Push-forward method for piecewise deterministic biochemical simulations

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