Ab initio folding of proteins with all-atom discrete molecular dynamics

Discrete molecular dynamics (DMD) is a rapid sampling method used in protein folding and aggregation studies. Until now, DMD was used to perform simulations of simplified protein models in conjunction with structure-based force fields. Here, we develop an all-atom protein model and a transferable force field featuring packing, solvation, and environment-dependent hydrogen bond interactions. We performed folding simulations of six small proteins (20-60 residues) with distinct native structures by the replica exchange method. In all cases, native or near-native states were reached in simulations. For three small proteins, multiple folding transitions are observed, and the computationally characterized thermodynamics are in qualitative agreement with experiments. The predictive power of all-atom DMD highlights the importance of environment-dependent hydrogen bond interactions in modeling protein folding. The developed approach can be used for accurate and rapid sampling of conformational spaces of proteins and protein-protein complexes and applied to protein engineering and design of protein-protein interactions.     

Multiscale Coarse-Graining of the Protein Energy Landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states.     

Observation of two families of folding pathways of BBL

BBL is an independent folding domain of a large multienzyme complex, 2-oxoglutarate dehydrogenase. The folding mechanism of BBL is under debate between the views of noncooperative downhill-type and classical two-state. Extensive replica exchange molecular dynamics simulations of BBL in explicit solvent have shown some non-two-state behaviors despite no definitive evidence of downhill folding. In this work, we postprocess the replica exchange data using our roadmap-based MaxFlux reaction path algorithm to reveal atomically detailed folding pathways. A connected graph is used to organize and visualize the folding pathways initiated from random coils. High structural and transition heterogeneity is seen in the early stage of folding. Two main parallel folding pathways emerge in the later stage; one path shows that tertiary contact and helix formation develop at different stages of folding, whereas the other path exhibits concurrence of secondary and tertiary structure formation to some extent. Because the native state of BBL is sensitive to experimental conditions, we speculate that the relative predominance of the two pathways may vary with the protein construct and solvent conditions, possibly leading to the seeming discrepancy of experimental results. Our roadmap-based reaction path algorithm is a general tool to extract path information from replica exchange.     

Piecewise All-Atom SMD Simulations Reveal Key Secondary Structures in Luciferase Unfolding Pathway

Although the folding of single-domain proteins is well characterized theoretically and experimentally, the folding of large multidomain proteins is less well known. Firefly luciferase, a 550 residue three-domain protein, has been commonly used as a substrate to study chaperone reactions and as a model system for the study of folding of long polypeptide chains, including related phenomena such as cotranslational folding. Despite being characterized by various experimental techniques, the atomic-level contributions of various secondary structures of luciferase to its fold’s mechanical stability remain unknown. Here, we developed a piecewise approach for all-atom steered molecular dynamics simulations to examine specific secondary structures that resist mechanical unfolding while minimizing the amount of computational resources required by the large water box of standard all-atom steered molecular dynamics simulations. We validated the robustness of this approach with a small NI3C protein and used our approach to elucidate the specific secondary structures that provide the largest contributions to luciferase mechanostability. In doing so, we show that piecewise all-atom steered molecular dynamics simulations can provide novel atomic resolution details regarding mechanostability and can serve as a platform for novel mutagenesis studies as well as a point for comparison with high-resolution force spectroscopy experiments.     

All-atom ab initio folding of a diverse set of proteins

Natural proteins fold to a unique, thermodynamically dominant state. Modeling of the folding process and prediction of the native fold of proteins are two major unsolved problems in biophysics. Here, we show successful all-atom ab initio folding of a representative diverse set of proteins by using a minimalist transferable-energy model that consists of two-body atom-atom interactions, hydrogen bonding, and a local sequence-energy term that models sequence-specific chain stiffness. Starting from a random coil, the native-like structure was observed during replica exchange Monte Carlo (REMC) simulation for most proteins regardless of their structural classes; the lowest energy structure was close to native-in the range of 2-6 A root-mean-square deviation (rmsd). Our results demonstrate that the successful folding of a protein chain to its native state is governed by only a few crucial energetic terms.     

Free energy surfaces of miniproteins with a betabetaalpha motif: replica exchange molecular dynamics simulation with an implicit solvation model

Designed miniproteins with a betabetaalpha motif, such as BBA5, 1FSD, and 1PSV can serve as a benchmark set to test the validity of all-atom force fields with computer simulation, because they contain all the basic structural elements in protein folding. Unfortunately, it was found that the standard all-atom force fields with the generalized Born (GB) implicit solvation model tend to produce distorted free energy surfaces for the betabetaalpha proteins, not only because energetically those proteins need to be described by more balanced weights of the alpha- and beta-strands, but also because the GB implicit solvation model suffers from overestimated salt bridge effects. In an attempt to resolve these problems, we have modified one of the standard all-atom force fields in conjunction with the GB model, such that each native state of the betabetaalpha proteins is in its free energy minimum state with reasonable energy barriers separating local minima. With this modified energy model, the free energy contour map in each protein was constructed from the replica exchange molecular dynamics REMD simulation. The resulting free energy surfaces are significantly improved in comparison with previous simulation results and consistent with general views on small protein folding behaviors with realistic topology and energetics of all three proteins.     

Reproducible polypeptide folding and structure prediction using molecular dynamics simulations

The folding of a polypeptide from an extended state to a well-defined conformation is studied using microsecond classical molecular dynamics (MD) simulations and replica exchange molecular dynamics (REMD) simulations in explicit solvent and in vacuo. It is shown that the solvated peptide folds many times in the REMD simulations but only a few times in the conventional simulations. From the folding events in the classical simulations we estimate an approximate folding time of 1-2 micros. The REMD simulations allow enough sampling to deduce a detailed Gibbs free energy landscape in three dimensions. The global minimum of the energy landscape corresponds to the native state of the peptide as determined previously by nuclear magnetic resonance (NMR) experiments. Starting from an extended state it takes about 50 ns before the native structure appears in the REMD simulations, about an order of magnitude faster than conventional MD. The calculated melting curve is in good qualitative agreement with experiment. In vacuo, the peptide collapses rapidly to a conformation that is substantially different from the native state in solvent.     

Simulated annealing coupled replica exchange molecular dynamics—An efficient conformational sampling method

Molecular dynamics simulated annealing (SA-MD) simulations are frequently used for refinement and optimization of peptide and protein structures. Depending on the simulation conditions and simulation length SA-MD simulations can be trapped in locally stable conformations far from the global optimum. As an alternative replica exchange molecular dynamics (RexMD) simulations can be used which allow exchanges between high and low simulation temperatures at all stages of the simulation. A significant drawback of RexMD simulations is, however, the rapid increase of the replica number with increasing system size to cover a desired temperature range. A combined SA-MD and RexMD approach termed SA-RexMD is suggested that employs a small number of replicas (4) and starts initially with a set of high simulation temperatures followed by gradual cooling of the set of temperatures until a target temperature has been reached. The protocol has been applied for the folding of several peptide systems and for the refinement of protein model structures. In all the cases, the SA-RexMD method turned out to be significantly more efficient in reaching low energy structures and also structures close to experiment compared to continuous MD simulations at the target temperature and to SA-MD simulations at the same computational demand. The approach is well suited for applications in structure refinement and for systematic force field improvement.     

Coarse-grained models of protein folding: toy models or predictive tools?

Coarse-grained models are emerging as a practical alternative to all-atom simulations for the characterization of protein folding mechanisms over long time scales. While a decade ago minimalist toy models were mainly designed to test general hypotheses on the principles regulating protein folding, the latest coarse-grained models are increasingly realistic and can be used to characterize quantitatively the detailed folding mechanism of specific proteins. The ability of such models to reproduce the essential features of folding dynamics suggests that each single atomic degree of freedom is not by itself particularly relevant to folding and supports a statistical mechanical approach to characterize folding transitions. When combined with more refined models and with experimental studies, the systematic investigation of protein systems and complexes using coarse-grained models can advance our theoretical understanding of the actual organizing principles that emerge from the complex network of interactions among protein atomic constituents.     

An evolutionary strategy for all-atom folding of the 60-amino-acid bacterial ribosomal protein l20

We have investigated an evolutionary algorithm for de novo all-atom folding of the bacterial ribosomal protein L20. We report results of two simulations that converge to near-native conformations of this 60-amino-acid, four-helix protein. We observe a steady increase of "native content" in both simulated ensembles and a large number of near-native conformations in their final populations. We argue that these structures represent a significant fraction of the low-energy metastable conformations, which characterize the folding funnel of this protein. These data validate our all-atom free-energy force field PFF01 for tertiary structure prediction of a previously inaccessible structural family of proteins. We also compare folding simulations of the evolutionary algorithm with the basin-hopping technique for the Trp-cage protein. We find that the evolutionary algorithm generates a dynamic memory in the simulated population, which leads to faster overall convergence.     

From coarse-grain to all-atom: toward multiscale analysis of protein landscapes

Multiscale methods are becoming increasingly promising as a way to characterize the dynamics of large protein systems on biologically relevant time-scales. The underlying assumption in multiscale simulations is that it is possible to move reliably between different resolutions. We present a method that efficiently generates realistic all-atom protein structures starting from the C(alpha) atom positions, as obtained for instance from extensive coarse-grain simulations. The method, a reconstruction algorithm for coarse-grain structures (RACOGS), is validated by reconstructing ensembles of coarse-grain structures obtained during folding simulations of the proteins src-SH3 and S6. The results show that RACOGS consistently produces low energy, all-atom structures. A comparison of the free energy landscapes calculated using the coarse-grain structures versus the all-atom structures shows good correspondence and little distortion in the protein folding landscape.     

All-atom Monte Carlo simulation of GCAA RNA folding

We report a detailed all-atom simulation of the folding of the GCAA RNA tetraloop. The GCAA tetraloop motif is a very common and thermodynamically stable secondary structure in natural RNAs. We use our simulation methods to study the folding behavior of a 12-base GCAA tetraloop structure with a four-base helix adjacent to the tetraloop proper. We implement an all-atom Monte Carlo (MC) simulation of RNA structural dynamics using a Go potential. Molecular dynamics (MD) simulation of RNA and protein has realistic energetics and sterics, but is extremely expensive in terms of computational time. By coarsely treating non-covalent energetics, but retaining all-atom sterics and entropic effects, all-atom MC techniques are a useful method for the study of protein and now RNA. We observe a sharp folding transition for this structure, and in simulations at room temperature the state histogram shows three distinct minima: an unfolded state (U), a more narrow intermediated state (I), and a narrow folded state (F). The intermediate consists primarily of structures with the GCAA loop and some helix hydrogen bonds formed. Repeated kinetic folding simulations reveal that the number of helix base-pairs forms a simple 1D reaction coordinate for the I-->N transition.     

All-atom fast protein folding simulations: the villin headpiece

We provide a fast folding simulation using an all-atom solute, implicit solvent method that eliminates the need for treating solvent degrees of freedom. The folding simulations for the 36-residue villin headpiece exhibit close correspondence with the landmark all-atom explicit solvent molecular dynamics simulations by Duan and Kollman (Duan & Kollman, Science 1998;282:740-744; Duan, Wang, & Kollman, Proc Natl Acad Sci USA 1998;95:9897-9902). Our implicit solvent approach uses only an entry-level single CPU PC with comparable throughput ( approximately 4 nsec/day) to the DK supercomputer simulation. The native state is shown to be stable. Our 200-nsec folding trajectory agrees with the DK simulation in displaying a burst phase, a rapid initial shrinkage, a highly native-like binding site structure, and more.     

Enhanced sampling of peptide and protein conformations using replica exchange simulations with a peptide backbone biasing-potential

During replica exchange molecular dynamics (RexMD) simulations, several replicas of a system are simulated at different temperatures in parallel allowing for exchange between replicas at frequent intervals. This technique allows significantly improved sampling of conformational space and is increasingly being used for structure prediction of peptides and proteins. A drawback of the standard temperature RexMD is the rapid increase of the replica number with increasing system size to cover a desired temperature range. In an effort to limit the number of replicas, a new Hamiltonian-RexMD method has been developed that is specifically designed to enhance the sampling of peptide and protein conformations by applying various levels of a backbone biasing potential for each replica run. The biasing potential lowers the barrier for backbone dihedral transitions and promotes enhanced peptide backbone transitions along the replica coordinate. The application on several peptide cases including in all cases explicit solvent indicates significantly improved conformational sampling when compared with standard MD simulations. This was achieved with a very modest number of 5-7 replicas for each simulation system making it ideally suited for peptide and protein folding simulations as well as refinement of protein model structures in the presence of explicit solvent.     

Studies of folding and misfolding using simplified models

Computer simulations are as vital to our studies of biological systems as experiments. They bridge and rationalize experimental observations, extend the experimental "field of view", which is often limited to a specific time or length scale, and, most importantly, provide novel insights into biological systems, offering hypotheses about yet-to-be uncovered phenomena. These hypotheses spur further experimental discoveries. Simplified molecular models have a special place in the field of computational biology. Branded as less accurate than all-atom protein models, they have offered what all-atom molecular dynamics simulations could not--the resolution of the length and time scales of biological phenomena. Not only have simplified models proven to be accurate in explaining or reproducing several biological phenomena, they have also offered a novel multiscale computational strategy for accessing a broad range of time and length scales upon integration with traditional all-atom simulations. Recent computer simulations of simplified models have shaken or advanced the established understanding of biological phenomena. It was demonstrated that simplified models can be as accurate as traditional molecular dynamics approaches in identifying native conformations of proteins. Their application to protein structure prediction yielded phenomenal accuracy in recapitulating native protein conformations. New studies that utilize the synergy of simplified protein models with all-atom models and experiments yielded novel insights into complex biological processes, such as protein folding, aggregation and the formation of large protein complexes.     

Predicting Peptide Structures in Native Proteins from Physical Simulations of Fragments

It has long been proposed that much of the information encoding how a protein folds is contained locally in the peptide chain. Here we present a large-scale simulation study designed to examine the extent to which conformations of peptide fragments in water predict native conformations in proteins. We perform replica exchange molecular dynamics (REMD) simulations of 872 8-mer, 12-mer, and 16-mer peptide fragments from 13 proteins using the AMBER 96 force field and the OBC implicit solvent model. To analyze the simulations, we compute various contact-based metrics, such as contact probability, and then apply Bayesian classifier methods to infer which metastable contacts are likely to be native vs. non-native. We find that a simple measure, the observed contact probability, is largely more predictive of a peptide''s native structure in the protein than combinations of metrics or multi-body components. Our best classification model is a logistic regression model that can achieve up to 63% correct classifications for 8-mers, 71% for 12-mers, and 76% for 16-mers. We validate these results on fragments of a protein outside our training set. We conclude that local structure provides information to solve some but not all of the conformational search problem. These results help improve our understanding of folding mechanisms, and have implications for improving physics-based conformational sampling and structure prediction using all-atom molecular simulations.     

Peptide folding simulations

Developments in the design of small peptides that mimic proteins in complexity, recent advances in nanosecond time-resolved spectroscopy methods to study peptides and the development of modern, highly parallel simulation algorithms have come together to give us a detailed picture of peptide folding dynamics. Two newly implemented simulation techniques, parallel replica dynamics and replica exchange molecular dynamics, can now describe directly from simulations the kinetics and thermodynamics of peptide formation, respectively. Given these developments, the simulation community now has the tools to verify and validate simulation protocols and models (forcefields).     

Accelerating all-atom protein folding simulations through reduced dihedral barriers

Protein folding requires extensive changes of backbone and sidechain dihedral angles, whose energy barriers constitute obstacles for the folding kinetics. Folding of small proteins is furthermore thought to be path-independent. Here, we propose that time-consuming all-atom protein folding simulations may be accelerated through a reduction of the dihedral barriers of the force field. In order to investigate this hypothesis, we performed various folding simulations of two small proteins. We report an acceleration towards smaller root-mean-square deviations from the native protein structure using our proposed method.     

Greedy replica exchange algorithm for heterogeneous computing grids

Replica exchange molecular dynamics (REMD) has become a valuable tool in studying complex biomolecular systems. However, its application on distributed computing grids is limited by the heterogeneity of this environment. In this study, we propose a REMD implementation referred to as greedy REMD (gREMD) suitable for computations on heterogeneous grids. To decentralize replica management, gREMD utilizes a precomputed schedule of exchange attempts between temperatures. Our comparison of gREMD against standard REMD suggests four main conclusions. First, gREMD accelerates grid REMD simulations by as much as 40 %. Second, gREMD increases CPU utilization rates in grid REMD by up to 60 %. Third, we argue that gREMD is expected to maintain approximately constant CPU utilization rates and simulation wall-clock times with the increase in the number of replicas. Finally, we show that gREMD correctly implements the REMD algorithm and reproduces the conformational ensemble of a short peptide sampled in our previous standard REMD simulations. We believe that gREMD can find its place in large-scale REMD simulations on heterogeneous computing grids.

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Graphical Abstract Standard replica exchange molecular dynamics (REMD) typically requires all replicas to complete prior to initiation of the replica exchange protocol. Greedy REMD decentralizes this process and therefore only requires a replica and its predetermined exchange partner to have finished simulations prior to initiating replica exchange. Because greedy REMD reduces the idle time associated with replica exchange tasks, it becomes particularly well suited for performing REMD on heterogeneous distributed computing environments.

     

From helix-coil transitions to protein folding

An evolution of procedures to simulate protein structure and folding pathways is described. From an initial focus on the helix-coil transition and on hydrogen-bonding and hydrophobic interactions, our original attempts to determine protein structure and folding pathways were based on an experimental approach. Experiments on the oxidative folding of reduced bovine pancreatic ribonuclease A (RNase A) led to a mechanism by which the molecule folded to the native structure by a minimum of four different pathways. The experiments with RNase A were followed by development of a molecular mechanics approach, first, making use of global optimization procedures and then with molecular dynamics (MD), evolving from an all-atom to a united-residue model. This hierarchical MD approach facilitated probing of the folding trajectory to longer time scales than with all-atom MD, and hence led to the determination of complete folding trajectories, thus far for a protein containing as many as 75 amino acid residues. With increasing refinement of the computational procedures, the computed results are coming closer to experimental observations, providing an understanding as to how physics directs the folding process.