Hybrid Modelling of Reaction, Diffusion and Taxis Processes in Biology Seminar

I will discuss methods for spatio-temporal modelling in cellular and molecular biology. Three classes of models will be considered:
microscopic (molecular-based, individual-based) models which are based on the simulation of trajectories of individual molecules and their localized interactions (for example, reactions);
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 in each compartment; and
macroscopic (deterministic) models which are written in terms of reaction-diffusion-advection PDEs for spatially varying concentrations.

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