Modelling and analysis of non-Markovian biochemical reaction networks

Abstract: Modeling intracellular processes has long relied on the Markovian assumption. However, as soon as a reactant interacts with its environment, molecular memory definitely exists and its effects cannot be neglected. Since the Markov theory cannot translate directly to modeling and analysis of non-Markovian processes, this leads to many significant challenges. We develop a formulation, namely the stationary generalized chemical-master equation, to model intracellular processes with molecular memory. This formulation converts a non-Markovian question to a Markovian one while keeping the stationary probabilistic behavior unchanged. Both a stationary generalized Fokker–Planck equation and a generalized linear noise approximation are further developed for the fast evaluation of fluctuations. These formulations can have broad applications and may help us discover new biological knowledge.

Mathematics

Audience: researchers in the topic

ICCM 2020