A Model of Calcium-Induced Calcium Release from the Sarcoplasmic Reticulum in The Smooth Muscle Cell and its Investigation by Mathematical Modeling

A model of calcium-induced calcium release (CICR) from the sarcoplasmic reticulum was developed, simulating the behavior of the smooth muscle cell under conditions of its agonist stimulation. The mathematical model is a system of thirteen differential equations. In the initial (basal) state, the parameters of active and passive transport of Ca2+ through both the plasma membrane and the sarcoplasmic reticulum membrane are adjusted. A study of the model showed that, depending on the model parameters, the cell system can demonstrate two types of calcium concentration changes in the cytosol: a single Ca2+ transient and an oscillatory mode. After stimulation is completed, the cell system returns to the basal state (under in vivo conditions) or goes to a new steady-state level (under in vitro conditions), except when the cell system is in oscillatory mode. It is shown that the sarcoplasmic reticulum can act both as a passive participant in the process of Ca2+ accumulation in the cytosol, acting as a buffer, and play a major role by significantly increasing the Ca2+ concentration in the cytosol. As a result of calcium-induced calcium release, the sarcoplasmic reticulum is not completely emptied, but retains quite significant amounts of Ca2+. The possibility of Ca2+ redistribution between the three compartments (extracellular space, cytosol and sarcoplasmic reticulum) creates the possibility of oscillation of cytosolic Ca2+ concentration. The developed model qualitatively reproduces the results of experimental studies conducted to identify store-operated calcium channels using the inhibitors of the calcium pump of the sarcoplasmic reticulum in a calcium-free medium.