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  • Open Access

Variational Identification of Markovian Transition States

Linda Martini1, Adam Kells1, Roberto Covino2, Gerhard Hummer2,3, Nicolae-Viorel Buchete4, and Edina Rosta1,*

  • 1Department of Chemistry, King’s College London, SE1 1DB London, United Kingdom
  • 2Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany
  • 3Institute of Biophysics, Goethe University Frankfurt, 60438 Frankfurt am Main, Germany
  • 4School of Physics and Institute for Discovery, University College Dublin, Dublin 4, Ireland

  • *edina.rosta@kcl.ac.uk
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Phys. Rev. X 7, 031060 – Published 28 September, 2017

DOI: https://doi.org/10.1103/PhysRevX.7.031060

Abstract

We present a method that enables the identification and analysis of conformational Markovian transition states from atomistic or coarse-grained molecular dynamics (MD) trajectories. Our algorithm is presented by using both analytical models and examples from MD simulations of the benchmark system helix-forming peptide Ala5, and of larger, biomedically important systems: the 15-lipoxygenase-2 enzyme (15-LOX-2), the epidermal growth factor receptor (EGFR) protein, and the Mga2 fungal transcription factor. The analysis of 15-LOX-2 uses data generated exclusively from biased umbrella sampling simulations carried out at the hybrid ab initio density functional theory (DFT) quantum mechanics/molecular mechanics (QM/MM) level of theory. In all cases, our method automatically identifies the corresponding transition states and metastable conformations in a variationally optimal way, with the input of a set of relevant coordinates, by accurately reproducing the intrinsic slowest relaxation rate of each system. Our approach offers a general yet easy-to-implement analysis method that provides unique insight into the molecular mechanism and the rare but crucial (i.e., rate-limiting) transition states occurring along conformational transition paths in complex dynamical systems such as molecular trajectories.

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Popular Summary

State-of-the-art supercomputers and software have enabled unprecedented insight into complex molecular processes, such as the folding of proteins essential to the function of biological cells. But the vast amount of data from these simulations requires innovative techniques for analyzing all available information. Of particular interest is identifying so-called transition states, critical points in a chemical reaction that determine whether or not molecules will react to form a new molecule. Transition states are elusive, however, as they are intrinsically short lived and thus notoriously difficult to characterize experimentally or theoretically. We have developed a method that automatically identifies the key transition states, as well as all main metastable states, and their underlying kinetic network.

Our method relies on the optimal construction of Markov state models—an approach that takes the complex behavior of molecules and breaks it down into discrete states and transition rates between those states. Identifying the underlying network of metastable Markov states for molecular dynamics simulation data is a widely successful and increasingly popular approach for achieving a more automatic and statistically optimal analysis of complex molecular systems. The metastable and transition states identified by our method correspond to an optimal coarse-graining of the underlying conformational dynamics, accurately capturing the key slowest-relaxation processes intrinsic to the analyzed system.

Our approach may also be applicable to time series of complex systems beyond molecular trajectories—to identify rate-limiting transition states in the context of kinetic networks in general and in the analysis of complex data from molecular dynamics in particular.

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Phys. Rev. X 7, 031060– Published 28 September, 2017
  • Received 16 June 2016
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