Oscillations in cytoplasmic calcium concentration ([Ca2+]), mediated by repetitive openings and closings of inositol trisphosphate receptor (IP3R) channels situated on the membrane of the endo/sarcoplasmic reticulum, have been found to be important for modulating many physiological processes. Decades of effort has been made to elucidate the mechanisms of such calcium oscillations, focusing on understanding (1) the dynamical properties of single IP3R in response to binding of various ligands, such as IP3, Ca2+ and ATP; and (2) how the IP3R dynamics contribute to the formation of calcium oscillations. In this talk, I will present how we used mathematical modelling and simulations to advance our understanding of the problems. The talk will be focused on three aspects: (1) the introduction of a mathematical model of IP3R which we established through fitting to single channel measurements; (2) stochastic simulation of localized calcium puffs using our IP3R model; and (3) deterministic approximation of stochastic modeling in the application of predicting calcium oscillations in airway smooth muscle cells. Finally, I will post some existing challenges for modeling calcium oscillations, which would inspire more constructive discussions at the workshop.
