Hodgkin-Huxley Equations
The major equation used by Hodgkin-Huxley to mathematically model the nerve
action potential is given below. Integration of this equation gives the
membrane potential at any given time.
dV/dt=-1/C[gNa(Vm)(Vm-VNa)
+gK(Vm)(Vm-VK)]
where
dV/dt = the change in membrane potential with respect to time
C = membrane capacitance
gNa,K = conductance of Sodium and Potassium
Vm = membrane potential (mV)
VNa,K = membrane potential with respect to Sodium and Potassium
(mV)
The first step to calculate the total nerve action potential involves
calculating the potential of the nerve cell membrane initially or while
the membrane is at rest.
Vm = (RT/F)ln(PK+[K+]
e+PNa+[Na+]e) / (PK+[K+]
i+PNa+[Na+]i)
where
R = gas constant
T = temperature (Degrees Celsius)
F = Faraday's constant
PK+,Na+ = Sodium and Potassium permeabilities
at rest
K+e/Na+e = extracellular concentrations
of Sodium and Potassium
K+i/Na+i = intracellular concentrations
of Sodium and Potassium