ABSTRACT
In 1952, Alan Hodgkin and Andrew Huxley, two British physiologists, described a series of experiments conducted on a squid giant axon . The aim of these experiments was to develop a better understanding of the origin of action potentials. Eleven years later, their work led to the pair being awarded the Nobel Prize for physiology or medicine. Today the model stands as the foundation of the quantitative description of cellular dynamics. Initially they had worked with frog cells, but later moved to the squid giant axon (so named because it is a large axon in a normal-size squid — unlike the giant squid of Fig. 6.1) because this particularly large cell allowed them to apply the electrophysiological techniques available at the time to measure ionic currents — something which would not have been possible with smaller cells. The mathematical description of cellular dynamics put forward by Hodgkin
and Huxley is made all the more remarkable because of the way in which their work is the culmination of excellent experimental neurophysiology as well as brilliant mathematical insight and computational analysis. The computational analysis required integration with a mechanical calculator of the system of differential equations which was insolvable with analytic tools (see Fig. 6.2). Remarkably, although the digital computers of today make the task easier, it is still a highly nontrivial system. Here, we will provide a rather simplified description. As we did in the previous chapter, we start with a simple model of cellular
membrane potential V ,
Cm dV
dt + Iion(V, t) = 0, (6.1)
where Cm is the membrane capacitance (induced by the phospholipid bilayer), the membrane potential V = Vinside − Voutside is the difference between the potential inside and outside the cell, and Iion is some function of V and t which described the various ionic currents. Of course, the magnitude of the current due to some ions is significantly larger than others, and, just as in Chapter 5.1, the sodium and potassium currents are typically the most dominant. Hence,
Figure 6.1: A giant squid. Not to be confused with a squid giant axon. (Image obtained from https://commons.wikimedia.org/ and freely distributed in the public domain.)
Figure 6.2: The calculator. A mechanical calculator of the type used by Andrew Huxley to intergrate the Hodgkin-Huxley equations. This particular machine comes from the office of Alan Hodgkin. (Image reproduced with permission from Hugh Robinson of University of Cambridge, Department of Physiology, Development and Neuroscience).
