Principles of General Physiology

Suppose that the ions, newly produced, are free to diffuse. As we have seen DIAGRAM OF CIRCUIT USED IN ' BSERVATIONS AND MEASUREMENTS OF CHANGES B, Half-discharged accumulator cell, sending constant current through the stretched wire P, from which various fractions can be led off by the sliding contact. R, Reverser, or commutator, by which the direction of the electromotive force led off can be changed without changing the connections of the battery.

S, Standard cell, which can be put into the circuit by the key W. M, Spring key for momentary closure, in order not to take off any appreciable current from the standard cell. O, The instrument used for detecting the electrical disturbance, electrometer or galvanometer. It can be shortcircuited by turning the switch D into the position opposite to that shown. When the capillary electrometer is used, a key should be introduced which keeps the instrument always short-circuited except when in use.

E, Nonpolarisable electrodes, leading off from points on the muscle T. E and T together represent any source of potential difference, such as those in tissues or in a hydrogen electrode. (page 158), the more rapidly moving ions will proceed in advance of the slower ones, giving rise to a potential difference in proportion to the difference of their velocities. In the small spaces within cells through which this diffusion takes place, any difference of concentration will equalise itself very rapidly, and, except in the case of the hydrogen and hydroxyl ions, can never give rise to any considerable electromotive force. The factor expressing this occurs in the formula

for the electromotive force of concentration batteries (see Nernst's book, 1911, p. 752). It is which gives the electromotive force at the contact of two solutions of concentrations PJ and c.y, u and v being the velocities of the cation and anion respectively. When u and v are very nearly equal, as in potassium chloride, the potential difference due to this factor is very small. If u is hydrogen, with a molecular conductivity of 318, and v is carboxyl, as in formic acid, with a molecular

R is 0-861 x 10~4 and if we take ordinary logarithms and a ratio of concentration of 1 to 10, the expression becomes about 0'05 volt, and even this could only last an infinitesimally short time owing to rapid diffusion. We see that, to account for the values actually obtained experimentally in animal tissues, another source of potential difference must be found. The potentials of metallic electrodes naturally suggest themselves, so that one sometimes finds it stated that the electromotive activity of tissues is that of a concentration battery. But it is plain that there is nothing in living cells that could be taken as a metallic electrode. On the other hand, we have already seen (page 161) how we can obtain a permanent potential difference of fairly considerable amount when a membrane is present permeable to one only of the two ions of a binary electrolyte. There is formed a Helmholtz double layer, and the electromotive force is expressed by a formula similar to that of the concentration battery. This point of view was token by Bernstein (1902), on the basis of Ostwald's (1890) considerations regarding semiperrneable membranes, and is developed further by Bernstein in a paper of 1913.

It may enable this important conception to be grasped more easily if a simple illustration be given. Imagine two large pastures separated by a fence and that the spaces between the liars of the fence are wide enough to allow lambs to pass through, but too narrow for ewes. Introduce into one of these pastures a flock of sheep, each ewe with one lamb. In the course of their wanderings they will arrive at the fence. The propensity of the lambs to wander further will take them through the fence, while the ewes will be left behind. But the attractive forces, particularly that of food, will prevent the lambs from departing' from their mothers for any considerable distance. Similarly, the presence of the lambs in the adjoining field will prevent the ewes from wandering far from the fence. Regarding wool as electric charge, we see that the potential will be higher on the side of the fence occupied by the ewes. It may be said that the thickness of the layer would be considerable, but if we imagine molecules magnified to the size of sheep, the arrangement would not greatly differ from the molecular one.

Since the question is somewhat fundamental, it is well to consider the mathematical proof that a membrane of the kind postulated gives rise to a potential difference expressed by a formula similar to that of Nernst's concentration battery with metallic electrodes. There are two distinct ways in which the calculation can be made. We may take the work done in moving electricity from one solution to the other against electrostatic forces, as in the method used by Nernst, based on Helmholtz's theory of contact potential, and similar to that used on page 33 in calculating the work done in compressing a gas. But for the present purpose, in which we are regarding the phenomenon from the point of view of the potential difference in equilibrium, the following method is more appropriate, besides giving an opportunity for a new aspect of the case. The details of the treatment I owe to Mr W. B. Hardy.

For simplicity, we will consider the membrane as being infinitely thin, which is very nearly true for the cell membrane. Let it be situated, to begin with, between water and a solution containing a salt which is electrolytically dissociated into the ions B- and S', and be freely permeable to B-, but impermeable to S', in a purely mechanical way, as a filter or sieve, for example. The ions B- tend to pass from solution inside to water outside owing to their osmotic pressure-and to this alone. Since ions S' cannot pass through, in order that ions B' shall diffuse into the outer solvent, they must separate from their companions. This they cannot do for more than a minute distance, owing to the enormous electrostatic force between the oppositely charged ions. The amount of this force was calculated by Arrhenius, as we saw on page 179 above.

These ions B' are, therefore, acted on by two forces in opposite directions, and they will take up a position in which the two forces are equal and opposite. The osmotic pressure exerted on a membrane of area A is Ao?P, where P is the pressure per unit area. Let E be the potential difference between the two members S' and B' of the Helmholtz double layer. Then — - is the potential gradient, or rate of fall of Further, if q is the quantity of electricity carried by one gram-equivalent of

ion B', then the force acting on this gram-equivalent is q — . That this is so will be clear by consideration of the fact that the force is directly proportional to the quantity of electricity producing it, and the fact that the greater the difference of potential between the layers of B' and S', the greater will be the attractive force between them. Let c be the concentration of the diffusible ion B' in gram-equivalents per c.c. of solution. The volume of the space between the two layers is A&r, if the depth be &r, and the number of gram-equivalents of the ion B' contained in the space is A8xc.

Then the force acting upon them, due to the potential gradient — , is A8xc — q. This force is equal and opposite to their osmotic pressure, therefore — The treatment will be more general if we suppose that the concentration of the ion B' is a positive quantity on both sides the membrane. In that case, we must integrate between the limits, pl and pv which are the osmotic pressures of the ions B- on the two sides of the membrane. or, if c2 is the concentration of the stronger solution and c, that of the weaker solution,

Cj and c.,, of course, refer to concentrations of the ion concerned, that is, the one to which the membrane is permeable. Although there are certain experimental difficulties in the actual investigation of the question, especially when inorganic electrolytes are dealt with, some measurements which I made with Congo-red (1911, 2, pp. 245-247) gave results in satisfactory agreement with the formula. If the S3'8tem is not in osmotic equilibrium, so that there is a flow of solvent through the membrane, the electromotive force would not be given by the formula.

There is an interesting theoretical difficult}', analogous to that involved in electrolytic dissociation already referred to (page 180), which has not yet received satisfactory explanation. We know experimentally that a Helmholtz double layer is formed, owing to the fact that one ion cannot 'move far from the oppositely charged one. But it is not easy to see why this should be so. Suppose the electrolyte completely dissociated. On the kinetic theory, this means that the period during which any oppositely charged ions come within each other's sphere of influence is negligible, so far as electric stresses are concerned. The work required to separate the ions is therefore accomplished, and further separation should not require any more energy. So that, if such a solution be separated from pure solvent by a membrane permeable to one kind of ion only, these ions should be able to diffuse out freely, since they are already out of the range of influence of the opposite ions. Of course, if they did so there would be a large increase in the free energy of the sj-stem, which would infringe the second law of energetics. But if the force uniting the ions is purely electrical, it is difficult to understand why they cannot separate from one another after being dissociated. Larmor (1908) suggested that the energy for dissociation may be drawn from the volume energy of the solvent.

To return to the question of the electromotive force at a membrane. From the mode of its production, it will be seen to be an illustration of the rationale of metallic electrode potentials, if we regard the metallic ions as being free to escape from the surface of the metal, while the oppositely charged mass of metal cannot. Contrary to the contact potential difference of solutions free to diffuse, it is permanent. We may speak of a membrane of the kind described as being polarised. This form of expression is sometimes convenient.

In the application of the above theory to the living cell, we see that, if the membrane is permeable to both ions, no electromotive force can be present ; although if one ion be larger than the other, there might be only a small number of pores permeable to the larger ion, so that, for a considerable time, an electromotive force might exist. If, moreover, the membrane were impermeable to both ions, there could be no potential difference, since there would be no possibility of the ions separating to form a double layer.

In short, a membrane previously impermeable to both ions might give rise to an electromotive force if it became permeable to one only, but not if it became permeable to both. Also a membrane, previously permeable to both ions, might become a source of potential difference if it became permeable to one only. Such changes are, no doubt, taking place in the normal activities of the cell. The manner of origin of these potential differences is essentially the same as the "electrical forces at phase boundaries, ': discussed by Haber and Klemensiewicz (1909); the phenomena described by Beutner (1912 and 1913) are, no doubt, due to the same facts. Suppose that we have a layer of a liquid, immiscible with water, in contact with a solution in water of an electrolyte, of which one ion is soluble in the non-aqueous phase, the other insoluble. It is clear that the former ions will tend to pass into the non-aqueous liquid, but cannot get beyond the boundary, owing to the other ions being unable to do so. We have again a Helmholtz double layer. Thus Beutner finds a potential difference at the contact surface between a watery solution of potassium thiocyanate and a solution of toluidine thiocyanate in toluidine. This is readily accounted for if the potassium ion is insoluble in toluidine, SCN ion being soluble.

If, in any cell process, ions are newly formed, these will add to the concentration of those of the same sign already present, and increase the potential difference at a membrane of the kind described, as the formula shows. We have seen (page 161) that the concentrations expressed in the formula refer to the total concentration of all the diffusible ions of the same sign present, since interchange takes place freely at the contact surface. Thus the chemical nature of the ion does not appear to enter into consideration.

FIG. 205. DIPHASIC ELECTRICAL CHANGE IN UNINJURED SARTORIUS MUSCLE. A, Photograph of excursion of capillary electrometer. First with a single stimulus. Then, a second time, with an additional stimulus at 0'022 sec. later. The change due to the latter is fainter, because only recorded once. Time in 200 per second. B, Similar photograph with another additional stimulus at O'OIO sec. after the first, and between it and the In addition to the form of the diphasic response, as recorded by the capillary electrometer, these two figures show that a stimulus, occurring in the refractory period due to a previous one, has no effect on the result of a stimulus given just at the beginning of the return of excitability. That is, a stimulus in the refractory period does not set up any further refractory state.

C, Analysis of a capillary electrometer record of a diphasic response of the gastrocnemius muscle to a single stimulus applied to the sciatic nerve. Muscle led off from the middle and the tendinous end. Charges on the surface of membranes themselves, dealt with by Mines (1912, 1), and discussed in relation to those of colloids on pages 89-91 of the present work, are difficult to bring into relation with the electromotive phenomena of cells. Of course, if a membrane adsorbs preferentially one ion of an electrolyte with which it is in contact, owing to the greater decrease of surface energy by this ion than by the opposite one, the membrane will obtain the charge of the adsorbed ions. Whether this would show itself in the form of a potential difference between the two sides of the membrane seems doubtful.

Baur (1913), however, has described what he calls a model of the electric fish, in which such charges . on membranes appear to play a part. If a mixture of "turkey red oil" with three parts of acetylene tetrachloride, be shaken with water and allowed to stand, a separation into an oily phase and a watery phase takes place. The lipoid phase is said to contain some water, sodium sulpho-ricinoleate, sodium sulphate, castor oil, and acetylene tetra-chloride. This is saturated with mercurous sulphate and electrodes made by contact with mercury. Two such electrodes in potassium sulphate solution have, of course, equal and opposite potential differences : —

so that the combination has no electromotive force. If, however, to the potassium sulphate solution on the one side an electrolyte with a strongly adsorbed cation, such as quinine sulphate, is added, this electrode becomes positive to the other. If the sodium salt of fluorescein, with strongly adsorbed anion, is added, the electrode becomes negative. Thus, with quinine sulphate on one side and fluorescein on the other, an electromotive force of 0'36 volt was obtained. The system is somewhat complex, probably unnecessarily so, and may, perhaps, be equally explicable on the basis of solubility of one ion only in the lipoid phase. The result would be the same.

We may now proceed to refer briefly to some actual cases where electromotive phenomena have been found to accompany the activity of cells. Led off to string galvanometer from two uninjured places on the surface of the muscle. Sciatic nerve stimulated by a single shock at E on the signal line S. Nerve. — The electrical response in nerve has been discussed above (page 379). Fig. 101 shows its character in the olfactory nerve of the pike. An important use of the fact has been made in several cases already referred to. The measurements of the time relations of the kpee-jerk by Jolly (page 475), the impulses arising in the vagus nerve by distension and collapse of the lung by Einthoven (see Fig. 106, page 386), and the impulses in the depressor fibres caused by increase of pressure in the aorta, also by Einthoven (in Fig. 106), may be mentioned.

Keith Lucas (1912) examines the evidence that has been brought forward to show that the process gf excitation is not necessarily accompanied by an electrical change, and comes to the conclusion (p. 507) that none is free from objection. We are, at present, entitled to hold the view that one is an aspect of the other. Muscle. — This also has been already discussed (page 539). Fig. 205 is from a photograph by Keith Lucas of the diphasic response in the sartorius muscle, and Fig. 206 is one by Einthoven, with the string galvanometer. We have shown how it is to be explained on the basis of the theory of the origin of potential difference given in previous pages of the present chapter.

In muscle, just as in nerve, it appears that the electrical change is connected with the process of excitation ; the excitation process is possible in muscle without the contraction process (page 539). The latter is a result of the excitation process, but may be unable to follow it. Fig. 172 (page 539) (middle curve) shows that, in the absence of calcium, the electrical change in the heart muscle takes place without any mechanical change. The significance of this fact has been pointed out above (page 398).

As to the precise location of the membranes concerned, both in nerve and in muscle, we must not forget the possibility that such polarised surfaces may occur, not only at the cell membrane on the outside of the cell, but at phase boundaries within it. But much more knowledge is required of the cell mechanisms. The way in which the " demarcation " current, or current of injury, is to be explained has been described previously. A further word of explanation may be added here. If an uninjured cell, at rest, is led off from any two points on its outer surface, it is clear that they will be equipotential, since we are only dealing with the outer component of the double layer. If we could place one electrode inside the cell, we should obtain the potential difference between the two components of the layer, as in my experiments with Congo-red (1911, 2). This is, in fact, what we do when we cut through or injure a cell in contact with normal cells, leading off from the outer surface of the normal cells and from the injured cells. This latter contact is, in effect, the same as the interior of the cell.

We saw above (page 393) how the disappearance of this potential difference on stimulation (" negative variation ") is explained by the disappearance of the state of polarisation in the normal cells, owing to the membrane becoming Distance between electrodes— 50 mm. V, Electrode at which the wave first arrives becomes H,, The chief negative wave. £T2, Negativity of distant electrode. ff, Positivity of distant electrode. plete wave only is seen. The above four components are obvious. Time in seconds.

electrode, so that the electrical change under the first electrode only is shown, namely, the components V and //,. Time in fifths of seconds. Note that the figures are reproduced as sent me by Dr Orbeli. Those in the published paper are incorrectly given. permeable to both ions of salts within the cell. It will be clear that the demarcation current can only last as long as the contents of the injured cell remain in place, and more or less identical in amount with what they were normally. As soon as the electrolytes have been replaced by those of the electrodes, owing to diffusion, the injured cells naturally become mere extensions of the leading off electrodes, and, being in contact with the normal surface of uninjured cells, the potential difference disappears.

It is interesting to note that in tissues which contain as much as 99 per cent, of water, such as those of the fresh water Medusa, investigated by Cremer (1906), an electrical change in contraction can be detected. As an illustration of the phenomena in smooth muscle, we may take the ureter, in which the electrical changes accompanying a wave of contraction FIG. 208. ELECTRO-CARDIOGRAM OF TORTOISE. — Heart in^situ. Led off from sinus and ventricle apex to capillary electrometer. Movement of shadow upwards means negativity of sinus contact.

A, Diphasic auricular response. V, Diphasic ventricular response. were recorded by Orbeli and Briicke (1910). Fig. 207 gives three of their curves. In curve B one wave only is given, and is a copy of the actual photograph as obtained. In curve A there are two waves, one of which is marked for description. A movement downwards means that the electrode under which the wave first passes becomes negative, and we notice that the large wave Hj is in this direction, and that it is followed by another, H2, in the opposite direction, as the wave of contraction leaves the first electrode and arrives at the second. This corresponds exactly to what happens in nerve and skeletal muscle. But what are the waves marked v and N ? It is suggested by Orbeli and Briicke that they represent a wave of inhibition preceding the contraction, as we have seen in the case of the intestine (page 367). It is clear that, if the ureter were in a state of tonus or partial contraction, inhibition would cause the first electrode to become less negative than the second, and appear as a positive deflection. If, however, the deflection N is also due to progress of the wave of inhibition . to the second electrode, as would appear from its opposite direction, it must have travelled at a slower rate than the excitation

a. Electrical change of the dog's ventricle in situ. Led off by contacts on apex and base. Simple diphasic response, base becoming negative first. Time, Jth sec. above. • 6, Reversed response with cold air for respiration. In middle curve, a trace of a preliminary short base negativity. c, An intermediate stage between a and b. The heart beats are indicated by a tambour giving the tracing between the time signal, and the electrical change, and are not to be taken as showing anything but the fact of the occurrence