Migrating ion channels

It is common in people suffering from multiple sclerosis that the distance they can walk without a rest is a lot less than what a healthy person can do. While walking a certain kind of fatigue arises which is different from the ordinary tiredness of muscles. Continuing for long enough leads to a state where the muscles just do not seem to respond any more. If this state has been approached too closely it can take many hours for normality to be restored. What is the mechanism of this kind of fatigue? It does not seem to be mentioned in most texts on the subject.

Some years ago I read an account of a patient suffering from the neuromuscular disease myasthenia gravis. She could walk normally in the morning but was confined to a wheelchair in the afternoon. Superficially this sounds like an extreme version of the fatigue in MS mentioned above. In this case more is known about what is going on. Myasthenia gravis is an autoimmune disease where the target of the attack mounted by the immune system is the acetylcholine receptors of muscles. Normally acetylcholine released by nerve cells carries the signal to the muscle cells that they should contract. This is interfered with by antibodies against the receptors. The result of this is that when the nerves responsible for directing the action of muscles are stimulated too often there is not enough acetylcholine present. It then takes a long time before the system can recover. It is clear that this cannot be the mechanism working in MS but I wondered whether in that case neurotransmitters could be depleted in some other way. In fact it seems that this is not the right explanation. In the book ‘McAlpine’s Multiple Sclerosis’ I found another alternative for which there is some evidence. It has to do with ion channels.

The mechanism of propagation of electrical signals in nerve cells was discovered in the early 1950’s by Alan Hodgkin and Andrew Huxley. It got them a Nobel prize in 1963. The basis of the phenomenon are flows of potassium and sodium ions across the cell membrane. In the resting state of the axon there is an electrical potential across the cell membrane which results from the difference in concentration of potassium ions on both sides. When a nerve signal (action potential) passes the permeability of the membrane to sodium and potassium ions changes in response to the changes in potential. This is a non-trivial dynamical process. A natural mathematical model would be a system of reaction-diffusion equations which admits travelling wave solutions. The study of this may be simplified by going to the “space-clamped” case. This comes down to studying solutions which only depend on time. It gives rise to a system of nonlinear ordinary differential equations. A possibility of studying this situation experimentally was found in the giant axon of the squid Loligo. This was used by Hodgkin and Huxley to get information about the coefficients of the ODE system. Once they had that information they had to solve the equations numerically in order to compare theory with experiment. In those days this numerical work had to be done by hand although a couple of years later they were able to apply some of the first ever computers, then being developed in Cambridge. In the Nobel lecture of Huxley we find a vivid description of doing this calculation. He says: “This was a laborious business … a propagated action potential took a matter of weeks. But it was often quite exciting. … an important lesson I learned from these manual computations was the complete inadequacy of one’s intuition in trying to deal with a system of this degree of complexity.” The Hodgkin-Huxley model is one of the most notable successes of mathematical biology. It is an example of the concept of an excitable system mentioned in a previous post. Now we know that the changes of permeability of the membrane are due to ion channels which regulate the movement of ions through the cell membrane. Ion channels are made by molecules embedded in the membrane which undergo conformational changes as a result of various stimuli. In the case of nerve conduction the stimuli are electrical. These changes are not deterministic. What changes with the applied potential is the probability of a channel being open, closed or inactivated.

The propagation speed of nerve impulses increases with the diameter of the axon and the unusually large diameter of the axon in the squid is its method of achieving fast signalling. Vertebrates like ourselves have found another method, which is to insulate the axon using myelin. It is the myelin which is damaged in MS. The rate of travel of nerve signals along the axon is not uniform. There are small regions along the axon, the nodes of Ranvier, where myelin is absent. The nerve impulse jumps from one node to the next. Associated to this is the fact that under normal circumstances most of the sodium and potassium channels are concentrated near the nodes of Ranvier. They are kept there by the oligodendrocytes which are also the cells which produce myelin. In fact myelin consists of layers of cell membrane of the oligodendrocytes.

In MS myelin is removed from the axons and nerve conduction no longer works properly, if it works at all in a given axon. There may be remyelination but this generally only produces a thin layer of myelin whose insulating properties are limited. Now it seems, and here I come back to what I read in ‘McAlpine’s Multiple Sclerosis’, that the nerve cells have developed another strategy to restore conduction to some extent. This is that ion channels migrate along the axon from the nodes of Ranvier. The general mechanism of conduction is then a different one from that of the fully myelinated axon. One disadvantage is that the nerve conduction is not so fast. The other is that ions may accumulate on one side of the cell membrane and the resting potential cannot be reestablished in an efficient way. Each firing of the nerve cell only results a small change in the concentration of ions after it has passed. If, however, these small changes are not being corrected for regularly they can add up to a serious change. This is a possible explanation for the fatigue. I would not claim that this is definitive explanation. On p. 628ff of ‘McAlpine’s Multiple Sclerosis’ a zoo of different ion channels is dicussed. From the short section on fatigue on p. 643 it seems clear that there are a lot of theories around. I would like to penetrate into the matter further.

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