of FAK phosphorylation and signaling to the downstream pathways is not understood. In this work, we carried out homology modeling and domain assembly of full length human iFAK and aFAK. 100 ns classical molecular dynamic simulations were performed using AMBER14 and effect of S910 phosphorylation on FAK was investigated. The iFAK model superposed on a small angel X-ray scattering (SAXS) derived model with RMSD of 1.18 Å for 590 Cα atoms. aFAK showed S910 phosphorylation site in L2 shielded by FERM. S910 phosphorylation in hFAK led to its exposure accompanied by a large conformational change and exposing the previously buried Grb2 interaction site responsible for causing cardiac hypertrophy. The models of FAK are in agreement with diverse experimental data and observed differences in biological action. Understanding the structure activity relationships of FAK in response to phosphorylation is important for its future therapeutic modulation.

Aryl-aryl interactions in designed peptide folds: Spectroscopic characteristics and optimal placement for structure stabilization

We have extended our studies of Trp/Trp to other Aryl/Aryl through-space interactions that stabilize hairpins and other small polypeptide folds. Herein we detail the NMR and CD spectroscopic features of these types of interactions. NMR data remains the best diagnostic for characterizing the common T-shape orientation. Designated as an edge-to-face (EtF or FtE) interaction, large ring current shifts are produced at the edge aryl ring hydrogens and, in most cases, large exciton couplets appear in the far UV circular dichroic (CD) spectrum. The preference for the face aryl in FtE clusters is W ≫ Y ≥ F (there are some exceptions in the Y/F order); this sequence corresponds to the order of fold stability enhancement and always predicts the amplitude of the lower energy feature of the exciton couplet in the CD spectrum. The CD spectra for FtE W/W, W/Y, Y/W, and Y/Y pairs all include an intense feature at 225-232 nm. An additional couplet feature seen for W/Y, W/F, Y/Y, and F/Y clusters, is a negative feature at 197-200 nm. Tyr/Tyr (as well as F/Y and F/F) interactions produce much smaller exciton couplet amplitudes. The Trp-cage fold was employed to search for the CD effects of other Trp/Trp and Trp/Tyr cluster geometries: several were identified. In this account, we provide additional examples of the application of cross-strand aryl/aryl clusters for the design of stable β-sheet models and a scale of fold stability increments associated with all possible FtE Ar/Ar clusters in several structural contexts. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 337-356, 2016.

Aggregation of Chameleon Peptides: Implications of α-Helicity in Fibril Formation

We investigate the relationship between the inherent secondary structure and aggregation propensity of peptides containing chameleon sequences (i.e., sequences that can adopt either α or β structure depending on context) using a combination of replica exchange molecular dynamics simulations, ion-mobility mass spectrometry, circular dichroism, and transmission electron microscopy. We focus on an eight-residue long chameleon sequence that can adopt an α-helical structure in the context of the iron-binding protein from Bacillus anthracis (PDB id 1JIG ) and a β-strand in the context of the baculovirus P35 protein (PDB id 1P35 ). We show that the isolated chameleon sequence is intrinsically disordered, interconverting between α-helical and β-rich conformations. The inherent conformational plasticity of the sequence can be constrained by addition of flanking residues with a given secondary structure propensity. Intriguingly, we show that the chameleon sequence with helical flanking residues aggregates rapidly into fibrils, whereas the chameleon sequence with flanking residues that favor β-conformations has weak aggregation propensity. This work sheds new insights into the possible role of α-helical intermediates in fibril formation.

How Efficient Is Replica Exchange Molecular Dynamics? An Analytic Approach

Replica exchange molecular dynamics (REMD) has become a standard technique for accelerating relaxation in biosimulations. Despite its widespread use, questions remain about its efficiency compared with conventional, constant temperature molecular dynamics (MD). An analytic approach is taken to describe the relative efficiency of REMD with respect to MD. This is applied to several simple two-state models and to several real proteins-protein L and the B domain of protein A-to predict the relative efficiency of REMD with respect to MD in actual applications. In agreement with others, we find the following: as long as there is a positive activation energy for folding, REMD is more efficient than MD; the effectiveness of REMD is strongly dependent on the activation enthalpy; and the efficiency of REMD for actual proteins is a strong function of the maximum temperature. Choosing the maximum temperature too high can result in REMD becoming significantly less efficient than conventional MD. A good rule of thumb appears to be to choose the maximum temperature of the REMD simulation slightly above the temperature at which the enthalpy for folding vanishes. Additionally, we find that the number of replicas in REMD, while important for simulations shorter than one or two relaxation times, has a minimal effect on the asymptotic efficiency of the method.

NXO beta structure mimicry: an ultrashort turn/hairpin mimic that folds in water

An NXO building block derived tetrapeptide mimic emulates a natural proline-glycine β-turn/hairpin in polar media, including water at room temperature.

Improved Generalized Born Solvent Model Parameters for Protein Simulations

The generalized Born (GB) model is one of the fastest implicit solvent models and it has become widely adopted for Molecular Dynamics (MD) simulations. This speed comes with tradeoffs, and many reports in the literature have pointed out weaknesses with GB models. Because the quality of a GB model is heavily affected by empirical parameters used in calculating solvation energy, in this work we have refit these parameters for GB-Neck, a recently developed GB model, in order to improve the accuracy of both the solvation energy and effective radii calculations. The data sets used for fitting are significantly larger than those used in the past. Comparing to other pairwise GB models like GB-OBC and the original GB-Neck, the new GB model (GB-Neck2) has better agreement to Poisson-Boltzmann (PB) in terms of reproducing solvation energies for a variety of systems ranging from peptides to proteins. Secondary structure preferences are also in much better agreement with those obtained from explicit solvent MD simulations. We also obtain near-quantitative reproduction of experimental structure and thermal stability profiles for several model peptides with varying secondary structure motifs. Extension to non-protein systems will be explored in the future.

A GLOBAL OPTIMIZATION SCHEME: KERNEL REPLICA EXCHANGE SIMULATION METHOD FOR PROTEIN FOLDING

A global optimization scheme which utilizes the framework of replica-exchange simulation and replaces the system exchange probability for jumping between different temperature replicas with the kernel exchange probability is brought out. The kernel exchange probability is calculated by taking into account the kernel part interaction, including protein–protein interactions only, with protein–solvent and solvent–solvent interactions approximated by a continuum solvation model. All the configurations are sampled with potential energies explicitly considering water molecules during the simulation while the energies obtained from continuum solvation model play as a scoring function to rank the conformation during the exchange process. It is shown that this method gives nearly identical total potential energy distribution in the solvated alanine dipeptide system compared with the results of the standard replica-exchange simulation in which much more number of replicas has to be employed. This optimization method is highly demonstrated in successfully folding a β-hairpin peptide, C-terminus (residue 41-56) of protein G, from the extended structure to native conformation.

Temperature-induced unfolding of epidermal growth factor (EGF): insight from molecular dynamics simulation

Thermal disruption of protein structure and function is a potentially powerful therapeutic vehicle. With the emerging nanoparticle-targeting and femtosecond laser technology, it is possible to deliver heating locally to specific molecules. It is therefore important to understand how fast a protein can unfold or lose its function at high temperatures, such as near the water boiling point. In this study, the thermal damage of EGF was investigated by combining the replica exchange (136 replicas) and conventional molecular dynamics simulations. The REMD simulation was employed to rigorously explore the free-energy landscape of EGF unfolding. Interestingly, besides the native and unfolded states, we also observed a distinct molten globule (MG) state that retained substantial amount of native contacts. Based on the understanding that which the unfolding of EGF is a three-state process, we have examined the unfolding kinetics of EGF (N-->MG and MG-->D) with multiple 20-ns conventional MD simulations. The Arrhenius prefactors and activation energy barriers determined from the simulation are within the range of previously studied proteins. In contrast to the thermal damage of cells and tissues which take place on the time scale of seconds to hours at relatively low temperatures, the denaturation of proteins occur in nanoseconds when the temperature of heat bath approaches the boiling point.

Modeling of peptides connecting the ligand-binding and transmembrane domains in the GluR2 glutamate receptor

Ligand-gated Glutamate receptors (GluR) mediate synaptic signals in the nervous system. Ionotropic GluRs of AMPA type, the subject of this study, are tetrameric assemblies of monomer subunits, each of which is constructed in a modular fashion from functional subdomains. The extracellular ligand-binding domain (LBD) changes its conformation upon binding of an agonist ligand followed by opening of a transmembrane (TM) ion channel. Peptides connecting the LBD and TM domains facilitate gating of the channel, and their structure and composition are important for the receptor functioning. In this study, we used replica exchange molecular dynamics (REMD) simulations to model S1M1 and S2M3 connecting peptides of the GluR2 receptor in two implicit solvents, water and interfacial water/lipid medium characterized by lower polarity. Propensity of these peptides to form helical structures was analyzed using helicity measure derived from the free energy of the simulated ensembles of structures. The S1M1 and S2M3 connecting peptides were not helical in our simulations in both dielectric environments in the absence of the rest of the protein. The structures of the LBD fragment with known high-resolution alpha-helical structure and of the TM3 helix were successfully predicted in the simulations, which in part validate our results. The S2M3 peptide, which is important in gating, formed a well-defined coil structure and salt-bridges with the S2 domain. The S1M1 peptide formed a loop structure via formation of internal salt-bridges. Potential implications of these structures on function of the receptor are discussed.

Computational approaches for the design of peptides with anti-breast cancer properties

Background: Breast cancer is the most common cancer among women. Tamoxifen is the preferred drug for estrogen receptor-positive breast cancer treatment, yet many of these cancers are intrinsically resistant to tamoxifen or acquire resistance during treatment. Therefore, scientists are searching for breast cancer drugs that have different molecular targets. Methodology: Recently, a computational approach was used to successfully design peptides that are new lead compounds against breast cancer. We used replica exchange molecular dynamics to predict the structure and dynamics of active peptides, leading to the discovery of smaller bioactive peptides. Conclusions: These analogs inhibit estrogen-dependent cell growth in a mouse uterine growth assay, a test showing reliable correlation with human breast cancer inhibition. We outline the computational methods that were tried and used along with the experimental information that led to the successful completion of this research.

Probing the nanosecond dynamics of a designed three-stranded beta-sheet with a massively parallel molecular dynamics simulation

Recently a temperature-jump FTIR study of a designed three-stranded sheet showing a fast relaxation time of approximately 140 +/- 20 ns was published. We performed massively parallel molecular dynamics simulations in explicit solvent to probe the structural events involved in this relaxation. While our simulations produce similar relaxation rates, the structural ensemble is broad. We observe the formation of turn structure, but only very weak interaction in the strand regions, which is consistent with the lack of strong backbone-backbone NOEs in previous structural NMR studies. These results suggest that either (D)P(D)P-II folds at time scales longer than 240 ns, or that (D)P(D)P-II is not a well-defined three-stranded beta-sheet. This work also provides an opportunity to compare the performance of several popular forcefield models against one another.

Structural insights for designed alanine-rich helices: comparing NMR helicity measures and conformational ensembles from molecular dynamics simulation

The temperature dependence of helical propensities for the peptides Ac-ZGG-(KAAAA)(3)X-NH(2) (Z = Y or G, X = A, K, and D-Arg) were studied both experimentally and by MD simulations. Good agreement is observed in both the absolute helical propensities as well as relative helical content along the sequence; the global minimum on the calculated free energy landscape corresponds to a single alpha-helical conformation running from K4 to A18 with some terminal fraying, particularly at the C-terminus. Energy component analysis shows that the single helix state has favorable intramolecular electrostatic energy due to hydrogen bonds, and that less-favorable two-helix globular states have favorable solvation energy. The central lysine residues do not appear to increase helicity; however, both experimental and simulation studies show increasing helicity in the series X = Ala --> Lys --> D-Arg. This C-capping preference was also experimentally confirmed in Ac-(KAAAA)(3)X-GY-NH(2) and (KAAAA)(3)X-GY-NH(2) sequences. The roles of the C-capping groups, and of lysines throughout the sequence, in the MD-derived ensembles are analyzed in detail.

Recent advances in implicit solvent-based methods for biomolecular simulations

Implicit solvent-based methods play an increasingly important role in molecular modeling of biomolecular structure and dynamics. Recent methodological developments have mainly focused on the extension of the generalized Born (GB) formalism for variable dielectric environments and accurate treatment of nonpolar solvation. Extensive efforts in parameterization of GB models and implicit solvent force fields have enabled ab initio simulation of protein folding to native or near-native structures. Another exciting area that has benefited from the advances in implicit solvent models is the development of constant pH molecular dynamics methods, which have recently been applied to the calculations of protein pK(a) values and the studies of pH-dependent peptide and protein folding.

Protein folding and unfolding by all-atom molecular dynamics simulations

Computational protein folding can be classified into pathway and sampling approaches. Here, we use the AMBER simulation package as an example to illustrate the protocols for all-atom molecular simulations of protein folding, including system setup, simulation, and analysis. We introduced two traditional pathway approaches: ab inito folding and high-temperature unfolding. The popular replica exchange method was chosen to represent sampling approaches. Our emphasis is placed on the analysis of the simulation trajectories, and some in-depth discussions are provided for commonly encountered problems.

Implicit modeling of nonpolar solvation for simulating protein folding and conformational transitions

Accurate description of the solvent environment is critical in computer simulations of protein structure and dynamics. An implicit treatment of solvent aims to capture the mean influence of water molecules on the solute via direct estimation of the solvation free energy. It has emerged as a powerful alternative to explicit solvent, and provides a favorable compromise between computational cost and level of detail. We review the current theory and techniques for implicit modeling of nonpolar solvation in the context of simulating protein folding and conformational transitions, and discuss the main directions for further development. It is demonstrated that the current surface area based nonpolar models have severe limitations, including insufficient description of the conformational dependence of solvation, over-estimation of the strength of pair-wise nonpolar interactions, and incorrect prediction of anti-cooperativity for three-body hydrophobic associations. We argue that, to improve beyond current level of accuracy of implicit solvent models, two important aspects of nonpolar solvation need to be incorporated, namely, the length-scale dependence of hydrophobic association and solvent screening of solute-solute dispersion interactions. We recognize that substantial challenges exist in constructing a sufficiently balanced, yet reasonably efficient, implicit solvent protein force field. Nonetheless, most of the fundamental problems are understood, and exciting progress has been made over the last few years. We believe that continual work along the frontiers outlined will greatly improve one's ability to study protein folding and large conformational transitions at atomistic detail.

Protein folding by zipping and assembly

How do proteins fold so quickly? Some denatured proteins fold to their native structures in only microseconds, on average, implying that there is a folding "mechanism," i.e., a particular set of events by which the protein short-circuits a broader conformational search. Predicting protein structures using atomically detailed physical models is currently challenging. The most definitive proof of a putative folding mechanism would be whether it speeds up protein structure prediction in physical models. In the zipping and assembly (ZA) mechanism, local structuring happens first at independent sites along the chain, then those structures either grow (zip) or coalescence (assemble) with other structures. Here, we apply the ZA search mechanism to protein native structure prediction by using the AMBER96 force field with a generalized Born/surface area implicit solvent model and sampling by replica exchange molecular dynamics. Starting from open denatured conformations, our algorithm, called the ZA method, converges to an average of 2.2 A from the Protein Data Bank native structures of eight of nine proteins that we tested, which ranged from 25 to 73 aa in length. In addition, experimental Phi values, where available on these proteins, are consistent with the predicted routes. We conclude that ZA is a viable model for how proteins physically fold. The present work also shows that physics-based force fields are quite good and that physics-based protein structure prediction may be practical, at least for some small proteins.

Computational design and experimental discovery of an antiestrogenic peptide derived from alpha-fetoprotein

Breast cancer is the most common cancer among women, and tamoxifen is the preferred drug for estrogen receptor-positive breast cancer treatment. Many of these cancers are intrinsically resistant to tamoxifen or acquire resistance during treatment. Consequently, there is an ongoing need for breast cancer drugs that have different molecular targets. Previous work has shown that 8-mer and cyclic 9-mer peptides inhibit breast cancer in mouse and rat models, interacting with an unsolved receptor, while peptides smaller than eight amino acids did not. We show that the use of replica exchange molecular dynamics predicts the structure and dynamics of active peptides, leading to the discovery of smaller peptides with full biological activity. Simulations identified smaller peptide analogues with the same conserved reverse turn demonstrated in the larger peptides. These analogues were synthesized and shown to inhibit estrogen-dependent cell growth in a mouse uterine growth assay, a test showing reliable correlation with human breast cancer inhibition.

Two-stage folding of HP-35 from ab initio simulations

Accurate ab initio simulation of protein folding is a critical step toward elucidation of protein-folding mechanisms. Here, we demonstrate highly accurate folding of the 35 residue villin headpiece subdomain (HP35) by all-atom molecular dynamics simulations using AMBER FF03 and the generalized-Born solvation model. In a set of 20 micros long simulations, the protein folded to the native state in multiple trajectories, with the lowest C(alpha) RMSD being 0.39 A for residues 2-34 (excluding residues 1 and 35). The native state had the highest population among all sampled conformations, and the center of most populated cluster had a C(alpha) RMSD of 1.63 A. Folding of this protein can be described as a two-stage process that followed a well-defined pathway. In the first stage, formation of helices II and III as a folding intermediate constituted the rate-limiting step and was initiated at a folding nucleus around residues Phe17 and Pro21. The folding intermediate further acted as a template that facilitated the folding and docking of helix I in the second stage. Detailed descriptions of the folding kinetics and the roles of key residues are presented.

Coupling of replica exchange simulations to a non-Boltzmann structure reservoir

Computing converged ensemble properties remains challenging for large biomolecules. Replica exchange molecular dynamics (REMD) can significantly increase the efficiency of conformational sampling by using high temperatures to escape kinetic traps. Several groups, including ours, introduced the idea of coupling replica exchange to a pre-converged, Boltzmann-populated reservoir, usually at a temperature higher than that of the highest temperature replica. This procedure reduces computational cost because the long simulation times needed for extensive sampling are only carried out for a single temperature. However, a weakness of the approach is that the Boltzmann-weighted reservoir can still be difficult to generate. We now present the idea of employing a non-Boltzmann reservoir, whose structures can be generated through more efficient conformational sampling methods. We demonstrate that the approach is rigorous and derive a correct statistical mechanical exchange criterion between the reservoir and the replicas that drives Boltzmann-weighted probabilities for the replicas. We test this approach on the trpzip2 peptide and demonstrate that the resulting thermal stability profile is essentially indistinguishable from that obtained using very long (>100 ns) standard REMD simulations. The convergence of this reservoir-aided REMD is significantly faster than for regular REMD. Furthermore, we demonstrate that modification of the exchange criterion is essential; REMD simulations using a standard exchange function with the non-Boltzmann reservoir produced incorrect results.

Folding free-energy landscape of villin headpiece subdomain from molecular dynamics simulations

High-accuracy ab initio folding has remained an elusive objective despite decades of effort. To explore the folding landscape of villin headpiece subdomain HP35, we conducted two sets of replica exchange molecular dynamics for 200 ns each and three sets of conventional microsecond-long molecular dynamics simulations, using AMBER FF03 force field and a generalized-Born solvation model. The protein folded consistently to the native state; the lowest C(alpha)-rmsd from the x-ray structure was 0.46 A, and the C(alpha)- rmsd of the center of the most populated cluster was 1.78 A at 300 K. ab initio simulations have previously not reached this level. The folding landscape of HP35 can be partitioned into the native, denatured, and two intermediate-state regions. The native state is separated from the major folding intermediate state by a small barrier, whereas a large barrier exists between the major folding intermediate and the denatured states. The melting temperature T(m) = 339 K extracted from the heat-capacity profile was in close agreement with the experimentally derived T(m) = 342 K. A comprehensive picture of the kinetics and thermodynamics of HP35 folding emerges when the results from replica exchange and conventional molecular dynamics simulations are combined.

Understanding the folding and stability of a zinc finger-based full sequence design protein with replica exchange molecular dynamics simulations

Full sequence design protein FSD-1 is a designed protein based on the motif of zinc finger protein. In this work, its folding mechanism and thermal stability are investigated using the replica exchange molecular dynamics model with the water molecules being treated explicitly. The results show that the folding of the FSD-1 is initiated by the hydrophobic collapse, which is accompanied with the formation of the C-terminal alpha-helix. Then the folding proceeds with the formation of the beta-hairpin and the further package of the hydrophobic core. Compared with the beta-hairpin, the alpha-helix has much higher stability. It is also found that the N-capping motif adopted by the FSD-1 contributes to the stability of the alpha-helix dramatically. The hydrophobic contacts made by the side chain of Tyr3 in the native state are essential for the stabilization of the beta-hairpin. It is also found that the folding of the N-terminal beta-hairpin and the C-terminal alpha-helix exhibits weak cooperativity, which is consistent with the experimental data. Meanwhile, the folding pathway is compared between the FSD-1 and the target zinc finger peptide, and the possible role of the zinc ion on the folding pathway of zinc finger is proposed. Proteins 2007. (c) 2007 Wiley-Liss, Inc.

Measuring cooperativity in the formation of a three-stranded beta sheet (double hairpin)

Recently validated chemical shift measures of hairpin structuring have been applied to a series of turn mutants of the Schenck-Gellman three-strand beta-sheet model with the aim of measuring the entropic advantage associated with aligning an additional strand onto an existing hairpin versus aligning the same two strands in an initial hairpin formation. In a four-state analysis (unfolded, 2 single hairpins, and the double hairpin fold in equilibrium) a cooperativity index can be defined as the factor by which the equilibrium constant for hairpin formation is improved when one strand is prestructured. This cooperativity index is 2.7 +/- 0.7 for hairpin formation about a stable D-Pro-Gly turn locus and increases to 7.6 +/- 1.2 for an Asn-Gly turn locus. The latter corresponds to a cooperativity induced DeltaDeltaG increment of 4.9 kJ/mol for the folding of a hairpin. Although larger than previous experimental measures of folding cooperativity in three-stranded sheets, the magnitude of this effect (which is considerably less than the TDeltaDeltaS expectation for prestructuring three or more beta-strand residue sites) likely reflects the intrinsic preference of these designed sequences for extended conformations. If similar or larger effects apply to protein beta-sheet folding, it is not surprising that particularly favorable hairpin alignments serve as nucleation sites in protein folding pathways.

Model systems for β-hairpins and β-sheets

beta-Sheets and alpha-helices are the two principal secondary structures in proteins. However, our understanding of beta-sheet structure lags behind that of alpha-helices, largely because, until recently, there was no model system to study the beta-sheet secondary structure in isolation. With the development of well-folded beta-hairpins, this is changing rapidly. Recent advances include: increased understanding of the relative contributions of turn, strand and sidechain interactions to beta-hairpin and beta-sheet stability, with the role of aromatic residues as a common subtheme; experimental and theoretical kinetic and thermodynamic studies of beta-hairpin and beta-sheet folding; de novo protein design, including all-beta structures, mixed alpha/beta motifs and switchable systems; and the creation of functional beta-hairpins.

The unfolded state of the villin headpiece helical subdomain: computational studies of the role of locally stabilized structure

The 36 residue villin headpiece helical subdomain (HP36) is one of the fastest cooperatively folding proteins, folding on the microsecond timescale. HP36's simple three helix topology, fast folding and small size have made it an attractive model system for computational and experimental studies of protein folding. Recent experimental studies have explored the denatured state of HP36 using fragment analysis coupled with relatively low-resolution spectroscopic techniques. These studies have shown that there is apparently only a small tendency to form locally stabilized secondary structure. Here, we complement the experimental studies by using replica exchange molecular dynamics with explicit solvent to investigate the structural features of these peptide models of unfolded HP36. To ensure convergence, two sets of simulations for each fragment were performed with different initial structures, and simulations were continued until these generated very similar final ensembles. These simulations reveal low populations of native-like structure and early folding events that cannot be resolved by experiment. For each fragment, calculated J-coupling constants and helical propensities are in good agreement with experimental trends. HP-1, corresponding to residues 41 to 53 and including the first alpha-helix, contains the highest helical population. HP-3, corresponding to residues 62 through 75 and including the third alpha-helix, contains a small population of helical turn residing at the N terminus while HP-2, corresponding to residues 52 through 61 and including the second alpha-helix, formed little to no structure in isolation. Overall, HP-1 was the only fragment to adopt a native-like conformation, but the low population suggests that formation of significant structure only occurs after formation of specific tertiary interactions.

Folding, misfolding, and amyloid protofibril formation of WW domain FBP28

We study the folding mechanism of a triple beta-strand WW domain from the Formin binding protein 28 (FBP28) at atomic resolution with explicit water model using replica exchange molecular dynamics computer simulations. Extended sampling over a wide range of temperatures to obtain the free energy, enthalpy, and entropy surfaces as a function of structural coordinates has been performed. Simulations were started from different configurations covering the folded and unfolded states. In the free energy landscape a transition state is identified and its structures and -values are compared with experimental data from a homologous protein, the prolyl-isomerase Pin1 WW domain. A stable intermediate state is found to accumulate during the simulation characterized by the carboxyl-terminal beta-strand 3 having misregistered hydrogen bonds and where the structural heterogeneity is due to nonnative turn II formation. Furthermore, the aggregation behavior of the FBP28 WW domain may be related to one such misfolded structure, which has a much lower free energy of dimer formation than that of the native dimer. Based on the misfolded dimer, aggregation to form protofibril structure is discussed.

A Second Look at Canonical Sampling of Biomolecules using Replica Exchange Simulation

The replica exchange approach, also called parallel tempering, is gaining popularity for biomolecular simulation. We ask whether the approach is likely to be efficient compared to standard simulation methods for fixed-temperature equilibrium sampling. To examine the issue, we make a number of straightforward observations on how "fast" high-temperature molecular simulations can be expected to run, as well as on how to characterize efficiency in replica exchange. Although our conclusions remain to be fully established, based on a range of results in the literature and some of our own work with a 50-atom peptide, we are not optimistic for the efficiency of replica exchange for canonical sampling of biomolecules.

Chemical shifts provide fold populations and register of beta hairpins and beta sheets

A detailed analysis of peptide backbone amide (H(N)) and H alpha chemical shifts reveals a consistent pattern for beta hairpins and three-stranded beta sheets. The H alpha's at non-hydrogen-bonded strand positions are inwardly directed and shifted downfield approximately 1 ppm due largely to an anisotropy contribution from the cross-strand amide function. The secondary structure associated H alpha shift deviations for the H-bonded strand positions are also positive but much smaller (0.1-0.3 ppm) and the turn residues display negative H alpha chemical shift deviations (CSDs). The pattern of (H(N)) shift deviations is an even better indicator of both hairpin formation and register, with the cross-strand H-bonded sites shifted downfield (also by approximately 1 ppm) and with diagnostic values for the first turn residue and the first strand position following the turn. These empirical observations, initially made for [2:2]/[2:4]-type-I' and -II' hairpins, are rationalized and can be extended to the analysis of other turns, hairpin classes ([3:5], [4:4]/[4:6]), and three-stranded peptide beta-sheet models. The H alpha's at non-hydrogen-bonded sites and (H(N))'s in the intervening H-bonded sites provide the largest and most dependable measures of hairpin structuring and can be used for melting studies; however the intrinsic temperature dependence of (H(N)) shifts deviations needs to reflect the extent of solvent sequestration in the folded state. Several observations made in the course of this study provide insights into beta-sheet folding mechanisms: (1) The magnitude of the (H(N)) shifts suggests that the cross-strand H-bonds in peptide hairpins are as short as those in protein beta sheets. (2) Even L-Pro-Gly turns, which are frequently used in unfolded controls for hairpin peptides, can support hairpin populations in aqueous fluoroalcohol media. (3) The good correlation between hairpin population estimates from cross-strand H-bonded (H(N)) shift deviations, H alpha shift deviations, and structuring shifts at the turn locus implies that hairpin folding transitions approximate two-state behavior.