A Biophysically Based Mathematical Model for the Kinetics of Mitochondrial Na-Ca Antiporter

Sodium-calcium antiporter is the primary efflux pathway for Ca²⁺ in respiring mitochondria, and hence plays an important role in mitochondrial Ca²⁺ homeostasis. Although experimental data on the kinetics of Na⁺-Ca²⁺ antiporter are available, the structure and composition of its functional unit and kinetic mechanisms associated with the Na⁺-Ca²⁺ exchange (including the stoichiometry) remains unclear. To gain a quantitative understanding of mitochondrial Ca²⁺ homeostasis, a biophysical model of Na⁺-Ca²⁺ antiporter is introduced that is thermodynamically balanced and satisfactorily describes a number of independent data sets under a variety of experimental conditions. The model is based on a multistate catalytic binding mechanism for carrier-mediated facilitated transport and Eyring's free energy barrier theory for interconversion and electrodiffusion. The model predicts the activating effect of membrane potential on the antiporter function for a 3Na⁺:1Ca²⁺ electrogenic exchange as well as the inhibitory effects of both high and low pH seen experimentally. The model is useful for further development of mechanistic integrated models of mitochondrial Ca²⁺ handling and bioenergetics to understand the mechanisms by which Ca²⁺ plays a role in mitochondrial signaling pathways and energy metabolism.