The Sodium Fluxes in the Muscle Fibres of A Marine and A Freshwater Lamellibranch

The body fluids of most animals are rich in sodium whilst the tissues are generally rich in potassium and poor in sodium. In those tissues which have been examined in detail, such as striated muscle, nerve or red blood cells, it has been found that the ionic contents of the cells are determined by the active extrusion of sodium and sometimes by the active accumulation of potassium, combined with a Donnan equilibrium of some of the ions. The active extrusion of sodium from a cell against an electrochemical potential requires energy. This energy can be calculated for any tissue from the electrochemical potentials of the sodium in the intracellular and extracellular fluids and from the rate of extrusion of sodium from the tissue.

The sodium concentrations in the blood of marine invertebrates are very much higher than in the blood of freshwater and terrestrial animals, and for this reason it seemed probable that the flux of sodium through the tissues of a marine invertebrate would be greater than the flux of sodium through the comparable tissues of a freshwater animal. The energy required to extrude the sodium from the cells might be considerably greater in a marine invertebrate than in a freshwater form as the energy required is a product of the flux of sodium and the electrochemical potentials of the sodium.

Tracer techniques have been used to measure the movement of sodium through amphibian and mammalian muscle (Keynes, 1954; Creese, 1954) and vertebrate and invertebrate nerve (Dainty & Kmjevic, 1955; Keynes, 1951, etc.), but no results are available for comparable tissues of a related marine and freshwater invertebrate. This paper records the results of experiments designed to measure the rate of exchange of sodium in the muscles of a marine lamellibranch, Mytilus edulis, in which the sodium concentration in the blood is similar to that of sea water, and of a freshwater lamellibranch, Anodonia cygnaea, in which the concentration of sodium in the blood is less than 3 % of that in sea water.

The rate of exchange of sodium between the cells and the blood was determined by equilibrating a piece of muscle with a saline containing ²⁴Na and then measuring the declining activity of the sodium in the muscle when the muscle was exposed to a current of tracer-free saline. In order to determine the rate constant of the exchange of sodium in the intracellular phase it is necessary that the loss of ²⁴Na by diffusion from the extracellular phase should be very rapid, otherwise some of the labelled sodium leaving the cells may re-enter other cells instead of escaping from the tissue. The slower the rate of loss from the extracellular fraction the greater the error from this cause. If the rate of loss from the extracellular phase is too low it becomes impossible to distinguish between the intracellular and the extracellular phases.

A suitable tissue for the experiment must have two properties. It must be in the form of a thin sheet so that the rate of loss from the extracellular phase will be rapid, and it must survive well in vitro so that the ionic composition at the end of the experiment is similar to that of the fresh tissue, otherwise the results are of doubtful value. Preliminary experiments with Mytilus byssus retractor and with slices of the adductor muscles of Mytilus and Anodonta showed that these tissues were unsuitable as they lost a large part of their potassium during one hour’s perfusion with saline. However, the ventricles of both Anodonta and Mytilus fulfilled the necessary requirements. They are easily isolated (Pilgrim, 1953) and consist of thin sheets of muscle less than 1 mm. thick even when contracted. They maintain an almost constant sodium and potassium content for several hours after isolation (Tables 2, 3), and according to Pilgrim will maintain mechanical activity for several days.

The ventricles were isolated by Pilgrim’s method and suspended by a fine nylon thread in the active saline which was kept stirred at 15° C. After 2 hr. in the active solution the ventricles were removed, blotted carefully to remove surface fluid and immersed in a current of tracer-free saline in a pyrex tube 5 mm. in diameter. Preliminary experiments showed that the activity associated with the nylon thread was less than 1 % of the total activity and was washed away in less than 1 min. The isolated ventricle showed some tendency to roll into a tube so it was essential to maintain a high rate of flow of saline to ensure an adequate washing of all the surfaces of the muscle. The normal rate of flow was 1·0 011./sec. and tests with coloured solutions showed that the saline was completely replaced about every 15 sec.

Counting was by a G.M. 4 end-window counter and a scaler. Corrections were made for the dead time of the counter, the activity of the background and the decay of the ²⁴Na.

At the end of the experiment the ventricle was analysed for sodium and potassium. The muscle was weighed, dissolved in a drop or two of concentrated nitric acid, evaporated to dryness on a water bath and the residue dissolved in 5 or 10 ml. of distilled water. The sodium and potassium contents were measured by an EEL flame photometer. Experiments were carried out at both 5° and 15° C.

Mytilus blood is similar in composition to sea water but contains more potassium to the extent of about 2 mM/kg. water (Potts, 1954). Mytilus ventricle was eluted with filtered sea water to which had been added 2 mM/1. of KC1 and 1 mM/1. Of glucose. The final solution contained 480 mM Na/1., 12·1 HIM K/l. and 560 mM Cl/1. The pH was in the range 7·8-8·1.

The radioactive saline containing ²⁴Na was prepared by dissolving 20 mg. of irradiated sodium carbonate, pile factor 10, in excess N-HCI and evaporating to dryness and then dissolving in o·66 ml. of water containing 12·1 mM KC1/L This produced a solution containing about 570 mM NaCl/1. and 12·1 mM KC1/1. which was then diluted to 10 ml. with the non-radioactive saline to produce a balanced salt solution. The pH of both solutions was always in the range 7·5-8·o.

Anodonta muscle was eluted with a saline containing 14 mM/1. NaCl, 0·5 HIM/I. KC1, 5 HIM/1. CaCl₂, 0-25 mM/1. Na₂HPO₄, and 1 HIM/1. glucose. The pH was adjusted, with dilute NaOH, to 7·5. The solution resembles the average composition of Anodonta blood except that Cl^- has been substituted for $HCO3−$⁠. Anodonta blood normally contains about 10 mM/1. of bicarbonate, but solutions containing so much bicarbonate are unstable and lose CO₂ to the atmosphere.

The radioactive saline was prepared by dissolving 20 mg. of irradiated sodium carbonate, pile factor 10, in 10 ml. of water and adding sufficient o·1 N-HCI to bring the pH to 7·5. 1 ml. of 12 mM/1. KC1 solution and 2 ml. of 65 mM/1. CaCl₂ solution were added and the solution was diluted to 26 ml. The final concentrations were: Na, 14·5 mM/1., K, 0·5 mM/1., and Ca, 5 mM/1. The composition closely resembled the average composition of Anodonta blood (Potts, 1954) but the solution slowly lost carbon dioxide and became more alkaline. HC1 was added at intervals to keep the pH between 7·5 and 8·o.

In a previous paper (Potts, 1958) details have been given of the inulin space, water content and inorganic composition of Mytilus and Anodonta ventricles. The water content of Mytilus ventricle is 8o·8±o·6% (w/vf) and of Anodonta ventricle 87·8 ±o·8%. The inulin space of Mytilus ventricle is 26·0 + 3-4% of the total water content and of Anodonta ventricle 30·5 ± 2·5 %. The intracellular concentrations of sodium, potassium and chloride in the two muscles are given in Table 1 together with the average composition of the extracellular fluids. The intracellular chloride content of Anodonta ventricle is unfortunately too small to be determined with accuracy.

The average diameters of the muscle fibres of the ventricles of both Mytilus and Anodonta were determined so that the sodium fluxes through the fibre membranes could be calculated. The ventricles of both Mytilus and Anodonta are so thin that with good illumination the diameter of the individual fibres can be measured directly in fresh tissue.

The diameters of the muscle fibres were measured as follows. A ventricle was extended under a cover-slip and observed with a $112$ in. water-immersion objective.

The diameters of twenty adjacent fibres lying in one transect were then measured with a calibrated graduated eye-piece. This was repeated for four ventricles of Mytilus and four of Anodonta.

Errors may arise for the following reasons. When the fibres are crowded together some confusion may occur between the edges of the fibres. The sites chosen for the transects are necessarily ones where the fibres are well spaced and therefore perhaps not typical of the ventricles. The pressure of the cover-slip may extend the ventricle and therefore slightly reduce the diameters of the fibres. These errors are not likely to be very large and the method is preferable to fixing and staining the tissues which usually involves some shrinkage of the fibres.

The average diameter of the muscle fibres of Mytilus ventricle was 9·5 ±0·3/4 and of Anodonta ventricle 13·5 ±0·7μ.

The concentrations of sodium and potassium in the ventricles used in the experiments are given in Tables 2 and 3. In some of the experiments both the initial and final sodium and potassium concentrations of the ventricles were measured, but in most experiments the whole of the ventricle was used and so only the final concentrations could be determined. The sodium content of Anodonta blood is rather variable and some of the changes in the sodium content of the ventricle during the course of the experiment may be caused by differences between the sodium content of the blood and the eluting saline. The results in Tables 2 and 3 show clearly that the ionic contents of the ventricles at the end of the experiments were similar to those of fresh material. In particular there is practically no fall in the potassium content of either Mytilus or Anodonta ventricles. The sodium content of the eluting saline for Mytilus ventricle, 480 mM/1., was not identical with the sodium content of the blood of Mytilus quoted in Table 1, namely 490 mM/kg. water. Any effect this may have had on the intracellular concentration of sodium has been neglected in the subsequent calculations in which it has been assumed that the intracellular concentrations of the ions are those given in Table 1.

At 5° C. in all experiments the time course of the decay of the activity of the muscle, when eluted with a non-radioactive saline, approximates to the sum of two exponentials which may be represented by the expression $Ae−K1t+Be−K2t$⁠. This is clearly seen when the results are plotted semi-logarithmically (Figs. 1, 3). The more rapidly declining part of the activity may be attributed to the sodium in the extracellular spaces, while the more slowly exchanging part may be attributed to the intracellular sodium (see Appendix). At 5° C. the distinction between the two parts is quite clear and after about 10 min. the activity in the extracellular sodium has become insignificant and the activity of the muscle declines as a simple exponential function of the time $Be−K2t$⁠, At 15° C. (Fig. 2) the rate of exchange of sodium between the fibres and the extracellular fluid is considerably faster than at 5° C. (Fig. 1), but the rate of diffusion from the extracellular spaces is not appreciably altered and the distinction between the two phases is not so clear. The rate of turnover of sodium inside the fibres of Anodonta muscle is rather faster than in Mytilus muscle and at 15° C. the extracellular and intracellular parts are not distinguishable, although at 5° C. they are still clear (Fig. 3). For this reason the sodium flux in Anodonta muscle at 15° C. could not be measured.

After the first ten minutes, in all experiments, the activity declines exponentially and so all the points lie on a straight line, $Be−K2t$⁠. By extrapolating this line back to t = o, B can be obtained. The difference between the experimental curve and the straight line represents, to a first approximation, the diffusion of sodium from the extracellular fluid. The diffusion of a substance into, or out of, a thin sheet has been investigated by Hill (1928). The rate of decline is most rapid at first but the fall becomes a simple exponential after about one-quarter of the substance has diffused out. In these experiments A and K₁ have been calculated on the assumption that the loss from the extracellular spaces is a simple exponential function of time since the sodium in the extracellular water declined so rapidly that the exact shape of the curve could not be determined.

The results of the experiments are summarized in terms of K₁K₂, A and B in Table 4. In all cases the rate constant K₁ is several times larger than K₂. is almost independent of temperature while K₂ is lower at 5° C. than at 15° C.

The analysis of the efflux of sodium from a muscle containing both an extracellular and an intracellular phase is complicated because most of the fibres communicate not with the tracer-free saline but with the intracellular fluid which contains a degree of radioactivity depending on K₁, K₂, A and t. Some of the ions leaving the fibres re-enter the fibres before they are swept away.

For this reason the apparent rate constant for the efflux of sodium from the fibres, K₂, will be less than the real rate constant k₂.

The mathematics of this system has been discussed by Harris & Bum (1949) and Keynes (1954) and Keynes has derived equations relating k₃ to K₃. Unfortunately these equations involve the thickness of the muscle and both Mytilus and Anodonta ventricles are so variable in thickness that it is convenient to rearrange the equations to eliminate the thickness of the muscle and some other quantities (see Appendix). &₂ may then be calculated from K₂K₃, C_o, C_i and e, where C_o and C_t are the extracellular and intracellular concentrations of sodium and e is the fraction by volume of the extracellular fluid.

The equations are only strictly applicable to a plane sheet of muscle and are not completely accurate even for that simple case, but the corrected values are probably to be preferred to the uncorrected K₂. The corrected values of the rate constant of the efflux from the intracellular fraction, k₂, are given in Table 4.

Using the corrected values of k₂, M, the flux of sodium through unit area of fibre surface can be calculated from the expression

For an infinite cylinder V/A = $12$r, where r is the radius of the cylinder.

For Mytilus

Hence

For Anodonta,

Hence

The sodium removed from the muscle is secreted against both a concentration gradient, $ENa$⁠, and an electrical potential, E_v.

Most of the previous measurements of sodium fluxes have been made either on vertebrate tissues, in which the extracellular concentration of sodium is of the order of from 100 to 150 mM/1. or on Sepia axons in which surface/volume ratio of the cells is much smaller than in the lamellibranch muscle fibre, so those results are not exactly comparable with the results reported here. The sodium fluxes per unit area of the fibre surface of the lamellibranch muscles are of the same order as those reported for vertebrate muscles. At 5° C. the sodium flux through Mytilus ventricle fibre is about 12 × 10^-8 mM/cm.²/sec. and at 15° C. is about 27 × 10^-8 mM/cm.²/sec. Harris & Bum (1949) and Keynes (1954) reported sodium fluxes of 10 and 5-4 × 10⁻⁸ mM/cm.²/sec. at 16° and 17° C. respectively, through the fibres of the frog sartorius. The difference between the frog and the marine lamellibranch may well arise from the much greater concentration of sodium in Mytilus blood. In Anodonta the sodium flux, 3·1 × 10^-8 mM/cm.^s/sec. is less than in the frog. In the frog sartorius the rate constant for the exchange of sodium is much smaller than in Mytilus but the fibres are much larger with a diameter of about 8oμ. In the rat diaphragm the fibres are only about 20 μ in diameter and k₂ is 3·75 hr.^-1 at 37° C. (Creese, 1954). In the rat diaphragm the sodium flux/unit area of fibre surface at 37° C. is as high as in Mytilus at 15° C., 27 mM/cm.²/sec. The 20° C. temperature difference compensates for the fourfold difference in sodium concentrations in the external fluids. The only measurements of sodium fluxes in tissues for marine animals are of the giant axons of Sepia where the sodium flux through the surface of the axon is even larger than in Mytilus muscle and amounts to 40 mM/cm.’/sec. during recovery from stimulation (Hodgkin & Keynes, 1954).

Although the sodium fluxes per unit surface area of lamellibranch muscles are comparable with those reported for other tissues, the theoretical energy required to maintain the flux is much larger in Mytilus than any previously reported. This is the result of the combination of a very narrow fibre, and hence a large surface volume ratio with a high concentration of sodium in the blood. The theoretical energy requirements of Mytilus muscle at 15° C. is 0·62 cal./g./hr. Keynes & Maisel (1954) calculated that in frog muscle only about 0·04 cal./g./hr. were required. Hodgkin & Keynes (1954) estimated that Sepia axons required about 0·08 cal./g./hr. In Anodonta muscle, where the ambient sodium concentration is much lower, only about 0·046 cal./g./hr. are required.

Levi & Ussing (1948) considered that the efflux of sodium from the frog sartorius was too large to represent an active process and suggested that part of it might be caused by an exchange diffusion requiring no energy. Hodgkin & Keynes (1955) have shown that in Sepia axons the sodium flux was not reduced even in the absence of external sodium under which conditions exchange diffusion would not occur. However, more recently Swan & Keynes (1956) have shown that the substitution of choline for sodium reduced the sodium efflux from frog muscle by more than half. In this case the energy requirement would be correspondingly reduced.

It is probable that in the lamellibranchs exchange diffusion is responsible for part of the efflux, but the apparent energy requirements of Mytilus ventricle are more than five times as great as those of Anodonta ventricle and exchange diffusion, if it occurs, is likely to take place in Anodonta ventricle as well. It is, therefore, very probable that the energy required for sodium extrusion is substantially greater in the marine species.

Measurements of the oxygen consumption of the two muscles, which will be reported in a later paper, show that in both animals the metabolic energy available is about twice as great as the apparent energy requirements for sodium extrusion, but the metabolic rate of the marine animal is several times greater than that of the freshwater animal.

This has a number of interesting implications in the field of osmotic regulation. It suggests, for example, that a freshwater animal may perform less ionic work than a marine animal; for although it has to perform a certain amount of ionic work at the body surface it may be saved a large amount of ionic work at the surface of each cell. Conversely the many marine animals which maintain a salt concentration in the blood which is less than that of sea water, for example teleosts, selachians, lampreys, sturgeons, grapsoid crabs and many shrimps, may be more efficient than otherwise appears.

Keynes (1954) derived the following equations:

λ and D’ can be eliminated as follows.

The intracellular fraction of sodium in Mytilus ventricle is 30 %, calculated from the chemical data. When calculated as BI(A + B) it is slightly higher, 35 %. For Anodonta the corresponding values are 52 and 55 %. The similarity of these values confirms the identity of the faster moving fraction with the extracellular fraction and the slower with the intracellular fraction.

I am indebted to the Director of the Marine Laboratory, Plymouth, for facilities given to me during my visits. I am also grateful to Dr B. C. Abbott of the Plymouth Laboratory for help and advice and to Dr J. C. Bevington of the Chemistry Department, Birmingham University, for the loan of a counter and scaler.