THE TONICITY-VOLUME RELATIONS FOR SYSTEMS CONTAINING HUMAN RED CELLS AND THE CHLORIDES OF MONOVALENT CATIONS BY ERIC PONDER (From The Nassau Hospital, Mineola, Long Island) (Received for publication, September 28, 1948) It has been recognized since the time of the earliest investigations into the osmotic behavior of red cells that different values for volume may be found when the cells are suspended in solutions of different ionic composition but of the same depression of freezing point. The problem as to why this should occur is of historical interest because it was an observation of this type which led Moore and Roaf (Moore and Roar, 1908; Roaf, 1912) to think of the ion distribution between the red cell and its environment as regulated by ion- binding processes rather than by permeability processes as ordinarily under- stood; these early observations, however, have been largely discounted, partly because there are serious technical difficulties attached to the determination of the freezing point of plasma and of hemolyzed red cells, and partly because of doubt as to the purity of the salts used and as to the reliability of the methods for measuring volume. Ege (1921) investigated the phenomenon as it presents itself when the solutions are those of salts of the monovalent anions (NaCI, KC1, KNO3, NaSO4, etc.). He observed differences in equilibrium volume, sometimes as great as 10 per cent, in solutions of the same depression of freezing point; he believed that these differences are best explained by assuming the rate of penetration of the different anions to be different, but was unable to account for the order in which the monovalent anions produce the anomalous effects on volume. Ponder and Saslow (1930, 1931) also noticed discrepancies in the relation between tonicity and volume when rabbit red cells are suspended in hypotonic NaC1, KC1, and LiCI, and attributed the differences to the loss of cell K being greater into some media than into others; this explanation has since been abandoned, but no other has been suggested in its place. This paper is concerned with the tonicity-volume relations of human red cells in solutions of the salts of the monovalent cations LiCt, NaC1, KC1, RbC1, and CsC1. 1. Red Cell Fragility in Equimolar Solutions of the Chlorides of the Monovalent Cations Table I gives the tonicity To in which there is just commencing hemolysis and the tonicity Ts0 in which there is 50 per cent hemolysis is systems at 22°C. containing human red cells and hypotonic LiC1, NaC1, KC1, RbC1, and CsC1. 391
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`392 TONICITY-VOLIYME RELATIONS OF RED CELLS Description of the Hemolytic Systems.--The hemolytic systems in which To and T~0 are measured are composed of 2 ml. of a series of solutions of the chlorides of the monovalent cations, descending in tonicity from T = 1.0 to T = 0.4 by steps of T = 0.05, to each of which 0.5 ml. of a suspension of washed human red cells is added. The washed cells of 2.5 (0.4/p) ml. of heparinized blood are finally suspended in 25 ml. of 1 per cent NaCI to make the suspension. After the addition of the red cells, the tonicities of the descending series become 1.0, 0.96, 0.92,... 0.44. The chlorides of the monovalent cations, after being dried at 60°C. for several days, are freshly prepared in 0.172 ~r solution in water. Specimens from two sources were used: LiC1, NaCI, KC1, RbCI, and Cs from the Amend Chemical Company, and LiC1, NaCI, and CsC1 prepared by Dr. Theodore Shedlovsky for conductivity work. The two sets of preparations have slightly different effects on red cell swelling and hemolysis; the swelling observed with the Amend Chemical Company preparation of TABLE I Te ~o LiC1 NaC1 KCI RbC1 CsCI 0.65 0.56 0.60 0.61 0.59 0.53 0.45 0.49 0.49 0.47 Order, Li > K ~ Rb > Cs > Na. LiC1, for example, is a little greater than that observed with Dr. Shedlovsky's prepara- tion, and so the latter was used in the experiments of section 2. In all cases the tonicity of the 0.172 ~ solution was taken as T = 1.0, the hypotonic solutions being made by the addition of water. The pit of the solutions varied from pH 6.6 to pH 6.8 (freshly prepared solutions, glass electrode); after the addition of the cell suspen- sion, the pH of the systems was 7.1 4- 0.05. The completed hemolytic systems are allowed to stand at 22°C. for 5 hours, with occasional mixing by inversion. At the end of that time the cells are thrown dowra, and the amount of lysis is determined from the concentration of Hb in the supernatant fluids; this is found colorimetrically, the whole procedure being very like that already described (Ponder, 1948 a). Table I shows that the tonicities To and Ts0 are not identical in their effects in the case of all the 0.172 ~ chlorides of the monovalent cations, and that the fragility of the ceils is least in 0.172 ~ LiC1 and greatest in 0.172 ~ NaC1. The order of the salts, with respect to the fragility of human red cells in them, is Li > K -> Rb > Cs > Na, which is not the order of either the hydrated or the crystal radius of the ions. 1 1 The introduction of corrections for differences in the activity coefficients makes matters worse instead of better, for the order of the activity coefficients is Li > Na > K > Rb > Cs, and LiC1, the strongest electrolyte, is the one which is isoplethechontic
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`ER~ PONDER 393 2. The Tonicity-Volume Relations in ttypotonic NaCl and in ttypotonic LiCl Systems The tonicity in which a red cell hemolyzes in a hypotonic system is that in which it reaches its critical volume Vh, a volume determined principally, al- though not exclusively, by red cell shape. When the quantity of the hypotonic medium is very great, the expression which gives the volume as a function of the tonicity T is in which the initial volume V0 of the cell is represented by unity, in which W is the water in the cell expressed as a fraction of unity, and in which R is a constant which varies from system to system. There are accordingly several ways in which variations in the fragility of a red cell, as measured by the tonicity in which i1: hemolyzes, can occur. The critical volume Vh itself may vary, the value of R may vary, as when there are changes from one metastable form of the red cell to another (Ponder, 1945), changes in the amount of "bound water," or when there is an escape of osmotically active substances from the cell into the hypotonic medium, ~ or the value of W may vary. The point which is apt to be confusing is that tonicity is classically defined in terms of the volume of the ceils of the system under consideration, a solution being isotonic with plasma when it maintains the same cell volume as plasma does, i.e., when it is isoplethechontic with plasma; 3 we are not entitled to expect, however, that the freezing point or the activity of water will be equally de- pressed in all isoplethechontic solutions unless the red cell can be represented by a model of a special kind. From a technical point of view, the analysis of the difference between the volume-tonicity relations in hypotonic NaC1 and in hypotonic LiC1 involves the simultaneous measurement of Vn, R, and W. Measurement o/R and W.--The red cells of human heparinized blood are washed 3 times with 0.172 M NaC1, and are then suspended (a) in 0.172 ~ NaC1 and (b) in 0.172 ~ LiC1, in such proportions that the volume concentration of the ceils is 0.4. with plasma when present in the highest concentration (equimolar with 1.1 gm./100 ml. NaC1). NaC1, a weaker electrolyte, is isoplethechontic with plasma in a concen- tration of only 0.93 gm./100 ml. 2 An escape of K from the red cell can be held responsible for a change in the value of R only if the escape is rapid, and only ff it is not compensated for by an entry of an equivalent amount of Na. This point has been fury discussed elsewhere (Ponder, 1948 0. * This word ("volume maintaining") was introduced by Ponder and Saslow (1930) to avoid the ambiguity associated with the word "isotonic," which is often used with- out the realization that isosmotic solutions are not always isoplethechontic.
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`394 TONICITY-VOLUM~ RELATIONS OF RED CELLS A series of solutions of NaCI and LiC1, varying in tonicity from T -- 1.0 to T = 0.4, are prepared, a 0.172 M solution of each salt being considered, for the time being, as hav- ing a tonicity of 1.0; the hypotonic solutions are made by the addition of water. To 2 ml. of each is added 0.5 ml. of the appropriate red cell suspension (red cells suspended in isotonic NaC1 being added to the series of NaCI solutions, cells suspended in iso- tonic LiC1 being added to the series of LiC1 solutions). After standing for 5 hours at 25°C., with occasional mixing by inversion, small volumes of each system are trans- ferred to Hamburger hematocrit tubes, in which the relative cell volumes, together with the amount of hemolysis, if any, are determined (cf. Ponder, 1948 c). 4 The expression for the volume of the red cell, regarded as an osmometer of initial volume V0 -- 1.0 and immersed in a limited volume of a medium of tonicity T, 5 RW(a -- aT) V = + 1 (2) (aT + 1) can be rewritten as V = RW r + l/a r + l/a + I = RW'/(T'a) + I (3) where a is the ratio of the volume of the surrounding medium to the volume of the cell water. This expression becomes identical with expression (1) when a is infinitely great; when a has a comparatively small value, a series of values off(T, a) is calculated and used to replace values of 1/T (see abscissa of Fig. 1). If the red cell can be treated as an osmometer, a straight line will result when values of V are plotted against values off(T,a); this line will pass through the origin T = 1.O,f(T,a) ---- 0, V = 1.0, and its slope will be RW. The value of R can be calculated from the slope RW of the straight line when the value of W is known. It can be found by drying a small mass of red cells to constant weight at 60-80°C. As the tonicity is reduced, a value T ~(0) is finally reached at which the least resistant cell in the system hemolyzes. The volume which corresponds to this critical tonicity 4 These determinations are made by spinning with a force of 2.7 × 103 G, main- tained for 30 minutes. Differences in the centrifugal force applied (and, to a minor extent, differences in the duration of spinning) result in differences in the value of R as well as in differences in the absolute lengths of the columns of packed cells. The most likely explanation for this is that the packing forces change when the cell undergoes swelling and decreases in density. A reduction of the centrifugal force to 0.7 X 103 G results in an increase of from 0.1 to 0.15 in R. I have not been able to obtain the high values of R (average value of 0.98) found by Guest (1948) for human red cells in hypotonic NaC1, except at relatively low rates of spinning. Recently I had the experience of obtaining, in a succession of determinations, R values between 0.85 and 0.95 instead of the usual 0.7 to 0.8 (systems of human red cells in hypotonic NaC1). This was traced to the hematocrit motor needing oil. 5 The addition of the 0.5 ml. of suspension, which contains 0.3 ml. of NaCI or of LiCI of a tonicity of 1.0 (0.172 M), raises the tonicity of the hypotonic medium to which the cells are added, so that the final tonicities in the series are 1.0, 0.913, 0.826... (common difference 0.087) instead of 1.0, 0.9, 0.8... (common difference 0.1). It is the tonicity of the mixture which is denoted by T.
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`ERIC PONDER 395 is Vh(0), the critical volume for the least resistant cell in the system. If the tonicity is reduced further, there is hemolysis in the system and we are concerned with the volume of the cells which remain intact; this is V/(1 -p), where p is the amount of lysis in the system (p = 1.0 for complete hemolysis). The tonicity in which p = 0.5 is the tonicity Th(50) with its corresponding critical volume Vn(~0) for the cell of average resistance. The true critical volumes are V~(o)/Vp and Vh(5o)/Vp, for Vv, the volume of the cells in plasma, is not generally equal to the volume in the solution which has the tonicity denoted by 1.0 (see below). Adjustments near the Origin.--In some types of experiment, it may be desirable to compare V0 with a special value of V, the volume Vv of the same number of red cells in plasma. If V0 = Vv, the salt solution of tonicity T = 1.0 is isotonic (isoplethechontic) with plasma. If the salt solution of T = 1.0 is not isoplethechontic with plasma, V0 will equal Vv -4- AW, and AW, which can be either positive or negative, will be the amount of water which enters (or leaves) the cell when it is transferred from plasma to the solution for which T has been put equal to 1.0. There will be a point on the linear tonicity-volume relation which has coordinates Vv and a special value of f(T, a); from this special value can be calculated a value of T which can be used as a number by which the concentration of the salt solution under consideration must be multiplied in order to give a salt solution isotonic with plasma. When the salt solution of T = 1.0 is not isoplethechontic with plasma, two con- sequences follow upon the taking of T = 1.0 as the origin of the coordinates of the tonicity-volume relation. The first is that red cells immersed in the solution of T = 1.0 (supposedly isoplethechontic with plasma, but not really so) will gain (or lose) water; this will change the slope of the line relating V andf(T,a) from RW to RWI. 6 If Vv is less than V0, the cell will appear to behave as a better osmometer than it really is; alternatively, if V v is greater than Vo, the cell will appear to behave as a poorer osmometer than it really is. The second is that if the cells begin to hemolyze at a critical volume Vh, and if the ratio Vh/Vo is calculated from the value of V0 found in the solution of tonicity 1.0 (not isoplethechontic with plasma) instead of from Vh/Vp, the critical volume will appear to be spuriously small in relation to the initial cell volume if Vv is less than V0 and spuriously great if Vv is larger than V0. Serious dis- crepancies can be introduced by an error of this kind. 7 , wl = (w ± aVo)/(Vo ± AV0). 7 It is not the purpose of this paper to discuss the concentrations of NaC1 and of other salts which have been found to be isoplethechontic with normal human plasma collected under oil. This aspect of the problem has been dealt with by Christensen and Warburg (1928) and by Kirk, Sorensen, Trier, and Warburg (1941); the concen- tration of NaC1 which they found to be isoplethechontic with plasma is about 0.150 M. Other values found, usually with fewer precautions as regards preventing the escape of CO.o, vary from 0.145 M to 0.190 M. The pH of NaC1 solutions is generally less than that of plasma and particularly of plasma which has been exposed to air, and so it is to be expected that the cation content of an NaC1 solution isoplethechontic with plasma would be somewhat greater than that of plasma itself. The point which this paper emphasizes is that the cation content of a LiC1 solution isoplethechontic with plasma would be greater still, the difference between the concentrations of NaC1 and of LiC1 not being attributable to differences in pH.
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`396 TONICITY-VOLUME RELATIONS OF RED CELLS Fig. 1 shows the results obtained with NaC1 and with LiC1. The points for the NaC1 systems lie on a straight line passing through the origin with a slope RW = 0.50; assuming W to be 0.7, R = 0.72. The tonicity in which the cells have the same volume V~ as they have in plasma is 0.93 gm./100 ml., and in the tonicity T = 1.0 (1.0 gin./100 ml.) the cells have decreased in volume from 1.04 to 1.0 units of volume. Allowance for this loss of water would increase the value of R from 0.72 to 0.75. At the upper end of the line, p = 0.0 when V = 1.35; remembering that the cell in plasma has a volume of 1.04 on the scale in use, the critical volume for the cell of least resistance is V~(o) = 1.30 V~. p=o5 v.05 1.6F 'P" O'OI ,, I , , ~ I," i i I i I , f(%¢) -04 .0.2 | (tS 0.4 0.6 0.8 1.0 i, I i i = , I , , ~ T FIG. I. Volume-tonicity relations for systems containing NaC1 (filled circles) and LiC1 (crosses). Ordinate, cell volume; abscissa, tonicity T and its function f(T,a). Commencing hemolysis at p = 0.0; 50 per cent hemolysis at p = 0.5. The volume of the cells in plasma is Vp. The points for the LiCI systems lie on a straight line passing through the point (T = 1.0, V = 1.10) and having a slope RW = 0.56; assuming W to be 0.7, R = 0.80. The tonicity in which the cells have the same volume Vp as they have in plasma is equimolar with 1.1 gin./100 ml. Nacl, and in a tonicity of T = 1.0 the cells have increased from 1.04 to 1.10 units of volume. Allow- ance for this entry of water reduces the value of R from 0.80 to 0.78, which is not significantly greater than the corrected value of R, 0.75, for the NaC1 system. At the upper end of the line, p = 0.0 when V = 1.38, and so the critical volume for the ceils of average resistance is almost the same as that found in the NaC1 system, s 8 The volumes at which p = 0.5 in the two systems may also be compared. They are 1.68 Vv in each case. Once the cells begin to hemolyze, however, the relation of V/(1-p) to tonicity becomes dependent on factors which are not yet sufficiently defined. Often the relation continues along the same straight line (as in the experi- ment illustrated in Fig. 1) until p is 0.7 or even 0.8; after this the measurements be-
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`~gIc PONDER 397 The difference between the tonicity-volume relations found in NaC1 and in LiC1 respectively is accordingly almost entirely accounted for by the concen- trations of isotonic (isoplethechontic with plasma) solutions of NaCI and of LiC1 differing by about 18 per cent. This is essentially the same result as Ege obtained with his series of monovalent anions, and it does not seem possible at present to state it in any simpler form. Equimolar concentrations of the chlorides of the monovalent cations unquestionably have specific effects on the volume which red cells attain when immersed in them. One would expect these specific effects to be related to properties such as the hydration of the cations, but this explanation would be tenable only if additional specific prop- erties were ascribed to K and Na, so as to make the effect of K equal to that of Rb and to move Na to the end of the series. It is true that K and Na are special ions so far as the red cell is concerned, since they are normal constituents, but one cannot have much confidence in a type of explanation which allows of two exceptions in a series of five. It can be shown that the effect of equimolar concentrations of NaC1 and LiC1 on red cell volume is reversible; there are also small differences in the rate at which K is lost by red cells into solutions of the two salts. R~versibility of the E~ect.--This can be demonstrated by preparing suspensions of identical numbers of cells in (1) 1.0 gm./100 ml. NaCI, (2) 0.72 gm./100 ml. LiC1, and (3) suspended in 0.72 gm./100 ml. LiC1 for an hour, then washed with 1.0 gm./100 ml. NaC1, and finally suspended in the latter medium. Identical suspensions are most easily made by weighing 2 gm. of a red cell suspension of volume concentration p -- 0.4 (in 1.0 gm./'100 ml. NaC1) into three weighed tubes, The cells in the three tubes are thrown down and the supernatant fluids are removed; 1.0 gm./100 ml. NaC1 is then added to the first tube, and 0.72 gm./100 ml. LiC1 to the second, until the weight of the contents of each tube is 2 gnh. About 10 ml. of 0.72 gin./100 mt. LiC1 is added to the third tube, the contents of which are allowed to stand for about an hour; the cells are thrown down, washed once with 1.0 gm./100 NaC1, thrown down again, and then made up to a weight of 2 gm. with 1.0 gm./100 ml. NaCI. The volume concen- trations of the cell suspensions in the three tubes are found by spinning at 2.7 X 108 G for 30 minutes. They will be found to be in the ratio 1.00, 1.10, and 1.00, which shows that the effect of 0.72 gm./100 ml. LiCI on volume is reversible by wash- ing with equimolar NaC1. K Losses.--The full effect of LiC1 on red cell volume can be observed if the cell volume is measured, by the hematocrit, as soon after the addition of the cells to 0.172 ~¢ LiC1 as the hematocrit method allows one to measure it, and allowing the cells to come unreliable. Sometimes the values of V/(1-p) corresponding to p -- 0.5 and more are unexpectedly great and lie on a curve concave to thef(T,a) axis instead of on a continuation of the straight line. In still other systems, the values of V/(1-p) go through a maximum when p has a value in the neighborhood of 0.5 (Ponder, 1948 c). The cause of these troublesome variations in the apparent volume-tonicity relations of the intact cells requires further study.
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`398 TONICITY-VOLUME RELATIONS O~F RED CELLS stand for periods up to 5 hours in 0.172 M LiC1 does not increase the magnitude of the effect appreciably. It is accordingly not surprising to find that the losses of K which take place into isotonic or hypotonic LiC1 are so small and take place so slowly that they cannot be held responsible for the phenomena under discussion. At 25°C., K losses amounting to 0.08, 0.08, 0.05, and 0.06 when expressed as fractions of the initial cell K are observed in the first 24 hours into 0.172 ,J NaC1, 0.172 M LiC1, hypo- tonic NaC1 (T =* 0.6), and hypotonic LiC1 (T -~ 0.6), respectively. SUMMARY 1. Differences in the fragility of human red cells are observed in equimolar solutions of the chlorides of the monovalent cations. The cells are most fragile in LiC1 and least fragile in NaC1, the salts falling in the order Li > K >- Rb > Cs > Na. 2. The difference between the tonicity-volume relations in systems containing LiC1 and systems containing NaC1 lies in the molarity of the solution of LiC1 which is isotonic (isoplethechontic) with plasma being considerably greater (0.189 ~) than the molarity of the solution of NaCI which is isotonic (iso- plethechontic) with plasma (0.160 M). The difference cannot be stated mean- time in any simpler terms than these; if the activity coefficients are taken into account, it becomes even greater. The tonicity-volume relations for the two systems are otherwise almost identical; the value of R for the two systems is almost the same, the critical volumes at which the cells of least resistance hemolyze are almost identical, and the critical volumes at which the cells of average resistance hemolyze are almost identical. 3. The LiC1 effect on volume occurs as soon after the addition of the cells to 0.172 M LiCI as the hematocrit method allows one to measure it. It is reversible by washing with 0.172 ~ NaC1. REFERENCES Christensen, I., and Warburg, E., 1928, Aaa me.d. Scan&, 50, 286. Ege, R., 1921, Biochem. Z., 115, 109. Guest, G. M., 1948, Blood, 3, 541. Kirk, E., S~rensen, G., Trier, M., and Warburg, E., 1941, Acta meal. Stand., 109, 321. Moore, B., and Roar, H. E., 1908, Biochem. J., 3, 55. Ponder, E., 1945, J. Gen. Physiol., $9, 89. Ponder, E., 1948 a, Blood, 3, 556. Ponder E., 1948 b, Hemolysis and Related Phenomena, New York, Grune and Stratton. Ponder, E., 1948 c, J. Gen. Physiol., 31,325. Ponder, E., and Saslow, G., 1930, J. Physiol., 70, 169. Ponder, E., and Saslow, G., 1931, J. Physiol., 73, 267. Roaf, H. E., 1912, Quart. J. Exp. Physiol., 5, 129.
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`Petition for Inter Partes Review of US 8,338,470
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