Marmarelis P Z, Naka K I
Biophys J. 1972 Nov;12(11):1515-32. doi: 10.1016/S0006-3495(72)86179-4.
An analytical solution is obtained for the three-dimensional spatial distribution of potential inside a flat cell, such as the layer of horizontal cells, as a function of its geometry and resistivity characteristics. It was found that, within a very large range of parameter values, the potential is given by [Formula: see text] where r = rho/rho(0), z = z/rho(0), rho = (R(i)/R(m)).rho(0), delta = h/rho(0); K is a constant; J is the assumed synaptic current; rho, z are cylindrical coordinates; rho(0) is the radius of the synaptic area of excitation; h is the cell thickness; and R(i), R(m) are the intracellular and membrane resistivities, respectively. Formula A closely fits data for the spatial decay of potential which were obtained from the catfish internal and external horizontal cells. It predicts a decay which is exponential down to about 40% of the maximum potential but is much slower than exponential below that level, a characteristic also exhibited by the data. Such a feature in the decay mode allows signal integration over the large retinal areas which have been observed experimentally both at the horizontal and ganglion cell stages. The behavior of the potential distribution as a function of the flat cell parameters is investigated, and it is found that for the range of the horizontal cell thicknesses (10-50 mu) the decay rate depends solely on the ratio R(m)/R(i). Data obtained from both types of horizontal cells by varying the diameter of the stimulating spot and for three widely different intensity levels were closely fitted by equation A. In the case of the external horizontal cell, the fit for different intensities was obtained by varying the ratio R(m)/R(i); in the case of the internal horizontal cell it was found necessary, in order to fit the data for different intensities, to vary the assumed synaptic current J.
得到了扁平细胞（如水平细胞层）内部电势三维空间分布的解析解，该解析解是其几何形状和电阻率特性的函数。研究发现，在非常大的参数值范围内，电势由[公式：见原文]给出，其中r = ρ/ρ(0)，z = z/ρ(0)，ρ = (R(i)/R(m))·ρ(0)，δ = h/ρ(0)；K为常数；J为假定的突触电流；ρ、z为柱坐标；ρ(0)为激发突触区域的半径；h为细胞厚度；R(i)、R(m)分别为细胞内电阻率和膜电阻率。公式A与从鲶鱼内、外水平细胞获得的电势空间衰减数据非常吻合。它预测电势衰减在达到最大电势的约40%之前呈指数形式，但在该水平以下比指数衰减慢得多，这也是数据所表现出的特征。衰减模式中的这种特征允许在水平细胞和神经节细胞阶段通过实验观察到的大视网膜区域上进行信号整合。研究了电势分布随扁平细胞参数的变化情况，发现对于水平细胞厚度范围（10 - 50微米），衰减率仅取决于R(m)/R(i)的比值。通过改变刺激点直径并针对三种差异很大的强度水平从两种类型的水平细胞获得的数据，都能很好地用公式A拟合。对于外水平细胞，通过改变R(m)/R(i)的比值来拟合不同强度的数据；对于内水平细胞，为了拟合不同强度的数据，发现有必要改变假定的突触电流J。
