A mathematical sequence representing tonic action potential spike trains

This is a study outlining the regularity of action potential spikes. Through a stochastic study, we observed a series of strong correlations between the intervals of tonically firing spikes generated by injecting constant currents of varying intensities into layer V pyramidal neurons of the ferret medial prefrontal cortex. Based on this, we derived a formulaic relationship 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 factors in the history of all previous ISIs. The sequence element exhibited minimal variation in value against the stimulation intensity in a neuron, serving as a precursor to timing. In contrast, the first ISI decreased logarithmically with the intensity of the injected current, acting as a scale factor. Finally, using these rules, we successfully predicted the timing of spikes, illustrating that this approach can reflect changes in ion conductance which affects the spike timing. These findings expand our insight into neural coding and increase research efficacy using neural modeling.