Probability Distributions of Markovian Sodium Channel States During Propagating Axonal Impulses With or Without Recovery Supernormality

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This study addressed a macroscopic neurophysiological phenomenon — supernormality during the recovery phase of propagating axonal impulses — in explicit chemical terms. Excitation was reconstructed numerically using the kinetic scheme of multiple-state probabilistic transitions within a population of voltage-dependent sodium channels (NaCh) derived by Vandenberg and Bezanilla (“PC” scheme). Each NaCh transition was characterized as a reversible Markov process with voltage-dependent rate constants associated with each respective directional transition. While recovery reconstructed with the Hodgkin–Huxley formalism included a supernormal period, the PC scheme did not. The present analysis showed that the occurrence and degree of supernormality with the PC scheme was determined by the relative speed of the transitions within the closed loop of the kinetic scheme; supernormality was promoted by speeding these kinetics. The analysis also showed that concurrent with supernormality, the faster loop kinetics caused (1) an elevation in the C1 → C2 transitions, and (2) a reduction in the I4 → I5 transitions. Thus, macroscopic functionality in information processing could be expressed in terms of probabilistic interstate transitions among a population of NaCh molecules.