Correction of end-plate potentials and currents for nonlinear summation

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Abstract
When transmitter substance acts to increase ionic conductance of a subsynaptic membrane, the resulting potential change is not linearly related to the conductance change. Peak potential changes (v) were computed for an equivalent circuit corresponding to the neuromuscular junction: the postsynaptic cell was simulated as a 'cable' with distributed capacitance and the conductance change was made to fall exponentially from an initial peak. For this model it was found that the quantity v/(1 − vE−1 a−1) is very nearly proportional to peak synaptic conductance, where E is the difference between synaptic equilibrium potential and membrane potential, and a is close to unity. That is, Martin's relation remains applicable even when the synaptic conductance is brief. The same equation holds, but with reduced a, when recording is nonfocal and (or) when the rate of decline of the synaptic conductance change is increased by the change of potential that it induces. Therefore, exact correction of end-plate potentials for nonlinearity is not possible. However, for recording that is close to focal and v/E less than 20%, there should be little error in the above 'correction' using a = 1 − 0.00135E, where E is expressed in millivolts. In the case of a 'point' voltage clamp, the recorded current is equal to the synaptic current only if the clamping electrodes are placed exactly focally, which may be technically impossible. Otherwise, the relation between recorded current and conductance is similar to that between v and conductance: nonlinearity may be quite large even when a clamp is very nearly focal, when synaptic conductance is large.