Mathematics Colloquium

WHEN:
Wednesday April 26 at 2:30 PM

WHERE:
Durham Science Center, Room DSC256

WHAT:

ABSTRACT:
Changes to the relative separation of molecules or other interacting species on account of diffusion accompany their associative or dissociative reaction. The molecules are symbolized, for two distinct types, A, B, by the relations A + B <=> AB and, if [A], [B] and [AB] denote the corresponding densities, the equation d/dt([AB]) = (k_+)[AB] specifies an associative process with a so-called forward rate constant (k_+). An approximate version of the preceding takes the form of a linear differential equation, which can be employed to obtain significant estimates for both (k_+) and the flux function d[AB]/dt. Such estimates are presented in different circumstances, including the localization of A, B on a common planar surface or their distribution in space; and also when the domain of A is a half space whereas that of B is an adjacent plane boundary surface. It proves advantageous to reformulate the last, a mixed boundary value problem, in terms of a linear integral equation. Biologically motivated reactions are analyzed in this manner and the theoretical methods employed to model the basal state of receptor phosphorylation in RBL cells and the initiation of phototransduction in rod photoreceptors.

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