%0 Journal Article %1 Huer_2007_332 %A Huertas, Marco A %A Smith, Gregory D %D 2007 %J J. Theor. Biol. %K Animals; Biological; Calcium Calcium; Carlo Channel Channels; Cytosol; Endoplasmic Gating; Ion Mathematics; Method; Models, Monte Probability; Processes Reticulum; Sarcoplasmic Signaling; Statistical; Stochastic %N 2 %P 332--354 %R 10.1016/j.jtbi.2007.01.003 %T The dynamics of luminal depletion and the stochastic gating of Ca$^2+$-activated Ca$^2+$ channels and release sites. %U http://dx.doi.org/10.1016/j.jtbi.2007.01.003 %V 246 %X 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$^2+$.

@article{Huer_2007_332, abstract = {Single channel models of intracellular calcium ({C}a$^{2+}$) channels such as the 1,4,5-trisphosphate receptor and ryanodine receptor often assume that {C}a$^{2+}$-dependent transitions are mediated by constant background cytosolic [{C}a$^{2+}$]. This assumption neglects the fact that {C}a$^{2+}$ released by open channels may influence subsequent gating through the processes of {C}a$^{2+}$-activation or inactivation. Similarly, the influence of the dynamics of luminal depletion on the stochastic gating of intracellular {C}a$^{2+}$ channels is often neglected, in spite of the fact that the sarco/endoplasmic reticulum [{C}a$^{2+}$] near the luminal face of intracellular {C}a$^{2+}$ channels influences the driving force for {C}a$^{2+}$, the rate of {C}a$^{2+}$ release, and the magnitude and time course of the consequent increase in cytosolic domain [{C}a$^{2+}$]. Here we analyze how the steady-state open probability of several minimal {C}a$^{2+}$-regulated {C}a$^{2+}$ channel models depends on the conductance of the channel and the time constants for the relaxation of elevated cytosolic [{C}a$^{2+}$] and depleted luminal [{C}a$^{2+}$] to the bulk [{C}a$^{2+}$] 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 [{C}a$^{2+}$] and depleted luminal [{C}a$^{2+}$] 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 {C}a$^{2+}$ puff/spark termination in release sites composed of {C}a$^{2+}$ channels that are activated, but not inactivated, by cytosolic {C}a$^{2+}$. The probability density approach shows that such minimal {C}a$^{2+}$ 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 {C}a$^{2+}$ 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 {C}a$^{2+}$.}, added-at = {2009-06-03T11:20:58.000+0200}, author = {Huertas, Marco A and Smith, Gregory D}, biburl = {https://www.bibsonomy.org/bibtex/2c73bb2b488626f842a3a356bc2bd61b7/hake}, description = {The whole bibliography file I use.}, doi = {10.1016/j.jtbi.2007.01.003}, file = {Huer_2007_332.pdf:Huer_2007_332.pdf:PDF}, interhash = {3a3dee3c2a6b691ee5b2801fc51bbc15}, intrahash = {c73bb2b488626f842a3a356bc2bd61b7}, journal = {J. Theor. Biol.}, keywords = {Animals; Biological; Calcium Calcium; Carlo Channel Channels; Cytosol; Endoplasmic Gating; Ion Mathematics; Method; Models, Monte Probability; Processes Reticulum; Sarcoplasmic Signaling; Statistical; Stochastic}, month = May, number = 2, pages = {332--354}, pii = {S0022-5193(07)00007-0}, pmid = {17286986}, timestamp = {2009-06-03T11:21:15.000+0200}, title = {The dynamics of luminal depletion and the stochastic gating of {C}a$^{2+}$-activated {C}a$^{2+}$ channels and release sites.}, url = {http://dx.doi.org/10.1016/j.jtbi.2007.01.003}, volume = 246, year = 2007 }