Hodgkin-Huxley Equations

Next, the conductance of Sodium and Potassium is calculated using the following equations:

g_Na = (120(m³)h) g_K = (36(n⁴))

where m, n and h are values that represent the gates that provide access through the Sodium and Potassium channels. (Refer to Biological Background for more details on these channels) The following equations are used to determine the values for m, n and h.

dm/dt = alpha_m(V_m(1-m)-(Beta_m(V_m)(m))
dn/dt = alpha_n(V_m(1-n)-(Beta_n(V_m)(n))
dh/dt = alpha_h(V_m(1-h)-(Betah(V_m)(h))

where

alpha_m = (.1(V_m+25)/(exp((Vm+25)/10)-1)
alpha_n = (.01(V+10)/exp((V_m+10)/10)-1)
alpha_h = (.07(exp(V_m/20)
Beta_m = 4exp(V_m/18)
Beta_n = ((1/(exp((V_m+30)/10)+1)
Beta_h = .125exp(V_m/80)
and m, n and h are initial values calculated using the resting membrane potential

After obtaining conductance, the membrane current can be calculated using the following equation