Stochastic properties of discrete waves of the limulus photoreceptor

In the dark-adapted photoreceptor of the horseshoe crab, Limulus, transient discrete depolarizations of the cell membrane, discrete waves, occur in total darkness and their rate of occurrence is increased by illumination. The individual latencies of the discrete waves evoked by a light stimulus often cannot be resolved because the discrete waves overlap in time. The latency of the first discrete wave that follows a stimulus can be determined with reasonable accuracy. We propose a model which allows us to make an estimate of the distribution of the latencies of the individual light-evoked discrete waves, and to predict the latency distribution of the first discrete wave that follows a stimulus of arbitrary intensity-time course from the latency distribution of the first discrete wave that follows a brief flash of light. For low intensity stimuli, the predictions agree well with the observations. We define a response as the occurrence of one or more discrete waves following a stimulus. The distribution of the peak amplitudes of responses suggests that the peak amplitude of individual discrete waves sometimes has a bimodal distribution. The latencies of the two types of discrete waves, however, follow similar distributions. The area under the voltage-time curve of responses that follow equal energy long (1.25 sec) and short (10 msec) light stimuli follows similar distributions, and this suggests that discrete waves summate linearly.