Ab initio simulation of a 57-residue protein in explicit solvent reproduces the native conformation in the lowest free-energy cluster

An enhanced conformational sampling method, multicanonical molecular dynamics (McMD), was applied to the ab intio folding of the 57-residue first repeat of human glutamyl- prolyl-tRNA synthetase (EPRS-R1) in explicit solvent. The simulation started from a fully extended structure of EPRS-R1 and did not utilize prior structural knowledge. A canonical ensemble, which is a conformational ensemble thermodynamically probable at an arbitrary temperature, was constructed by reweighting the sampled structures. Conformational clusters were obtained from the canonical ensemble at 300 K, and the largest cluster (i.e., the lowest free-energy cluster), which contained 34% of the structures in the ensemble, was characterized by the highest similarity to the NMR structure relative to all alternative clusters. This lowest free-energy cluster included native-like structures composed of two anti-parallel α-helices. The canonical ensemble at 300 K also showed that a short Gly-containing segment, which adopts an α-helix in the native structure, has a tendency to be structurally disordered. Atomic-level analyses demonstrated clearly that inter-residue hydrophobic interactions drive the helix formation of the Gly-containing segment, and that increasing the hydrophobic contacts accompanies exclusion of water molecules from the vicinity of this segment. This study has shown, for the first time, that the free-energy landscape of a structurally well-ordered protein of about 60 residues is obtainable with an all atom model in explicit water without prior structural knowledge.     

Molecular mechanism for stabilizing a short helical peptide studied by generalized-ensemble simulations with explicit solvent

We study the folding mechanism of an analog of the C-peptide of ribonuclease A in explicit water by a replica-exchange multicanonical molecular dynamics simulation based on all-atom models. The multicanonical weight factor was determined by the combined use of the multicanonical replica-exchange method and the replica-exchange multicanonical algorithm. Using statistically reliable data thus obtained, we have examined the free-energy landscape of the peptide system. The global-minimum free-energy state in the landscape at room temperature has an alpha-helix structure with a distortion near the N-terminus. The state also has a salt bridge between Glu(-)-2 and Arg(+)-10 and an aromatic-aromatic interaction between Phe-8 and His(+)-12, both of which have been observed in x-ray and other experimental measurements. Principal component analysis clearly shows the different roles of these side-chain interactions in the peptide folding. The side-chain interaction between Phe-8 and His(+)-12 greatly enhances the stability of helical structure toward the C-terminal end, whereas the salt bridge between Glu(-)-2 and Arg(+)-10 mainly works as a restraint to prevent the alpha-helix structure from extending to the N-terminus. The free-energy landscape of C-peptide reveals a funnel-like shape where all of these interactions consistently exist only in the global-minimum state. This is the major reason why the native structure of the short helical peptide shows significant stability at low temperatures.     

Free-energy landscape of a chameleon sequence in explicit water and its inherent alpha/beta bifacial property

A sequence in yeast MATalpha2/MCM1/DNA complex that folds into alpha-helix or beta-hairpin depending on the surroundings has been known as "chameleon" sequence. We obtained the free-energy landscape of this sequence by using a generalized-ensemble method, multicanonical molecular dynamics simulation, to sample the conformational space. The system was expressed with an all-atom model in explicit water, and the initial conformation for the simulation was a random one. The free-energy landscape demonstrated that this sequence inherently has an ability to form either alpha or beta structure: The conformational distribution in the landscape consisted of two alpha-helical clusters with different packing patterns of hydrophobic residues, and four beta-hairpin clusters with different strand-strand interaction patterns. Narrow pathways connecting the clusters were found, and analysis on the pathways showed that a compact structure formed at the N-terminal root of the chameleon sequence controls the cluster-cluster transitions. The free-energy landscape indicates that a small conditional change induces alpha-beta transitions. Additional unfolding simulations done with replacing amino acids showed that the chameleon sequence has an advantage to form an alpha-helix. Current study may be useful to understand the mechanism of diseases resulting from abnormal chain folding, such as amyloid disease.     

Conformational energy landscape of the acyl pocket loop in acetylcholinesterase: a Monte Carlo-generalized Born model study

The X-ray crystal structure of the reaction product of acetylcholinesterase (AChE) with the inhibitor diisopropylphosphorofluoridate (DFP) showed significant structural displacement in a loop segment of residues 287-290. To understand this conformational selection, a Monte Carlo (MC) simulation study was performed of the energy landscape for the loop segment. A computational strategy was applied by using a combined simulated annealing and room temperature Metropolis sampling approach with solvent polarization modeled by a generalized Born (GB) approximation. Results from thermal annealing reveal a landscape topology of broader basin opening and greater distribution of energies for the displaced loop conformation, while the ensemble average of conformations at 298 K favored a shift in populations toward the native by a free-energy difference in good agreement with the estimated experimental value. Residue motions along a reaction profile of loop conformational reorganization are proposed where Arg-289 is critical in determining electrostatic effects of solvent interaction versus Coulombic charging.     

Simulation study on the disordered state of an Alzheimer's beta amyloid peptide Abeta(12 36) in water consisting of random-structural, beta-structural, and helical clusters

The monomeric Alzheimer's beta amyloid peptide, Abeta, is known to adopt a disordered state in water at room temperature, and a circular dichroism (CD) spectroscopy experiment has provided the secondary-structure contents for the disordered state: 70% random, 25% beta-structural, and 5% helical. We performed an enhanced conformational sampling (multicanonical molecular dynamics simulation) of a 25-residue segment (residues 12-36) of Abeta in explicit water and obtained the conformational ensemble over a wide temperature range. The secondary-structure contents calculated from the conformational ensemble at 300 degrees K reproduced the experimental secondary-structure contents. The constructed free-energy landscape at 300 degrees K was not plain but rugged with five clearly distinguishable clusters, and each cluster had its own characteristic tertiary structure: a helix-structural cluster, two beta-structural clusters, and two random-structural clusters. This indicates that the contribution from the five individual clusters determines the secondary-structure contents experimentally measured. The helical cluster had a similarity with a stable helical structure for monomeric Abeta in 2,2,2-trifluoroethanol (TFE)/water determined by an NMR experiment: The positions of helices in the helical cluster were the same as those in the NMR structure, and the residue-residue contact patterns were also similar with those of the NMR structure. The cluster-cluster separation in the conformational space indicates that free-energy barriers separate the clusters at 300 degrees K. The two beta-structural clusters were characterized by different strand-strand hydrogen-bond (H-bond) patterns, suggesting that the free-energy barrier between the two clusters is due to the H-bond rearrangements.     

Free-energy function for discriminating the native fold of a protein from misfolded decoys

In this study, free-energy function (FEF) for discriminating the native fold of a protein from misfolded decoys was investigated. It is a physics-based function using an all-atom model, which comprises the hydration entropy (HE) and the total dehydration penalty (TDP). The HE is calculated using a hybrid of a statistical-mechanical theory applied to a molecular model for water and the morphometric approach. The energetic component is suitably taken into account in a simple manner as the TDP. On the basis of the results from a careful test of the FEF, which have been performed for 118 proteins in representative decoy sets, we show that its performance is distinctly superior to that of any other function. The FEF varies largely from model to model for the candidate models for the native structure (NS) obtained from nuclear magnetic resonance experiments, but we can find models or a model for which the FEF becomes lower than for any of the decoy structures. A decoy set is not suited to the test of a free-energy or potential function in cases where a protein isolated from a protein complex is considered and the structure in the complex is used as the model NS of the isolated protein without any change or where portions of the terminus sides of a protein are removed and the percentage of the secondary structures lost due to the removal is significantly high. As these findings are made possible, we can assume that our FEF precisely captures the features of the true NS.     

Folding free-energy landscape of a 10-residue mini-protein, chignolin

Chignolin is an artificial mini-protein composed of 10 residues (GYDPETGTWG) that has been shown to cooperatively fold into a beta-hairpin structure in water. We extensively explored the conformational space of chignolin using a 180-ns multicanonical molecular dynamics (MD) simulation and analyzed its folding free-energy landscape. In the MD trajectory, we found structures that satisfy 99% of the experimental restraints and are quite close to the experimentally determined structures with C(alpha) root-mean-square-deviations of less than 0.5 Angstroms. These structures formed a large cluster in the conformational space with the largest probability of existence, agreeing well with the experiment.     

Transition state of a SH3 domain detected with principle component analysis and a charge-neutralized all-atom protein model

The src SH3 domain has been known to be a two-state folder near room temperature. However, in a previous study with an all-atom model simulation near room temperature, the transition state of this protein was not successfully detected on a free-energy profile using two axes: the radius of gyration (R(g)) and native contact reproduction ratio (Q value). In this study, we focused on an atom packing effect to characterize the transition state and tried another analysis to detect it. To explore the atom packing effect more efficiently, we introduced a charge-neutralized all-atom model, where all of the atoms in the protein and water molecules were treated explicitly, but their partial atomic charges were set to zero. Ten molecular dynamics simulations were performed starting from the native structure at 300 K, where the simulation length of each run was 90 ns, and the protein unfolded in all runs. The integrated trajectories (10 x 90 = 900 ns) were analyzed by a principal component analysis (PCA) and showed a clear free-energy barrier between folded- and unfolded-state conformational clusters in a conformational space generated by PCA. There were segments that largely deformed when the conformation passed through the free-energy barrier. These segments correlated well with the structural core regions characterized by large phi-values, and the atom-packing changes correlated with the conformational deformations. Interestingly, using the same simulation data, no significant barrier was found in a free-energy profile using the R(g) and Q values for the coordinate axes. These results suggest that the atom packing effect may be one of the most important determinants of the transition state.     

Equilibrium conformational dynamics in an RNA tetraloop from massively parallel molecular dynamics

Conformational equilibrium within the ubiquitous GNRA tetraloop motif was simulated at the ensemble level, including 10 000 independent all-atom molecular dynamics trajectories totaling over 110 µs of simulation time. This robust sampling reveals a highly dynamic structure comprised of 15 conformational microstates. We assemble a Markov model that includes transitions ranging from the nanosecond to microsecond timescales and is dominated by six key loop conformations that contribute to fluctuations around the native state. Mining of the Protein Data Bank provides an abundance of structures in which GNRA tetraloops participate in tertiary contact formation. Most predominantly observed in the experimental data are interactions of the native loop structure within the minor groove of adjacent helical regions. Additionally, a second trend is observed in which the tetraloop assumes non-native conformations while participating in multiple tertiary contacts, in some cases involving multiple possible loop conformations. This tetraloop flexibility can act to counterbalance the energetic penalty associated with assuming non-native loop structures in forming tertiary contacts. The GNRA motif has thus evolved not only to readily participate in simple tertiary interactions involving native loop structure, but also to easily adapt tetraloop secondary conformation in order to participate in larger, more complex tertiary interactions.     

An accurate, residue-level, pair potential of mean force for folding and binding based on the distance-scaled, ideal-gas reference state

Structure prediction on a genomic scale requires a simplified energy function that can efficiently sample the conformational space of polypeptide chains. A good energy function at minimum should discriminate native structures against decoys. Here, we show that a recently developed, residue-specific, all-atom knowledge-based potential (167 atomic types) based on distance-scaled, finite ideal-gas reference state (DFIRE-all-atom) can be substantially simplified to 20 residue types located at side-chain center of mass (DFIRE-SCM) without a significant change in its capability of structure discrimination. Using 96 standard multiple decoy sets, we show that there is only a small reduction (from 80% to 78%) in success rate of ranking native structures as the top 1. The success rate is higher than two previously developed, all-atom distance-dependent statistical pair potentials. Applied to structure selections of 21 docking decoys without modification, the DFIRE-SCM potential is 29% more successful in recognizing native complex structures than an all-atom statistical potential trained by a database of dimeric interfaces. The potential also achieves 92% accuracy in distinguishing true dimeric interfaces from artificial crystal interfaces. In addition, the DFIRE potential with the C(alpha) positions as the interaction centers recognizes 123 native structures out of a comprehensive 125-protein TOUCHSTONE decoy set in which each protein has 24,000 decoys with only C(alpha) positions. Furthermore, the performance by DFIRE-SCM on newly established 25 monomeric and 31 docking Rosetta-decoy sets is comparable to (or better than in the case of monomeric decoy sets) that of a recently developed, all-atom Rosetta energy function enhanced with an orientation-dependent hydrogen bonding potential.     

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. I. Backbone structure of enkephalin

A new methodology for theoretically predicting the native, three-dimensional structure of a polypeptide is presented. Based on equilibrium statistical mechanics, an algorithm has been designed to determine the probable conformation of a polypeptide by calculating conditional free-energy maps for each residue of the macromolecule. The conditional free-energy map of each residue is computed from a set of probability integrals, obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. By locating the region(s) of lowest free energy for each map, the probable conformation for each residue can be identified. The native structure of the polypeptide is assumed to be the combination of the probable conformations of the individual residues. All multidimensional probability integrals are evaluated by an adaptive Monte Carlo algorithm (SMAPPS —Statistical-Mechanical Algorithm for Predicting Protein Structure). The Monte Carlo algorithm searches the entire conformational space, adjusting itself automatically to concentrate its sampling in regions where the magnitude of the integrand is largest (“importance sampling”). No assumptions are made about the native conformation. The only prior knowledge necessary for the prediction of the native conformation is the amino acid sequence of the polypeptide. To test the effectiveness of the algorithm, SMAPPS was applied to the prediction of the native conformation of the backbone of Met-enkephalin, a pentapeptide. In the calculations, only the backbone dihedral angles (? and ψ) were allowed to vary; all side-chain (χ) and peptide-bond (ω) dihedral angles were kept fixed at the values corresponding to the alleged global minimum energy previously determined by direct energy minimization. For each conformation generated randomly by the Monte Carlo algorithm, the total conformational energy of the polypeptide was obtained from established empirical potential energy functions. Solvent effects were not included in the computations. With this initial application of SMAPPS , three distinct low-free-energy β-bend structures of Met-enkephalin were found. In particular, one of the structures has a conformation remarkably similar to the one associated with the previously alleged global minimum energy. The two additional structures of the pentapeptide have conformational energies lower than the previously computed low-energy structure. However, the Monte Carlo results are in agreement with an improved energy-minimization procedure. These initial results on the backbone structure of Met-enkephalin indicate that an equilibrium statistical-mechanical procedure, coupled with an adaptive Monte Carlo algorithm, can overcome many of the problems associated with the standard methods of direct energy minimization.     

Identification of cooperative folding units in a set of native proteins.

Cooperative unfolding penalties are calculated by statistically evaluating an ensemble of denatured states derived from native structures. The ensemble of denatured states is determined by dividing the native protein into short contiguous segments and defining all possible combinations of native, i.e., interacting, and non-native, i.e., non-interacting, segments. We use a novel knowledge-based scoring function, derived from a set of non-homologous proteins in the Protein Data Bank, to describe the interactions among residues. This procedure is used for the structural identification of cooperative folding cores for four globular proteins: bovine pancreatic trypsin inhibitor, horse heart cytochrome c, French bean plastocyanin, and staphylococcal nuclease. The theoretical folding units are shown to correspond to regions that exhibit enhanced stability against denaturation as determined from experimental hydrogen exchange protection factors. Using a sequence similarity score for related sequences, we show that, in addition to residues necessary for enzymatic function, those amino acids comprising structurally important folding cores are also preferentially conserved during evolution. This implies that the identified folding cores may be part of an array of fundamental structural folding units.     

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

Molecular dynamics (MD) simulations using all-atom and explicit solvent models provide valuable information on the detailed behavior of protein–partner substrate binding at the atomic level. As the power of computational resources increase, MD simulations are being used more widely and easily. However, it is still difficult to investigate the thermodynamic properties of protein–partner substrate binding and protein folding with conventional MD simulations. Enhanced sampling methods have been developed to sample conformations that reflect equilibrium conditions in a more efficient manner than conventional MD simulations, thereby allowing the construction of accurate free-energy landscapes. In this review, we discuss these enhanced sampling methods using a series of case-by-case examples. In particular, we review enhanced sampling methods conforming to trivial trajectory parallelization, virtual-system coupled multicanonical MD, and adaptive lambda square dynamics. These methods have been recently developed based on the existing method of multicanonical MD simulation. Their applications are reviewed with an emphasis on describing their practical implementation. In our concluding remarks we explore extensions of the enhanced sampling methods that may allow for even more efficient sampling.     

Refinement of comparative models of protein structure by using multicanonical molecular dynamics simulations

Comparative modelling is a powerful method that easily predicts a considerably accurate structure of a protein by using a template structure having a similar amino-acid sequence to the target protein. However, in the region where the amino-acid sequence is different between the target and the template, the predicted structure remains unreliable. In such a case, the model has to be refined. In the present study, we explored the possibility of a molecular dynamics-based method, using the human SAP Src Homology 2 (SH2) domain as the modelling target. The multicanonical method was used to alleviate the multiple-minima problem and the generalised Born/surface area model was used to reduce the computational cost. In addition, position restraints were imposed on the atoms in the reliable regions to avoid unnecessary conformational sampling. We analyzed the conformational distribution of the ligand-recognition loop of the domain and found that the most populated conformational clusters in the ensemble of the model agreed well with one of the two major clusters in the ensemble of the reference simulation starting from the crystal structure. This demonstrates that the current refinement method can significantly improve the accuracy of an unreliable region in a comparative model.     

Application of Enhanced Sampling Monte Carlo Methods for High-Resolution Protein-Protein Docking in Rosetta

The high-resolution refinement of docked protein-protein complexes can provide valuable structural and mechanistic insight into protein complex formation complementing experiment. Monte Carlo (MC) based approaches are frequently applied to sample putative interaction geometries of proteins including also possible conformational changes of the binding partners. In order to explore efficiency improvements of the MC sampling, several enhanced sampling techniques, including temperature or Hamiltonian replica exchange and well-tempered ensemble approaches, have been combined with the MC method and were evaluated on 20 protein complexes using unbound partner structures. The well-tempered ensemble method combined with a 2-dimensional temperature and Hamiltonian replica exchange scheme (WTE-H-REMC) was identified as the most efficient search strategy. Comparison with prolonged MC searches indicates that the WTE-H-REMC approach requires approximately 5 times fewer MC steps to identify near native docking geometries compared to conventional MC searches.     

A Correspondence Between Solution-State Dynamics of an Individual Protein and the Sequence and Conformational Diversity of its Family

Conformational ensembles are increasingly recognized as a useful representation to describe fundamental relationships between protein structure, dynamics and function. Here we present an ensemble of ubiquitin in solution that is created by sampling conformational space without experimental information using “Backrub” motions inspired by alternative conformations observed in sub-Angstrom resolution crystal structures. Backrub-generated structures are then selected to produce an ensemble that optimizes agreement with nuclear magnetic resonance (NMR) Residual Dipolar Couplings (RDCs). Using this ensemble, we probe two proposed relationships between properties of protein ensembles: (i) a link between native-state dynamics and the conformational heterogeneity observed in crystal structures, and (ii) a relation between dynamics of an individual protein and the conformational variability explored by its natural family. We show that the Backrub motional mechanism can simultaneously explore protein native-state dynamics measured by RDCs, encompass the conformational variability present in ubiquitin complex structures and facilitate sampling of conformational and sequence variability matching those occurring in the ubiquitin protein family. Our results thus support an overall relation between protein dynamics and conformational changes enabling sequence changes in evolution. More practically, the presented method can be applied to improve protein design predictions by accounting for intrinsic native-state dynamics.     

Protein-Protein Docking with Dynamic Residue Protonation States

Protein-protein interactions depend on a host of environmental factors. Local pH conditions influence the interactions through the protonation states of the ionizable residues that can change upon binding. In this work, we present a pH-sensitive docking approach, pHDock, that can sample side-chain protonation states of five ionizable residues (Asp, Glu, His, Tyr, Lys) on-the-fly during the docking simulation. pHDock produces successful local docking funnels in approximately half (79/161) the protein complexes, including 19 cases where standard RosettaDock fails. pHDock also performs better than the two control cases comprising docking at pH 7.0 or using fixed, predetermined protonation states. On average, the top-ranked pHDock structures have lower interface RMSDs and recover more native interface residue-residue contacts and hydrogen bonds compared to RosettaDock. Addition of backbone flexibility using a computationally-generated conformational ensemble further improves native contact and hydrogen bond recovery in the top-ranked structures. Although pHDock is designed to improve docking, it also successfully predicts a large pH-dependent binding affinity change in the Fc–FcRn complex, suggesting that it can be exploited to improve affinity predictions. The approaches in the study contribute to the goal of structural simulations of whole-cell protein-protein interactions including all the environmental factors, and they can be further expanded for pH-sensitive protein design.     

Interaction of human leukocyte elastase with a N-aryl azetidinone suicide substrate: Conformational analyses based on the mechanism of action of serine proteinases

The three-dimensional interaction of the enzyme-activated (suicide) inhibitor AA 231-1 [N(2-chloromethyl)-3,3-difluoro-azetidin-2-one] with human leukocyte elastase has been studied using computer graphics and molecular mechanics. Systematic conformational analyses and energy minimizations have been performed for the inhibitor AA 231-1 and its presumed complexes formed during the enzymatic process of inactivation, i.e., the Michaelis complex, the acyl-enzyme, and the inactivated enzyme with the covalently bound inhibitor. The β-lactam ring characteristics of modeled AA 231-1 were in agreement with crystallo-graphic data of related structures. Lowest energy conformatinos were found when the angle between the planes of the β-lactam ring and that of its phenyl substituent was about −60 or 60°. To study the interaction with the enzyne, the enzyme-inhibitor complexes were constructed by docking the inhibitor in the active site using enzyme coordinates from an X-ray crystallographic structure. The whole enzyme structure was used for conformational analyses and energy mechanics. Favorable conformations for the Michaelis complex have been obtained in which the carbonyl oxygen of the inhibitor was located in the oxyanion hole and the hydroxyl of Ser195 was in position to interact with the β-lactam carbonyl carbon on the α face of AA 231-1. Simulations of the approach of the benzylic carbon by the nucleophilic amino acid His40 or His57 through an S_N2 displacement on the halomethyl group of AA 231-1 were performed. The results agreed with the alkylation of the imidazole nitroge Nϵ2 of His57 leading to the inactivated enzyme (bis-adduct form).