# Radek Erban

Radek Erban abstract

Radek Erban, Mathematical Institute, Oxford University:

Title: Mathematical Methods for Multiscale Modelling in Molecular, Cell andPopulation Biology

Abstract:I will discuss methods for spatio-temporal modelling in molecular, celland population biology. Three classes of models will be considered:

** **(i) microscopic (molecular-based, individual-based) models which are based on the simulation of trajectories of molecules (individuals) and their localized interactions (for example, reactions);

** **(ii) mesoscopic (lattice-based) models which divide the computational domain into a finite number of compartments and simulate the time evolution of the numbers of molecules (numbers of individuals) in each compartment; and

** **(iii) macroscopic (deterministic) models which are written in terms of mean-field reaction-diffusion-advection partial differential equations (PDEs) for spatially varying concentrations.

In the first part of my talk, I will discuss connections between themodelling frameworks (i)-(iii). I will consider chemical reactions bothat a surface and in the bulk. In the second part of my talk, I willpresent hybrid (multiscale) algorithms which use models with a differentlevel of detail in different parts of the computational domain.The main goal of this multiscale methodology is to use a detailedmodelling approach in localized regions of particular interest(in which accuracy and microscopic detail is important) and a lessdetailed model in other regions in which accuracy may be tradedfor simulation efficiency. I will also discuss hybrid modellingof chemotaxis where an individual-based model of cells is coupledwith PDEs for extracellular chemical signals.