Vincent A. Voelz

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.

Taming the complexity of protein folding.

Protein folding is an important problem in structural biology with significant medical implications, particularly for misfolding disorders like Alzheimers disease. Solving the folding problem will ultimately require a combination of theory and experiment, with theoretical models providing a comprehensive view of folding and experiments grounding these models in reality. Here we review progress towards this goal over the past decade, with an emphasis on recent theoretical advances that are empowering chemically detailed models of folding and the new results these technologies are providing. In particular, we discuss new insights made possible by Markov state models (MSMs), including the role of non-native contacts and the hub-like character of protein folded states.

Unfolded-State Dynamics and Structure of Protein L Characterized by Simulation and Experiment

While several experimental techniques now exist for characterizing protein unfolded states, all-atom simulation of unfolded states has been challenging due to the long time scales and conformational sampling required. We address this problem by using a combination of accelerated calculations on graphics processor units and distributed computing to simulate tens of thousands of molecular dynamics trajectories each up to approximately 10 mus (for a total aggregate simulation time of 127 ms). We used this approach in conjunction with Trp-Cys contact quenching experiments to characterize the unfolded structure and dynamics of protein L. We employed a polymer theory method to make quantitative comparisons between high-temperature simulated and chemically denatured experimental ensembles and find that reaction-limited quenching rates calculated from simulation agree remarkably well with experiment. In both experiment and simulation, we find that unfolded-state intramolecular diffusion rates are very slow compared to highly denatured chains and that a single-residue mutation can significantly alter unfolded-state dynamics and structure. This work suggests a view of the unfolded state in which surprisingly low diffusion rates could limit folding and opens the door for all-atom molecular simulation to be a useful predictive tool for characterizing protein unfolded states along with experiments that directly measure intramolecular diffusion.

Blind test of physics-based prediction of protein structures

We report here a multiprotein blind test of a computer method to predict native protein structures based solely on an all-atom physics-based force field. We use the AMBER 96 potential function with an implicit (GB/SA) model of solvation, combined with replica-exchange molecular-dynamics simulations. Coarse conformational sampling is performed using the zipping and assembly method (ZAM), an approach that is designed to mimic the putative physical routes of protein folding. ZAM was applied to the folding of six proteins, from 76 to 112 monomers in length, in CASP7, a community-wide blind test of protein structure prediction. Because these predictions have about the same level of accuracy as typical bioinformatics methods, and do not utilize information from databases of known native structures, this work opens up the possibility of predicting the structures of membrane proteins, synthetic peptides, or other foldable polymers, for which there is little prior knowledge of native structures. This approach may also be useful for predicting physical protein folding routes, non-native conformations, and other physical properties from amino acid sequences.

Exploring zipping and assembly as a protein folding principle

It has been proposed that proteins fold by a process called “Zipping and Assembly” (Z&A). Zipping refers to the growth of local substructures within the chain, and assembly refers to the coming together of already‐formed pieces. Our interest here is in whether Z&A is a general method that can fold most of sequence space, to global minima, efficiently. Using the HP model, we can address this question by enumerating full conformation and sequence spaces. We find that Z&A reaches the global energy minimum native states, even though it searches only a very small fraction of conformational space, for most sequences in the full sequence space. We find that Z&A, a mechanism‐based search, is more efficient in our tests than the replica exchange search method. Folding efficiency is increased for chains having: (a) small loop‐closure steps, consistent with observations by Plaxco et al. 1998;277;985–994 that folding rates correlate with contact order, (b) neither too few nor too many nucleation sites per chain, and (c) assembly steps that do not occur too early in the folding process. We find that the efficiency increases with chain length, although our range of chain lengths is limited. We believe these insights may be useful for developing faster protein conformational search algorithms. Proteins 2007.

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 peptides 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.

Probing antibody internal dynamics with fluorescence anisotropy and molecular dynamics simulations

The solution dynamics of antibodies are critical to antibody function. We explore the internal solution dynamics of antibody molecules through the combination of time-resolved fluorescence anisotropy experiments on IgG1 with more than two microseconds of all-atom molecular dynamics (MD) simulations in explicit water, an order of magnitude more than in previous simulations. We analyze the correlated motions with a mutual information entropy quantity, and examine state transition rates in a Markov-state model, to give coarse-grained descriptors of the motions. Our MD simulations show that while there are many strongly correlated motions, antibodies are highly flexible, with Fab and Fc domains constantly forming and breaking contacts, both polar and non-polar. We find that salt bridges break and reform, and not always with the same partners. While the MD simulations in explicit water give the right time scales for the motions, the simulated motions are about 3-fold faster than the experiments. Overall, the picture that emerges is that antibodies do not simply fluctuate around a single state of atomic contacts. Rather, in these large molecules, different atoms come in contact during different motions.

Calculation of rate spectra from noisy time series data

As the resolution of experiments to measure folding kinetics continues to improve, it has become imperative to avoid bias that may come with fitting data to a predetermined mechanistic model. Toward this end, we present a rate spectrum approach to analyze timescales present in kinetic data. Computing rate spectra of noisy time series data via numerical discrete inverse Laplace transform is an ill‐conditioned inverse problem, so a regularization procedure must be used to perform the calculation. Here, we show the results of different regularization procedures applied to noisy multiexponential and stretched exponential time series, as well as data from time‐resolved folding kinetics experiments. In each case, the rate spectrum method recapitulates the relevant distribution of timescales present in the data, with different priors on the rate amplitudes naturally corresponding to common biases toward simple phenomenological models. These results suggest an attractive alternative to the “Occams razor” philosophy of simply choosing models with the fewest number of relaxation rates. Proteins 2012.

A multiscale approach to sampling nascent peptide chains in the ribosomal exit tunnel.

We present a new multiscale method that combines all-atom molecular dynamics with coarse-grained sampling, towards the aim of bridging two levels of physiology: the atomic scale of protein side chains and small molecules, and the huge scale of macromolecular complexes like the ribosome. Our approach uses all-atom simulations of peptide (or other ligand) fragments to calculate local 3D spatial potentials of mean force (PMF). The individual fragment PMFs are then used as a potential for a coarse-grained chain representation of the entire molecule. Conformational space and sequence space are sampled efficiently using generalized ensemble Monte Carlo. Here, we apply this method to the study of nascent polypeptides inside the cavity of the ribosome exit tunnel. We show how the method can be used to explore the accessible conformational and sequence space of nascent polypeptide chains near the ribosome peptidyl transfer center (PTC), with the eventual aim of understanding the basis of specificity for co-translational regulation. The method has many potential applications to predicting binding specificity and design, and is sufficiently general to allow even greater separation of scales in future work.