Vijay S. Pande

Current Status of the AMOEBA Polarizable Force Field

Molecular force fields have been approaching a generational transition over the past several years, moving away from well-established and well-tuned, but intrinsically limited, fixed point charge models toward more intricate and expensive polarizable models that should allow more accurate description of molecular properties. The recently introduced AMOEBA force field is a leading publicly available example of this next generation of theoretical model, but to date, it has only received relatively limited validation, which we address here. We show that the AMOEBA force field is in fact a significant improvement over fixed charge models for small molecule structural and thermodynamic observables in particular, although further fine-tuning is necessary to describe solvation free energies of drug-like small molecules, dynamical properties away from ambient conditions, and possible improvements in aromatic interactions. State of the art electronic structure calculations reveal generally very good agreement with AMOEBA for demanding problems such as relative conformational energies of the alanine tetrapeptide and isomers of water sulfate complexes. AMOEBA is shown to be especially successful on protein-ligand binding and computational X-ray crystallography where polarization and accurate electrostatics are critical.

Absolute comparison of simulated and experimental protein-folding dynamics

Protein folding is difficult to simulate with classical molecular dynamics. Secondary structure motifs such as α-helices and β-hairpins can form in 0.1–10 µs (ref. 1), whereas small proteins have been shown to fold completely in tens of microseconds. The longest folding simulation to date is a single 1-µs simulation of the villin headpiece; however, such single runs may miss many features of the folding process as it is a heterogeneous reaction involving an ensemble of transition states. Here, we have used a distributed computing implementation to produce tens of thousands of 5–20-ns trajectories (700 µs) to simulate mutants of the designed mini-protein BBA5. The fast relaxation dynamics these predict were compared with the results of laser temperature-jump experiments. Our computational predictions are in excellent agreement with the experimentally determined mean folding times and equilibrium constants. The rapid folding of BBA5 is due to the swift formation of secondary structure. The convergence of experimentally and computationally accessible timescales will allow the comparison of absolute quantities characterizing in vitro and in silico (computed) protein folding.

Accelerating molecular dynamic simulation on graphics processing units

We describe a complete implementation of all‐atom protein molecular dynamics running entirely on a graphics processing unit (GPU), including all standard force field terms, integration, constraints, and implicit solvent. We discuss the design of our algorithms and important optimizations needed to fully take advantage of a GPU. We evaluate its performance, and show that it can be more than 700 times faster than a conventional implementation running on a single CPU core.

On the transition coordinate for protein folding

To understand the kinetics of protein folding, we introduce the concept of a “transition coordinate” which is defined to be the coordinate along which the system progresses most slowly. As a practical implementation of this concept, we define the transmission coefficient for any conformation to be the probability for a chain with the given conformation to fold before it unfolds. Since the transmission coefficient can serve as the best possible measure of kinetic distance for a system, we present two methods by which we can determine how closely any parameter of the system approximates the transmission coefficient. As we determine that the transmission coefficient for a short-chain heteropolymer system is dominated by entropic factors, we have chosen to illustrate the methods mentioned by applying them to geometrical properties of the system such as the number of native contacts and the looplength distribution. We find that these coordinates are not good approximations of the transmission coefficient and therefore, cannot adequately describe the kinetics of protein folding.

Molecular simulation of ab initio protein folding for a millisecond folder NTL9(1–39)

To date, the slowest-folding proteins folded ab initio by all-atom molecular dynamics simulations have had folding times in the range of nanoseconds to microseconds. We report simulations of several folding trajectories of NTL9(1-39), a protein which has a folding time of approximately 1.5 ms. Distributed molecular dynamics simulations in implicit solvent on GPU processors were used to generate ensembles of trajectories out to approximately 40 micros for several temperatures and starting states. At a temperature less than the melting point of the force field, we observe a small number of productive folding events, consistent with predictions from a model of parallel uncoupled two-state simulations. The posterior distribution of the folding rate predicted from the data agrees well with the experimental folding rate (approximately 640/s). Markov State Models (MSMs) built from the data show a gap in the implied time scales indicative of two-state folding and heterogeneous pathways connecting diffuse mesoscopic substates. Structural analysis of the 14 out of 2000 macrostates transited by the top 10 folding pathways reveals that native-like pairing between strands 1 and 2 only occurs for macrostates with p(fold) > 0.5, suggesting beta(12) hairpin formation may be rate-limiting. We believe that using simulation data such as these to seed adaptive resampling simulations will be a promising new method for achieving statistically converged descriptions of folding landscapes at longer time scales than ever before.

Solvation free energies of amino acid side chain analogs for common molecular mechanics water models.

Quantitative free energy computation involves both using a model that is sufficiently faithful to the experimental system under study (accuracy) and establishing statistically meaningful measures of the uncertainties resulting from finite sampling (precision). In order to examine the accuracy of a range of common water models used for protein simulation for their solute/solvent properties, we calculate the free energy of hydration of 15 amino acid side chain analogs derived from the OPLS-AA parameter set with the TIP3P, TIP4P, SPC, SPC/E, TIP3P-MOD, and TIP4P-Ew water models. We achieve a high degree of statistical precision in our simulations, obtaining uncertainties for the free energy of hydration of 0.02-0.06 kcal/mol, equivalent to that obtained in experimental hydration free energy measurements of the same molecules. We find that TIP3P-MOD, a model designed to give improved free energy of hydration for methane, gives uniformly the closest match to experiment; we also find that the ability to accurately model pure water properties does not necessarily predict ability to predict solute/solvent behavior. We also evaluate the free energies of a number of novel modifications of TIP3P designed as a proof of concept that it is possible to obtain much better solute/solvent free energetic behavior without substantially negatively affecting pure water properties. We decrease the average error to zero while reducing the root mean square error below that of any of the published water models, with measured liquid water properties remaining almost constant with respect to our perturbations. This demonstrates there is still both room for improvement within current fixed-charge biomolecular force fields and significant parameter flexibility to make these improvements. Recent research in computational efficiency of free energy methods allows us to perform simulations on a local cluster that previously required large scale distributed computing, performing four times as much computational work in approximately a tenth of the computer time as a similar study a year ago.

Everything you wanted to know about Markov State Models but were afraid to ask

Simulating protein folding has been a challenging problem for decades due to the long timescales involved (compared with what is possible to simulate) and the challenges of gaining insight from the complex nature of the resulting simulation data. Markov State Models (MSMs) present a means to tackle both of these challenges, yielding simulations on experimentally relevant timescales, statistical significance, and coarse grained representations that are readily humanly understandable. Here, we review this method with the intended audience of non-experts, in order to introduce the method to a broader audience. We review the motivations, methods, and caveats of MSMs, as well as some recent highlights of applications of the method. We conclude by discussing how this approach is part of a paradigm shift in how one uses simulations, away from anecdotal single-trajectory approaches to a more comprehensive statistical approach.

Simulation of Folding of a Small Alpha-helical Protein in Atomistic Detail using Worldwide- distributed Computing

By employing thousands of PCs and new worldwide-distributed computing techniques, we have simulated in atomistic detail the folding of a fast-folding 36-residue alpha-helical protein from the villin headpiece. The total simulated time exceeds 300 micros, orders of magnitude more than previous simulations of a molecule of this size. Starting from an extended state, we obtained an ensemble of folded structures, which is on average 1.7A and 1.9A away from the native state in C(alpha) distance-based root-mean-square deviation (dRMS) and C(beta) dRMS sense, respectively. The folding mechanism of villin is most consistent with the hydrophobic collapse view of folding: the molecule collapses non-specifically very quickly ( approximately 20ns), which greatly reduces the size of the conformational space that needs to be explored in search of the native state. The conformational search in the collapsed state appears to be rate-limited by the formation of the aromatic core: in a significant fraction of our simulations, the C-terminal phenylalanine residue packs improperly with the rest of the hydrophobic core. We suggest that the breaking of this interaction may be the rate-determining step in the course of folding. On the basis of our simulations we estimate the folding rate of villin to be approximately 5micros. By analyzing the average features of the folded ensemble obtained by simulation, we see that the mean folded structure is more similar to the native fold than any individual folded structure. This finding highlights the need for simulating ensembles of molecules and averaging the results in an experiment-like fashion if meaningful comparison between simulation and experiment is to be attempted. Moreover, our results demonstrate that (1) the computational methodology exists to simulate the multi-microsecond regime using distributed computing and (2) that potential sets used to describe interatomic interactions may be sufficiently accurate to reach the folded state, at least for small proteins. We conclude with a comparison between our results and current protein-folding theory.

Progress and challenges in the automated construction of Markov state models for full protein systems

Markov state models (MSMs) are a powerful tool for modeling both the thermodynamics and kinetics of molecular systems. In addition, they provide a rigorous means to combine information from multiple sources into a single model and to direct future simulations/experiments to minimize uncertainties in the model. However, constructing MSMs is challenging because doing so requires decomposing the extremely high dimensional and rugged free energy landscape of a molecular system into long-lived states, also called metastable states. Thus, their application has generally required significant chemical intuition and hand-tuning. To address this limitation we have developed a toolkit for automating the construction of MSMs called MSMBUILDER (available at https://simtk.org/home/msmbuilder). In this work we demonstrate the application of MSMBUILDER to the villin headpiece (HP-35 NleNle), one of the smallest and fastest folding proteins. We show that the resulting MSM captures both the thermodynamics and kinetics of the original molecular dynamics of the system. As a first step toward experimental validation of our methodology we show that our model provides accurate structure prediction and that the longest timescale events correspond to folding.

Alchemical free energy methods for drug discovery: progress and challenges

Improved rational drug design methods are needed to lower the cost and increase the success rate of drug discovery and development. Alchemical binding free energy calculations, one potential tool for rational design, have progressed rapidly over the past decade, but still fall short of providing robust tools for pharmaceutical engineering. Recent studies, especially on model receptor systems, have clarified many of the challenges that must be overcome for robust predictions of binding affinity to be useful in rational design. In this review, inspired by a recent joint academic/industry meeting organized by the authors, we discuss these challenges and suggest a number of promising approaches for overcoming them.