Colloquium, Program in Applied Mathematics- Multiscale Stochastic Transcription Models

Abstract:   The formalism of stochastic reaction networks (SRNs) provides building blocks for number of models in mathematical biology both at molecular and population levels (e.g., gene transcription or epidemic outbreak). In particular the SRNs allow to naturally incorporate both delay and multi-scale phenomena. In the first case the resulting models may be often expressed in the language of queuing theory, in the second case they lead to stochastic diffusions and ODE/PDE approximations. In this talk I will provide a brief overview of the applications of SRNs to modeling molecular biological systems emphasizing the recent work on multi-scaling for simple stochastic gene transcription model.