A Calcium Diffusion-Reaction Model for Facilitation

Abstract

At many synapses, repeated presynaptic action potentials often evoke increased neurotransmitter release to successive spikes. This enhancement of released neurotransmitter accumulates in a train of action potentials, rises with time constants of 30 and 300 ms, decays with similar time constants after the last spike in the train and is called (homosynaptic) facilitation. An early hypothesis for facilitation (Katz & Miledi, 1968), the “single-site/nonlinear-summation/residual-calcium” hypothesis, states that facilitation is due to a residuum of calcium remaining in the terminal from the first action potential that summates with calcium that enters during the second action potential, which facilitates the release of neurotransmitter due to the nonlinear dependence of transmitter release on calcium. However, this simple model (facilitation occurs at the secretory trigger) cannot account for the large magnitude of facilitation (several fold increase for a few action potentials). Other models (Yamada & Zucker, 1992) propose that calcium acts at distinct facilitation sites, with slow unbinding kinetics determining the time constants of facilitation. However these models contradict experimental results of Kamiya & Zucker (1994) implying that a small residual calcium acts with fast kinetics and high affinity to strongly facilitate release.