From previous studies with the squid axon membrane under electronic voltage clamp conditions (where Vm is forced to assume set values), where the potassium current was measured with the sodium channels blocked, it was observed that gK = Jk /Vm = gK (Vm, t).
From chemical kinetics considerations, Hodgkin and Huxley assumed that four "particles" must simultaneously occupy specific sites on the potassium gate protein in order to open it. Thus, they wrote:
where n is the K+ activation parameter ; it is taken as the probability of a K gate opening particle being at the active site. gKo is taken to be 36 mS/cm2, VK = 12 mV. n is given by the ODE:
n = -n(an +Pn) + an L4-8 an and Pn are exponential functions of membrane potential:
The sodium current is activated once Vm reaches a depolarization threshold voltage. The sodium current or conductance deactivates spontaneously, once its channels have been open. Hodgkin and Huxley observed that sodium channel activation had kinetics that suggested three "particles" (not necessarily the particles for potassium channel activation) were required. Deactivation of the sodium channels suggested monomolecular kinetics, where a single event of probability (1 - h) caused inactivation. Thus, the probability of Na+ channels being open was m3h, and the sodium current density was
gNao = 120 mS/cm2, VNa = - 115 mV. The ODEs for sodium activation and deacti-vation are m = -m(a +B ) + a 1.4-12
The four voltage-dependent parameters are am = 0.1(v + 25)/[exp(0.1v + 2.5) - 1] 1.4-14
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