Voltage gating by molecular subunits of Na+ and K+ ion channels: higher-dimensional cubic kinetics, rate constants, and temperature

The structural similarity between the primary molecules of voltage-gated Na and K channels (alpha subunits) and activation gating in the Hodgkin-Huxley model is brought into full agreement by increasing the model's sodium kinetics to fourth order (m(3) → m(4)). Both structures then virtually imply activation gating by four independent subprocesses acting in parallel. The kinetics coalesce in four-dimensional (4D) cubic diagrams (16 states, 32 reversible transitions) that show the structure to be highly failure resistant against significant partial loss of gating function. Rate constants, as fitted in phase plot data of retinal ganglion cell excitation, reflect the molecular nature of the gating transitions. Additional dimensions (6D cubic diagrams) accommodate kinetically coupled sodium inactivation and gating processes associated with beta subunits. The gating transitions of coupled sodium inactivation appear to be thermodynamically irreversible; response to dielectric surface charges (capacitive displacement) provides a potential energy source for those transitions and yields highly energy-efficient excitation. A comparison of temperature responses of the squid giant axon (apparently Arrhenius) and mammalian channel gating yields kinetic Q10 = 2.2 for alpha unit gating, whose transitions are rate-limiting at mammalian temperatures; beta unit kinetic Q10 = 14 reproduces the observed non-Arrhenius deviation of mammalian gating at low temperatures; the Q10 of sodium inactivation gating matches the rate-limiting component of activation gating at all temperatures. The model kinetics reproduce the physiologically large frequency range for repetitive firing in ganglion cells and the physiologically observed strong temperature dependence of recovery from inactivation.