The conduction of electrical impulses by nerves is a chemical nrocess which has intrigued scientists for many years. ~ l t h b u ~the h general understanding of the mechkism is disseminated more among physiologists than chemists, the characteristics of rhe nervPa;~dtheexperiments done on them art: usually explained utiliping principles familiar to chemists and by analogies to some better characterized chemical systems. s sizes. tbev While newe cells mow in a varietv of s h a ~ eand can generally he described as a cell body wiih small fingkr~ikk extensions called dendrites. The cell bodv extends into a (generally) long tuhe called the axon. At th;other end of this axon are the svname endincs connected to the dendrites of the next nerve-celi or to a muscle cell. (See Fig. 1.) Once an electrical signal is started, it travels from one end of the cell to the otherualong the axon. I t is this conduction which we will consider. Ph~siologistsrecognize that the process is as well understood aB it is only because of the existence of aiant axons in a few sea animals-notably the squid-which may be up to a millimeter in diameter. Tbis compares with most mammalian axons which are less than a hundredth the size. The following discussion will then apply in detail to squid axons and by inference to newes of other species. In order to clarifv what is understood about the conduction of nerve impulses,&e should understand the system when it is not conducting, that is, in its resting state which is a dynamic equilibrium. We consider the axon system to be a relatively imnermeahle memhrane separating "inside" and "outside" flGd reservoirs. Inside the fluid co&tainsnumerous organic ions and a high potassium concentration-about twenty times that outside. Outside is the extracellular fluid which is similar to seawater, principally a solution of sodium chloride with about ten times more sodium than on the inside. There is, in addition, ten times more chloride on the outside than on the ~~~
Hy innt.rting an electrode intorhe inner solutimof the axon, the inside is fuund to he ahout 70 mV more negative than the outside. This vt~ltayeis rnllrd the resting potential.
Figure 1. Representative Mammalian Nerve. D label is dendrite area. A is the axon which may be between 1 p and 1 m long.
The ion concentration changes across the memhrane cause this potential difference in the following manner. Most chemists are familiar with the Nernst equation relating the voltage of a concentration half-cell with the ratio of ion concentrations on either side of a cell connected with a porous plug
where R is the gas constant, T the absolute temperature, z the ion charge, F the Faraday constant, and the a's the ion activities. I t is, from its derivation, a measure of the diffusion potential: the more concentrated side tends to diffuse into the less concentrated. The equation can be used under limited conditions and not when more than one ionic snecies must be considered simultaneously. In that case, since the different inns tend todiffuseat dittbrent rates.ean. . . ( 1 ) must be modified to give
For convenience, Ci, the concentration of ion "i", has been substituted for the activities. ti is the transference number for the ion and equals the fraction of the current carried by a given ion. I t is equal to t.=- u.C. (3) nGc, where the u's are the ionic mohilities (m2s-'v-' in SI units). In this case we consider the necessary "j"species to he Na+, K+, and C1-. We see from eqn. (2) that for an ion with a given concentration gradient, the potential across the plug (here the nerve membrane) depends on the concentrations and mohilities of the other ions as seen in eqn. (3).The smaller the relative flow of a eiven ion. the smaller its contribution to the voltaee " " across the membrane. Experiments on nerves show that varying the CI- or Na+ concentrations hardlv affects the restine ~otential but that changing K+ makes a Lrge difference. S& results lead us to helieve that the memhrane selectively allows transference mostly to K+ and mostly prevents transference of Na+ and C1-. Physidogists generally descrihe this phenomenon using the Goldman-Hodekin-Katzenuntionwhich can be derived from a sum of half-potentials lik; eqn. (2) and some mathematical tricks ( 1 ) .The equation is
where the Pi, the permeahilities, are related to the ion mobilities in a straightforward way. We note that the organic anions which reside inside the axon cannot penetrate through the memhrane. Thus in detailed consideration of ion concentrations and voltage, Donnan equilibria need to be considered, (e.g., aee Ref. (2)). As an aside, we note that since the axon at rest is leaky to small ions, the inside of the nerve constantly loses K+ and eainsNa+.. the . potential would soon run down. However. the Fans are continually replenished by ion "pumps" which, &ing metabolic energy, transport K+ and Na+ against their reVolume 54, Number 6, June 1977 / 345
spective concentration gradients. The molecule that does this is called sodium-potassium ATPase and is a major subject in itself. A number related to ionic transference across a membrane is called, reasonably, permeability, and a membrane having different ionic mobilities for the different ions going across is said to be selectively permeable. We have seen cow klective permeability explains reasonably the resting potential of the axon. The cause of this selectivity is excellently reviewed by Diamond and Wriebt (3).and interested readers are ureed to read their a r t i c k i n general, the selectivity depends i n the free energy difference between the binding of an ion to the surrounding waters compared to binding on, in, or near some part of the membrane which is oppositely charged. Since the Ions are charged the interactions are ~ainly~coulombic or monopole-dipole as opposed to dipole-dipole or van der Wads type. Thus for a membrane with highly charged or small (high-electric field) sites, the ion-site interaction is larger than ion-water interaction and so controls the selection. Since the ion partially dehydrates as it binds to the membrane sites, the binding is stronger for smaller ions which have centers of charge closer to the site, and the site is thus selective for small ions. On the other hand, for a weakly charged or largesite, the water-ion interaction energy controls the selectivity. A more easily dehydrating system will bind to the membrane more strongly causing larger ions to be selected over smaller ones. Thus the membrane selects for K+ over Na+ using a "weak" membrane binding mechanism and selects for N;+ over K+ with a "strong" binding site. The mechanism causing the permeabilities (as opposed to ion binding) difference is vague without specific structural information, but it could be either from a partitioning effect similar to solvent extraction or a change in mohility through numerous interactions in analogy with an ion exchange column (4). Now, armed with the information concerning the internal and external solutions, the selectively permeable membrane between them, and a concept of how potentials across the membrane can varv with relative uermeabilitv changes, we can proceed to a de&iption of the nerve impulse itself. If the voltaee across the membrane is chemicallv or electricallvtaken closer to zero-a "depolarizationn-the membrane's permeabilitv to sodium is observed to increase. Since the sodium Rradi&t is opposite to that of potassium, the memhrane is further deudarized h v the flow of sodium ions, the sodium's relative p&meabilit;increases more, and the process continues until the sodium permeability is larger than that of potassium. (For those familiar with the jargon, this is positive feedback.) Then the potential is largely determined by the sodium gradient which yields a potential around +50 mV, the opposite sense to the resting potential. This change in sodium permeability, and the concomitant swing from a K+ potential to an opposing Na+ potential, occurs over a time of about 1 msec, after which time the sodium permeability decreases, but more slowly (about 10 msec) and the potential across the membrane reverts back to its resting state. This "repolarization" is speeded by some extra K+ flowing outward as well. The voltage swing described above is the nerve impulse. But how is it propagated? Consider one place on the axon t o be at, say, +50 mV and a t another point at the resting potential, -70 mV, with the membrane potential smoothlv vawine between these two points. Then somewhere in betwe&-the exact place depending on the conductivitv of the electrolvte solutions and ;he dielectric of ;he memhrane, [he nerve is depolarized enouah to initiate the change in sodium permeabilitv, .. and the pulse occurs further alongthe nerve. Both the mechanism and the sites which r e a l a t e the voltage dependent sodium permeability change & together called the "sodium channels", although without further structural data they must be considered only sites of low activation enerw for sodium uermeabilitv. These sites are extremely ~~&&-between i 0 and 500ipz of membrane de346 1 Journal of ChemicalEducafion
Figure 2. Left is a figure of the vonage clamp system. Rlght is a schematic picture of a lhree-elecbode potentinstalas used for oxidatiweduction stwdies. Similarly lettered parts serve the same function in each. Left: A, wire current electrode: 6. KC1 filled electrodes for potential measuring: C, current follower: D, working elemode: E, axon, V. voltage generatw relative to bansmembrane potential. Right: A, auxiliary or counter electrode; 6, reference electrode: 6. current follower; 0,working electrode: V, voltage generatw relative to reference.
I
I liMLlmrK,
Figure 3. Example of dam from voltage clamp when K+ current has been suppress%. Top is the trace of the voltage shift wilh time-a step potential. Bottom is the sodium current as it changes with time.
pending on animal species and nerve size. Taking the membrane to be 100 A thick, this is equivalent to a concentration M. between 1and 50 X Many chemical tools have been developed to understand this mmt dramatic chemical entity and the effects it produces, some of which will now be discussed. The fundamental evidence for the existence of the above-mentioned ionic currents was obtained by Hodgkin, Huxley and Katz (5) using what physiologists call a voltage clamp and what electrochemists call a three electrode uotentiostat (6)(see Fie. 2). This auuaratus enables the vol&e across the &braneto'be fixedikd the ionic currents and their chanees in time to be monitored. This is usually done by holding
