An Expanded Markov State Model–Transition Path Theory Framework for Ion Conduction Reactive Pathways through Membrane Channels

The combination of Markov State Models (MSMs), which approximate the dynamics of a system as stochastic transitions among a finite set of microstates, with transition path theory (TPT) enables a rigorous identification of the dominant reactive pathways controlling slow processes in complex systems. Although the MSM/TPT framework has been successfully applied to a wide range of problems, its use in analyzing unbound processes such as ion conduction through channels presents special conceptual challenges. The standard formulation of MSM/TPT, built on a picture of reactive transitions between two metastable basins, is incompatible with an unbound process such as ion conduction. An expanded formulation of the MSM/TPT framework is introduced to enable characterization of ion channels. The expanded framework is general and could also be applied to a wide range of open systems such as pumps, motors, and molecular machines.