Nikola Popovic abstract
Nikola Popovic, School of Maths, UoE
A geometric analysis of fast-slow models for stochastic gene expression
Stochastic models for gene expression frequently exhibit dynamics on different time-scales. One potential scale separation is due to significant differences in the lifetimes of mRNA and the protein it synthesises, which allows for the application of perturbation techniques.Here, we develop a dynamical systems framework for the analysis of a family of "fast-slow" models for gene expression that is based on geometric singular perturbation theory. We illustrate our approach by giving a complete characterisation of a standard two-stage model which assumes transcription, translation, and degradation to be birth-and-death processes of first order. In particular, we develop a systematic expansion procedure for the resulting propagator probabilities that can in principle be taken to any order in the perturbation parameter.Finally, we verify our asymptotics by numerical simulation, and we explore its practical applicability, as well as the effects of a variation in the system parameters and the scale separation.