Kyle A. Beauchamp

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.

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.

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.

To Milliseconds and Beyond: Challenges in the Simulation of Protein Folding

Quantitatively accurate all-atom molecular dynamics (MD) simulations of protein folding have long been considered a holy grail of computational biology. Due to the large system sizes and long timescales involved, such a pursuit was for many years computationally intractable. Further, sufficiently accurate forcefields needed to be developed in order to realistically model folding. This decade, however, saw the first reports of folding simulations describing kinetics on the order of milliseconds, placing many proteins firmly within reach of these methods. Progress in sampling and forcefield accuracy, however, presents a new challenge: how to turn huge MD datasets into scientific understanding. Here, we review recent progress in MD simulation techniques and show how the vast datasets generated by such techniques present new challenges for analysis. We critically discuss the state of the art, including reaction coordinate and Markov state model (MSM) methods, and provide a perspective for the future.

MDTraj: A Modern Open Library for the Analysis of Molecular Dynamics Trajectories

As molecular dynamics (MD) simulations continue to evolve into powerful computational tools for studying complex biomolecular systems, the necessity of flexible and easy-to-use software tools for the analysis of these simulations is growing. We have developed MDTraj, a modern, lightweight, and fast software package for analyzing MD simulations. MDTraj reads and writes trajectory data in a wide variety of commonly used formats. It provides a large number of trajectory analysis capabilities including minimal root-mean-square-deviation calculations, secondary structure assignment, and the extraction of common order parameters. The package has a strong focus on interoperability with the wider scientific Python ecosystem, bridging the gap between MD data and the rapidly growing collection of industry-standard statistical analysis and visualization tools in Python. MDTraj is a powerful and user-friendly software package that simplifies the analysis of MD data and connects these datasets with the modern interactive data science software ecosystem in Python.

Markov State Model Reveals Folding and Functional Dynamics in Ultra-Long MD Trajectories

Two strategies have been recently employed to push molecular simulation to long, biologically relevant time scales: projection-based analysis of results from specialized hardware producing a small number of ultralong trajectories and the statistical interpretation of massive parallel sampling performed with Markov state models (MSMs). Here, we assess the MSM as an analysis method by constructing a Markov model from ultralong trajectories, specifically two previously reported 100 μs trajectories of the FiP35 WW domain (Shaw, D. E. Science 2010, 330, 341-346). We find that the MSM approach yields novel insights. It discovers new statistically significant folding pathways, in which either beta-hairpin of the WW domain can form first. The rates of this process approach experimental values in a direct quantitative comparison (time scales of 5.0 μs and 100 ns), within a factor of ∼2. Finally, the hub-like topology of the MSM and identification of a holo conformation predicts how WW domains may function through a conformational selection mechanism.

Simple few-state models reveal hidden complexity in protein folding

Markov state models constructed from molecular dynamics simulations have recently shown success at modeling protein folding kinetics. Here we introduce two methods, flux PCCA+ (FPCCA+) and sliding constraint rate estimation (SCRE), that allow accurate rate models from protein folding simulations. We apply these techniques to fourteen massive simulation datasets generated by Anton and Folding@home. Our protocol quantitatively identifies the suitability of describing each system using two-state kinetics and predicts experimentally detectable deviations from two-state behavior. An analysis of the villin headpiece and FiP35 WW domain detects multiple native substates that are consistent with experimental data. Applying the same protocol to GTT, NTL9, and protein G suggests that some beta containing proteins can form long-lived native-like states with small register shifts. Even the simplest protein systems show folding and functional dynamics involving three or more states.

Investigating How Peptide Length and a Pathogenic Mutation Modify the Structural Ensemble of Amyloid Beta Monomer

The aggregation of amyloid beta (Aβ) peptides plays an important role in the development of Alzheimers disease. Despite extensive effort, it has been difficult to characterize the secondary and tertiary structure of the Aβ monomer, the starting point for aggregation, due to its hydrophobicity and high aggregation propensity. Here, we employ extensive molecular dynamics simulations with atomistic protein and water models to determine structural ensembles for Aβ(42), Aβ(40), and Aβ(42)-E22K (the Italian mutant) monomers in solution. Sampling of a total of >700 microseconds in all-atom detail with explicit solvent enables us to observe the effects of peptide length and a pathogenic mutation on the disordered Aβ monomer structural ensemble. Aβ(42) and Aβ(40) have crudely similar characteristics but reducing the peptide length from 42 to 40 residues reduces β-hairpin formation near the C-terminus. The pathogenic Italian E22K mutation induces helix formation in the region of residues 20-24. This structural alteration may increase helix-helix interactions between monomers, resulting in altered mechanism and kinetics of Aβ oligomerization.

MSMBuilder: Statistical Models for Biomolecular Dynamics

MSMBuilder is a software package for building statistical models of high-dimensional time-series data. It is designed with a particular focus on the analysis of atomistic simulations of biomolecular dynamics such as protein folding and conformational change. MSMBuilder is named for its ability to construct Markov state models (MSMs), a class of models that has gained favor among computational biophysicists. In addition to both well-established and newer MSM methods, the package includes complementary algorithms for understanding time-series data such as hidden Markov models and time-structure based independent component analysis. MSMBuilder boasts an easy to use command-line interface, as well as clear and consistent abstractions through its Python application programming interface. MSMBuilder was developed with careful consideration for compatibility with the broader machine learning community by following the design of scikit-learn. The package is used primarily by practitioners of molecular dynamics, but is just as applicable to other computational or experimental time-series measurements.

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.