Hodgkin-Huxley Models

In the 1950's, Alan Hodgkin and Andrew Huxley won the Nobel Prize in Physiology for their study of signal transmission in squid axons. They effectively modeled propagation of an action potential through the use of electrical analogs and non linear ordinary differential equations.  The model approximates the lipid bilayer, voltage gated voltage channels, ion leak channels, and ion pumps.

                  Figure 6:  A.F. Huxley                                 Figure 7:  A.L. Hodgkin            Figure 8:  Hodkin-Huxley Gaint Squid axon

Electrical analogs

Because the lipid bilayer retains a potential between the extracellular and intracellular ionic concentrations, it can be modeled as a capacitor whose storage is dependent upon the other components of the circuit, or cell. Voltage gated ion channels and ion leak channels are represented by two conductors in parallel, accurately depicting their position and function within the membrane. Both conductors are subsequently dependent upon voltage across the membrane, but voltage gated ion channels are modeled as time dependent, meaning their response is nonlinear, which is a   valid representation of the carrier protein activity within the mechanism. Leak channels are represented by linear conductors whose response is solely dependent upon the voltage across the membrane. Each conductor is modeled in series with a "battery”, or electrochemical gradient that drives the flow of ions across the membrane.  Ionic pumps are modeled as current sources that can alter the flow of ions across the membrane.  The model was used to demonstrate that the change in membrane potential can be approximated as a sum of the currents in a circuit.

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