Abstract
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$^2+$.
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