Markov dynamic models for long-timescale protein motion

Abstract

Molecular dynamics (MD) simulation is a well-established method for studying protein motion at the atomic scale. However, it is computationally intensive and generates massive amounts of data. One way of addressing the dual challenges of computation efficiency and data analysis is to construct simplified models of long-timescale protein motion from MD simulation data. In this direction, we propose to use Markov models with hidden states, in which the Markovian states represent potentially overlapping probabilistic distributions over protein conformations. We also propose a principled criterion for evaluating the quality of a model by its ability to predict long-timescale protein motions. Our method was tested on 2D synthetic energy landscapes and two extensively studied peptides, alanine dipeptide and the villin headpiece subdomain (HP-35 NleNle). One interesting finding is that although a widely accepted model of alanine dipeptide contains six states, a simpler model with only three states is equally good for predicting long-timescale motions. We also used the constructed Markov models to estimate important kinetic and dynamic quantities for protein folding, in particular, mean first-passage time. The results are consistent with available experimental measurements.

Fig. 1.

Five synthetic energy landscapes and the corresponding models.

Fig. 2.

Average log-likelihood scores of the models for synthetic energy landscapes.

Fig. 3.

Average log-likelihood scores of alanine dipeptide models.

Fig. 4.

Conformations generated from the 3-state model A3 (a) and the 6-state model M6 (b).

Fig. 5.

Average log-likelihood scores for the villin headpiece models.

Fig. 6.

(a) Main state transitions of the 20-state villin headpiece model. The size of each node is proportional to the probability of the corresponding state in the stationary distribution. The width of each edge is proportional to the transition probability. States with probability <0.01 in the stationary distribution, self-transitions and transitions with probability <0.002 are not shown to avoid cluttering the diagram. The initial conformations most likely belong to state 12, and the native conformation most likely belongs to state 15. (b) Example conformations from states 7, 12, 13, 15 and 18. The residues forming helix 1 are drawn in red. (c) The most likely state transition sequences from states 12 to 15.