Intercellular Ca 2+ Wave Propagation through Gap-Junctional Ca 2+ Diffusion: A Theoretical Study

Abstract

Intercellular regenerative calcium waves in systems such as the liver and the blowfly salivary gland have been hypothesized to spread through calcium-induced calcium release (CICR) and gap-junctional calcium diffusion. A simple mathematical model of this mechanism is developed. It includes CICR and calcium removal from the cytoplasm, cytoplasmic and gap-junctional calcium diffusion, and calcium buffering. For a piecewise linear approximation of the calcium kinetics, expressions in terms of the cellular parameters are derived for 1) the condition for the propagation of intercellular waves, and 2) the characteristic time of the delay of a wave encountered at the gap junctions. Intercellular propagation relies on the local excitation of CICR in the perijunctional space by gap-junctional calcium influx. This mechanism is compatible with low effective calcium diffusivity, and necessitates that CICR can be excited in every cell along the path of a wave. The gap-junctional calcium permeability required for intercellular waves in the model falls in the range of reported gap-junctional permeability values. The concentration of diffusive cytoplasmic calcium buffers and the maximal rate of CICR, in the case of inositol 1,4,5-trisphosphate (IP 3) receptor calcium release channels set by the IP 3 concentration, are shown to be further determinants of wave behavior.