Alan Hodgkin, Andrew Huxley, Equations, and Prizes

In 1932 Alan Hodgkin became a graduate researcher at Trinity College, Cambridge, and by that time he was already interested in measuring electrical signals from cell membranes. Hodgkin was exposed to Julius Bernstein’s membrane theory of electrical conductance by reading the published work of a friend of his father, Keith Lucas, in part because both his father and Lucas had been killed in the first world war. Briefly, Bernstein’s membrane theory holds that when a change in voltage in one part of a cell propagates to other parts of the cell, the propagation is caused by the change in voltage. Today this is accepted by everyone, and at the time it was suspected to be true by many. During his graduate work in the mid 1930’s Hodgkin found a way experimentally to test and verify the theory, and to do broad ranging investigations into cellular biophysics. Most of this work he did while at the Marine Biological Laboratory in Plymouth. In 1938 Hodgkin met Huxley. At the time, Andrew Huxley was an undergraduate in his last year at Trinity College, Cambridge. He was only three years younger than his teacher Hodgkin, and they formed a fruitful scientific partnership over the following years, interrupted only by the second world war.

Remember from our story about Young and Cole that in the summer of 1938, Hodgkin had met with Kenneth Cole at the MBL in Woods Hole. Cole exposed Hodgkin to his methods of preparing the squid giant axon, and together they made measurements of the resting potential of the nerve fiber. Within a year, Huxley was back at the Marine Biological Laboratory in Plymouth, using the methods Hodgkin had learned and adapted from his time with Cole at the MBL. In 1939, while working at Plymouth, Huxley successfully inserted a microelectrode along the axis of the nerve fiber in such a careful way that the process of inserting the electrode did not disturb the electrical readings obtained from the membrane of the axon. Kenneth Cole and his collaborator, Howard J Curtis, managed to do the same that year at the MBL with slightly different methods. But, in his Nobel lecture, Huxley remarked that while Cole and Curtis’s data was useful and their methods innovative, the results weren’t accurate enough to use to formulate a precise biophysical equation of the action potential of an enervated nerve fiber. A precise biophysical equation is exactly what he and Hodgkin were able to formulate several years later, and what they would go on to win the Nobel Prize for.

The exact methods of these experiments are quite detailed. Basically two wires are inserted down the narrow tube of the squid giant axon, with careful attention not to damage the membrane of the nerve fiber. A third wire is placed outside of the axon, near the membrane, in whatever solution the membrane is also in. As we saw in our last story, a typical solution was sodium citrate. This is called the “voltage clamp method”, and it was a revolutionary technology when applied to biophysics. Huxley detailed the method in his Nobel lecture, but there are also beautiful recordings of Hodgkin demonstrating the technique in the 1970 documentary The Squid and its Giant Nerve Fiber. The documentary is now long out of print and only a few clips of it are extant. Those that exist are aggregated by Smith College and freely available online.  There is no better way to understand the mechanics of the methods involved in these foundational experiments than by seeing them performed by the scientists who won the Nobel Prize using them. And pictorial and verbal descriptions certainly pale in comparison. So I will omit any more of those here. Instead we can focus on the elegance of Hodgkin and Huxley’s biophysical equations.

Tragically, several weeks after Huxley and Hodgkin were successful in taking intracellular readings of an action potential in the squid giant axon, Hitler invaded Poland. Over the next seven years both men variously contributed to the war effort. Hodgkin worked on designing oxygen masks for airmen, and Huxley worked to improve ballistic targeting methods. The war delayed Huxley and Hodgkin, but thankfully didn’t stop either of them.

After the war, Huxley and Hodgkin started doing more sophisticated experiments, and built upon earlier work that showed that potassium ions played a large role in the reversibility of the action potential back to its resting potential state. By this time, it was clear that the action potential was caused when a change in voltage allowed sodium ions from outside of the membrane of the nerve fiber to interact with the membrane of the nerve somehow, causing the change in voltage along the membrane of the axon. It was also clear that potassium ions inside the axon were responsible for the resting potential of the nerve fiber. The exact mechanism which allowed sodium and potassium ions to cause this activity were not yet known. Now we know that little voltage gated ion channels allow sodium and potassium ions in and out of the cell in a very specific way. These voltages gated channels are like little dikes in the cell membrane, which open and shut depending on the electrical charge of the membrane, selectively allowing sodium and potassium to move in and out of the nerve fiber.

In 1952 Hodgkin and Huxley published five papers detailing the precise biophysics of the squid giant axon. The central equation of this biophysical account is usually given as follows:

From Schwiening 2008

One of the remarkable things about Huxley and Hodgkin’s equation is that without knowing the biological mechanism by which sodium and potassium move in and out of the nerve cell, they were able to model precisely the results of the then unknown voltage gates. Again, there are many detailed explanations of the Hodgkin-Huxley equation freely available. And I will not take the time to walk through each term of it here. Yet from a cursory glance at the equation we see that there are parameters for the probability of some amount of potassium (the K in the second chunk of the equation after the equal sign) and some amount of sodium (the Na in the third chunk of the equation after the equal sign) acting dynamically with the change in voltage of the membrane over time (the first chunk of the equation after the equal sign). Today we interpret these terms in the equation as capturing the likelihood of voltage gated ion channels opening and closing and how that changes with voltage and time. Yet it was researchers working with Huxley and Hodgkin’s equation who later came to discover these little opening and closing gates in the cell wall of the nerve fiber. This is exactly how Hodgkin and Huxley talked about the issue during their Nobel lectures. They both thought that their equation should “be regarded as a first approximation which needs to be refined and extended in many ways in the search for the actual mechanism”. They thought they were contributing to a process of discovery, rather than solving a problem once and for all.