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Talk Abstract
Presynaptic [Ca] Diffusion Simulations and Models of Synaptic Facilitation

Robert Zucker, Univ. of Califonia, Berkeley

We are trying to understand the basis for a form of short-term synaptic plasticity called facilitation. During a train of presynaptic action potentials, successive postsynaptic responses increase due to an increase in transmitter release per spike. This effect rises with time constants of 30 and 300 ms, and decays with similar time constants after the last spike in the train (when measured by single test spikes at later intervals). Katz & Miledi (1968) showed that facilitation requires Ca entry, and proposed that it is a simple consequence of the highly cooperative action of 4 Ca ions binding at the site causing exocytosis combined with residual Ca remaining present during the facilitation period adding to the transient rise in [Ca] in an action potential. However, this simple model cannot account for the large magnitude of facilitation (several fold increase for a few spikes) in the face of a very small increase in the rate of secretion during the facilitation period. Yamada & Zucker (1992) and Bertram, Sherman & Stanley (1996) proposed that Ca acts at distinct facilitation sites, with slow unbinding kinetics determining the time constants of facilitation. However, Kamiya & Zucker (1994) found that rapid reduction of residual Ca by photolytic release of a presynaptic Ca buffer rapidly eliminated facilitation, implying that a small residual Ca (less than 1 µM) acts with fast kinetics and high affinity to strongly facilitate release elicited by local brief rises in [Ca] to about 100 µM. And Atluri & Regehr (1996) found that facilitation has intrinsic kinetics of tens of ms, and is normally rate limited by equilibrium reaction of low levels of residual Ca.

We are using simulations of Ca dynamics in the active zone and models of reaction schemes to search for possible models of facilitation. Ca enters presynaptic boutons through an array of Ca channels in active zones on the presynaptic surface, and diffuses in three dimensions into the bouton. Numerical simulations involve solution of the diffusion equation, with mobile and immobile presynaptic buffers, and surface extrusion of Ca by pumps, to produce a spatio-temporal profile of [Ca] during and after a short train of action potentials. A facilitation site with kinetics and affinities consistent with experimental results at the same location as the exocytosis binding site (20 nm from the nearest open Ca channel) is saturated by each action potential, and cannot cause facilitation. But such a site located 60 nm away produces facilitation similar to what is observed experimentally. This distance may reflect the mean free path of Ca ions from the nearest open Ca channel to a physically obscured binding site on the backside of the proteins that dock vesicles to release sites.

This is joint work with Thomas Schlumpberger.

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