Spatial distribution of potential in a flat cell. Application to the catfish horizontal cell layers

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.