In a succession of articles published over 65 years ago, Sir Alan Lloyd Hodgkin and Sir Andrew Fielding Huxley established what now forms our physical understanding of excitation in nerve, and how the axon conducts the action potential. They uniquely quantified the movement of ions in the nerve cell during the action potential, and demonstrated that the action potential is the result of a depolarizing event across the cell membrane. They confirmed that a complete depolarization event is followed by an abrupt increase in voltage that propagates longitudinally along the axon, accompanied by considerable increases in membrane conductance. In an elegant theoretical framework, they rigorously described fundamental properties of the Na+ and K+ conductances intrinsic to the action potential.
Notwithstanding the elegance of Hodgkin and Huxley’s incisive and explicative series of discoveries, their model is mathematically complex, relies on no small number of stochastic factors, and has no analytical solution. Solving for the membrane action potential and the ionic currents requires integrations approximated using numerical methods. In this article I present an analytical formalism of the nerve action potential,