A comment on Martin's relation

Abstract

In the limit of slowly varying synaptic conductance changes, a quantity proportional to the quantal content of a synaptic potential is provided by Martin's formula: 1/(VO/Vp-1), where Vp is the peak amplitude of the synaptic potential and Vo is the synaptic equilibrium potential. If the synaptic conductance change is not slowly varying on the time scale of the postsynaptic cell's membrane time constant, Martin's formula overestimates the effects of nonlinear summation and provides an upper limit for the actual quantal content. In the limit of rapidly varying synaptic conductance changes the quantity ln(1/[1-Vp/Vo]) is proportional to the quantal content. This formula underestimates the effects of nonlinear summation and gives a lower limit for the quantal content for cases in which the synaptic conductance is not rapidly varying. These two formulas used together provide upper and lower bounds to the correction for nonlinear summation of postsynaptic potentials.