Barry P H
J Membr Biol. 1984;82(3):221-39. doi: 10.1007/BF01871632.
Many neurones are extremely invaginated and possess branching processes, axons and dendrites. In general, they are surrounded by a restricted diffusion space. Many of these cells exhibit large, slow potential changes during the passage of current across their membranes. Whenever currents cross membranes separating aqueous solutions, differences in transport numbers of the major permeant ions give rise to local concentration changes of these ions adjacent to the membranes, which will result in various electrical and osmotic effects. These transport number effects are expected to be enhanced by the presence of membrane invaginations. Dendrites are equivalent to reversed invaginations and there should be significant changes in concentrations of permeant ions within them. In general, the effects of such changes on the electrical response of a cell will be greater when the concentration of a major permeant ion is low. The effects have been modelled in terms of two nondimensional parameters: the invagination transport number parameter beta and the relative area occupied by the invaginations delta A. If these two parameters are known, the magnitudes and time course of the slow potential changes can immediately be estimated and the time course converted to real time, if the length of the invaginations (l) and ionic diffusion coefficient (D) within them are alos known. Both analytical and numerical solutions have been given and predictions compared. It is shown that in the case of large currents and potentials the analytical solution predictions will underestimate the magnitudes and rates of onset of the voltage responses. The relative magnitude of the transport number effect within the invaginations (or dendrites) and other transport number contributions to slow potential changes have also been assessed and order-of-magnitude values of these are estimated for some biological data.
许多神经元具有高度内陷的结构，并拥有分支状的突起、轴突和树突。一般来说，它们被一个受限的扩散空间所包围。在电流通过这些细胞膜的过程中，许多此类细胞会表现出大的、缓慢的电位变化。每当电流穿过分隔水溶液的细胞膜时，主要渗透离子的迁移数差异会导致这些离子在膜附近的局部浓度变化，这将产生各种电效应和渗透效应。膜内陷的存在预计会增强这些迁移数效应。树突相当于反向的内陷，其中渗透离子的浓度应该会有显著变化。一般来说，当主要渗透离子的浓度较低时，这种变化对细胞电反应的影响会更大。这些效应已根据两个无量纲参数进行建模：内陷迁移数参数β和内陷所占的相对面积ΔA。如果知道这两个参数，就可以立即估计缓慢电位变化的幅度和时间进程，并且如果还知道内陷的长度（l）和其中的离子扩散系数（D），就可以将时间进程转换为实际时间。已经给出了解析解和数值解，并对预测结果进行了比较。结果表明，在大电流和高电位的情况下，解析解预测会低估电压响应的幅度和起始速率。还评估了内陷（或树突）内迁移数效应的相对大小以及对缓慢电位变化的其他迁移数贡献，并针对一些生物学数据估计了它们的数量级值。
