Diffusive transport: theory and application

In this thesis we investigate the behaviour of diffusing particles in a variety of scenarios. We are primarily interested in the case of molecules diffusing inside a cell in the context of biological processes where the mechanism by which a cell responds to an event occurring on its surface may involve the transport of molecular complexes from the cellular surface to the nucleus, and the transport of synthesised molecules from the nuclear surface to the cellular surface.

We find the Green's functions for diffusions in two and three dimensions, respectively, on a domain bounded by non-concentric surfaces, one absorbing and one reflecting. Exact expressions are also found for mean hitting times and hitting densities. Our motivation is diffusive transport from a nuclear surface, to a cellular surface and back. Hence, we consider cases where the initial condition is uniformly distributed on the nuclear or cellular surface, and where the hitting density of the outward leg is the density of initial conditions for the return leg. Mean times are calculated by integrating the Green's functions over the domain.

Additionally, we create a mathematical model for a specific type of assay experiments where Coxiella burnetii bacteria are placed inside a well and are allowed to be phagocytosed by a monolayer of monocytes on the bottom of the well. We obtain an expression for the intracellular bacterial load at any point during the experiment.