The use of Monte Carlo methods in modelling synaptic function
by
Bill Gibson
School of Mathematics and Statistics, Sydney University
Coauthors: Max Bennett (Physiology, Sydney University), Les Farnell (Mathematics, Sydney University)

Neurons communicate principally via synaptic connections at which electrical impulses are transmitted using complicated electrochemical mechanisms. Two important aspects of this transmission are the influx of calcium ions into the presynaptic terminal and their binding to vesicle-associated proteins and then the subsequent release and diffusion of neurotransmitter substances across the synaptic cleft.

We have modelled both these processes using Monte Carlo techniques, in which a computer tracks the motion of individual molecules (up to 50, 000) as they diffuse and bind. The diffusion processes are modelled by mimicking the random walk that each molecules undergoes. Other processes that require special attention are reflection from cell walls, binding to receptors and buffers, pumping through membranes, etc.

The Monte Carlo method is an alternative to the usual continuous differential-equation approach, which works in terms of average concentrations of substances. Advantages of the Monte Carlo method are insights into the essentially stochastic nature of synaptic processes and the ability to handle complex geometries with little increase in programming complexity.

Date received: May 17, 1999