Modelling non-Markovian dynamics in biochemical reactions

Biochemical reactions are often modelled as discrete-state continuous-time stochastic processes evolving as memoryless Markov processes. However, in some cases, biochemical systems exhibit non-Markovian dynamics. We propose here a methodology for building stochastic simulation algorithms which model more precisely non-Markovian processes in some specific situations. Our methodology is based on Constraint Programming and is implemented by using Gecode, a state-of-the-art framework for constraint solving.

Our technique allows us to randomly sample waiting times from probability density functions that not necessarily are distributed according to a negative exponential function. In this context, we discuss an important case-study in which the probability density function is inferred from single-molecule experiments that describe the distribution of the time intervals between two consecutive enzymatically catalysed reactions. Noticeably, this feature allows some types of enzyme reactions to be modelled as non-Markovian processes.

We show that our methodology makes it possible to obtain accurate models of enzymatic reactions that, in specific cases, fit experimental data better than the corresponding Markovian models.