Richard D. Keynes

The potassium permeability of a giant nerve fibre

The experiments described in the preceding paper (Hodgkin & Keynes, 1955) show that metabolic inhibitors like dinitrophenol and cyanide produce large changes in the relative magnitude of the fluxes of potassium moving inwards and outwards across the membranes of giant axons from Sepia officinalis. For normal fibres recovering from stimulation the influx is 15-30 pmole/cm2 sec, while the efflux is 20-40 pmole/cm2 sec. On poisoning with dinitrophenol, which virtually abolishes the sodium efflux, the potassium influx is reduced to 2-3 pmole/cm2 sec, while the efflux remains the same or is slightly increased. These facts may be explained by supposing that in normal fibres there is, in addition to the passive potassium movements seen by themselves in poisoned fibres, an activeuptake ofpotassium, coupled to the extrusion ofsodium, and amounting to about 20 pmole/cm2 sec. This hypothesis is attractive in that it provides a reasonable explanation ofthe further observation that the sodium efflux drops by some 20 pmole/cm2 sec when external potassium is removed, but it raises one serious difficulty which needs to be resolved. According to the equation derived by Ussing (1949b) for independent passive transport of ions, the influx (Mi) and the efflux (M0) of a monovalent cation such as potassium should be related in the following way:

The ionic fluxes in frog muscle

Methods are described for determining the absolute sizes of the inward and outward fluxes of radioactive sodium and potassium in frog muscle fibres. Most of the work was concerned with a small muscle from the frog’s foot, the M. extensor longus dig. IV, but the fluxes in sartorius and abdominal muscles were also measured. In normal Ringer’s solution (containing 2·5 mM-K) the mean potassium flux in the toe muscle was estimated as 4·5 pmole/cm2s, the influx being slightly smaller than the efflux. In 5 mM-K the fluxes were nearly doubled. A simplified theoretical treatment of the error in the potassium flux likely to arise from the slowness of diffusion in the extracellular space of the muscle, showed that in this small cylindrical muscle it was only about 10 %. Similar calculations for sartorius muscles suggested that the true flux was about 12 pmole/cm2s in normal Ringer, but this result depended on a rather large correction for the diffusion effect. It proved difficult to make really satisfactory measurements of the sodium fluxes, because, as has been noted by other authors, the time course of the exchange of 24Na in a whole muscle did not conform exactly to that for a simple two-stage process. However, the sodium fluxes in the toe muscle were estimated to be of the order of 10 pmole/cm2s. There were several possible causes for the observed deviations from ideal behaviour, but there was insufficient evidence to decide between them. The self-diffusion coefficient of sodium ions in the extracellular space of the muscle was found to be 3·1 x 10-6cm2/s. Sartorius muscles gave fluxes and diffusion coefficients of the same order. It was shown that the sodium efflux in frog muscle was reduced in potassium-free Ringer, and increased in a potassium-rich medium. This suggests that there may be, as in cephalopod axons, some form of coupling between sodium efflux and potassium influx.

The screw–helical voltage gating of ion channels

In the voltage–gated ion channels of every animal, whether they are selective for K+, Na+ or Ca2+, the voltage sensors are the S4 transmembrane segments carrying four to eight positive charges always separated by two uncharged residues. It is proposed that they move across the membrane in a screw–helical fashion in a series of three or more steps that each transfer a single electronic charge. The unit steps are stabilized by ion pairing between the mobile positive charges and fixed negative charges, of which there are invariably two located near the inner ends of segments S2 and S3 and a third near the outer end of either S2 or S3. Opening of the channel involves three such steps in each domain.

The leakage of radioactive potassium from stimulated nerve.

There are good reasons for believing that the energy for the transmission of the nervous impulse is derived from the exchange of a small amount of sodium and potassium across the nerve membrane (Hodgkin & Katz, 1949). Most of the evidence, however, has been obtained from studies of the electrical behaviour of nerve membranes and, although experiments of this type are the only means by which the transient events of the single action potential can be investigated, they do not usually provide unambiguous information about the accompanying or causative ionic movements. The conclusions drawn from them therefore need to be confirmed by more direct methods. It was shown some years ago (Cowan, 1934) that Maia nerve lost an appreciable quantity of potassium when stimulated to fatigue, and a similar potassium leakage has been demonstrated in medullated nerve (Arnett & Wilde, 1941). There is also some evidence of a loss of potassium and gain of sodium in active muscles (Fenn, 1940). None of these experiments proved conclusively that there was always a leakage of potassium during activity, since the potassium observed to escape from the nerves might have come only from those fibres which had been reduced to a state of complete exhaustion. Nor did this work give any reliable indication as to the magnitude of the effect. Hodgkin & Huxley (1947) used the dependence of the membrane resistance of Carcinus axons on the external potassium concentration to make a more accurate measurement of the amount which leaked out during the impulse. While their method was free from the objection that the leakage might have been due to total fatigue of the axon, it was indirect, and they were unable to exclude the possibility that the substance which accumulated outside the axon during stimulation was not potassium, but something else which affected the membrane resistance in a similar fashion. In the preceding paper (Keynes & Lewis, 1951 a) a method was described for studying the passage of potassium through nerve membranes with the aid of the radioactive isotope K42. This technique offered the prospect of measuring the potassium leakage during activity in a way which was not open to any of the criticisms which could be made of the earlier work. The object of the experiments

Modelling the activation, opening, inactivation and reopening of the voltage–gated sodium channel

A model of the voltage–gated sodium channel is put forward suggesting that the four S4 voltage–sensors behave as screw–helices making a series of discrete transitions that carry one elementary charge for each notch of the screw helix. After the channel has been activated by the first two steps R ⇌ P ⇌ A in all four domains, followed by a voltage–independent rearrangement, it is opened by a third cooperative step A ⇌ B in domains I, II and III in conjunction with hydration. Inactivation is a voltage–dependent process controlled by the third step A ⇌ I in sensor IVS4, and the closing of the channel is brought about its dehydration. From the inactivated steady state the channel may be reopened by a fourth step, I ⇌ C in sensor IVS4 and rehydration. The computed kinetics of the model are shown to conform closely with those observed experimentally.

Kinetic analysis of the sodium gating current in the squid giant axon

A critical study has been made of the characteristics of the kinetic components of the sodium gating current in the squid giant axon, of which not less than five can be resolved. In addition to the principal fast component Ig2, there are two components of appreciable size that relax at an intermediate rate, Ig3a and Ig3b, Ig3a has a fast rise, and is present over the whole range of negative test potentials. Ig3babsent below -40 mV, exhibits a delayed onset and disappears on inactivation of the sodium system. There are also two smaller components, Ig1 and Ig4, with very fast and much slower relaxation time constants, respectively.

A new look at the mechanism of activation and inactivation of voltage-gated ion channels

Studies on the kinetics of activation and inactivation of the sodium channels of the squid giant axon, on the sodium gating current, and on the properties of the non-inactivating steady-state current, are briefly reviewed. Taken in conjunction with recent evidence on the structure of voltage-gated ion channels, they have led to the development of a series-parallel model of the sodium channel that can be regarded as a modernized version of the Hodgkin-Huxley model, with some novel features. It is suggested that activation results from conformational changes brought about by the four S4 voltage sensors operating in parallel, each of which makes two discrete steps to reach the fully activated state of the channel. There follows a voltage-independent hydration step, and the channel is ready to open. Inactivation is a potential-dependent process involving a third transition of voltage sensor S4d alone, which, rather than bringing a ball and chain blocking group into position to close the channels, serves to switch the system so that it passes from an initial activated mode, in which there is a high probability of arriving at an open state with a brief latency, to a second steady-state mode, in which the probability of opening is very much lower.

On the voltage dependence of inactivation in the sodium channel of the squid giant axon

Measurements of the macroscopic sodium current in the squid giant axon show that the inactivation gate carries around 1.3 units of electronic charge. The contrary evidence from single-channel studies is considered, and a modified series—parallel model of the sodium channel is proposed that might help to resolve the disagreement.

Bimodal gating of the Na+ channel

Inactivation of voltage-gated ion channels, whether they are selective for Na+, K+ or Ca2+, probably never involves their total closure, and some flow of ion current persists if large enough test pulses are applied. Incomplete inactivation was first reported for the Na+ channels of the squid giant axon, but has since been observed in other types of peripheral nerve and, more recently, in muscle fibres and the neurons of mammalian brain. The phenomenon is therefore widespread and has important implications for the functioning of voltage-gated channels in a variety of situations. It is best described in terms of a gating mechanism that switches the channel from an initial mode in which it has a high probability of opening to one in which the probability is greatly lowered, but not reduced to zero.

On the slowly rising phase of the sodium gating current in the squid giant axon

High–resolution records of the sodium gating current in the squid giant axon demonstrate the existence of a slowly rising phase that is first apparent at pulse potentials slightly below zero, and becomes increasingly pronounced at more positive potentials. At +80 mV the current reaches its peak with a delay of 30 μs at 10°C. It is suggested that this current is generated by the first two steps labelled R ←P and P ←A in the S4 units of all four domains of the series–parallel gating system, activating the channel before its opening by the third steps A ←B in domains I, II and III in conjunction with hydration. The kinetics of the slowly rising phase can only be explained by the incorporation of an appropriate degree of voltage–dependent cooperativity between the S4 voltage–sensors for their two initial transitions.