Cooperativity can reduce stochasticity in intracellular calcium dynamics

The opening of inositol (1,4,5)-triphosphate (IP(3)) receptors, clustered at discrete sites on the endoplasmic reticulum, can lead to large-scale intracellular calcium waves. Recent experiments in Xenopus oocytes have shown that the inter-wave intervals for these waves have a standard deviation that is much smaller than their mean and that the background calcium concentration exhibits a slow rise during the interwave interval. Using a simple mathematical model, we examine the possibility that this slow rise increases the cooperativity between the openings of the clusters. We find that our model, coupled to the usual assumption that the pumps on the endoplasmic reticulum are activated instantaneously, is unable to explain the observed data: the clusters are found to fire independently and the inter-wave interval distribution is a Poisson distribution with a standard deviation that is approximately equal to its mean. On the other hand, we find that incorporating pumps that slowly activate leads to a slow increase in the background calcium concentration which makes global events progressively more likely to occur. We show that this cooperativity results in much smaller standard deviations and inter-wave interval distributions that are clearly not Poisson distributions.