The task of theory in cell biology is to predict behavior from system parameters. The general features of IP3-induced Ca2+ spiking we find experimentally are: (1) interspike intervals are random; (2) cell-to-cell variability is very large; (3) the agonist concentration-response relation of the average interspike interval is exponential; (4) the moment relation between the average interspike interval and its standard deviation is linear; (5) the moment relation and the agonist sensitivity are cell type and pathway-specific and not subject to cell variability. Identification of the mathematical structure to which a system corresponds is the first and most important step in the development of a theory. The mathematical (some say dynamical) structure corresponding to IP3-induced Ca2+ signaling is an array of noisy excitable (maybe bistable) elements coupled by a diffusion process. There is strong coupling within clusters and weak coupling between clusters. Global feedbacks and processes set long time scales. Starting from there, we can develop a simple theory showing the moment relation and its robustness properties. We find that on a single-cell level in several cases, long time scales may arise from small spike probabilities and not from slow processes, but slow processes are required to obtain a small coefficient of variation for the interspike interval.
