# Mariya Ptashnyk

Mariya Ptashnyk abstract

Department of Mathematics, University of Dundee

Gene Regulatory Network and Functional Analysis: Mathematical modelling and analysis of signalling processes in cells and tissues.

Abstract: In this talk I would like to present some ideas on bifurcation analysis for a simple model of a gene regulatory network and on multiscale analysis of a receptor-based model for transport of signalling molecules in a tissue. Gene regulatory networks lie at the heart of many important intracellular signal transduction processes. We consider a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). Such intracellular negative feedback systems are known to exhibit oscillatory behaviour. Applying linearised stability analysis, we study the stability of a (spatially inhomogeneous) steady state of the model equations. Our results show that the diffusion coffiecient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. The main diculty of the analysis is that the steady state of the model is not constant. In a microscopic model for transport of signalling molecules in a tissue we consider interactions between signalling molecules (i.e. growth factors, hormones) diffusing in the intercellular space and receptors located in the cell membrane. Using multiscale analysis techniques we derive a macroscopic averaged model for transport of signalling molecules on a tissue level. This approach allow us to analyse the impact of the microscopic structure and microscopic properties of a cell tissue on macroscopic signalling processes.