An Analysis of the Validity of Markov State Models for Emulating the Dynamics of Classical Molecular Systems and Ensembles.

Markov state models parametrized using molecular simulation data are powerful tools for the investigation of conformational changes in biomolecules and in recent years have gained increasing popularity. However, a Markov state model is an approximation to the true dynamics of the complete system. We show how Markov state models are derived from the generalized Liouville equation identifying the assumptions and approximations involved and review the mathematical properties of transition matrices. Using two model systems, a two-bit flipping model consisting of only four states, and molecular dynamics simulations of liquid butane, we subsequently assess the influence of the assumptions, for example, of the marginal degrees of freedom, used in the derivation on the validity of the Markov state model.