具有间隙连接耦合的电池中扩散的局部累积时间
Local accumulation time for diffusion in cells with gap junction coupling
摘要：
在本文中，我们分析了在一对细胞间隙连接耦合的细胞内扩散的弛豫到稳态。缝隙连接普遍存在于大多数动物器官和组织中，为细胞之间的电和化学通讯提供直接扩散途径。大多数间隙连接的分析模型集中在稳态扩散通量和相关的有效扩散率。在这里，我们调查的松弛到稳定状态的所谓的本地积累时间。后者通常用于估计在形态发生期间形成蛋白质浓度梯度的时间。其基本思想是将稳态浓度的分数偏差视为局部累积时间的累积分布。局部累积时间的有用特征之一是它考虑了不同空间区域可以以不同速率弛豫的事实。我们考虑静态和动态间隙连接模型。前者将间隙连接视为具有有效磁导率$μ$的电阻性通道，而后者将间隙连接表示为在打开和关闭状态之间随机切换的随机门。通过在拉普拉斯空间中求解扩散方程，然后取小- $s$极限来计算局部累积时间。我们表明，积累时间是一个单调增加的函数的空间位置，跳跃不连续的间隙连接。这种不连续性在静态结的极限$μ\rightarrow \infty$和随机门控结的极限$β\rightarrow 0$中消失，其中$β$是门关闭的速率。最后，我们的结果被推广到最近邻间隙结耦合的线性阵列的情况。
英文摘要：
In this paper we analyze the relaxation to steady-state of intracellular diffusion in a pair of cells with gap-junction coupling. Gap junctions are prevalent in most animal organs and tissues, providing a direct diffusion pathway for both electrical and chemical communication between cells. Most analytical models of gap junctions focus on the steady-state diffusive flux and the associated effective diffusivity. Here we investigate the relaxation to steady state in terms of the so-called local accumulation time. The latter is commonly used to estimate the time to form a protein concentration gradient during morphogenesis. The basic idea is to treat the fractional deviation from the steady-state concentration as a cumulative distribution for the local accumulation time. One of the useful features of the local accumulation time is that it takes into account the fact that different spatial regions can relax at different rates. We consider both static and dynamic gap junction models. The former treats the gap junction as a resistive channel with effective permeability $μ$, whereas the latter represents the gap junction as a stochastic gate that randomly switches between an open and closed state. The local accumulation time is calculated by solving the diffusion equation in Laplace space and then taking the small-$s$ limit. We show that the accumulation time is a monotonically increasing function of spatial position, with a jump discontinuity at the gap junction. This discontinuity vanishes in the limit $μ\rightarrow \infty$ for a static junction and $β\rightarrow 0$ for a stochastically-gated junction, where $β$ is the rate at which the gate closes. Finally, our results are generalized to the case of a linear array of cells with nearest neighbor gap junction coupling.
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