Colloquium
3:30 p.m., Monday
Math 100
Richard Bertram
Institute of Molecular Biophysics
Florida State University
Mathematical Analysis of Deterministic and Stochastic Models
of Synaptic Transmitter Release
In the brain, information is transmitted from one nerve cell to another
by the secretion of neurotransmitters. We have developed mathematical
models of neurotransmitter secretion, and the shortterm enhancement of
secretion that is an important part of the signal processing done
at nerve terminals. Although some information can be obtained from simple
deterministic models, the biological process is inherently stochastic, so
stochastic models are required to capture many important features.
Development and analysis of one such model will be described. With this
model, shortterm enhancement is due to the interaction of two populations
of transmitter release sites, each described by probability density
functions that evolve according to hyperbolic conservation equations.
Equations for the means of these density functions are derived, yielding
a system of ordinary differential equations that is much simpler to
analyze. Finally, a multiple scale analysis is used to explain
several properties of transmitter release observed in experiments.
