A molecular dynamics (MD) simulation of protein folding tracks every atom in space at sub-nanosecond time intervals as the protein folds and unfolds, generating millions of protein conformations. However, this massive amount of data can be difficult to summarize in a statistically robust way that is easy to interpret, understand, and experimentally validate. Markov state models (MSMs) represent an important advance in the analysis of MD datasets: by assigning each frame in a simulation to a smaller set of states, we can analyze the state populations and pairwise transitions to determine the thermodynamics and kinetics of the system, respectively. However, even MSMs containing just hundreds of states may be too fine-grained to pair with experimental validation or prospective predictions. Therefore, it is important to coarse-grain MSMs such that they contain just a handful of states—for protein folding, these might correspond to “folded,” “unfolded,” and “misfolded”—and are thus more amenable to comparison with coarser experimental methods. Most MSM coarse-graining methods, however, fail to produce qualitatively reasonable results, or are not robust to statistical artifacts. Here, we present a robust, interpretable coarse-graining method for MSMs. By leveraging the fact that each state is represented by a probability distribution, we first assess state similarity using the information theoretic Jensen-Shannon divergence of their probability distributions. We then employ agglomerative hierarchical clustering to merge similar states using a minimum variance criterion. By monitoring the increase in variance at every merge step, we can also automatically determine the appropriate number of coarse-grained macrostates for a system. We demonstrate our method’s effectiveness in identifying protein folding macrostates and its robustness to statistical artifacts. Finally, we highlight the versatility of this method by showing how it can be extended to grouping sets of MSMs, such as a protein folding simulation performed in several different force fields, according to dynamical similarity.

Constructing interpretable computational models of protein dynamics using information theory and variance minimization

256th National Meeting (2018)

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