Modelling Cellular Reaction-Diffusion Kinetics

Accurate modeling of reaction kinetics is important for understanding the functionality of biological cells. Depending on the particle concentrations and on the relation between particle mobility and reaction rate constants, different mathematical models are appropriate. In the limit of slow diffusion and small concentrations, both discrete particle numbers and spatial inhomogeneity must be taken into account. The most detailed model consists of particle-based reaction-diffusion dynamics, where all individual particles are explicitly resolved in time and space, and particle positions are propagated by diffusion equations, and reaction events may occur only when reactive species are adjacent. For rapid diffusion or large concentrations, the model may be coarse-grained in different ways. Rapid diffusion leads to mixing and implies that spatial resolution is not needed below a certain length scale. This permits the system to be modeled via a spatiotemporal chemical Master equation (STCME), i.e. a coupled set of chemical Master equations acting on spatial sub-volumes. The talk will discuss these different models; in particular, we will see how the STCME description can be derived from particle-based reaction-diffusion dynamics.

Joint work with Stefanie Winkelmann (FU Berlin)