Metabolic efficiency with fast spiking in the squid axon

Fundamentally, action potentials in the squid axon are consequence of the entrance of sodium ions during the depolarization of the rising phase of the spike mediated by the outflow of potassium ions during the hyperpolarization of the falling phase. Perfect metabolic efficiency with a minimum charge needed for the change in voltage during the action potential would confine sodium entry to the rising phase and potassium efflux to the falling phase. However, because sodium channels remain open to a significant extent during the falling phase, a certain overlap of inward and outward currents is observed. In this work we investigate the impact of ion overlap on the number of the adenosine triphosphate (ATP) molecules and energy cost required per action potential as a function of the temperature in a Hodgkin-Huxley model. Based on a recent approach to computing the energy cost of neuronal action potential generation not based on ion counting, we show that increased firing frequencies induced by higher temperatures imply more efficient use of sodium entry, and then a decrease in the metabolic energy cost required to restore the concentration gradients after an action potential. Also, we determine values of sodium conductance at which the hydrolysis efficiency presents a clear minimum.