SEMINAR: Spatial Effects Arising from Multi-Scale Stochastic Dynamics

In this talk I will explore some interesting features that can arise within reaction networks which are stochastic and spatial. I will present a useful measure-valued framework for modelling stochastic networks with spatial heterogeneity. In this model reactions rates at a spatial location are proportional to the mass of different species present locally, and to a location specific chemical rate that is allowed to be a function of the local or global mass of different species. I will explain the benefit of the framework in establishing approximation limits that exploit multi-scale aspects of the system. Some interesting features arise from spatial heterogeneity that can be explored, I will mention an example of protein production with spatially dependent transcription and translation rates where noisy oscillations are sustained by a time delay caused by spatial arrangements.