(nonmyelinated neurons fire in a continuous fashion, without the jumps; ion
leakage allows effectively complete circuits, but slows the rate of propagation).
The Hodgkin-Huxley model
The current flow across the cell membrane depends on the capacitance of the
membrane and the resistance of the ion channels. The total ionic current is
represented by the sum of the sodium current, potassium current and a small
leakage current. The leakage current represents the collective contribution of
ions such as chloride and bicarbonate.
The Hodgkin-Huxley (HH) model is of an isopotential membrane patch or a single
electrical compartment i.e. there are no spatial effects on the potential (Hodgkin
& Huxley, 1952a; 1952b; 1952c). The units of the model are per membrane unit
area, and it is then straightforward to scale the model to a single compartment of
any desired membrane area.
The total membrane current is the sum of the ionic currents and the capacitive
current,
(79) Im (t) = Iionc (t) + CMdVmΓ-
(80) Iionic(t)=INa(t)+IK (t)+IL (t)
where Im is the membrane current density, Iionic are the ionic currents
densities, CM is the membrane capacity per unit area and Vm is the membrane
voltage. The two main ionic conductances, sodium and potassium are
independent of each other, and a third, leak conductance does not depend on
any of the other conductances or the membranal voltage. Thus, the total ionic
current is the sum of the separate ionic currents.
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