A Mathematical Sequence Representing Tonic Action Potential Spike Trains

Abstract

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 two factors: the timing precursor and the scale factor. Those arise from a linear relationship between activities of ion channels that modulate spike frequency adaptation and spike timing. Using this rule, we successfully predicted spike timing and demonstrated that the spike timing can be determined by the linear combination of various ion channel activities, reflecting different cellular signaling pathways such as G-protein coupled receptor (GPCR) activation. These findings not only aid studies on cellular signaling but also expand our insight into neural coding, while increasing research efficacy through neural modeling. Significant StatementWhile the action potential (AP) pattern may appear simple at first glance, no rule has been discovered in the nearly 100 years since it was first recorded. Building on this finding, we have developed a method to intuitively measure the activity of various ion channels responsible for determining spike timing from the AP spikes, as well as the associated intracellular and extracellular signaling pathways.