Diffusion Limited Reactions

Source 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 $A+B \leftrightharpoons AB$, and, if $[A]$, $[B]$, and $[AB]$ denote the corresponding densities, the equation $\frac{d}{dt} [AB] = k_+ [A][B]$ specifies an associative process with 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 a bounding planar surface. It proves advantageous to reformulate the last, a mixed boundary value problem, in terms of a linear integral equation. Biological applications are discussed, including the mechanism for the observed phosphorylation of proteins in resting cells and the incipience of phototransduction in rod photoreceptors.