Quantitative comparison of villin headpiece subdomain simulations and triplet-triplet energy transfer experiments.

As the fastest folding protein, the villin headpiece (HP35) serves as an important bridge between simulation and experimental studies of protein folding. Despite the simplicity of this system, experiments continue to reveal a number of surprises, including structure in the unfolded state and complex equilibrium dynamics near the native state. Using 2.5 ms of molecular dynamics and Markov state models, we connect to current experimental results in three ways. First, we present and validate a novel method for the quantitative prediction of triplet-triplet energy transfer experiments. Second, we construct a many-state model for HP35 that is consistent with previous experiments. Finally, we predict contact-formation time traces for all 1,225 possible triplet-triplet energy transfer experiments on HP35.

Factors determining electrostatic fields in molecular dynamics simulations of the Ras/effector interface.

Using molecular dynamics simulations, we explore geometric and physical factors contributing to calculated electrostatic fields at the binding surface of the GTPase Ras with a spectroscopically labeled variant of a downstream effector, the Ras-binding domain of Ral guanine nucleotide dissociation stimulator (RalGDS). A related system (differing by mutation of one amino acid) has been studied in our group using vibrational Stark effect spectroscopy, a technique sensitive to electrostatic fields. Electrostatic fields were computed using the AMBER 2003 force field and averaged over snapshots from molecular dynamics simulation. We investigate geometric factors by exploring how the orientation of the spectroscopic probe changes on Ras-effector binding. In addition, we explore the physical origin of electrostatic fields at our spectroscopic probe by comparing contributions to the field from discrete components of the system, such as explicit solvent, residues on the Ras surface, and residues on the RalGDS surface. These models support our experimental hypothesis that vibrational Stark shifts are caused by Ras binding to its effector and not the structural rearrangements of the effector surface or probe reorientation on Ras-effector binding, for at least some of our experimental probes. These calculations provide physical insight into the origin, magnitude, and importance of electrostatic fields in protein-protein interactions and suggest new experiments to probe the field's role in protein docking.

Vibrational Stark effect spectroscopy at the interface of Ras and Rap1A bound to the Ras binding domain of RalGDS reveals an electrostatic mechanism for protein-protein interaction.

Electrostatic fields at the interface of the Ras binding domain of the protein Ral guanine nucleotide dissociation stimulator (RalGDS) with the structurally analogous GTPases Ras and Rap1A were measured with vibrational Stark effect (VSE) spectroscopy. Eleven residues on the surface of RalGDS that participate in this protein-protein interaction were systematically mutated to cysteine and subsequently converted to cyanocysteine in order to introduce a nitrile VSE probe in the form of the thiocyanate (SCN) functional group. The measured SCN absorption energy on the monomeric protein was compared with solvent-accessible surface area (SASA) calculations and solutions to the Poisson-Boltzmann equation using Boltzmann-weighted structural snapshots from molecular dynamics simulations. We found a weak negative correlation between SASA and measured absorption energy, indicating that water exposure of protein surface amino acids can be estimated from experimental measurement of the magnitude of the thiocyanate absorption energy. We found no correlation between calculated field and measured absorption energy. These results highlight the complex structural and electrostatic nature of the protein-water interface. The SCN-labeled RalGDS was incubated with either wild-type Ras or wild-type Rap1A, and the formation of the docked complex was confirmed by measurement of the dissociation constant of the interaction. The change in absorption energy of the thiocyanate functional group due to complex formation was related to the change in electrostatic field experienced by the nitrile functional group when the protein-protein interface forms. At some locations, the nitrile experiences the same shift in field when bound to Ras and Rap1A, but at others, the change in field is dramatically different. These differences identify residues on the surface of RalGDS that direct the specificity of RalGDS binding to its in vivo binding partner, Rap1A, through an electrostatic mechanism.

Bayesian inference for Brownian dynamics.

We present a Bayesian method for inferring the potential energy experienced by a particle subject to Brownian dynamics. Assuming polynomial potentials, the best polynomial order can be determined by analytical computation of a series of Bayes factors. The coefficients can be estimated from marginal posterior distributions. The method is applicable not only for the motion of an actual Brownian particle but to many kinds of single degree-of-freedom trajectories with Gaussian noise and short, nonzero correlation times.

Enhanced modeling via network theory: Adaptive sampling of Markov state models.

Computer simulations can complement experiments by providing insight into molecular kinetics with atomic resolution. Unfortunately, even the most powerful supercomputers can only simulate small systems for short timescales, leaving modeling of most biologically relevant systems and timescales intractable. In this work, however, we show that molecular simulations driven by adaptive sampling of networks called Markov State Models (MSMs) can yield tremendous time and resource savings, allowing previously intractable calculations to be performed on a routine basis on existing hardware. We also introduce a distance metric (based on the relative entropy) for comparing MSMs. We primarily employ this metric to judge the convergence of various sampling schemes but it could also be employed to assess the effects of perturbations to a system (e.g. determining how changing the temperature or making a mutation changes a system's dynamics).

Bayesian detection of intensity changes in single molecule and molecular dynamics trajectories.

Single molecule spectroscopy experiments and molecular dynamics simulations have several profound features in common, chief among which is that both follow the dynamics of some degrees of freedom of a single molecule over time. The analysis is essentially the same: one investigates the changes in the degrees of freedom followed. For instance, in a single molecule fluorescence experiment, the degree of freedom is often the number of photons detected in some time period. In this article, we introduce a straightforward Bayesian method for detecting if and when changes occurred. In contrast to methods based upon maximum likelihood estimates, a Bayesian approach allows for a more systematic means not only to change point detection but also to cluster the data into states. Most importantly, the Bayesian method supplies a simpler hypothesis testing framework. Although we focus on Poisson-distributed data, the Bayesian methods outlined here can in principle be applied to data sampled from any distribution.

Bayesian single-exponential kinetics in single-molecule experiments and simulations.

In this work, we develop a fully Bayesian method for the calculation of probability distributions of single-exponential rates for any single-molecule process. These distributions can even be derived when no transitions from one state to another have been observed, since in that case the data can be used to estimate a lower bound on the rate. Using a Bayesian hypothesis test, one can easily test whether a transition occurs at the same rate or at different rates in two data sets. We illustrate these methods with molecular dynamics simulations of the folding of a beta-sheet protein. However, the theory presented here can be used on any data from simulation or experiment for which a two-state description is appropriate.

Combining molecular dynamics with bayesian analysis to predict and evaluate ligand-binding mutations in influenza hemagglutinin.

Influenza virus attaches to and infects target cells via binding of cell-surface glycans by the viral hemagglutinin. This binding specificity is considered a major reason why avian influenza is typically poorly transmitted between humans, while swine influenza is better transmitted due to glycan similarity between the human and swine upper respiratory tract. Predicting mutations that control glycan binding is thus important to continued surveillance against new pandemic influenza strains. We have designed a molecular-dynamics approach for scoring potential mutants with predictive power for both receptor-binding-domain and allosteric mutations similar to those identified from clinical isolates of avian influenza. We have performed thousands of simulations of 17 different hemagglutinin mutants totaling >1 ms in length and employ a bayesian model to rank mutations that disrupt the stability of the hemagglutinin-ligand complex. Based on our simulations, we predict a significantly increased k(off) for seven of these mutants. This means of using molecular dynamics analysis to make experimentally verifiable predictions offers a potentially general method to identify ligand-binding mutants, particularly allosteric ones. Our analysis of ligand dissociation provides a means to evaluate mutants prior to experimental mutagenesis and testing and constitutes an important step toward understanding the determinants of ligand binding by H5N1 influenza.

The Fip35 WW domain folds with structural and mechanistic heterogeneity in molecular dynamics simulations.

We describe molecular dynamics simulations resulting in the folding the Fip35 Hpin1 WW domain. The simulations were run on a distributed set of graphics processors, which are capable of providing up to two orders of magnitude faster computation than conventional processors. Using the Folding@home distributed computing system, we generated thousands of independent trajectories in an implicit solvent model, totaling over 2.73 ms of simulations. A small number of these trajectories folded; the folding proceeded along several distinct routes and the system folded into two distinct three-stranded beta-sheet conformations, showing that the folding mechanism of this system is distinctly heterogeneous.

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.

Accelerating molecular dynamic simulation on the cell processor and Playstation 3.

Implementation of molecular dynamics (MD) calculations on novel architectures will vastly increase its power to calculate the physical properties of complex systems. Herein, we detail algorithmic advances developed to accelerate MD simulations on the Cell processor, a commodity processor found in PlayStation 3 (PS3). In particular, we discuss issues regarding memory access versus computation and the types of calculations which are best suited for streaming processors such as the Cell, focusing on implicit solvation models. We conclude with a comparison of improved performance on the PS3's Cell processor over more traditional processors.

Heterogeneity even at the speed limit of folding: large-scale molecular dynamics study of a fast-folding variant of the villin headpiece.

We have performed molecular dynamics simulations on a set of nine unfolded conformations of the fastest-folding protein yet discovered, a variant of the villin headpiece subdomain (HP-35 NleNle). The simulations were generated using a new distributed computing method, yielding hundreds of trajectories each on a time scale comparable to the experimental folding time, despite the large (10,000 atom) size of the simulation system. This strategy eliminates the need to assume a two-state kinetic model or to build a Markov state model. The relaxation to the folded state at 300 K from the unfolded configurations (generated by simulation at 373 K) was monitored by a method intended to reflect the experimental observable (quenching of tryptophan by histidine). We also monitored the relaxation to the native state by directly comparing structural snapshots with the native state. The rate of relaxation to the native state and the number of resolvable kinetic time scales both depend upon starting structure. Moreover, starting structures with folding rates most similar to experiment show some native-like structure in the N-terminal helix (helix 1) and the phenylalanine residues constituting the hydrophobic core, suggesting that these elements may exist in the experimentally relevant unfolded state. Our large-scale simulation data reveal kinetic complexity not resolved in the experimental data. Based on these findings, we propose additional experiments to further probe the kinetics of villin folding.

Bayesian update method for adaptive weighted sampling.

Exploring conformational spaces is still a challenging task for simulations of complex systems. One way to enhance such a task is weighted sampling, e.g., by assigning high weights to regions that are rarely sampled. It is, however, difficult to estimate adequate weights beforehand, and therefore adaptive methods are desired. Here we present a method for adaptive weighted sampling based on Bayesian inference. Within the framework of Bayesian inference, we develop an update scheme in which the information from previous data is stored in a prior distribution which is then updated to a posterior distribution according to new data. The method proposed here is particularly well suited for distributed computing, in which one must deal with rapid influxes of large amounts of data.