The spontaneous rhythmical impedance changes that occur in fertilized and unfertilized eggs of the rainbow trout after about 7 hr. immersion in tap water have been analysed. They are found to be almost entirely capacitative and correspond to a change of between 5 and 10 % when measured at a frequency of about 1.0 kc. The possibility of any associated resistance change being virtually unobservable is discussed.
These changes, which have not so far been recorded in other living material, are compared with the impedance changes that occur in nerve cells and Nitella.
Fertilized and unfertilized trout eggs exhibit periodic structural changes in their protoplasmic membranes after being in tap water for about 7 hr. The frequency of these changes is increased by an increase in temperature, while the changes themselves can be reversibly abolished by phenyl urethane (Hubbard & Rothschild, 1939; Rothschild, 1940). These periodic changes can best be measured electrically in terms of the impedance of the cell membrane, which is found to vary in an approximately sinusoidal manner, with a period of about 1-5 min. Measurement of impedance provides little information about membrane structure, as it involves both resistance and capacitance in living systems.* If, however, the observed impedance can be resolved into its resistive and capacitative components, information may be obtained about the structure and properties of the cell membrane. This has been done with great success in the case of Nitella and the squid nerve (Cole & Curtis, 1938, 1939), in which the propagated action potentials are associated with impedance variations which have been resolved into their resistive and capacitative components by an analytical method outlined later. It is found that the impedance variation is almost entirely resistive, the capacitance of the membrane remaining nearly, but not quite, constant. The fall in resistance during the propagation of an action potential provides an elegant electrical demonstration of the breakdown of membrane impermeability during activity. If, however, the impedance variation had been found to be mainly due to a change in capacitance, the whole picture of membrane reactivity during the passage of an action potential might have had to be modified.
In the case of the trout egg, there is no evidence of periodic changes in potential across the membrane, and it is therefore of special interest to resolve the periodic impedance changes into components which can be considered in terms of membrane structure. The experiments described in this paper were done just before the war and their analysis has therefore been delayed. They are in a sense preliminary, but the results are sufficiently definite to warrant publication.
Fertilized and unfertilized eggs of Salmo irideus Gibbons and of S.fario were used. The egg is about 4-5 mm. in diameter. It resembles a plant cell in that the living part is restricted to a thin spherical shell, a few micra thick, within which there is a yolky globulin-containing solution whose electrical resistance varies between 100 and 200 ohm-cm. (Gray, 1920; Rothschild, 1946). Outside the living membrane, known as the vitelline membrane, there is a further membrane, the chorion, separated from the vitelline membrane by the perivitelline space. The chorion and perivitelline space are about 100/x thick in normal conditions. As, the chorion is freely permeable to water and small molecules, the perivitelline space has approximately the same composition as the external medium.
The impedance of the vitelline membrane was measured by placing the egg in an electrolytic cell in the unknown arm of an alternating current bridge, and balancing this unknown arm at different frequencies by a resistance Rp in parallel with a capacitance Cp in the standard arm. The apparatus has been fully described elsewhere (Hubbard & Rothschild, 1939). In previous experiments the electrolytic cell was usually cubical, with platinized platinum electrodes forming two opposite faces of the cell. In these experiments, hollow hemispherical platinized platinum electrodes, whose separation could be adjusted, were used, close up to the egg surface. This procedure makes Maxwell’s well-known equation involving the resistance of suspensions of spheres inapplicable. This only affects the quantitative measurements of membrane resistance and capacitance with which we are not directly concerned in this paper.
At any given frequency, the impedance of the egg in its electrolytic cell can be expressed in terms of the parallel resistance Rp and capacitance Cp in the standard arm of the a.c. bridge, provided that the impedance does not vary. If the values of Rp and Cp so obtained are converted into the equivalent series form, Ra and—jXa, where Ra is the equivalent series resistance and —jXa is the equivalent series reactance [Æ, = i /coCg, where u> = ZTT. v (frequency)], the locus of the co-ordinates Ra, —jXa at various frequencies will be an arc of a semicircle, cutting the resistance axis at infinite and zero frequency. The phase angle of the capacitative part of the membrane will be half the angle formed by the radii from Ra at v = 00 and Ra at v = o. Each co-ordinate Ra, —jXa is the terminal of the impedance vector at the frequency in question, as , where \ Z\ is the absolute magnitude of the impedance. A description of the ‘Circle Diagram ‘analytical technique has been given in further detail by Cole (1928).
This analysis holds good for any combination of resistances and a single capacitative element, or as it is sometimes called when the phase angle of the capacitative element is constant and less than , a dielectric impedance element.
Suppose that a circle diagram has been obtained (Fig. 1a), and that the cell membrane is treated in some way so that only its resistance falls, impedance measurements being made at times t0, t1, t2, …, during the change of resistance. Cole & Curtis (1938) showed that at each frequency the locus of the terminals of the impedance vectors corresponding to measurements at t0, t1, t2,…, will be part of another semicircle, the circumference of which passes through the terminal of the t0 impedance vector, and is tangent to the resistance axis at The effect on the ‘resting ‘circle diagram of a change with time in membrane resistance is shown in Fig. 1b.
If, however, the treatment of the membrane results only in a change of capacitance, the terminals of the impedance vectors at each frequency and at t0, t1,t2, … remain on the original arc of a circle but move round the perimeter towards when the capacitance decreases, and towards R∞ when it increases.
Although the effect on the ‘resting’ circle diagram of a change in membrane resistance is easy to see in Fig. 1 b, the effect of a change in capacitance is somewhat confusing because time and reactance are both plotted in the R3, X8 plane. As a result, during a pure capacitance change with time, the terminal of the impedance vector at a particular frequency vj at time t0 looks as if it becomes the terminal of another impedance vector at another frequency vi, but at the same time t0. In reality it is the same impedance vector, at the same frequency vj, but at a different time tr. If, however, the capacitance change is plotted in three dimensions, R8, X8 and t, the situation becomes clearer. A sinusoidal variation of capacitance with time is plotted in this way in Fig. 2.
If the change in the membrane is due to a change of resistance and capacitance, the terminals of the time impedance vectors will occupy positions intermediate between the two extremes. This was found in the case of Nitella (Cole & Curtis, 1938), in which the membrane capacitance changes by 15% and the membrane resistance by a factor of 200, during the passage of an action potential.
When the impedance of the vitelline membrane of a trout egg is changing rhythmically, the detector across the a.c. bridge varies as in Fig. 3 a. The reason that the record is bilaterally symmetrical with respect to the time axis has been explained in a previous paper (Hubbard & Rothschild, 1939).* The actual variation of impedance with time is shown in Fig. 3 b, which is a tracing from the envelope curve in Fig. 3 a. If instead of photographing the impedance change, the a.c. bridge is kept balanced by hand adjustment of the parallel resistance and capacitance in the bridge standard arm, a series of If and Cp values which repeat every 1·5 min., will be obtained. This is shown in Fig. 4. The periodic variations in Rp and Cp can also be obtained by the * ellipse ‘method of analysis (Cole & Curtis, 1938 ; Rothschild, 1940), but thefrequency of the changes in the trout egg are sufficiently low to permit hand balancing.
This procedure is repeated at a number of frequencies, and it is obvious from the section entitled ‘Analytical procedure’ that if the change in membrane impedance is due to a change in resistance, a series of impedance vector terminals, in the positions shown in Fig. 1 b, will be obtained ; while if the change is capacitative, the terminals will be as in Figs. 1 c or 2 ; and if the change is due to a change in resistance and capacitance, the terminals will occupy positions intermediate between these two extremes. As the trout egg undergoes spontaneous changes in impedance, it cannot, as it were, be kept quiet while a static circle diagram is made, and then have its impedance changed for comparison of the resistive and capacitative parameters with the resting condition. Consequently, there is no ‘resting circle ‘diagram for the trout egg, but nevertheless it is easy to see whether the maximum and minimum values of Rp and Cp, converted into the equivalent R8, —jX8 form, are in the capacitance-change or the resistance-change positions. Two actual runs at various frequencies are shown in Fig. 5, * from which it is clearly seen that the impedance change is almost entirely capacitative. Three eggs were examined in this way over the whole frequency spectrum, which for this system is 0-2-50 kc. It is, however, also possible to tell whether the change is capacitative or resistive when the effect is examined at only one frequency, and particularly if the frequency in question is not too far in either direction from the ‘characteristic frequency’, at which —jXa is a maximum. Near this frequency, a resistance change in the membrane will cause the terminal of the impedance vector to oscillate almost vertically with time, while a capacitance change will cause an almost horizontal oscillation with time. Ten eggs have been examined in this way and all show the same result : that the rhythmical impedance change is almost entirely capacitative.
where c31 = capacitance in μF.cm.−2 at a frequency vt=i eye. sec.−1,
a = radius in cm.,
r∞= R3/k at v = o,
k = electrolytic cell constant,
r∞= R3/k at v = ∞,
r1 = specific resistance of external medium,
ω i=2 π × vi,where vi= i cye. sec.-1,
, where at which X8 is a maximum,
ϕ = phase angle between current and voltage across the capacitative part of the cell membrane,
and α = 2ϕ/π.
This equation involves the assumption that the membrane resistance is infinite and that the membrane impedance can be expressed in the form Z3= Kω −α, where K is a constant. The validity of these assumptions does not affect the experiments described in this paper.*
where ω and α can be measured in the circle diagram.
From this equation and measurements in Fig. 5, the maximum percentage change in capacitance per cycle is found to be between 5 and 10% at about 1 kc. This maybe compared with the percentage changes in Rp and Cp in the a.c. bridge standard arm which are 0-4 and 4-0 respectively. It is hardly necessary to mention that a change in resistance in the bridge standard arm in no way implies a resistance change in the unknown arm, because the equivalent circuit in the unknown arm can be represented as, while that in the standard arm is .
Capacitance is considered to be a characteristic of the cell membrane which remains constant under widely different conditions, and the periodic capacitance changes that occur in the trout egg are therefore of special interest. In discussing the membrane capacitance, Cole (1940) says: ‘The singularly small changes of this ion impermeable part of the cell membrane in injury, death, current flow and excitation—where the ion permeability may change ten or a thousand fold—leads us to picture the ion impermeable structure as a massive, inert and durable framework, occupying almost the entire bulk of the membrane, with the ion permeability represented by at most a small percentage of the membrane volume.
‘In contrast to the ion impermeability, the ion permeability as measured electrically has considerable functional significance and its changes reflect—or perhaps cause—a variety of physiological and pathological phenomena.’
The number of different types of cells whose plasma membranes have been electrically examined at all is small, and within this group there are few whose membranes can be made to alter their properties, and even fewer whose membranes do so spontaneously. In those that have been examined, membrane reactivity is almost entirely associated with changes in resistance rather than capacitance, though as mentioned earlier, there is a 15% change in membrane capacitance during the propagation of an action potential in Nitella-, in the squid axon, the decrease in membrane capacitance during activity is only 2% (Cole & Curtis, 1939). The relationship between resistance and capacitance changes in active muscle membranes may well be of the same order. The only other cases in which changes in membrane structure are associated with changes of capacitance are in the eggs of Hipponoe escalentas and Arbacia punctulata, in which there is an increase of over 100% in capacitance after fertilization (Cole, 1938). In other eggs, however, fertilization has no effect on membrane capacitance (Cole & Guttman, 1942; Rothschild, 1).
The question arises as to what functional importance is to be attached to the capacitance changes in Nitella and the squid axon during activity, and similarly what importance is to be attached to the spontaneous capacitance changes in the trout egg. The relatively great size of the resistance change during activity in the former is not necessarily a reason for ignoring the changes in capacitance or considering them as of little functional interest. The recent work of Hodgkin & Huxley (1945) on the variation of potential across the squid axon membrane during activity, where the potential not only decreases to zero but actually reverses in sign to the extent of 15 mV., shows that the ‘uncorking’ picture of the membrane during activity, with release of potassium into the external medium, may not be adequate. In the present state of our knowledge of the cell membrane it is difficult to say what effect a change in an oriented layer on the cell surface, causing a change in potential of 15 mV., would have on the capacitance. Conversely it is difficult to prophesy what effect a change of 5 % in capacitance would have on the potential.
In all cells so far examined, with the exception of the trout egg, a change in impedance has been found to be associated with a decrease in resistance and potential. The position is not the same in the trout’s egg because there is no evidence of periodic potential changes across the vitelline membrane, though it is possible that the insertion of a micro-electrode into the inside of the egg, which is involved in such measurements (Pumphrey, 1931), might interfere with such changes. Apart from this, the capacitance change is small and potential changes associated with it might have been too small to notice, particularly as the experiments were done with a quite different end in view.
If, however, one argues that a small change in capacitance may only be associated with a small change in potential, it is hardly consistent to argue at the same time that the significant reversal of potential during squid axon activity may only be associated with a diminutive change in capacitance.
Further experiments, particularly involving variations in the environment, may shed some light on the origin and significance of these spontaneous rhythmical changes in capacitance, both as regards their spontaneity and the fact that they are capacitative. Most cells which are capable of propagating action potentials exhibit spontaneous rhythmical potential changes under certain environmental conditions ; but as the impedance changes associated with their potential fluctuations will probably be found to be mainly resistive, they are unlikely to assist much in the interprétât on of the experiments recorded in this paper.
When the membrane resistance is very high, a relatively small change in it may be difficult to see in the circle diagram. Close inspection of Fig. 5 shows some very slight indications of a change in membrane resistance. The existence or otherwise of a change in membrane resistance during the impedance cycle could probably be determined more easily by d.c. than a.c. measurements.
Cole (1941) interprets the electrical behaviour of nerve membranes as being due to inductance as well.
This can be explained briefly as follows. The oscilloscope measures the potential across the bridge. At balance this potential is zero; at off balance the potential oscillates around zero, because the source is alternating. Therefore in every cycle the potential is positive (‘above ‘zero), and negative (‘below ‘zero).
It also involves the assumption that Maxwell’s equation, referred to earlier on, is applicable. This is not the case because of the shape of the electrodes and their proximity to the egg, but the equation can be used to get a rough idea of the order of magnitude of the change.
Prof. K. S. Cole has drawn my attention to the fact that if the membrane impedance can be expressed in the form Z3= K ω− α, where if is a constant, and log Z3/K. is plotted against log <u, there is a discrepancy between the slope of this line (− α) and the phase angle across the capacitance of the membrane as measured in the circle diagram . This discrepancy, which only occurs significantly in the first of the circle diagrams in Fig. 5, may be due to trout eggs not always obeying the empirical Z3= K ω− α rule; on the other hand, this particular batch of eggs had unusually variable phase angles. Whether this was due to an inherent variability in the eggs or to an extraneous factor is not known.