AM. ZOOLOGIST, 2:5-25 (1962). COMPARATIVE PHYSIOLOGY OF CONDUCTION IN NERVE AND MUSCLE C. HOVI.K Department of Zoology, University of (llasgow INTRODUCTION It sometimes helps us to understand a natural mechanism more deeply if we consider its function teleologically and I hope you will permit an introductory recourse to this approach. A nerve fiber must be able to transmit a message, or as we now say, a quantity of information, in the form of a code, over distances varying from less than a millimeter (in the case of a small insect) up to several meters (in the case of a large whale). This has to be achieved with minimal loss of accuracy. To do this the nerve cell uses its capacity for producing propagated electrical potential changes. Speed as well as accuracy is desirable; faster conduction permits the evolutionary development of larger, more complex and efficient organisms. In principle, a system using signals individually graded in regard to both magnitude and time-course (like the message in a telephone cable) would transmit information most economically and swiftly. But this demands a capacity for accurate reproduction at all points along the length of the nerve. Even a highly stable, well-insulated telephone cable is unable to do this, and a long one requires "booster" stages at intervals. Biological systems are notoriously full of randomly-fluctuating or "noisy" elements and so can be expected to have difficulty in maintaining the degree of accuracy desired. They are very badly insulated and need continuous "boosting" along their length. It is not surprising, then, that nerve fibers have adopted—uniformly as far as we know at the present time—a system of coded signalling in which the transmitted unit is a simple, all-or-nothing pulse and so indicates merely "on" or "off," as do the functional units of a digital computer. There is no message in the pulse itself except this indication; the primary coding of the message Author's present address: Dept. of Biology, University of Oregon, Eugene, Oregon. (5) in the nerve is contained in the duration of the intervals between successive pulses. It cannot be emphasized too strongly that this method is unlike that used by computers, for unlike computers, the nervous system must in effect utilize an accurate clock with which to compare the arrival of these signals, in order to interpret their message. The amount of information which can be transmitted in unit time by a pulse-time system is increased if the signal itself is very brief, and hence the nerve impulse must be of short duration. Muscles receive instructions from their motor nerves in the form of these all-ornothing impulses, coded so as to be translated by the muscle into controlled contraction. It is at this point that we see how a coded message is interpreted and translated into functional terms, in this case the development of force and movement by the muscle. If the signals were handed on to the contractile machinery unaltered, all-ornothing excitations of the contractile mechanism would result. In order to grade tension development the muscle would then have to adopt one of two possible alternatives. The simplest is to break down the contractile mechanism into small steps, each actuated by an all-or-nothing signal. The alternative is to break down the muscle into separately-innervated sub-units, each of which can be included or withdrawn independently from participation in contraction. Each method has certain disadvantages. The former must cause a reduction in the maximum speed of response by the muscle to nervous command, owing to the time required for summation of the small steps, though it might well be adequate for some situations. The latter is quite sound in principle but it is intrinsically unsuitable for small muscles composed of few fibers since the number of sub-units into which a small muscle can be divided is small. Nevertheless, it has been utilized by G. HOYIE many muscles, especially in vertebrates. A quite different type of control is possible in principle, and that is to have a dual or multiple mechanism for each muscle liber. One channel may then be used for exciting very large contractile responses, another for giving graded responses. It should be possible to do this with a common contractile mechanism, if this in turn can be activated in a graded fashion; but it would certainly require dual or multiple innervation of each muscle fiber, with corresponding dual or multiple transmission mechanisms. Then one nerve could be used when the fastest response is called for and another for slower responses requiring careful gradation. In spite of the complication in innervation and mechanism, this method is widespread throughout the animal kingdom; phylogenetically it may well be the oldest. It is the one almost exclusively utilized in arthropods, for it permits excellent control with only two nerve fibers per muscle and arthropods, especially small ones, have very few nerve fibers to utilize. Employment of graded responses does, however, lead to the difficulty of initiating and propagating a variable-sized signal in the muscle fiber membrane. This has been partly overcome by carrying the coded nerve message to all parts of the muscle fiber via nerve branches. Each nerve-ending liberates an approximately similar quantity of transmitter-substance, which is adequate only for the production of a small, local electrical change (post-synaptic potential). Post-synaptic potentials (p.s.ps.) are graded in height, depending on the quantity of transmitter released. The muscle membrane in the multiply-innervated type of system must then be without the capacity for responding to the graded post-synaptic potentials with all-or-nothing signals. It may lose its electrical excitability completely, as has the slow skeletal muscle of the frog. Or it may reduce its responsiveness from all-ornothing to a graded nature, so that the electrical response of the muscle fiber membrane is a function of the size of the postsynaptic potential. In that way a varied range of information is transmitted by single signals, the graded p.s.ps. Integration, or initial translation of the signal messages, is then achieved at the synapse. The height of a post-synaptic potential depends on the interval between it and the immediatelypreceding signal, and on other aspects of recent history of the junction. Like all transmissive stages utilized by the nervous system p.s.ps. are intimately linked with the time-clock. There are two other places in the nei-vous system where graded, rather than all-ornothing, responsiveness is desirable in principle and in fact found. Firstly, in sensory nerve terminals, many fine branches may converge on a single axon, so that if each gave discrete all-or-nothing signals a chaos of impulses would pass into the main trunk. An initial section of the main trunk acts as an integrating region and impulses originate there, but the signals arising in the branches are graded. Secondly, in the dendritic branches of central nerve cells (and in some cases the nerve cell bodies) which receive multiple synaptic contacts, possibly from many cells, a similar argument applies. The post-synaptic potentials are graded responses and impulses originate in the axon hillock region. The dendrites are probably not electrically excitable. Since the cells of the nervous system are discrete units it is necessary for them to be able to transmit excitatory events among themselves, and also to the muscle cells. To this end special forms of contact (synapses) occur between them. The transmissive process at these points is usually chemical in nature. In one instance very close physical contact between adjacent nerve cells permits electrical transmission (Furshpan and Potter, ^59) but this is probably very rare. The giant axons of earthworms, unlike those of the squid, are formed by the fusion of segmentally-produced units in which the points of contact remain partitioned. At these points of contact the transmission is also electrical in nature (Kao and Grundfest, 1957). We may now summarize the major requirements of excitable membranes of different nerve and muscle cells, or different parts of these cells as follows: 1. Axons of nerve cells must produce rap- CONDUCTION IN NERVE AND MUSCLE idly-propagating, brief, all-or-nothing electrical signals. 2. Muscle cells may be required to produce signals comparable to nerve impulses, or they may be required to give only graded electrical signals in response to electrical stimulation, or they may be electrically unresponsive to electrical stimulation. 3. Regions of nerve or muscle cells underlying special points of contact (synapses) from nerve cell branches must be capable of responding by giving electrical changes to chemical substances released by the terminals. In summary, four different capabilities are called for: all-or-nothing pulsatile responsiveness, graded electrical responsiveness, electrical unresponsiveness, and responsiveness (by electrical change) to chemical stimuli. THE NATURE OF ELECTRICAL ACTIVITY IN NERVE AND MUSCLE CELLS Our problem is to discover how excitable cells can provide for each of these different functions. We may assume that they probably have achieved this result by a process of evolution starting from a common ancestral cellular mechanism. A general theory of impulse activity in nerve and muscle was first produced in 1902 by Bernstein. By that time the all-or-nothing, brief nature of the nerve impulse had been established and it was thought that a similar impulse was utilized in muscles. According to Bernstein, the impulse is due to a brief, temporary obliteration of a resting membrane potential. The latter is produced across a (at that time hypothetical) semi-permeable plasma membrane, a layer of differentiated cytoplasm about 100 A thick forming the functional skin of the nerve fiber or muscle cell and containing within it the fluid and structural components of the cell. The resting voltage could be measured, albeit reduced in magnitude by short-circuiting, between an electrode placed on the outside of a nerve or muscle and a second one placed in a freshly-made cut, which permitted fairly good electrical contact with the inside of the cells. This potential difference approximated 1/10 volt in the best measurements (Tschachotin, 1907). It was reduced progressively by gradually raising the external potassium ion concentration of the bathing fluid. Bernstein made this observation the basis of his hypothesis. The interior of both nerve and muscle cells contains a high concentration of potassium ions; the fluid surrounding the cells in the body does not, for sodium is the major cation. Potassium ions must, therefore, be accumulated by the cells and sodium excluded from them. Chloride ions form the major anion in the body fluids but are virtually absent from the inside of the nerve or muscle cell. Hence, Bernstein proposed that the membrane is not permeable to sodium or chloride but markedly so to potassium ions. The major internal constituents of the cells must be protein, which at the pH of the cells is in anionic form. These large anions are unable to diffuse out across the cell membrane and so a dynamic equilibrium is established; potassium ions enter the cells to neutralize the negative charges on the immobile internal anions, but tend to move outwards down the concentration gradient. The tendency to move outwards is just balanced by a small net negative charge on the interior. At equilibrium, which will quickly be established if the ionic permeabilities are not too low, the potential difference will approach the theoretical potential for a potassium concentration cell (potassium equilibrium potential). The first theoretical treatment of this kind of system had been due to Donnan, and the state was named after him a Donnan equilibrium. The value of the potential difference was determined theoretically by Nernst (1911) as: Em = RT/F logft [Ki]/[Ko] (Nernst equation) R = gas constant T = absolute temperature F = Faraday's constant [Ki] = potassium activity inside cell (approximately = concentration) [Ko] = potassium activity outside cell. Following excitation, according to the Bernstein hypothesis, the membrane struc- G. HOYLE ture would be temporarily altered, affecting the general permeability to all ions. Sodium and chloride would be permitted to enter and potassium would leave. The resting potential would fall towards zero, the whole membrane behaving like an injured one. The time-course of this change must be extremely rapid, occupying barely one millisecond. But even more remarkably, recovery occurs in an only slightly longer period. This was supposed to be simply due to an immediate return of the original properties of the membrane. As an explanation of resting and conducted activity in nerve and muscle this hypothesis lasted unchanged for almost four decades. The possibility of chemical activation at synapses did not become fully established until about the end of this era. Most of the later experiments designed to test the hypothesis confirmed its probable validity, although alternative theories were proposed. One alternative theory was that the resting potential was directly associated with metabolic activity, perhaps in the form of a redox potential. Since the possible nature of this activity was not specified in detail, the theory has not offered any serious challenge to the ionic model. The action potential has often been regarded as having a pharmacological basis in terms of a highly active organic substance (commonly regarded as acetylcholine) moving inwards across the membrane (Nachmansohn, 1959). There might well be some such release and movement in connection with the structural changes, but these would not invalidate the general hypothesis, because the ionic gradients and currents of action due to the concentration-cell effects of unequally-distributed mineral-ions would still play the fundamental role in conduction. The Bernstein hypothesis underwent a setback when it was found that the resting membrane is in fact permeable to sodium ions (Fenn, 1940), but this difficulty was soon countered by endowing the membrane with a "sodium pump" capable of ejecting intruding Na+ ions as fast as they enter (Dean, 1941). A much more serious blow was delivered when the first directly-recorded membrane potentials were meas- ured. These were obtained following the introduction of the squid giant axon by Young, (1938) which permitted measuring the membrane potential of a single nerve fiber with the aid of an electrode directly inserted inside it. Cole and Curtis (1939) used this method to show that there is in fact a marked fall in membrane resistance during the action potential, as predicted by the Bernstein theory. But these, and other investigators (Hodgkin and Huxley, 1939) were in for a big surprise when they looked at the action potential, for it turned out that this did not simply fall to zero, as proposed by the theory, but actually reversed in sign by an appreciable amount. It is not possible to detect a reversal of membrane potential using external electrodes only. The second world war interrupted further research on the nerve impulse for a few years, but soon after a penetrating attack was initiated by the British group. Starting with the Bernstein hypothesis as their basis, they considered the possibility that by including the sodium ion in the formation of the action potential it might be possible to explain the observed course of events. As early as 1902, in the same volume of Pfliigers Archiv as that in which the Bernstein hypothesis was stated, Overton had proposed that sodium must be involved in the action potential and might be exchanged for potassium. Since the simpler Bernstein theory seemed perfectly adequate the Overton proposals were neglected. If the membrane were suddenly made permeable to sodium ions selectively, argued Hodgkin (1949), the inequality of distribution of these ions across the membrane would certainly ensure a fall in resting potential. Furthermore, the equilibrium potential for sodium ions is of opposite electrical sign to potassium. This meant that if the sodium ion permeability change were sufficiently drastic, so that relative to the other ions it made a very large contribution to the potential, there could be a reversal of membrane potential. The voltage on the membrane would swing from a value close to the equilibrium potential for potassium to that of the equilibrium potential for sodium (Fig. 1). Visualizing the possibility CONDUCTION IN NERVE AND MUSCLE RESTING MEMBRANE ACTIVE MEMBRANE V Drastic rise in Na conductance FIG. 1. The "ion-batteries" underlying electrical activity. At rest the potassium battery (En) dominates the membrane potential (Em) owing to a relatively high potassium conductance (gk). Following excitation the sodium conductance (gN«) undergoes a drastic rise and so the sodium battery (ENn) comes instead to determine the membrane potential. An increase in chloride conductance (gcl) would act in the opposite direction to sodium. of a specific chemical transporting or carrier mechanism, the phenomenon of sodium permeability increase was termed sodiwn activation, the carrier mechanism in effect being activated. The principal consequence of this hypothesis is that the magnitude of the action potential and, in particular, that of the overshoot, should depend on the external concentration of sodium ions. Hodgkin and Katz (1949) showed that this is true for squid giant axon and soon after it was demonstrated for frog sartorius muscle (Nastuk and Hodgkin, 1950). Since then it has been demonstrated to apply to mammalian and a number of other nerves and muscles (Shanes, 1958a,b—review). The fall in magnitude of the action potential occurs in accordance with the equation: V = 58 log "Na-substitute'yNao where "Na-substitute" is the concentration of an "inert" ion substituted for sodium. The rate of rise of the action potential should, and does, also fall as the external sodium concentration is increased. The new explanation of the recovery phase of the action potential also differs from the original Bernstein one, which postulated a simple return to status quo in regard to the general ionic permeability of the membrane. The new hypothesis proposed a specific increase in permeability to potassium ions, occurring soon after the sodium permeability increase, but with a delayed rise. This may be called potassium activation. By itself potassium activation would not cause a return to the resting potential if the sodium conductance remained high, so a further effect was proposed, to ensure a cutting off of the inward current due to sodium ions. This was termed sodium inactivation, and visualized as a sudden stoppage of the inward sodium ion transport mechanism. As the membrane becomes charged again during the period in which K+ flows outwards, the potassium conductance may be expected to fall automatically, so it is not necessary to postulate specific inactivation in addition, although this might occur. On this new hypothesis the time-course of the action potential is determined by the G. HOYLE 10 calculated action potent ial which alter the ionic permeabilities and so also the effective membrane resistance. The machine produces an oscillographically-displayed current which exactly matches that flowing across the membrane and so parallels the permeability changes (Hodgkin and Huxley, ]952a,b) By measuring the current changes with time, first in the presence of a normal concentration of external Na and second in its absence, and subtracting the second values FIG. 2. Ionic changes underlying the action potential of the squid giant axon. The actual conduct- from the first, the time-course of the sodium ance changes to the sodium and potassium ions as current can be determined. This current determined by the "voltage clamp" method are starts immediately the voltage across the given by solid lines. The calculated action poten- membrane is displaced in the depolarizing tial based on these conductance changes is given by direction and rises rapidly to a peak in 0.5 the broken line. The action potential starts in advance of the local conductance changes owing to msec, returning to zero inside four msec the electiotonic spread of current in advance of the (Fig. 2). The current is in the inward (depermeability changes. (From Hodgkin and Huxley, polarizing) direction and thereby assists the 1952&, J. Physiol.) applied voltage. In the absence of sodium the current is entirely in the outward direcsum of the sodium-ion and potassium-ion tion and is considered to be carried very conductance changes, along the lines illus- largely by potassium ions. In the squid trated in Fig. 2. The great advantage of this giant axon it starts to rise as soon as the hypothesis was that it was possible to sub- voltage is lowered, but at a much slower ject it to experimental tests, especially on rate than that for sodium, and it takes the squid giant axon. There should be a many milliseconds to reach completion. By net gain of sodium ions about equalled by taking the measured values for Na conducta net loss of potassium ions during the pas- ance changes and combining them with the sage of a nerve impulse. By using Na24 and K conductance changes a theoretical action K4- as tracers Keynes (1951) was able to potential can be constructed. This has a show that a squid giant axon takes up about time-course which is in good agreement 3.7 p. /A mol Na ions per sq. cm. of mem- with the actual action potential. In some recent experiments it has been brane per impulse, while it loses 4.3 /j. ^ mol K ions per sq. cm. so that the gain in found possible to verify the ionic hypothesodium is balanced by the loss in potassium sis for the squid giant axon in a satisfying way. On this hypothesis, solely the surface as predicted. The actual sodium- and potassium-ion membrane is concerned with conducted acconductance changes were measured by an tivity and the core is important only as the ingenious device called the 'voltage clamp.' storehouse for potassium ions. If the axoIn this technique two electrodes are in- plasm can be squeezed out without doing serted down the center of the axon and a irrecoverable damage to the surface mempre-determined voltage is applied suddenly brane it should be possible to replace it across it by passing current through one of with a simple potassium salt solution of apthem from an amplifying device regulated propriate concentration and obtain normal by feed-back from the actual membrane resting and action potentials. This has now voltage, which is recorded from the other. been achieved (Baker, Hodgkin, and Shaw, The electronic device measures the inten- 1961) using potassium sulphate or potassity and time-course of the current which sium isethionate under 2-3 cm hydrostatic the machine has to provide in order to pressure, in the cannulated giant axon of maintain constant voltage in the face of Loligo forbesi. The resting potential is prochanges taking place in the membrane portional to the logarithm of the inter- 11 CONDUCTION IN NERVE AND MUSCLE nal potassium (sulphate)-ion concentration when the external potassium concentration is kept constant, as required by the theory (Fig. 3). When sodium ions were used to replace part of the internal potassium, the resulting action potential was also reduced in height as predicted. Conducted action pote7itials in insect nerves. The explanation of the nerve action potential outlined above seemed to be D -60 -C —=2 -o • -50 tiali £ -40 [K]0 = 10mM ^> g -30 - 1 / •3 -20 .2 « -10 0 + 10 —i A1 i i i 1 600 i 500 100 200 300 400 Internal potassium concentration (mAf) mV. + 50 0 FIG. 3. Experiments on squid giant axons from which all the axoplasm has been extruded, and refilled with artificial salines. Upper: effect of internal potassium concentration on resting potential of axon bathed in sea water. Lower, left: upper, action potential (internal electrode) with isotonic potas- 1 2 3 4 5 msec. 6 7 8 sium sulphate as internal medium; lower, normal axon. Lower, right: effect of replacing some of internal potassium by sodium ions. A—normal, B— 25% replaced, C—50% replaced. (From Baker et al., 1961, Nature.) 12 G. HOYI.K Direction of impulse Local current after potential Local current FIG. 4. The propagating action potential. Left: distribution of the wave of electrical disturbance along the nerve fibre showing way in which electrotonic current flows from resting region into active region and in so doing depolarizes in advance of the main wave. Right: appearance of action potential wave as recorded oscillographically with an internal electrode. Local current initiates spike when threshold is exceeded. capable of wide application, but not to phytophagous insects. In them the blood (hemolymph) sodium and potassium concentrations may be present in inverse ratio compared to that in all other body fluids, there being high potassium and a low sodium concentration (Bone, 1944). Nevertheless, the insect nerve action potential has been found to be dependent on the presence of sodium, or a suitable sodium-substitute, and the recovery of normal membrane potential can only occur in a low external potassium concentration (Hoyle, 1953; Yamasaki and Narahashi, 1959a). Evidently a normal ionic mechanism is utilized, but the axons are surrounded by a sheath which keeps out (or actively extrudes) potassium ions while retaining sodium ions. (Hoyle, 1952; Twarog and Roeder, 1956) spread of the potential evoked away from the site, decreasing exponentially with distance. If the action potential mechanism is blocked, for example by intense cold, this purely electrical spread can be detected beyond the block (Hodgkin, 1937). It is this action, spreading in advance of the wave of permeability change, which acts as a stimulus to further depolarization and the initiation of progressive, propagated change (Fig. 4). The membrane in the wake of the advancing depolarization wave is still recovering its resting potential (and excitability) after the wave has passed too far away to re-excite it. Otherwise the whole membrane would change permanently from the polarized to the depolarized state. A long nerve fiber can carry several impulses at the same time, spaced 2-3 cm apart. CABLE THEORY AND LOCAL-CIRCUIT ACTION SALTATORY CONDUCTION IN MYELINATED NERVE FIBERS The general theory described above accounts for the changes which occur in active nerve fibers but it does not explain the process of propagation. The theory for this is that the membrane has certain passive electrical properties which permit purely electrical (electrotonic) conduction of an applied potential change. The membrane has the property of a condenser and electric charge tends to spread along it evenly. But it also has a finite transverse resistance so the charge must leak away in time. Following activation at a given site, there is a In myelinated nerve fibers of vertebrates the electrical resistance of the myelin is so high that local electrotonic spread of current across it cannot occur to the extent necessary for initiation of further activity. Nor is there sufficient space for these currents to pass underneath it. Instead, the current flows round the myelin and through the nearest gap, i.e., the node of Ranvier. The nodes are sufficiently close to each other to ensure a reasonable safety-factor for the depolarization produced, in exceed- CONDUCTION IN NERVE AND MUSCLE Membrane under myelin remains inactive Outward current depolarizes next node of Ranvier 13 the same shape as that of the squid giant axon. That of the frog sartorius muscle fibers is similar in shape, but on a slightly slower time scale. Differences of this order of magnitude can be accounted for largely on the basis of a longer electrical time constant (product of transverse resistance and Current flows capacitance) of the membrane, which will Reverse ' potential ^ outside myelin at active node slow down the electrotonic rise and decay. BIG. 5. Conduction in myelinated nerve fiber. Only By contrast muscle fibers of hearts have the membrane in nodal regions becomes active. very differently shaped action potentials Current flows frorn the next nearest resting node (Draper and Weidmann, 1951; Irisawa et back over the outside of the myelin and returns in the core of the fiber. al.; 1961). The rising phase occurs similarly and goes straight into an overshoot, but aling the threshold for firing the sodium-cur- though repolarization starts immediately rent avalanche. The spread of simple elec- following the peak of the action potential trotonic current is much more rapid than it soon slows down markedly, forming a the propagation of action potentials in bare plateau which lasts for some 300-400 msec. membrane, so faster overall conduction is The plateau has an important functional achieved. The reversed membrane poten- significance. Once a nerve or muscle fiber tial associated with full sodium activation of the ordinary kind has recovered its full is developed only at the nodes; hence the resting potential following activity it is caaction potential as it were "jumps" from pable of being again excited so as to give node to node, a process therefore referred another action potential. In muscle the recovery time is short compared with the duto as saltatory conduction. The events occurring at the node itself ration of a twitch, and this permits the fuappear to be substantially the same as those sion of contractions leading to the very usefound in the squid giant axon. The rising ful tetanus. For a heart muscle to go into phase of the action potential is certainly tetanus would, however, spell disaster for due to sodium-ion entry. There is, how- most animals and a mechanism ensuring a ever, some doubt as to whether the mem- period of inexcitability between contracbrane resting potential is a potassium con- tions sufficient to allow full relaxation, is centration potential, and this has been cate- clearly desirable. This is" the purpose of the gorically denied recently (Stampfli, 1959). plateau. How is it achieved? Instead, it may be dominated by the chloIt can be shown experimentally that the ride ion. This would not invalidate the duration of the plateau is greatly affected general theory, on which the chloride ion by the external potassium-ion concentramay easily be expected to be able to replace tion (Weidmann, 1957). Also, the height potassium as a source of resting voltage. In of the overshoot is reduced by lowering the many muscle cells the chloride ion probab- external sodium-ion concentration (Weidly makes a major contribution (Hodgkin mann, 1957). Thus it is possible to explain and Horowicz, 1959). Chloride-ion permea- the rising phase on the normal basis of a bility increases are probably involved in specific increase in sodium conductance (socertain kinds of inhibitory activity and may dium activation) and the sharp peak as due be associated with increases in membrane to sodium inactivation. Meanwhile the popotential. They can act in a similar man- tassium conductance is rising only very ner to potassium as a restorer of resting po- slowly, but after about 300 msec starts to tential. rise rapidly, so bringing the plateau to an end and depolarizing the fiber (Fig. 6). OTHER KINDS OF CONDUCTED POTENTIALS, This does not mean that a final solution of HEART MUSCLE the nature of the potential changes in heart Not all propagated action potentials have muscle fibers has been reached, but merely Direction on of impulse 14 G. HOYLE O 100 20O 300 4.00ms FIG. 6. Typical action potential from heart muscle fiber and time-courses of hypothetical sodium and potassium conductance changes which could underly it. that changes in ionic permeability, if suitably timed, could explain them. PACEMAKER ACTIVITY Another feature of heart muscle cells is their spontaneous "pacemaker" depolarization. Of course it is not difficult to simply postulate a fluctuating conductance to one of the ions. The equations derived by Hodgkin and Huxley (19526) to describe the action potential in terms of ionic conductance changes include a value m which is a variable describing sodium activation. Noble (1960) has shown that merely by inserting in these equations a different, appropriate value for m, the system is made theoretically unstable during diastole. The instability would be of the kind required to lead to pacemaker activity. GRADED RESPONSIVENESS AND DECREMENTAL CONDUCTION Electrical responses which are graded, not all-or-nothing in magnitude, can be obtained from the normal nerve membrane discussed previously, but only over a very narrow range of depolarizations, just below the threshold for the initiation of conducted spikes. They can readily be obtained from fatigued, damaged, anoxic or lightly- poisoned membranes. This section is, however, concerned with those membranes in which gradedness is the normal situation, for functional reasons. Subsynaptic membranes are always gradedly responsive to the chemical substances which actuate them, the magnitude of the response being a function of the concentration of the transmitter agent liberated in their vicinity. It appears, however, that they are not electrically excitable (Grundfest, 1957) and so they cannot conduct the resulting potential changes except in so far as electrotonic spread occurs. The slow skeletal muscle fibers of the frog are formed exclusively of this kind of membrane (Burke and Ginsborg, 1956). Functionally significant, gradedly-excitable electrogenic membrane occurs in nerve in post-synaptic dendrites and possibly in some pre-synaptic ones (Grundfest, 1960). It also occurs in fine sensory nerve terminals (Grundfest, 1960). In all these cases its function is to permit integration of incoming signals, in the former converting coded information from digital-time to analogue-time form. In muscle this kind of membrane is best known from the arthropods, where it is probably the only type present. It is, however, probably widespread throughout the invertebrate phyla (Hoyle, 1957) and in vertebrates it may occur in fish (Takeuchi, 1960), birds (Ginsborg, 1960) and in the contractile portions of some intrafusal muscle spindles in mammals (Boyd, 1958). Membrane which is electrically excitable but gives only graded, not all-or-nothing responses is characterized by responsiveness to depolarizing electrical stimuli over a wide range of magnitudes, even exceeding the resting potential. The responses may go as far as the full overshoot position (sodium equilibrium potential), but at no stage does the response become regenerative. Although the excitation initiates a response in adjacent regions of the fiber the latter is always smaller than the stimulus. The process is illustrated in Fig. 7 and should be compared with the all-or-nothing situation. Such a response is conducted actively, but with a progressive decrement, so that it rapidly decays to zero, as it propa- CONDUCTION IN NERVE AND MUSCLE Graded spike responses --n-rrm--Vt- threshold FIG. 7. Graded responses and the hypothetical conductance changes underlying them. Upper: responses of typical insect muscle fiber to depolarizing pulse of constant duration and progressively increasing strength. Height of response increases progressively but never comes to exceed stimulus height so response will propagate only decrementally. Lower: hypothetical sodium and potassium conductances changes to increasing stimulus strength. Sodium current increases with each step, and so also does potassium. Potential change does not reach sodium equilibrium value. gates away from the stimulated region. In a maximally stimulated insect (Romalea) muscle fiber a 30 mV response was reduced to only 5 raV over 2.1 mm (Cerf et al., I960). Where this type of responsiveness occurs, information is changed in quality, from digital partly to analogue form, and integration can occur in these membranes. Graded responsiveness can only be utilized though, when a relatively small area is to be activated, close to the point of innervation. That is why it is necessary, with this mechanism, to employ multi-terminal innervation. Why, in that case, complicate the picture by graded electrical responses, since presumably the primary post-synaptic potentials could serve for the excitation transfer as they do in frog slow skeletal muscles and some crustacean muscles? It is not yet possible to give a full answer to this question, but it may be that the electrical response of an electrically excitable membrane is the only method of ensuring really quick subsequent activation of the 15 contractile machinery, in which case the membrane would, in many muscles, need to retain as much electric responsiveness as was consistent with fine gradation of excitation at the membrane level. It would, of course, be very satisfying if we could explain graded electrical responsiveness, as well as other varieties of responsiveness, in terms of the general ionic model by permitting some minor changes. One way in which this can be done is to postulate that the potassium conductance change rises much more steeply in this type of membrane, other changes being of the standard kind. This simple alteration gives a surprisingly adequate account. If the potassium conductance rises almost as steeply as the sodium conductance, then the membrane will not be able to depolarize to any extent under the influence of increased sodium conductance before a rising potassium conductance will cause potential changes in the opposite direction. The rising voltage will be cut off before there is time to swing over to the sodium-equilibrium-potential level. The process would be aided if sodium-inactivation also occurred either earlier or more readily. The dependence of the magnitude of the response on the magnitude of the depolarization, which is the essential feature of gradedly-responsive-membrane, follows from this hypothesis. The sodium current is proportional to the depolarization in the squid giant axon membrane, and likewise in graded membrane. Thus the stronger the stimulus the greater the extent of sodium activation and current flow. This will lead to progressively greater responses, but the potassium current will likewise increase progressively and so still cut off potential change before it swings over to the sodium-equilibrium-potential value. The graded responses have the shape of abortive spikes, never forming plateaus. This strongly suggests a link between sodium inactivation and rising potassium current. The proposed mechanism is illustrated in Fig. 6. On this explanation very slight changes in the timing of the conductance changes, which might be expected to occur naturally, would be reflected in relatively 16 G. HOYLE large differences in the size and shape of graded responses. Considerable variations are usually encountered in successive graded responses recorded from a fixed site. So far, the validity of this proposed modification of the general ionic hypothesis has not been subjected to rigorous testing, although there is substantial evidence in its favor. One consequence of the proposal is that it should be possible to make the normally graded membrane give all-or-nothing responses. All that would be necessary would be to impede potassium ion movement selectively. Even a slight increase in membrane resistance might do this. In fact, several arthropod muscle fibers have been made to give propagated all-or-nothing responses simply by adding barium or strontium ions to the medium. (Fatt and Ginsborg, 1958; McCann et al., 1958; Werman and Grundfest, 1958) These ions cause an increase in membrane resistance. The potentials which result are greatly prolonged compared with normal action potentials, as would be expected if repolarization was difficult owing to impeded potassium-ion movement. It would be nice to be able to achieve a more normal-looking action potential than the Sr/Ba one, perhaps by the action of a drug applied in a minute dose. This has recently been achieved in insects using the mild insectide ryanodine (Fig. 8; Hoyle, unpublished). Some minutes after the application of this drug to gradedly responsive locust muscle fibers, the fibers give allor-nothing spikes having a shape resembling that of normal action potentials of nerve, or of ordinary vertebrate skeletal muscle fibers. Even fibers which in normal saline showed no sign of electrical responsiveness gave large spikes after ryanodine treatment. Alternative explanations for graded responsiveness have been offered, particularly in terms of more thinly-distributed areas of selective sodium-permeability increase (sodium "trap-doors"), compared with all-ornothing membrane. On this basis an increase in general electrical resistance might be expected to bring about all-or-nothing activity by carrying the initial excitation to more trap-doors. However, in arthropod muscle there are so many distributed nerve endings that the surface membrane is equally excited all over by each impulse; therefore an increased resistance is not going to cause a greater spread than occurs normally. INHIBITION AND OTHER SYNAPTIC EVENTS Inhibitory activity is often conducted to the site of action by normal nerve impulses, in which case it is a property of particular synaptic sites. Chemical diffusion of inhibitory activity over a wide area also occurs, for example, in spreading "depression" in mammalian brains; but most inhibitory phenomena are highly local and are not conducted except electrotonically. That is, there is no evidence that inhibitory changes are in any way regenerative, capable of exciting further inhibitory-type response. The inhibitory change occurs only in chemically excitable membrane. Although inhibitory phenomena are not strictly within the scope of this article, it is desirable to ask if it is possible to explain inhibition in terms of the ionic theory. Excitatory synaptic activity, too, must be explicable in terms of the ionic hypothesis for it to have full validity. A post-synaptic potential rises rapidly and decays slowly; often the decay is exponential, determined by the purely electrical characteristics of the membrane. (Fatt and Katz, 1951; Takeuchi and Takeuchi, I960). Synaptic-potential height is increased if the resting potential is artificially raised, and lowered if it is reduced, in a linear manner (Fatt and Katz, 1951; del Castillo et al., 1953). The synaptic potential is associated with a temporary low resistance in the membrane region. Fatt and Katz explain it as a sudden increase in the permeability of the subsynaptic membrane caused by the combination with it of transmitter substance. The permeability change is certainly either a general one, or to several ion species, not just one kind of ion (del Castillo and Katz. 1954). This is analogous to the original Bernstein explanation of the nerve impulse, as a non-specific increase in permeabilitv to all ions, and must lead to a de- CONDUCTION IN NERVE AND MUSCLE 17 FIG. 8. Conversion of electrically-inexcitable membrane (muscle fiber of spiracular closing muscle, Schistocerca) to all-or-nothing responsive membrane by drug action (ryanodine, 10-"M). Muscle fiber re- sjxmded to nerve stimulation only by post-synaptic potentials before drug was applied. Under influence of drug all-or-nothing spikes arise; local responses when close to threshold. polamation towards, but not beyond, 2ero membrane potential. In fact post-synaptic potentials never reach the zero level. The resting nerve membrane in parallel with the synaptic membrane discharges into the depolarized synaptic region and gives a response if it is electrically excitable. Thus excitatory synaptic activity is readily explicable in terms of the ionic theory. Inhibitory activity is also associated with a fall in membrane resistance, and is affected by membrane potential (Fatt and Katz, 1953; Hutter and Trautwein, 1956; Boistel and Fatt, 1958; Hoyle and Wiersma, 1958). Sometimes potential change is associated with inhibitory transmission, particularly when the membrane potential is displaced above or below the normal resting level. This is always in the hyperpolarizing direction for membrane potentials at or below resting level, but quickly becomes depolarizing when the membrane is hyperpolarized. The potential at which no change occurs is called the change-over or reversal potential. Evidently the transmitter substance causes an increased permeability to an ion having an equilibrium potential near to the normal resting poten- 18 G. HOYLE tial. Inhibitory activity results in a displacement of the membrane potential towards this equilibrium potential. Either chloride or potassium ions could fill this requirement, or both acting together. It seems that either ion separately or both in concert may be involved in inhibitory activity in different situations. In crustacean muscle, although it is by no means clear what actually causes the mechanical inhibition, whether interference with ion flow or a more direct action, the electrical potential changes associated with it are probably due to a selective increase in permeability to chloride ions. In the sinus venosus of the heart, where comparable hyperpolarizing potentials appear, it seems also to be due to chloride ions. But in the sensory terminals of the stretch receptor of the crayfish, which receive an inhibitory efferent innervation, the inhibitory process appears to be due to an increase in potassium-ion conductance (Edwards and Hagiwara, 1959). The inhibitory process in nerve cells and in heart muscle has a similar basis in that the functional aim in each case is to keep the mean membrane potential high enough, even in the face of continuing excitatory disturbances, so that the level of potential at which action potentials are set up is not reached. UPSIDE-DOWN ACTION POTENTIALS The production of action potentials depends on the capacity of the membrane to change state suddenly from one mode to another and back again. The change in state is not only produced by depolarizing current, for starting with a nerve in the depolarized condition a comparable reaction can be induced by hyperpolarizing current. Segal (1958—squid giant axon) and Mueller (1958—node of Ranvier) discovered independently that nerve cells depolarized by potassium chloride react to hyperpolarizing pulses of adequate strength not merely by electrotonic changes but also by giving a large response in the same direction. The response is all-or-nothing and propagated, i.e., it is an upside-down action potential. In squid giant axon the upside-down action potential is about 1000 times longer than the normal one (Tasaki, 1959), but comparable reversed action potentials of crayfish nerve fibers last for only five milliseconds. In the latter preparation, long hyperpolarizing pulses give rise to repetitive responses (Tomita et al., 1961). On the ionic theory, raising the external potassium ion concentration must cause depolarization, but only as long as the potassium conductance is high. Should the potassium conductance fall greatly relative to the chloride conductance, then the chloride ion will dominate. It seems that this is what happens in the membrane. When it is hyperpolarized beyond a certain point it jumps from a condition in which the potassium conductance is high, to one in which it is low. In the depolarized membrane this leads to a large potential shift towards the chloride equilibrium potential value. These findings have some consequences for understanding the normal resting and action potentials. Plots of resting potential against external potassium concentration show non-linearity at low potassium concentration ( = high membrane potential). This is due to a great fall-off in potassium conductance, coupled with the fact that it is very difficult to reduce the external potassium value to zero. There is evidently another external layer, separated by a small space from the plasma membrane itself, which acts as a barrier to the free diffusion of ions. Diffusion of potassium out of this space takes time, and there is constant replacement by potassium leaking out into it from the cell (Harris and Sjodin, 1961). Many excitable membranes do not behave as simple ohmic resistors (over a range of potential change below the threshold for giving active responses) but show a marked change in the slope of the voltagecurrent curve at a membrane potential about equal to the resting potential (Yamasaki and Narahashi, 1959). Thereafter outward, or depolarizing current passes more readily, the membrane behaving like a rectifier. This behavior is probably largely concerned also with special behavior of the potassium ion, which is a principal carrier of current. It may be leaving as much as two hundred times more readilv than it en- CONDUCTION IN NERVE AND MUSCLE ters. This behavior recalls that of semiconductors. CONDUCTION IN SMOOTH MUSCLE The foregoing accounts of conduction processes are relevant to excitable cells in general, but certain special problems arise in regard to conduction in sheets of muscle which are not clearly divided into discrete, individually-innervated units. This includes all the different kinds of smooth muscle found in vertebrates, of the gut, ureter, uterus, pupil, blood vessels, etc. and also most of the muscles of invertebrates other than arthropods. A characteristic feature of all these very diverse muscles is that they are composed of non-striated (smooth) cells which are invariably thin, spindle-shaped, uninucleate and, with one or two exceptions, short. Their fine innervation appears to be by simple synaptic contacts (Caesar et al., 1957; Richardson, 1958) but very little is known about it. The general innervation is probably from a diffuse nerve net within the muscle in most cases (Stohr, 1954; Boeke, 1949; Hoyle, 1957). Conduction within the muscle may thus occur in the nerve net, in which case it is rather slow since at each of the synapses within the net delay occurs. Conduction in such nets may be apparently decremental (Pantin, 1935), but this is really due to a failure of the excitation to pass certain synapses which require facilitation by successive impulses. There may be through-conducting tracts in such nets, either determined by yielding synapses or special tracts of long fibers (Pantin, 1952) and thus the appearance of a dual or multiple innervation may be created (Pople and Ewer, 1954). Three other kinds of conduction have been proposed for various smooth muscles; electrical, by the muscle fibers themselves; by progressing stretch; and by diffusing chemicals. Three possible mechanisms have been suggested to explain the first of these alternatives: 1, ephaptic transmission between overlapping cells; 2, low resistance pathways between adjacent cells; 3, cytoplasmic continuity between cells. Regarding the latter, bridges have certainly been 19 located between smooth muscle cells (Prosser et al., I960) but these may be merely structural rather than special electrical pathways, although they undoubtedly facilitate electrical spread from one cell to another. All three alternatives must be regarded as possibilities. All excitable cells are affected by being stretched or relaxed and respond by membrane potential changes. In smooth muscle the extent of depolarization associated with stretch may be such as to lead to contraction (Biilbring, 1955). This affords a simple mechanical means by which conduction may occur in smooth muscles, since contraction initiated at one end will stretch the adjacent cells and so on down the length. Most smooth muscles are highly sensitive to certain chemical agents (Rosenblueth, 1950) and this is the basis of general control of involuntary muscle by humoral agents. Progressive diffusion is not, however, likely to be a major mode of conduction, but the influence of humoral agents is neverthless very important in other ways. Under their influence the excitability may rise greatly. The cells will then become more sensitive to stretch, and conduction by this means may become possible. Also, individual cells will become much more susceptible to electrical stimulation by current flowing from adjacent cells or groups of cells (Burnstock and Prosser, 1960). Thus there is probably no uniform pattern of conduction in smooth muscle. Not only different modes but also different combinations of conduction modes are possible arid different mechanisms may operate at different times, depending on humoral influences, degree of stretch, etc. The membranes of smooth muscle cells probably differ in their properties just as do those of striated muscle, being either electrically unresponsive, gradedly responsive, or all-or-nothing; and of course they may change according to local hormonal conditions and stretch. The smooth muscle cells of the vas deferens of the guinea-pig can undoubtedly give all-or-nothing action potentials (Burnstock and Holman, 1961). The membrane potential is probably mainly determined by the potassium-ion 20 G. HOYLE distribution, but with a large chloride-ion contribution. Sodium ions are probably mainly responsible for the action potential changes, but with a strong possibility of other, unknown ions playing a significant role (Holman, 1958). ANOMALIES A few anomalies have already been mentioned which are not easy to fit into the general scheme of the ionic hypothesis. There are others: for instance, artificial alteration of the internal concentration of potassium ions often does not have the predicted effect. Injection of potassium and sodium into frog sartorius muscle fibers did not affect the membrane potential (Falk and Gerard, 1953). These experiments were open to the objection that chloride, which would reduce the membrane potential, was injected at the same time. This objection was met by introducing these salts, as well as calcium and magnesium, along with aspartate and glutamate, into squid giant axons (Grundfest et al., 1954). However, no significant changes of potential were obtained. In view of the success of Baker et al., 1961) in replacing the extruded axoplasm by salt solutions, a procedure which gave results according perfectly with the hypothesis, it can only be concluded that a satisfactory injection of the salts cannot be made with the axoplasm or myoplasm still present. Some years ago Tobias (1950) reported that frog sartorius muscles soaked in distilled water until they had lost more than 99% of their potassium still developed a resting potential as high as 40% normal. Continuing this line of experiment, Stephenson (1957) soaked sartorius muscles in potassium-free saline until the potassium had fallen to one-third normal, and then transferred them to saline containing potassium chloride. They accumulated an average of 31 mE/1 potassium in 50 min., but the membrane potentials remained constant, although according to the ionic theory they should have risen to 10 mV. In this case the potassium measurements were made on whole muscles and the resting po- tential records were taken from outer fibers which may have deteriorated. Results more difficult to explain are provided by the demonstration that action potentials of unique shape may be developed by some membranes in the complete absence of sodium but in the presence of substitute ions. Lorente de No et al. (1947) reported that, in frog nerves which had lost the capacity to conduct by being soaked in sodium-deficient media, certain small fibers recovered their ability to conduct following soaking in solutions containing certain quaternary ammonium compounds but no sodium. The majority of the nerve fibers, and likewise frog ordinary skeletal muscle fibers and crab axons, failed to recover responsiveness. Crustacean muscle fibers, however, give larger responses than normally in completely sodium-free media, containing instead choline, tetraethylammonium or tetrabutylammonium (Fatt and Katz, 1953). Hydrazinium and hydroxylammonium ions, though not perfect substitutes, at least paritally restore propagated responses in mammalian nerve fibers (Sugaya and Laget, 1958). Frog spinal ganglion cells (Koketsu et al., 1959a) and insect muscle fibers (Wood, 1958; Hoyle, unpublished) may be added; and the list continues to grow. In none of these cases is it possible to regard the quaternary ammonium compound as a simple sodium substitute. Although the height of the overshoot is proportional to the concentration of the substitute ion, in some cases a very small fraction suffices to greatly prolong the action potential. In the case of the larger ions, especially tetrabutyl ammonium, the action is irreversible (crustacean muscle: Fatt and Katz, 1953). In some insect muscles, several hours of washing are required to restore a tetraethylammonium-treated muscle to normal. One possibility raised by Fatt and Katz to explain their results in crustacean muscle was that the action potential might be determined by the outward movement of internal anions, and this movement would be facilitated by the external substitution of the onium ions. Following their work on the squid giant axon Tasaki and Hagiwara (1957) thought that tetraethylammonium CONDUCTION IN NERVE AND MUSCLE might exert its influence only after penetrating the membrane to the inside of the axon. It has no effect when added to the bathing fluid but only when injected. In confirmation of this possibility, typical, prolonged potentials are evoked by intracellular stimulation of frog spinal ganglion cells following the injection of tetraethylammonium or hydrazine into the cells, although in that case they are effective when applied externally also (Koketsu et al., 1959a; Koketsu and Nishi, 1960). These responses occurred even when the cells were bathed in medium containing no ions but only sucrose (Koketsu et al., 19596). Evidently either some ions capable of carrying current remain trapped outside the plasma membrane but beneath some relatively impermeable sheath, or else an action potential mechanism supported entirely by the outward movement of internal anions must be postulated. DISCUSSION The experiments mentioned in the last section remind us rather forcibly that the ionic explanation of electrical activity in nerve and muscle is still only a convenient hypothesis. If any cellular mechanism were discovered which could produce a resting potential without recourse to concentration-cell effects, it would not be difficult to bring the facts of ion distribution and movement into line with it. At the same time the anamolies are not so compelling that we must abandon the hypothesis and say "we simply do not know." Tt has been shown that many of the most significant variations in the shapes of action potentials can probably be accounted for quite satisfactorily on the basis of different time-courses of permeability changes to various ion species. Some of the other phenomena, including action potentials in the absence of external cations, can be explained if we postulate that outwardlyflowing anions can cany sufficient current to give the observed changes. It does not follow that this is the normal mechanism. These ion changes probably do occur normally, but they are masked by the much more massive inward movement of sodium 21 ions, or may even be inhibited by the sodium inflow. It may be argued from this that it is the structural changes in the membrane which are the most significant ones in regard to the functioning of excitable cells. The production of a resting potential is clearly important, but it is produced only in order that it can be reduced by excitatory events and thereby transduce and permit transmission of the stimulus. So far very little attention has been paid to this problem of the structural changes, although some attempts are now being made in this direction (Tobias, 1958; Tobias and Nelson, 1959). The Nachmanson group maintains that the structural changes occurring in electrically excitable membrane are analogous to those occurring in post-synaptic membrane; i.e., they are the result of a combination between structural molecules of the cell membrane and some active agent released locally by depolarizing current flow. This group, although maintaining that this substance is in fact acetylcholine, fails to explain why it is only at the synaptic regions that this drug can initiate action potentials. Apart from the structural transformations which must occur in association with excitation, the principal physiological phenomenon providing a basis for excitability and conduction must be the sodium pump mechanism. At one time it was suggested that the activity of the sodium pump might be the direct cause of membrane potentials (Grundfest, 1955) as it may well be in frog skin (Ussing and Zerahn, 1951) but this idea has been abandoned; it is unlikely that the pump can produce more than a few mV difference in potential especially if, as is probable in nerve, it is a coupled pump, taking in one potassium ion for each sodium ion extruded. Unfortunately there is no suitable molecular model for the pump, or any other ion transport mechanism, although the way in which energy is supplied to the pump is being discovered. High-energy phosphate bonds generated by metabolism are carried to the membrane as arginine phosphate and ATP (Caklwell et al., 1960r;). These in some way drive the so- 22 G. high Na* high CI" low K + External medium I coupled \"Sut T ci ;ut? transfer/ Internal medium REST HOYLE A'CI" An" Na + . in high K+ high nondiffusible anion low CI" low No4 ACTIVITY FIG. 9. Summary of principal ion movements determining activity in membrane. The clotted lines in "inhibition" indicate permeability increases, not RECOVERY INHIBITION necessarily resulting in any net movement in or out. Passive ion movements occur at all times in addition. dium pump, and arginine phosphate also ance appreciably delayed, the potential maintains at the same time the potassium change goes far towards the sodium, equiuptake process which is coupled to sodium librium (reversal) potential and, since the change is greater than the stimulus causing extrusion (Caldwell et al., 19606). In summary, there is overwhelming evi- it, it is regenerative and propogated in the dence that the normal resting potential of form of an all-or-nothing impulse. The nerve and muscle cells throughout the ani- final shape of this propagated disturbance mal kingdom is the result of the inequality depends on the rate of change of the potasof distribution of ions across the mem- sium conductance change. The principal brane. It is dominated by the potassium ion movements concerned in the electrical ion, rarely by the chloride ion, and never activities of membranes are shown in Fig. 9. by any other ion species. The inequality is maintained by metabolically-driven ion REFERENCES pumps which in particular extrude sodium Baker, P. F., A. L. Hodgkin, and T. I. Shaw. 1961. ions and take up potassium ions. TempoReplacement of the protoplasm of a giant nerve rary electrical changes are generated in exfibre with artificial solutions. Nature 190:885-886. citable membrane following changes which Bernstein, J. 1902. Untersuchungen zur Thermodynamik der biolektrischen Strome. Pfliig. Arrh. affect the conductance to ions. 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