Mapping interpuff interval distribution to the properties of inositol trisphosphate receptors

Tightly clustered inositol trisphosphate receptors (IP3Rs) control localized Ca2+ liberation from the endoplasmic reticulum to generate repetitive Ca2+ puffs. Distributions of the interpuff interval (IPI), i.e., the waiting time between successive puffs, are found to be well characterized by a probability density function involving only two parameters, lambda and xi, which represent the basal rate of puff generation and the recovery rate from refractoriness, respectively. However, how the two parameters depend on the kinetic parameters of single IP3Rs in a cluster is still unclear. In this article, using a stochastic puff model and a single-channel data-based IP3R model, we establish the dependencies of lambda and xi on two important IP3R model parameters, IP3 concentration ([IP3]) and the recovery rate from Ca2+ inhibition (rlow). By varying [IP3] and rlow in physiologically plausible ranges, we find that the xi-lambda plane is comprised of only two disjoint regions, a biologically impermissible region and a region where each parameter set (xi, lambda) can be caused by using two different combinations of [IP3] and rlow. The two combinations utilize very different mechanisms to maintain the same IPI distribution, and the mechanistic difference provides a way of identifying IP3R kinetic parameters by observing properties of the IPI.