Weinberg Seth H, Smith Gregory D
Department of Applied Science, The College of William & Mary, Williamsburg, Virginia.
Department of Applied Science, The College of William & Mary, Williamsburg, Virginia.
Biophys J. 2014 Jun 17;106(12):2693-709. doi: 10.1016/j.bpj.2014.04.045.
Intracellular calcium (Ca(2+)) plays a significant role in many cell signaling pathways, some of which are localized to spatially restricted microdomains. Ca(2+) binding proteins (Ca(2+) buffers) play an important role in regulating Ca(2+) concentration ([Ca(2+)]). Buffers typically slow [Ca(2+)] temporal dynamics and increase the effective volume of Ca(2+) domains. Because fluctuations in [Ca(2+)] decrease in proportion to the square-root of a domain's physical volume, one might conjecture that buffers decrease [Ca(2+)] fluctuations and, consequently, mitigate the significance of small domain volume concerning Ca(2+) signaling. We test this hypothesis through mathematical and computational analysis of idealized buffer-containing domains and their stochastic dynamics during free Ca(2+) influx with passive exchange of both Ca(2+) and buffer with bulk concentrations. We derive Langevin equations for the fluctuating dynamics of Ca(2+) and buffer and use these stochastic differential equations to determine the magnitude of [Ca(2+)] fluctuations for different buffer parameters (e.g., dissociation constant and concentration). In marked contrast to expectations based on a naive application of the principle of effective volume as employed in deterministic models of Ca(2+) signaling, we find that mobile and rapid buffers typically increase the magnitude of domain [Ca(2+)] fluctuations during periods of Ca(2+) influx, whereas stationary (immobile) Ca(2+) buffers do not. Also contrary to expectations, we find that in the absence of Ca(2+) influx, buffers influence the temporal characteristics, but not the magnitude, of [Ca(2+)] fluctuations. We derive an analytical formula describing the influence of rapid Ca(2+) buffers on [Ca(2+)] fluctuations and, importantly, identify the stochastic analog of (deterministic) effective domain volume. Our results demonstrate that Ca(2+) buffers alter the dynamics of [Ca(2+)] fluctuations in a nonintuitive manner. The finding that Ca(2+) buffers do not suppress intrinsic domain [Ca(2+)] fluctuations raises the intriguing question of whether or not [Ca(2+)] fluctuations are a physiologically significant aspect of local Ca(2+) signaling.
细胞内钙（Ca(2+)）在许多细胞信号通路中发挥着重要作用，其中一些信号通路定位于空间受限的微区。钙结合蛋白（钙缓冲蛋白）在调节钙离子浓度（[Ca(2+)]）方面发挥着重要作用。缓冲蛋白通常会减缓[Ca(2+)]的时间动态变化，并增加钙离子区域的有效体积。由于[Ca(2+)]的波动与区域物理体积的平方根成比例减小，因此有人可能推测缓冲蛋白会降低[Ca(2+)]的波动，从而减轻小区域体积对钙信号传导的影响。我们通过对理想化的含缓冲蛋白区域及其在自由钙离子流入过程中的随机动力学进行数学和计算分析来检验这一假设，其中钙离子和缓冲蛋白与大量浓度进行被动交换。我们推导了钙离子和缓冲蛋白波动动力学的朗之万方程，并使用这些随机微分方程来确定不同缓冲参数（例如解离常数和浓度）下[Ca(2+)]波动的幅度。与基于确定性钙信号模型中简单应用有效体积原理的预期形成显著对比的是，我们发现可移动且快速的缓冲蛋白通常会在钙离子流入期间增加区域[Ca(2+)]波动的幅度，而固定（不可移动）的钙离子缓冲蛋白则不会。同样与预期相反的是，我们发现在没有钙离子流入的情况下，缓冲蛋白会影响[Ca(2+)]波动的时间特征，但不会影响其幅度。我们推导了一个描述快速钙离子缓冲蛋白对[Ca(2+)]波动影响的解析公式，重要的是，确定了（确定性）有效区域体积的随机类似物。我们的结果表明，钙离子缓冲蛋白以一种非直观的方式改变了[Ca(2+)]波动的动力学。钙离子缓冲蛋白不会抑制区域内源性[Ca(2+)]波动这一发现提出了一个有趣的问题，即[Ca(2+)]波动是否是局部钙信号传导的一个生理上重要的方面。
