Directed kinetic transition network model.

Molecular dynamics simulations contain detailed kinetic information related to the functional states of proteins and macromolecules, but this information is obscured by the high dimensionality of configurational space. Markov state models and transition network models are widely applied to extract kinetic descriptors from equilibrium molecular dynamics simulations. In this study, we developed the Directed Kinetic Transition Network (DKTN)-a graph representation of a master equation which is appropriate for describing nonequilibrium kinetics. DKTN models the transition rate matrix among different states under detailed balance. Adopting the mixing time from the Markov chain, we use the half mixing time as the criterion to identify critical state transition regarding the protein conformational change. The similarity between the master equation and the Kolmogorov equation suggests that the DKTN model can be reformulated into the continuous-time Markov chain model, which is a general case of the Markov chain without a specific lag time. We selected a photo-sensitive protein, vivid, as a model system to illustrate the usage of the DKTN model. Overall, the DKTN model provides a graph representation of the master equation based on chemical kinetics to model the protein conformational change without the underlying assumption of the Markovian property.