Mathematical model of mitochondrial ionic homeostasis: three modes of Ca2+ transport.

Mitochondria play an important role in regulation of Ca2+ homeostasis in a cell. Here we present a mathematical model of mitochondrial ion transport and use this model to analyse different modes of Ca2+ uptake by mitochondria. The model includes transport of H+, Ca2+, K+, inorganic phosphate and oxidative substrates across the inner mitochondrial membrane harboring permeability transition pore (PTP). The detailed description of ion fluxes is based on the experimental ion kinetics in isolated mitochondria. Using the model we show that the kinetics of Ca2+ uptake by mitochondria is regulated by the total amount of Ca2+ in the system and the rate of Ca2+ infusion. Varying these parameters we find three different modes of ion transport. When the total amount of Ca2+ is below 140 nmol Ca2+/mg protein, all available Ca2+ is accumulated in the matrix without activation of the PTP. Between 140 and 160 nmol Ca2+/mg protein, accumulation of Ca2+ generates periodic opening and closure of the PTP and oscillations of ion fluxes. Higher levels of Ca2+ (> 160 nmol Ca2+/mg protein) result in a permanently open PTP, membrane depolarization and loss of small ions from the matrix. We show that in the intermediate range of Ca2+ concentrations the rate of Ca2+ infusion regulates the PTP state, so that slow Ca2+ infusion does not lead to PTP opening, while fast Ca2+ infusion results in an oscillatory state.