Nerve Pulses and Reaction-Diffusion Systems

Abstract

Five years after Russell’s now classic Report on Waves appeared in Great Britain in 1845 [833], a twenty-nine year old German physicist named Hermann Helmholtz published measurements of the propagation speed of electrical pulses along the sciatic nerve of frog, a bundle of fibers that carries signals from the spinal cord to leg muscles [420, 864]. Influenced by comments of Isaac Newton suggesting that the speed of propagation of nerve activity is very high (like that of light [706]), most scientists then considered the speed of a nerve pulse too large to measure. Helmholtz was further advised not to undertake this project by his father, a philosopher who believe that a muscular response was identical to its cause, theoretically precluding any time delay between the two pheomena. Hermann Helmholtz, characteristically, decided to ask Nature. Using a clever experimental device to measure the relevant time delay as the pulse passed two points on the nerve, he found the surprisingly low propagation speed of 27 meters per second, which is close to presently measured speeds [874]. In 1868, Julius Bernstein used an even more ingenious measurement apparatus to record the localized shape of a nerve pulse [80]. Following these experiments, therefore, neuroscientists were pressed to explain why the speed of a pulse is so low — a question they would puzzle over for a century.