The role of electricity in the nervous systems of animals was first observed in dissected frogs by Luigi Galvani, who studied it from 1791 to 1797. Galvani's results inspired Alessandro Volta to develop the Voltaic pile—the earliest-known electric battery—with which he studied animal electricity (such as electric eels) and the physiological responses to applied direct-current voltages.
In the 19th century scientists studied the propagation of electrical signals in whole nerves (i.e., bundles of neurons) and demonstrated that nervous tissue was made up of cells, instead of an interconnected network of tubes (a reticulum). Carlo Matteucci followed up Galvanis studies and demonstrated that injured nerves and muscles in frogs could produce direct current. Matteuccis work inspired the German physiologist, Emil du Bois-Reymond, who discovered in 1843 that stimulating these muscle and nerve preparations produced a notable diminution in their resting currents, making him the first researcher to identify the electrical nature of the action potential. The conduction velocity of action potentials was then measured in 1850 by du Bois-Reymond's friend, Hermann von Helmholtz. Progress in electrophysiology stagnated thereafter due to the limitations of chemical theory and experimental practice. To establish that nervous tissue is made up of discrete cells, the Spanish physician Santiago Ramón y Cajal and his students used a stain developed by Camillo Golgi to reveal the myriad shapes of neurons, which they rendered painstakingly. For their discoveries, Golgi and Ramón y Cajal were awarded the 1906 Nobel Prize in Physiology. Their work resolved a long-standing controversy in the neuroanatomy of the 19th century; Golgi himself had argued for the network model of the nervous system.
The 20th century saw significant breakthroughs in electrophysiology. In 1902 and again in 1912, Julius Bernstein advanced the hypothesis that the action potential resulted from a change in the permeability of the axonal membrane to ions. Bernsteins hypothesis was confirmed by Ken Cole and Howard Curtis, who showed that membrane conductance increases during an action potential. In 1907, Louis Lapicque suggested that the action potential was generated as a threshold was crossed, what would be later shown as a product of the dynamical systems of ionic conductances. In 1949, Alan Hodgkin and Bernard Katz refined Bernsteins hypothesis by considering that the axonal membrane might have different permeabilities to different ions; in particular, they demonstrated the crucial role of the sodium permeability for the action potential. They made the first actual recording of the electrical changes across the neuronal membrane that mediate the action potential. This line of research culminated in the five 1952 papers of Hodgkin, Katz and Andrew Huxley, in which they applied the voltage clamp technique to determine the dependence of the axonal membrane's permeabilities to sodium and potassium ions on voltage and time, from which they were able to reconstruct the action potential quantitatively. Hodgkin and Huxley correlated the properties of their mathematical model with discrete ion channels that could exist in several different states, including "open", "closed", and "inactivated". Their hypotheses were confirmed in the mid-1970s and 1980s by Erwin Neher and Bert Sakmann, who developed the technique of patch clamping to examine the conductance states of individual ion channels. In the 21st century, researchers are beginning to understand the structural basis for these conductance states and for the selectivity of channels for their species of ion, through the atomic-resolution crystal structures, fluorescence distance measurements and cryo-electron microscopy studies.
Julius Bernstein was also the first to introduce the Nernst equation for resting potential across the membrane; this was generalized by David E. Goldman to the eponymous Goldman equation in 1943. The sodium–potassium pump was identified in 1957 and its properties gradually elucidated, culminating in the determination of its atomic-resolution structure by X-ray crystallography. The crystal structures of related ionic pumps have also been solved, giving a broader view of how these molecular machines work.