A Mathematical Sequence Representing Tonic Action Potential Spike Trains
This is a study on the regularity of action potential spikes. Through a stochastic study, we found a series of strong correlations between the intervals of tonically firing spikes with the existence of spike frequency adaptation generated by injecting constant currents of varying intensities into layer 5 pyramidal neurons of the ferret medial prefrontal cortex. Based on this, we derived a relationship formula for the interspike intervals (ISIs). According to this formula, an ISI can be expressed as a product of the first ISI and a mathematical sequence that factorials the history of all previous ISIs. When this formula was applied to individual neurons, the sequence part exhibited minimal variation in value against the intensity of stimulation and was similar across injected current intensities, serving as a precursor to timing which is related to spike number rather than time after stimulation. In contrast, the first ISI decreased negative logarithmically with the intensity of injected current, acting as a scale factor. Finally, we successfully predicted the timing of spike occurrences based on the characteristics of this sequence formula and replicated spike train generated by strong stimulation using partial information from spike trains generated by weak stimuli.