GRadient Adaptive Decomposition (GRAD) Method: Optimized Refinement Along Macrostate Borders in Markov State Models

Markov state models (MSM) are used to model the kinetics of processes sampled by molecular dynamics (MD) simulations. MSM reduce the high dimensionality inherent to MD simulations as they partition the free energy landscape into discrete states, generating a kinetic model as a series of uncorrelated jumps between states. Here, we detail a new method, called GRadient Adaptive Decomposition, which optimizes coarse-grained MSM by refining borders with respect to the gradient along the free energy surface. The proposed method requires only a small number of initial microstates because it corrects for errors produced by limited sampling. Whereas many methods rely on fuzzy partitions for proper statistics, GRAD retains a crisp decomposition. Two test studies are presented to illustrate the method and assess its accuracy: the first analyzes MSM of idealized model potentials, while the second is a study of the dynamics of unstacking of the deoxyribose adenosine monophosphate dinucleotide.