Huertas Marco A, Smith Gregory D
Department of Applied Science, College of William and Mary, Williamsburg, VA 23187, USA.
J Theor Biol. 2007 May 21;246(2):332-54. doi: 10.1016/j.jtbi.2007.01.003. Epub 2007 Jan 11.
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+).
细胞内钙（Ca(2+)）通道的单通道模型，如三磷酸肌醇受体和雷诺丁受体，通常假定Ca(2+)依赖性转变是由恒定的胞质背景[Ca(2+)]介导的。这一假设忽略了开放通道释放的Ca(2+)可能通过Ca(2+)激活或失活过程影响后续门控的事实。同样，尽管细胞内Ca(2+)通道腔面附近的肌浆网/内质网[Ca(2+)]会影响Ca(2+)的驱动力、Ca(2+)释放速率以及随之而来的胞质区域[Ca(2+)]增加的幅度和时间进程，但腔室耗竭动力学对细胞内Ca(2+)通道随机门控的影响常常被忽视。在这里，我们分析了几种最小Ca(2+)调节的Ca(2+)通道模型的稳态开放概率如何取决于通道的电导以及胞质[Ca(2+)]升高和腔室[Ca(2+)]耗尽至两个隔室的总体[Ca(2+)]的弛豫时间常数。我们的方法包括蒙特卡罗模拟以及针对以随机门控通道的每个状态为条件的胞质[Ca(2+)]升高和腔室[Ca(2+)]耗尽的多元概率密度的对流反应方程组的数值解。随后，这两种方法都被用于研究腔室耗竭在由被胞质Ca(2+)激活但未失活的Ca(2+)通道组成的释放位点中Ca(2+)阵发/闪烁终止动力学中的作用。概率密度方法表明，这种最小Ca(2+)释放位点模型可能在两种不同的参数范围内表现出阵发/闪烁样动力学。在一种情况下，阵发/闪烁终止是由于随机磨损过程，并由快速的Ca(2+)域塌陷促进[参见DeRemigio, H., Smith, G., 2005. 被视为终止马尔可夫链上吸收时间的随机磨损动力学。细胞钙38, 73 - 86]。在第二种情况下，阵发/闪烁终止是由腔室Ca(2+)的局部耗尽促进的。
