Kinetic network in Milestoning: Clustering, reduction, and transition path analysis

We present a reduction of Milestoning (ReM) algorithm to analyze the high-dimensional Milestoning kinetic network. The algorithm reduces the Milestoning network to low dimensions but preserves essential kinetic information, such as local residence time, exit time, and mean first passage time between any two states. This is achieved in three steps. First, nodes (milestones) in the high-dimensional Milestoning network are grouped into clusters based on the metastability identified by an auxiliary continuous-time Markov chain. Our clustering method is applicable not only to time-reversible networks but also to non-reversible networks generated from practical simulations with statistical fluctuations. Second, a reduced network is established via network transformation, containing only the core sets of clusters as nodes. Finally, transition pathways are analyzed in the reduced network based on the transition path theory. The algorithm is illustrated using a toy model and a solvated alanine dipeptide in two and four dihedral angles.