Theoretical analysis of calcium wave propagation based on inositol (1,4,5)-trisphosphate (InsP 3) receptor functional properties

Abstract

In the presence of inositol (1,4,5)-trisphosphate (InsP 3) repetitive waves of elevated cytosolic free Ca 2+ (Ca waves) that travel through cellular cytoplasm are observed. Investigation of this phenomenon stimulated the view of cellular cytoplasm as ‘an excitable medium composed of Ca release processes (InsP 3R), coupled by a common stimulatory signal (Ca) through diffusion’ [Lechleiter JD. Clapham DE. (1992) Molecular mechanisms of intracellular calcium excitability in Xenopus laevis oocytes. Cell, 69, 283–294]. Using a kinetic model of InsP 3R gating, an analytical expression for the amplitude of Ca wave propagating through this excitable medium has been obtained. The ampiitude of the Ca wave is determined by the combination of cell-specific parameters and the functional properties of a single InsP 3R. An analytical expression for Ca wave propagation velocity has been also obtained using the Luther equation for diffusion-driven autocatalytic reaction. Both equations provided reasonable estimations for Ca wave amplitude (1.3 μM free Ca) and the velocity of the wave propagation (21 μm/s) for Ca waves in Xenopus oocytes when numerical values of parameters were used. The duration of refractory period has been shown to be determined mainly by the activity of CaATPase. Obtained results provide an insight into the mechanisms underlying the process of Ca wave propagation and define the interrelationship between different factors involved in this process. Some experimentally testable predictions can be done based on the analytical expressions obtained for Ca wave amplitude, the velocity of Ca wave propagation and the duration of refractory period.