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

Single channel models of intracellular calcium ( Ca 2 + ) channels such as the 1,4,5-trisphosphate receptor and ryanodine receptor often assume that Ca 2 + -dependent transitions are mediated by constant background cytosolic [ Ca 2 + ] . This assumption neglects the fact that Ca 2 + released by open channels may influence subsequent gating through the processes of Ca 2 + -activation or inactivation. Similarly, the influence of the dynamics of luminal depletion on the stochastic gating of intracellular Ca 2 + channels is often neglected, in spite of the fact that the sarco/endoplasmic reticulum [ Ca 2 + ] near the luminal face of intracellular Ca 2 + channels influences the driving force for Ca 2 + , the rate of Ca 2 + release, and the magnitude and time course of the consequent increase in cytosolic domain [ Ca 2 + ] . Here we analyze how the steady-state open probability of several minimal Ca 2 + -regulated Ca 2 + channel models depends on the conductance of the channel and the time constants for the relaxation of elevated cytosolic [ Ca 2 + ] and depleted luminal [ Ca 2 + ] to the bulk [ Ca 2 + ] 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 [ Ca 2 + ] and depleted luminal [ Ca 2 + ] 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 Ca 2 + puff/spark termination in release sites composed of Ca 2 + channels that are activated, but not inactivated, by cytosolic Ca 2 + . The probability density approach shows that such minimal Ca 2 + 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 Ca 2 + 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 Ca 2 + .