A Ca2+ puff model based on integrodifferential equations.

Abstract

The calcium signalling system is important for many cellular processes within the human body. Signals are transmitted within the cell by releasing calcium (Ca $_{}^{2+}$ ) from the endoplasmic reticulum (ER) into the cytosol via clusters of Ca $_{}^{2+}$ channels. Mathematical models of Ca $_{}^{2+}$ release via inositol 1,4,5-trisphosphate receptors (IP₃R) are used to compute Ca $_{}^{2+}$ transients in regions that are difficult to measure directly. In particular, accounting for the data on Ca $_{}^{2+}$ puffs as stochastic Ca $_{}^{2+}$ release events in models remains challenging. Parameterising Markov models for representing the IP₃R with steady-state single channel data obtained at fixed combinations of the ligands Ca $_{}^{2+}$ and inositol-trisphosphate (IP₃) has previously been demonstrated to be insufficient. However, by extending an IP₃R model based on steady-state data with an integral term that incorporates the delayed response of the channel to varying Ca $_{}^{2+}$ concentrations we succeed in generating realistic Ca $_{}^{2+}$ puffs. By interpreting the integral term as a weighted average of Ca $_{}^{2+}$ concentrations that extend over a time interval of length  $\tau$ into the past we conclude that the IP₃R requires a certain amount of memory of past ligand concentrations.