On the decay of lateral phase separations in biological membranes

A theory for the decay of a lateral phase separation in a biological membrane has been developed based upon the edge decay of a population of circular molecular domains of uniform size. The theory has been applied to the case of vesicle fusion at a presynaptic membrane. It is shown that the efficiency of fusion decays exponentially in time with a rate constant $\text{solπ}\text{2τ}\text{N}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ which decreases as the rate at which bonds are broken within each domain (τ^?1) decreases and as the number of molecules within each domain (N) increases. Moreover, it has been speculated that this mechanism may offer in part an explanation for the slow, exponential decay during post-tetanic potentiation where it is known that the efficiency of neurotransmitter release at the presynaptic membrane is rate-controlling and decays exponentially.