A NONSTATIONARY POISSON POINT PROCESS DESCRIBES THE SEQUENCE OF ACTION-POTENTIALS OVER LONG-TIME SCALES IN LATERAL-SUPERIOR-OLIVE AUDITORY NEURONS

The behavior of lateral-superior-olive (LSO) auditory neurons over lar ge time scales was investigated. Of particular interest was the determ ination as to whether LSO neurons exhibit the same type of fractal beh avior as that observed in primary VIII-nerve auditory neurons. It has been suggested that this fractal behavior, apparent on long time scale s, may play a role in optimally coding natural sounds. We found that a nonfractal model, the nonstationary dead-time-modified Poisson point process (DTMP), describes the LSO firing patterns well for time scales greater than a few tens of milliseconds, a region where the specific details of refractoriness are unimportant. The rate is given by the su m of two decaying exponential functions. The process is completely spe cified by the initial values and time constants of the two exponential s and by the dead-time relation. Specific measures of the firing patte rns investigated were the interspike-interval (ISI) histogram, the Fan o-factor time curve (FFC), and the serial count correlation coefficien t (SCC) with the number of action potentials in successive counting ti mes serving as the random variable. For all the data sets we examined, the latter portion of the recording was well approximated by a single exponential rate function since the initial exponential portion rapid ly decreases to a negligible value. Analytical expressions available f or the statistics of a DTMP with a single exponential rate function ca n therefore be used for this portion of the data. Good agreement was o btained among the analytical results, the computer simulation, and the experimental data on time scales where the details of refractoriness are insignificant. For counting times that are sufficiently large, yet much smaller than the largest time constant in the rate function, the Fano factor is directly proportional to the counting time. The nonsta tionarity may thus mask fractal fluctuations, for which the Fano facto r increases as a fractional power (less than unity) of the counting ti me.