Effects of quantal unit latency on statistics of poisson and binomial neurotransmitter release mechanisms

Abstract

Linear random sum theory was used to develop statistics of corrected end-plate potential amplitudes for end-plate potentials composed of coincident (fixed latency model) and non-coincident (variable latency model) unit potentials using the Poisson and the binomial distributions for the neurotransmitter release mechanism. Equations were derived for the mean, variance, variance to mean ratio and coefficient of variation of corrected end-plate potential amplitudes. Analysis of neuromuscular transmission using these equations revealed the following: The mean quantal content of end-plate potentials formed from coincident unit potentials is to a good approximation linearly related to, and less than the quantal content of end-plate potentials formed from non-coincident unit potentials for both release mechanisms. As quantal content increases, the variance to mean ratio of corrected end-plate potential amplitudes formed from noncoincident unit potentials under a Poisson release mechanism initially decreases with increasing quantal content and then asymptotically approaches a constant value; whereas, the ratio is a continuously decreasing function of quantal content for a binomial release mechanism. For the Poisson release mechanism this ratio remains constant and equal to the mean unit amplitude for all values of quantal content when end-plate potentials are composed of coincident unit potentials, but the ratio remains a decreasing function of quantal content for a binomial release mechanism. For the Poisson release mechanism the coefficient of variation of corrected end-plate potential amplitudes formed from non-coincident unit potentials is smaller than the coefficient of variation of corrected amplitudes formed from coincident unit potentials; thus, the inverse of the square of the coefficient of variation is a better approximation for quantal content than the ratio of mean end-plate potential amplitude to mean unit amplitude. For the binomial release mechanism and large values of quantal content, the coefficient of variation of end-plate potentials is smaller than the respective coefficient of variation of end-plate potentials formed from coincident and non-coincident unit potentials for the Poisson release mechanism. Thus, for the binomial release mechanism and large quantal contents, the inverse of the square of the coefficient of variation yields a value of quantal content that is too large.