Mathematical models of travelling calcium waves
by
James Sneyd
Massey University

In the past fifteen years or so, it has become clear that the concentration of calcium ions inside cells shows extremely complex dynamic behaviour in practically all cell types. In response to a variety of stimuli, the concentration of intracellular free calcium ions can form temporal oscillations, travelling waves, spiral waves, multiple spiral waves, periodic waves, or even waves that travel from cell to cell over large areas. It is not always clear what the exact functions of these behaviours are, but we do know they serve to control such diverse functions as hormone secretion, cell movement, gene expression, wound recovery, and intercellular coordination. Clearly, these calcium oscillations and waves are of great physiological importance; they are therefore studied intensively by many experimental groups around the world. But just as clear (to a mathematician at least) is that such complex dynamical behaviours cannot be well understood without a firm theoretical underpinning, a framework upon which hypotheses may he hung, and a detailed knowledge of the bifurcations and dynamics underlying the observed phenomena. Hence, this area of physiology is ideally suited for collaborative work between mathematicians and experimentalists. In my talk I shall begin by discussing some of the background physiology, and show some movies of experimental results. I'll then discuss some of the mathematical models in the field, and show how this modelling work, in close collaboration with experimental work, has answered a number of crucial questions. Finally, I'll briefly discuss some of the more complex bifurcations seen in more recent models, and outline the most important unsolved theoretical questions in the field today. Ideally, I'll be able to show how mathematicians and experimentalists working together can solve problems that would be inaccessible to each working on their own.

Date received: September 6, 2000