A theoretical and experimental study of the effects of non-uniform membrane resistance on the shape of single-cell charging curves

The isolated Muller glial cell of the neotenous tiger salamander retina is used as an experimental model for studying the effects of non-uniform membrane conductance on the shape of charging curves in response to step current inputs. A simple cable model of the Muller cell is formulated and used to interpret the experimental data. The Muller cell model is completely described by three parameters: (a) electrotonic length L; (b) the membrane time constant τ_m; and (c) the percentage of the total membrane conductance accounted for by the endfoot S. Model analysis indicates that increasing S produces monotonic decreases in the rise time of charging curves. This effect is greatest when L is small. In such cases charging curve rise time can be substantially faster than that of a semi-infinite cable. When S > 0, the first time constant obtained by fitting the late exponential tail of the charging curve is not the membrane time constant (as is the case when S = 0), but is instead an equalizing rime constant equal to the membrane time constant times a scale factor in the range of 0 to 1. This scaling factor becomes quite small as S approaches 100%. We describe a convergent numerical procedure for generating unique estimates of all three model parameters from charging curves. Application of the algorithm to experimentally measured Muller cell charging curves confirms Newman's finding that a large fraction of membrane conductance in these cells is accounted for by the endfoot (>90%). The model prediction that charging curve rise time may be substantially faster than that of the semi-infinite cable when S > 0 is also confirmed. The error that results from misinterpreting the first equalizing time constant τ₁, as the membrane time constant τ_m can have a significant effect on estimates of specific membrane resistance and capacitance. The algorithm described in this paper provides a means for obtaining direct estimates of the membrane time constant and will make possible more accurate estimates of specific membrane resistance and capacitance in Muller glial cells. The fact that the estimation procedure is based on a simple electrophysiological measurement suggests that it may be useful for studying asymmetry of membrane conductance in glial and neural elements of the intact nervous system.