Stochastic Subthreshold Processes in Photorecptors and Neuromuscular Junctions and a Shot Noise Model

Abstract

The apparently regular, deterministic functional properties of the arthropod photoreceptor potentials and frog neuromuscular endplate potentials are based on random and spontaneous microscopic activity. Because of this randomness, quantitative descriptions of that activity must be in statistical terms and in the form of a stochastic model. The paper presents such a model for the spontaneous miniature endplate potentials (m.e.p.p.) of the neuromuscular junction and the spontaneous slow potential fluctuations (SPF) of the Limulus photoreceptor ceptor.The shot process, a stochastic model originally applied to the shot noise in electron tubes, is the model adapted to describe the two examples of subthreshold neuroelectric activity mentioned above. It is used here to deal with the summation of random unitary events (m.e.p.p. and SPF) in the cell membrane which give rise to the fluctuating subthreshold potentials. The model allows one to describe statistical properties of the membrane potential fluctuations such as its amplitude probability density function (pdf), mean and variance, in terms of the statistical parameters of the unitary events such as average occurrence rate, amplitude distribution and time course.The paper presents a brief general description of the shot process including expressions for amplitude pdf as derived using the method of characteristic functions and using a stochastic integral equation. The second technique is used to solve directly for the pdf of a shot process with exponential shots that are reasonably realistic from the neurophysiological viewpoint. Analog and digital simulations are also used to obtain the pdf as a method of solution which may allow more flexibility in choice of unitary parameters.The results of neurophysiological experiments are presented in which the unitary parameters of the photoreceptor and endplate potentia1s were obtained and used to predict the summated fluctuating potentials on the basis of the shot process model. These predictions were compared to directly measured statistics of the neuroelectric activity. The predicted endplate potential statistics correlate very well with the directly measured values. Predictions of photoreceptor potential statistics correlated well with measured values of mean but showed discrepancies with variance measures. Such discrepancies are related to the nonindependence of SPF intervals with light stimulation and the effects of light adaptation on the SPF amplitude. The variability of visual threshold found in psychophysical experiments is also discussed in terms of the theoretical model and ecperimental findings