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Optimized parameter selection reveals trends in Markov state models for protein folding.

ABSTRACT: As molecular dynamics simulations access increasingly longer time scales, complementary advances in the analysis of biomolecular time-series data are necessary. Markov state models offer a powerful framework for this analysis by describing a system's states and the transitions between them. A recently established variational theorem for Markov state models now enables modelers to systematically determine the best way to describe a system's dynamics. In the context of the variational theorem, we analyze ultra-long folding simulations for a canonical set of twelve proteins [K. Lindorff-Larsen et al., Science 334, 517 (2011)] by creating and evaluating many types of Markov state models. We present a set of guidelines for constructing Markov state models of protein folding; namely, we recommend the use of cross-validation and a kinetically motivated dimensionality reduction step for improved descriptions of folding dynamics. We also warn that precise kinetics predictions rely on the features chosen to describe the system and pose the description of kinetic uncertainty across ensembles of models as an open issue.

SUBMITTER: Husic BE

PROVIDER: S-EPMC5116026 | biostudies-literature | 2016 Nov

REPOSITORIES: biostudies-literature

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Optimized parameter selection reveals trends in Markov state models for protein folding.

Husic Brooke E BE McGibbon Robert T RT Sultan Mohammad M MM Pande Vijay S VS

The Journal of chemical physics 20161101 19

As molecular dynamics simulations access increasingly longer time scales, complementary advances in the analysis of biomolecular time-series data are necessary. Markov state models offer a powerful framework for this analysis by describing a system's states and the transitions between them. A recently established variational theorem for Markov state models now enables modelers to systematically determine the best way to describe a system's dynamics. In the context of the variational theorem, we ...[more]

PMID: 27875868

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Project description:Understanding how kinetics in the unfolded state affects protein folding is a fundamentally important yet less well-understood issue. Here we employ three different models to analyze the unfolded landscape and folding kinetics of the miniprotein Trp-cage. The first is a 208 ?s explicit solvent molecular dynamics (MD) simulation from D. E. Shaw Research containing tens of folding events. The second is a Markov state model (MSM-MD) constructed from the same ultralong MD simulation; MSM-MD can be used to generate thousands of folding events. The third is a Markov state model built from temperature replica exchange MD simulations in implicit solvent (MSM-REMD). All the models exhibit multiple folding pathways, and there is a good correspondence between the folding pathways from direct MD and those computed from the MSMs. The unfolded populations interconvert rapidly between extended and collapsed conformations on time scales ?40 ns, compared with the folding time of ?5 ?s. The folding rates are independent of where the folding is initiated from within the unfolded ensemble. About 90% of the unfolded states are sampled within the first 40 ?s of the ultralong MD trajectory, which on average explores ?27% of the unfolded state ensemble between consecutive folding events. We clustered the folding pathways according to structural similarity into "tubes", and kinetically partitioned the unfolded state into populations that fold along different tubes. From our analysis of the simulations and a simple kinetic model, we find that, when the mixing within the unfolded state is comparable to or faster than folding, the folding waiting times for all the folding tubes are similar and the folding kinetics is essentially single exponential despite the presence of heterogeneous folding paths with nonuniform barriers. When the mixing is much slower than folding, different unfolded populations fold independently, leading to nonexponential kinetics. A kinetic partition of the Trp-cage unfolded state is constructed which reveals that different unfolded populations have almost the same probability to fold along any of the multiple folding paths. We are investigating whether the results for the kinetics in the unfolded state of the 20-residue Trp-cage is representative of larger single domain proteins.

Project description:CONSPECTUS: Protein function is inextricably linked to protein dynamics. As we move from a static structural picture to a dynamic ensemble view of protein structure and function, novel computational paradigms are required for observing and understanding conformational dynamics of proteins and its functional implications. In principle, molecular dynamics simulations can provide the time evolution of atomistic models of proteins, but the long time scales associated with functional dynamics make it difficult to observe rare dynamical transitions. The issue of extracting essential functional components of protein dynamics from noisy simulation data presents another set of challenges in obtaining an unbiased understanding of protein motions. Therefore, a methodology that provides a statistical framework for efficient sampling and a human-readable view of the key aspects of functional dynamics from data analysis is required. The Markov state model (MSM), which has recently become popular worldwide for studying protein dynamics, is an example of such a framework. In this Account, we review the use of Markov state models for efficient sampling of the hierarchy of time scales associated with protein dynamics, automatic identification of key conformational states, and the degrees of freedom associated with slow dynamical processes. Applications of MSMs for studying long time scale phenomena such as activation mechanisms of cellular signaling proteins has yielded novel insights into protein function. In particular, from MSMs built using large-scale simulations of GPCRs and kinases, we have shown that complex conformational changes in proteins can be described in terms of structural changes in key structural motifs or "molecular switches" within the protein, the transitions between functionally active and inactive states of proteins proceed via multiple pathways, and ligand or substrate binding modulates the flux through these pathways. Finally, MSMs also provide a theoretical toolbox for studying the effect of nonequilibrium perturbations on conformational dynamics. Considering that protein dynamics in vivo occur under nonequilibrium conditions, MSMs coupled with nonequilibrium statistical mechanics provide a way to connect cellular components to their functional environments. Nonequilibrium perturbations of protein folding MSMs reveal the presence of dynamically frozen glass-like states in their conformational landscape. These frozen states are also observed to be rich in ?-sheets, which indicates their possible role in the nucleation of ?-sheet rich aggregates such as those observed in amyloid-fibril formation. Finally, we describe how MSMs have been used to understand the dynamical behavior of intrinsically disordered proteins such as amyloid-?, human islet amyloid polypeptide, and p53. While certainly not a panacea for studying functional dynamics, MSMs provide a rigorous theoretical foundation for understanding complex entropically dominated processes and a convenient lens for viewing protein motions.

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Optimized parameter selection reveals trends in Markov state models for protein folding.

Publications

Optimized parameter selection reveals trends in Markov state models for protein folding.

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