The dynamics of luminal depletion and the stochastic gating of Ca2+Ca2+-activated Ca2+Ca2+ channels and release sites

Single channel models of intracellular calcium (Ca2+)(Ca2+) channels such as the 1,4,5-trisphosphate receptor and ryanodine receptor often assume that Ca2+Ca2+-dependent transitions are mediated by constant background cytosolic [Ca2+][Ca2+]. This assumption neglects the fact that Ca2+Ca2+ released by open channels may influence subsequent gating through the processes of Ca2+Ca2+-activation or inactivation. Similarly, the influence of the dynamics of luminal depletion on the stochastic gating of intracellular Ca2+Ca2+ channels is often neglected, in spite of the fact that the sarco/endoplasmic reticulum [Ca2+][Ca2+] near the luminal face of intracellular Ca2+Ca2+ channels influences the driving force for Ca2+Ca2+, the rate of Ca2+Ca2+ release, and the magnitude and time course of the consequent increase in cytosolic domain [Ca2+][Ca2+]. Here we analyze how the steady-state open probability of several minimal Ca2+Ca2+-regulated Ca2+Ca2+ channel models depends on the conductance of the channel and the time constants for the relaxation of elevated cytosolic [Ca2+][Ca2+] and depleted luminal [Ca2+][Ca2+] to the bulk [Ca2+][Ca2+] of both compartments. Our approach includes Monte Carlo simulation as well as numerical solution of a system of advection-reaction equations for the multivariate probability density of elevated cytosolic [Ca2+][Ca2+] and depleted luminal [Ca2+][Ca2+] conditioned on each state of the stochastically gating channel. Both methods are subsequently used to study the role of luminal depletion in the dynamics of Ca2+Ca2+ puff/spark termination in release sites composed of Ca2+Ca2+ channels that are activated, but not inactivated, by cytosolic Ca2+Ca2+. The probability density approach shows that such minimal Ca2+Ca2+ release site models may exhibit puff/spark-like dynamics in either of two distinct parameter regimes. In one case, puffs/spark termination is due to the process of stochastic attrition and facilitated by rapid Ca2+Ca2+ domain collapse [cf. DeRemigio, H., Smith, G., 2005. The dynamics of stochastic attrition viewed as an absorption time on a terminating Markov chain. Cell Calcium 38, 73–86]. In the second case, puff/spark termination is promoted by the local depletion of luminal Ca2+Ca2+.