poster: Analytic expressions of the mean time first passage times and hitting densitiy for diffusing particles in eccentric annular regions
speaker: Stana Remus (University of Leeds)abstract: Many cells of the immune system have receptors which are produced in the nucleus and these move under the influence of diffusion until they reach the outer membrane of the cell. Depending on the type of receptor, they might also diffuse on the surface of the cell until either a certain period of time has passed or the receptor encounters a peptide. After either of these events the receptors re-enter the cytoplasm and diffuse until they are absorbed by the nucleus. We are interested in the first passage properties of the receptors. Particularly, two quantities of great importance are the mean time $T$ from creation of a receptor to its absorption back into the nucleus and the distribution $\varepsilon$ of eventual hitting points on both the nucleus and the cytoplasm. We show how these quantities can be determined explicitly for two types of geometry, namely when the nucleus and membrane are concentric and eccentric, both in 2D and 3D. For this purpose, we derive an analytic expression for the Green's function of the Laplace equation for a domain bounded by non-concentric surfaces in two dimensions and three dimensions subject to absorbing outer surface and reflecting inner surface and vice versa. Utilizing the Green's function we derive an expression for $T$ and compare with previous results in the literature. Furthermore, using the Green's function we calculate exact formula for $\varepsilon$ and compare it with numerical results.
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