A collaboration between members of the School of Mathematics and Statistics and the Department of Physiology has been in place for over ten years. During this time, about 30 joint research papers have been published in major journals and competitive grants totalling over one million dollars have been awarded for joint projects.
Calcium plays a vital role in the nervous system, being the trigger for release of neurotransmitter at the synaptic connections between neurons. In addition, calcium is implicated in synaptic plasticity and hence in the way in which the brain learns and stores memories. Calcium enters a nerve terminal from outside during electrical stimulation, but there is increasing evidence that calcium sequestered in internal stores within neurons and terminals also plays a important part. We have developed models for many aspects of calcium function, the most recent being a comprehensive Monte Carlo computation scheme that allows detailed investigation of synaptic function at the ionic and molecular level. We are currently applying this method to a study of facilitation, which is the transient increase in the probability of transmitter release that follows an impulse.
Nerves and muscles communicate via electrical signals. Modern experimental techniques measure potentials that arise external to cell bodies during this communication but existing computational theories deal almost exclusively with internal potentials. We have developed methods for computing external potentials, using mathematical analysis of electrical circuits that mimic the physiological processes. These methods have been applied to amphibian motor-nerve terminals, boutons in sympathetic ganglia and to smooth muscle tissue in arterial walls and the vas deferens. The combination of theoretical and experimental procedures has led to important insights into the mechanisms of transmitter release in these systems.