Orateur
Description
Single-cell data have revealed the presence of biological variability between cells of identical genome and environment, highlighting not only epigenetic aspects but also the stochastic nature of gene expression. In the context of regulatory networks underlying cell states and types, we need to consider models that take into account both stochasticity and the interaction of genes with each other. Here we focus on two dynamical models of gene expression, formulated as a piecewise-deterministic Markov process (PDMP) and describing an arbitrary number of interacting genes. The first model simplifies the gene expression mechanism by considering that a gene is transcribed into messenger RNA, which in turn is translated into protein. While this stochastic model is able to reproduce the biological variability measured experimentally, it remains mathematically complex and difficult to study. For this reason, a simplified model involving only proteins is often considered. In this talk, we demonstrate using coupling methods that, in a specific parameter regime, the simplified model is an approximation of the model with two layers.