Application of Markov State Models to simulate long timescale dynamics of biological macromolecules.

Conformational changes of proteins are an*Author contributed equally with all other contributors. essential part of many biological processes such as: protein folding, ligand binding, signal transduction, allostery, and enzymatic catalysis. Molecular dynamics (MD) simulations can describe the dynamics of molecules at atomic detail, therefore providing a much higher temporal and spatial resolution than most experimental techniques. Although MD simulations have been widely applied to study protein dynamics, the timescales accessible by conventional MD methods are usually limited to timescales that are orders of magnitude shorter than the conformational changes relevant for most biological functions. During the past decades great effort has been devoted to the development of theoretical methods that may enhance the conformational sampling. In recent years, it has been shown that the statistical mechanics framework provided by discrete-state and -time Markov State Models (MSMs) can predict long timescale dynamics from a pool of short MD simulations. In this chapter we provide the readers an account of the basic theory and selected applications of MSMs. We will first introduce the general concepts behind MSMs, and then describe the existing procedures for the construction of MSMs. This will be followed by the discussions of the challenges of constructing and validating MSMs, Finally, we will employ two biologically-relevant systems, the RNA polymerase and the LAO-protein, to illustrate the application of Markov State Models to elucidate the molecular mechanisms of complex conformational changes at biologically relevant timescales.