Calcium wave propagation by calcium-induced calcium release: an unusual excitable system

We discuss in detail the behaviour of a model, proposed by Goldbeter et al. (1990. Proc. natn. Acad. Sci. 87, 1461-1465), for intracellular calcium wave propagation by calcium-induced calcium release, focusing our attention on excitability and the propagation of waves in one spatial dimension. The model with no diffusion behaves like a generic excitable system, and threshold behaviour, excitability and oscillations can be understood within this general framework. However, when diffusion is included, the model no longer behaves like a generic excitable system; the fast and slow variables are not distinct and previous results on excitable systems do not necessarily apply. We consider a piecewise linear simplification of the model, and construct travelling pulse and periodic plane wave solutions to the simplified model. The analogous behaviour in the full model is studied numerically. Goldbeter's model for calcium-induced calcium release is an excitable system of a type not previously studied in detail.