Coarse graining of biochemical systems described by discrete stochastic dynamics

TL;DR

This paper introduces a systematic method for simplifying finite Markov models of biological systems by merging states, preserving key steady-state properties, and providing criteria for optimal coarse graining, demonstrated on kinesin motor kinetics.

Contribution

It presents a novel state-merging approach for coarse graining Markov models that maintains steady-state fluxes and offers an optimal resolution criterion.

Findings

Method preserves steady-state probabilities and fluxes except between merged states.

Coarse graining levels can be iteratively refined independently of merging order.

Applied successfully to kinesin cycle kinetics.

Abstract

Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and all steady-state fluxes except the one between the merged states. Different levels of coarse graining of the underlying microscopic dynamics can be obtained by iteration, with the result being independent of the order in which states are merged. A criterion for the optimal level of coarse graining or resolution of the process is proposed via a tradeoff between the simplicity of the coarse-grained model and the information loss relative to the original model. As a case study, the method is applied to the cycle kinetics of the molecular motor kinesin.