Smith G D, Wagner J, Keizer J
Institute of Theoretical Dynamics, University of California, Davis 95616, USA.
Biophys J. 1996 Jun;70(6):2527-39. doi: 10.1016/S0006-3495(96)79824-7.
In the presence of rapid buffers the full reaction-diffusion equations describing Ca2+ transport can be reduced using the rapid buffering approximation to a single transport equation for [Ca2+]. Here we simulate the full and reduced equations, exploring the conditions necessary for the validity of the rapid buffering approximation for an isolated Ca2+ channel or a cluster of channels. Using a point source and performing numerical simulations of different durations, we quantify the error of the rapid buffering approximation as a function of buffer and source parameters as well as the time and spatial scale set by the resolution of confocal microscopic measurements. We carry out simulations of Ca2+ "sparks" and "puffs," both with and without the indicator dye Ca2+ Green-1, and find that the rapid buffering approximation is excellent. These calculations also show that the traditional calculation of [Ca2+] from a fluorescence signal may grossly underestimate the true value of [Ca2+] near a source. Finally, we use the full model to simulate the transient Ca2+ domain near the pore of an open Ca2+ channel in a cell dialyzed with millimolar concentrations of 1,2-bis(2-aminophenoxy)ethane-N,N,N,N-tetraacetic acid or EGTA. In this regime, where the rapid buffering approximation is poor. Neher's equation for the steady-state Ca2+ profile is shown to be a reliable approximation adjacent to the pore.
在存在快速缓冲剂的情况下，描述Ca2+转运的完整反应扩散方程可以通过快速缓冲近似简化为一个关于[Ca2+]的单一转运方程。在此，我们对完整方程和简化方程进行模拟，探究孤立的Ca2+通道或通道簇的快速缓冲近似有效性所需的条件。使用点源并进行不同持续时间的数值模拟，我们将快速缓冲近似的误差量化为缓冲剂和源参数以及由共聚焦显微镜测量分辨率设定的时间和空间尺度的函数。我们对有和没有指示剂染料Ca2+ Green-1的Ca2+“闪烁”和“阵发现象”进行模拟，发现快速缓冲近似非常出色。这些计算还表明，从荧光信号传统计算[Ca2+]可能会严重低估源附近[Ca2+]的真实值。最后，我们使用完整模型模拟在用毫摩尔浓度的1,2-双(2-氨基苯氧基)乙烷-N,N,N,N-四乙酸或乙二醇双四乙酸透析的细胞中开放Ca2+通道孔附近的瞬态Ca2+域。在这种快速缓冲近似不适用的情况下，表明用于稳态Ca2+分布的内尔方程在孔附近是一个可靠的近似。
