Geometric and many-particle aspects of transmitter binding.

We investigate the various reactivity patterns possible when several transmitter molecules, released at one side of a synaptic gap, diffuse and bind reversibly to a single receptor at the other end. In the framework of a one-dimensional approximation, the complete time, reactivity, concentration and gap-width dependence are determined, using a rigorous theoretical and computational approach to the many-body aspects of this problem. The time dependence of the survival probability is found to consist of up to four phases. These include a short delay followed by gaussian, power-law, and exponential decay phases. A rigorous expression is derived for the long-time exponent and approximate expressions are obtained for describing the short-time gaussian phase.