Christian R. Schwantes

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.

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.

Perspective: Markov models for long-timescale biomolecular dynamics.

Molecular dynamics simulations have the potential to provide atomic-level detail and insight to important questions in chemical physics that cannot be observed in typical experiments. However, simply generating a long trajectory is insufficient, as researchers must be able to transform the data in a simulation trajectory into specific scientific insights. Although this analysis step has often been taken for granted, it deserves further attention as large-scale simulations become increasingly routine. In this perspective, we discuss the application of Markov models to the analysis of large-scale biomolecular simulations. We draw attention to recent improvements in the construction of these models as well as several important open issues. In addition, we highlight recent theoretical advances that pave the way for a new generation of models of molecular kinetics.

Modeling molecular kinetics with tICA and the kernel trick.

The allure of a molecular dynamics simulation is that, given a sufficiently accurate force field, it can provide an atomic-level view of many interesting phenomena in biology. However, the result of a simulation is a large, high-dimensional time series that is difficult to interpret. Recent work has introduced the time-structure based Independent Components Analysis (tICA) method for analyzing MD, which attempts to find the slowest decorrelating linear functions of the molecular coordinates. This method has been used in conjunction with Markov State Models (MSMs) to provide estimates of the characteristic eigenprocesses contained in a simulation (e.g., protein folding, ligand binding). Here, we extend the tICA method using the kernel trick to arrive at nonlinear solutions. This is a substantial improvement as it allows for kernel-tICA (ktICA) to provide estimates of the characteristic eigenprocesses directly without building an MSM.

Complex Pathways in Folding of Protein G Explored by Simulation and Experiment

The B1 domain of protein G has been a classic model system of folding for decades, the subject of numerous experimental and computational studies. Most of the experimental work has focused on whether the protein folds via an intermediate, but the evidence is mostly limited to relatively slow kinetic observations with a few structural probes. In this work we observe folding on the submillisecond timescale with microfluidic mixers using a variety of probes including tryptophan fluorescence, circular dichroism, and photochemical oxidation. We find that each probe yields different kinetics and compare these observations with a Markov State Model constructed from large-scale molecular dynamics simulations and find a complex network of states that yield different kinetics for different observables. We conclude that there are many folding pathways before the final folding step and that these paths do not have large free energy barriers.

Dynamical Phase Transitions Reveal Amyloid-like States on Protein Folding Landscapes

Developing an understanding of protein misfolding processes presents a crucial challenge for unlocking the mysteries of human disease. In this article, we present our observations of β-sheet-rich misfolded states on a number of protein dynamical landscapes investigated through molecular dynamics simulation and Markov state models. We employ a nonequilibrium statistical mechanical theory to identify the glassy states in a proteins dynamics, and we discuss the nonnative, β-sheet-rich states that play a distinct role in the slowest dynamics within seven protein folding systems. We highlight the fundamental similarity between these states and the amyloid structures responsible for many neurodegenerative diseases, and we discuss potential consequences for mechanisms of protein aggregation and intermolecular amyloid formation.

Probing the origins of two-state folding

Many protein systems fold in a two-state manner. Random models, however, rarely display two-state kinetics and thus such behavior should not be accepted as a default. While theories for the prevalence of two-state kinetics have been presented, none sufficiently explain the breadth of experimental observations. A model, making minimal assumptions, is introduced that suggests two-state behavior is likely for any system with an overwhelmingly populated native state. We show two-state folding is a natural consequence of such two-state thermodynamics, and is strengthened by increasing the population of the native state. Further, the model exhibits hub-like behavior, with slow interconversions between unfolded states. Despite this, the unfolded state equilibrates quickly relative to the folding time. This apparent paradox is readily understood through this model. Finally, our results compare favorable with measurements of folding rates as a function of chain length and Keq, providing new insight into these relations.

Atomistic structural ensemble refinement reveals non-native structure stabilizes a sub-millisecond folding intermediate of CheY

The dynamics of globular proteins can be described in terms of transitions between a folded native state and less-populated intermediates, or excited states, which can play critical roles in both protein folding and function. Excited states are by definition transient species, and therefore are difficult to characterize using current experimental techniques. Here, we report an atomistic model of the excited state ensemble of a stabilized mutant of an extensively studied flavodoxin fold protein CheY. We employed a hybrid simulation and experimental approach in which an aggregate 42 milliseconds of all-atom molecular dynamics were used as an informative prior for the structure of the excited state ensemble. This prior was then refined against small-angle X-ray scattering (SAXS) data employing an established method (EROS). The most striking feature of the resulting excited state ensemble was an unstructured N-terminus stabilized by non-native contacts in a conformation that is topologically simpler than the native state. Using these results, we then predict incisive single molecule FRET experiments as a means of model validation. This study demonstrates the paradigm of uniting simulation and experiment in a statistical model to study the structure of protein excited states and rationally design validating experiments.