  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 AP 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.
