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.
