A mathematical model of the regulation mechanism of Ca2+ concentration in lens in vivo

In order to elucidate the regulation mechanism of homeostasis on intracellular Ca2+ concentration in lens in vivo, the authors proposed a new mathematical model based upon the model of Ca2+ active transport. The mathematical model has new factors: Ca2+ efflux and Ca2+ influx across the cell membrane related to the difference between intracellular and extracellular Ca2+ concentration. Changes in intracellular Ca2+ concentration were investigated by numerical simulation using this model. Ca2+ efflux (active transport) is increased with intracellular Ca2+ concentration and their relationship corresponds to a Michaelis-Menten reaction. Ca2+ influx increases with the Ca2+ permeable coefficient of cell membrane. These results are consistent with the experimental results is a qualitative way and indicate that the model is suitable to elucidate the regulation mechanism of intracellular Ca2+ concentration. From the theoretical point of view, therefore, it is suggested that intracellular Ca2+ concentration may depend on two factors: one is the Ca2+ dependence of the Ca2+ active transport system, the other the Ca2+ permeability of the cell membrane.