Push-forward method for piecewise deterministic biochemical simulations

TL;DR

This paper introduces a generalized push-forward simulation algorithm for piecewise-deterministic Markov processes, enabling efficient modeling of biochemical networks with stochastic and deterministic dynamics, applicable in biology and biotechnology.

Contribution

It extends previous push-forward methods to handle non-integrable systems, improving simulation efficiency for complex biochemical PDMP models.

Findings

The new algorithm works for non-integrable systems.

It enhances simulation speed and accuracy for biochemical networks.

Applicable in biological, biotechnological, and biocomputing contexts.

Abstract

A biochemical network can be simulated by a set of ordinary differential equations (ODE) under well stirred reactor conditions, for large numbers of molecules, and frequent reactions. This is no longer a robust representation when some molecular species are in small numbers and reactions changing them are infrequent. In this case, discrete stochastic events trigger changes of the smooth deterministic dynamics of the biochemical network. Piecewise-deterministic Markov processes (PDMP) are well adapted for describing such situations. Although PDMP models are now well established in biology, these models remain computationally challenging. Previously we have introduced the push-forward method to compute how the probability measure is spread by the deterministic ODE flow of PDMPs, through the use of analytic expressions of the corresponding semigroup. In this paper we provide a more general simulation algorithm that works also for non-integrable systems. The method can be used for biochemical simulations with applications in fundamental biology, biotechnology and biocomputing.This work is an extended version of the work presented at the conference CMSB2019.