Osmotic Properties of Living Cells

Osmotic Properties of Living Cells D . A . T. DICK Department of Hunznn Anatomy. Oxford University. Oxford. England1 Page

I. General Introduction .............................................. I1. Theory of Osmotic Pressure ....................................... A Introduction ................................................. B. Thermodynamic Derivation of Osmotic Pressure Laws ........ C. The Osmotic Coefficient ....................................... D . Units of Osmotic Pressure .................................... E. Summary ..................................................... I11. Osmotic Properties of Protein Solutions ........................... X . The Donnan Effect ........................................... B . Ion Binding by Proteins ...................................... C. Hydration of Proteins in Solution ............................. D . Entropy of Mixing of Protein Solutions ....................... E Summary .................................................... I V . The Relationship between Volume and Osmotic Pressure at Equilibrium in Living Cells ............................................ A . Theory ...................................................... B. Assumptions Underlying Theoretical Treatment ................. C. Techniques of Volume Measurement ............................ 1. Direct Measurement of Diameter of Spherical Cells .......... 2. Hematocrit Methods ...................................... 3 Measurement of Concentration of Nonpenetrating Solute ...... 4. Angular Diffraction of Light by Cell Suspensions (Halometry) 5 . Measurement of Conductivity of Cell Suspensions ............ 6 Measurement of Opacity of Cell Suspensions ................ 7. Measurement of Changes in the Solid and Water Contents of the Cell .................................................. D . Volume-Osmotic Pressure Relationships in Erythrocytes ........ E Volume-Osmotic Pressure Relationships in Cells Other than Erythrocytes ................................................. F. Osmotic Behavior of the Nucleus ............................... G. Conclusion ................................................... V . Kinetics of Osmotic Volume Changes in Living Cells ................. A Introduction .................................................. B. Theory of Osmotic Water Permeability ......................... C Methods of Measuring Osmotic Water Permeability ............. D Osmotic Permeability Coefficients of Cells ....................... E. Difference between Osmotic and Diffusion Methods of Measuring Water Permeability ........................................... F. The Rate of Diffusion of Water through the Cell Protoplasm .... G. Conclusion ................................................... VI . Acknowledgments ................................................. VII . References .......................................................

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388 388 388 389 392 393 395 395 396 398 399 399 403 404 404 407 413 414 414 415 415 416 416 417 418 422 426 427 427 427 428 431 432 436 438 442 443 443

1 Present address : Physiological Department, Carlsberg Laboratory, Copenhagen, Denmark .

387

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D. A. T. DICK

I. GENERAL INTRODUCTION The relation of the water content of cells to the osmotic pressure of the immersion medium has been much studied. Nevertheless the physicochemical principles underlying the osmotic properties of cells are still not well understood. It is the object of this review not so much to attempt a wide survey as to assemble information for the examination of some fundamental aspects of the subject from a limited point of view. Discussion has been confined to isolated cells maintained under normal or nearly normal physiological conditions. The review has further been limited to animal cells; the osmotic properties of plant cells are in general modified, except in hypertonic solutions, by their possession of a cell wall capable of withstanding considerable hydrostatic pressures. Discussion of the effect on the osmotic properties of the cell of various factors in the external environment-e.g., temperature, variation in ionic composition, damage to the cell membrane-has been omitted for reasons of space. The great advantages of a thermodynamic treatment of the osmotic properties of the cell have only recently been appreciated. Since so little is known with certainty of the structure and functioning of the cell membrane, it has seemed appropriate to avoid discussion of mechanism altogether and to take an empirical approach, using thermodynamic methods to do no more than reconcile the known properties of the cell with the properties of the cell membrane and the physicochemical properties of the cell constituents so far as these are known. 11. THEORY OF OSMOTIC PRESSURE

A . Introduction When a solution is separated from a quantity of the pure solvent by a membrane which is permeable to the solvent and not to the solute, then solvent tends to be drawn through the membrane into the solution so as to dilute it. The movement of solvent can be prevented by applying a certain hydrostatic pressure to the solution. This pressure is called the osmotic pressure. The osmotic pressure is thus defined in terms of certain experimental conditions ; it is an expression of a specific physical property of the solution, but it comes into existence only when the defined conditions are fulfilled. It does not refer to any particular theory of the mechanism of the phenomenon, such as the bombardment of solute or solvent molecules on the membrane. In the present state of knowledge discussion of the mechanism involved is in fact of no practical importance and is best avoided. It must be noted that the component whose movements are observed is the solvent and not the solute. I n the modern theoretical treatment

OSMOTIC PROPERTIES OF LIVING CELLS

389

of osmotic pressure, attention has therefore come to be directed to the solvent and not to the solute as in the classical treatment of van’t Hoff. Movement of solvent is described in terms of its chemical potential. The chemical potential is a thermodynamic quantity which is used to measure the tendency to flow. It is defined in such a way that a fluid always flows from a situation of higher to one of lower chemical potential; when no movement of a fluid takes place across a permeable membrane, then its chemical potential is the same on both sides and the system is said to be in equilibrium. The chemical potential of a solvent is commonly altered in two different ways (although other ways are possible) : by the admixture of a solute with the solvent, which lowers its chemical potential, and by the application of pressure to the solvent, which raises its chemical potential. Thus the flow of solvent across a semipermeable membrane (i.e., permeable only to the solvent) is associated with the lowering of the chemical potential of the solvent in the solution due to the presence of the solute ; and the flow is prevented by raising this chemical potential by the application of pressure until it is again equal to the chemical potential of solvent in the pure solvent, so that the system comes into equilibrium. The osmotic pressure may thus be accurately defined as the excess pressure which must be applied to a solution to bring it into equilibrium with the pure solvent when they are separated by a perfectly semipermeable membrane. Attention has been drawn by Hildebrand ( 1955), Babbitt ( 1955), and Chinard and Enns (1956) to the limitations of the original van’t Hoff law of osmotic pressure and to the great advances made by applying to osmotic pressure theory thermodynamic concepts such as the chemical potential in place of kinetic concepts based on analogy with the gas laws. The following is a simplified account of the main results of this approach. Thermodynamic treatments can be found in standard works on the subject (Glasstone, 1948 ; Butler, 1946 ; Guggenheim, 1950; Lewis and Randall, 1923). B. Thermodynamic Derivation of Osmotic Pressure Laws It has been seen that the chemical potential of a solvent can be altered in two principal ways, by addition of solute and by application of pressure. The mathematical relations expressing these facts are as follows. The relation between the change of chemical potential and the amount of solute added (if we assume that the solution is ideal, and that the temperature, pressure, and amount of solvent are kept constant) is given by the equation

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D. A. T. DICK

where p1 and plo are the chemical potentials of the solvent in the solution and in the pure solvent, respectively, and nl and n2 are the numbers of gram-molecules of solvent and solute in the solution. (The derivation of this and other equations used here is given in the works quoted above.) The quantity nl/(nl nz) is called the mole fraction and is a measure of concentration. Since its value is necessarily less than 1.0, its logarithm is negative, and thus pl is lower than pl0. The relation between the change of chemical potential and the applied pressure, when the temperature and composition of the solution are kept constant, is given by the equation

+

where P is the total applied pressure, and V1 is a quantity known as the partial molal volume of the solvent in the solution, which is approximately equal to the volume occupied by one gram-molecule of solvent in solution. The raising of the chemical potential of the solvent by increasing the applied pressure by an amount, TI, which equals the osmotic pressure, is obtained by integrating equation 2 thus :

If it is assumed that Yl remains constant with change of pressure, i.e., that the solvent is incompressible (this assumption is almost exactly true), then Apl

= (Po

+ TI)8,

- Po 81 = TIPI

(4)

Thus the increase of chemical potential is proportional to the increase of pressure. But since at osmotic equilibrium the reduction of the chemical potential of the solvent due to the presence of solute is exactly balanced by the increase of chemical potential produced by the osmotic pressure, then the net change of chemical potential of the solvent in the solution is zero ; the chemical potential of solvent in the solution is equal to that in the pure solvent. In mathematical terms, that is,

+ Apl

(due to pressure) = 0 On substituting equations 1 and 4 in equation 5, there results Apl (due to solute)

or

(5)

39 1

OSMOTIC PROPERTIES OF LIVING CELLS

This equation relates the osmotic pressure to the mole fraction of solvent in the solution. If it is assumed that nl is much greater than n2, i.e., that the solution is very dilute, the equation may be simplified as follows : Since

n2 (when nl

*

> n2)

then

or

But nlPl = V l , whic and thus

is the partial volume of solvent in the solution,

or

where m is the molal concentration of solvent in the solution (for definition, see below). Equations 9 and 10 are modified expressions of the Boyle-van’t Hoff law. By deriving them in this way and not as originally by analogy with the gas laws, which is now known to be invalid, it is seen first that the law is an approximation which is entirely dependent on the assumptions that the solution is both ideal and extremely dilute. (An ideal solution is one which obeys Raoult’s law.) Second, the quantity Vl in equation 9 is the volume of solvent in the solution and not the volume of the solution itself, Correspondingly m in equation 10 is a molal concentration [weight of solute/weight (* volume) of solvent] and not a molar concentration (weight of solute/volume of solution). This difference makes clear the significance of the quantity known as the “osmotically inactive volume” as it occurs in the simplified form of the Boyle-van? Hoff law conventionally applied to living cells :

II (Y- b ) = K ( a constant)

(11) where V is the total cell volume, and b is the “osmotically inactive volume.” I t can be seen that ( V - b ) corresponds to Vl in equation 9 and thus expresses the amount of solvent water in the cell ; b is merely that quantity which has to be subtracted from the total cell volume to obtain it and

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D. A. T. DICK

consists of the volume of the cell solute plus that of any solid in the cell which is not in solution. The term “osmotically inactive volume” as applied to this is meaningless and may even be misleading, since b includes the crystalloid fraction of the cell solute which is responsible for the major part of the intracellular osmotic pressure. The term “nonsolvent volume” has already been used for b, and its use is clearly preferable. It must be noted that b as used in the van der Waals gas equation is the co-volume, which is not the same as the actual volume of the gas molecules (it is approximately four times the volume of the molecules). The use of b in osmotic equations must therefore be clearly distinguished from the van der Waals b. Teorell (1952) has stated that b “clearly has nothing to do with the eigenvolume of the solutes.” This statement appears inconsistent with the thermodynamic derivation of the osmotic pressure law.

C . The Osmotic Coeficient

A further modification must be introduced into the Boyle-van’t Hoff law before it can be applied in practice. It has been seen that two basic assumptions underlie the law-first that the solution concerned is extremely dilute, and second that the solution shows ideal behavior. In order to overcome these limitations, a correction factor, the osmotic coefficient (+), is introduced into the equation so as to reconcile the predictions of theory with the behavior of real solutions. The modified forms of equations 9 and 10 are IIVl = + R T n 2 (12) and II = + R T m (13) As a consequence of this modification an assumption underlying the simple Boyle-van’t Hoff law of equation 11 is revealed. It is assumed that RT% = K ( a constant)

+

Here R is the gas constant; T, the absolute temperature, is usually kept constant during osmotic experiments ; n2 is constant, provided that there is no net passage of solute across the cell membrane during the experiment. The assumption of the constancy of here the average molal osmotic coefficient of the intracellular solute, is, however, not generally valid. In spite of the effects of electrostatic attraction between ions and of ionic hydration ( a good account of the treatment of these effects by means of the Debye-Huckel theory is given by Bull, 1951)’ the osmotic coefficients of the crystalloid fractions of the cell solute are indeed practically constant over the range of concentrations which occur in living cells (see Robinson and Stokes, 1955). But the osmotic coefficients of many

+,

OSMOTIC PROPERTIES OF LIVING CELLS

393

proteins have been shown to increase sharply with concentration, even when this is expressed in molal units (see Fig. 1 ) . This is partly due to the binding of water of solvation by protein molecules, thus diminishing the amount capable of acting as solvent to the protein molecules themselves or to other solutes. Ogston (1956) has, however, pointed out that water of solvation is in fact a purely theoretical concept used to interpret certain experimental results, and so the amount of its contribution to the observed osmotic coefficients remains uncertain. Another possible cause of the anomalous osmotic pressures of protein solutions is the large partial molar entropy of mixing of protein solutions (see Section 111.D). This has been explained and at least partly accounted for as a consequence of the great difference in the size of solute and solvent molecules in protein solutions. The osmotic properties of protein solutions and the theories used to account for them will be examined in greater detail in Section 111. Whatever the cause of the large osmotic coefficients of proteins, it is clear that they are likely to produce anomalies in the osmotic behavior of all cells which contain significant amounts of intracellular protein. One important result is that the contribution of the protein component to the total intracellular osmotic pressure may be unexpectedly high. For example, in the human erythrocyte, although the molar concentration of hemoglobin is only 0.005 (if we assume 33.5 g. of H b per 100 ml. of corpuscles and a molecular weight of 67,000), the corresponding molar osmotic coefficient is 3.55 (calculated from the data of Adair, 1929), so that the partial osmotic pressure of the hemoglobin in the cell is 17.5 m-osm. and not 5 m-osm. as expected. This is not an insignificant contribution to a total intracellular osmotic pressure of 300 m-osm. Second, when the concentration of the intracellular protein falls, as during osmotic swelling, the osmotic coefficient drops sharply. Thus the simple form of the Boylevan’t Hoff law will not be obeyed, since in the equation

n(V-b) = K K , which is equivalent to 4 RTn2, is no longer constant. The result is to make b appear to be larger than it actually is or, conversely, to make the apparent water content of the cell, as determined by measurements of osmotic equilibria, smaller than the water content determined by direct methods. D . Units of Osnzotk Pressure There is much confusion as to the use of the terms “osmole” and “milliosmole.” Milliosmoles have been frequently used merely as units of mass of solute; they have been defined as “the sum of the millimoles of undissociated solutes and the milliequivalents of dissociated solutes” (Deyrup, 1953) and used in concentration units such as milliosmoles per liter.

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D. A. T. DICK

2.

2.

:

I-

z w I. Y

0.5

t

LIMITS OF CONCENTRATIONS PRESENT IN ERYTHROCYTE.

SOL%; 0

I

I

0 I

I

CHLORID~qms{100ml. :[tolvent I

20

I

I

30 40 HAEMOCLOBIN qms/100mt.of solvent 10

I.

I

50

FIG.1. Variation of the molal osmotic coefficients of hemoglobin and sodium chloride with concentration. These must be carefully distinguished from molar osmotic coefficients (see Section 11. D ) . Dotted lines represent approximately the limits of concentration produced during osmotic swelling of the erythrocyte, sodium chloride being taken as typical ,in its osmotic behavior of the crystalloid fraction of the erythrocyte solute.

OSMOTIC PROPERTIES O F L IVI N G CELLS

395

Such a unit is tacitly assumed to express the osmotic pressure of the solution. This assumption is not correct, however, because no account is taken of the osmotic coefficients of the solutes. Since the osmotic coefficient relates a concentration to an osmotic pressure (see equation 13), two osmotic coefficients exist corresponding to the two methods of expressing concentration. If molal concentrations are used, then the molal osmotic coefficient must be applied to obtain the osmotic pressure; for molar concentrations the molar osmotic coefficient must be used. For dissociated electrolytes the osmotic coefficients must be applied to the total gram-ion concentration present. It is thus greatly preferable to use the milliosmole directly as a unit of osmotic pressure. One osmole is defined as the osmotic pressure of a 1.0 molal solution of an ideal nonelectrolyte, i.e., 22.4 atmospheres at 0°C. An osmolar solution so defined has a freezing-point depression of 1.86”C. The osmolarity of a real solution can thus be determined directly from freezing-point measurements, but to calculate it from the molality (or molarity) of the solute the appropriate molal (or molar) osmotic coefficient must be used. This unit has the advantage of being independent of the temperature, apart from very small variations due to the effect of temperature on the osmotic coefficient. The unit milliosmole, used in this review, is based on the above definition unless otherwise stated.

E. Summary An outline of the thermodynamic derivation of the laws of osmotic pressure is given. It is shown that the simple Boyle-van? Hoff law is based on a number of approximations which are not generally valid. The chief assumption is that the average osmotic coefficient of the intracellular solutes is constant. The osmotic coefficient of proteins in solution is usually large, however, and increases rapidly with concentration. This is due in part to the great difference in size of protein and water molecules and also to binding of water of solvation to the protein. In consequence, living cells which contain a significant amount of protein cannot be expected to obey the simple Boyle-van’t Hoff law. I t is seen that the so-called “osmotically inactive volume” is simply the volume of solute plus the volume of any solid in the cell which is not in solution. The unit “milliosmole” is used not as a unit of mass but as a unit of osmotic pressure, and a definition is given.

PROPERTIES OF PROTEIN SOLUTIONS 111. OSMOTIC Protein forms an important component of the solute in every living cell. It has been known since the classical work of Sgkensen (1917) that concentrated protein solutions show great departures from ideal

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D. A. T. DICK

behavior. For this reason a discussion of the osmotic properties of protein solutions is essential for an understanding of the osmotic behavior of living cells. The nonideality of protein solutions is due to a variety of causes of which the most important are ( 1 ) the Donnan effect, (2) ion binding by the protein, ( 3 ) hydration, and (4) nonideal entropy of mixing.

A . The Donmn Eflect When proteins are not at their isoelectric point, they discharge or combine with protons to form charged ions, usually of multiple valency. Since the p H of the body fluids and of the cell interior probably lies in the region 6.5 to 7.5 (Caldwell, 1956) and thus on the alkaline side of the isoelectric point of most proteins, the latter normally exist in the body fluids as multivalent anions. If a membrane is impermeable to one species of ion such as these protein ions, then an unequal distribution of the remaining permeable ions is set up across the membrane of a type first described and accounted for on a thermodynamic basis by Donnan (191 1 ) . It has not been clearly appreciated, however, that there are two kinds of Donnan equilibrium in physiological systems: (1) with a difference in osmotic pressure across the membrane, and (2) without a difference of osmotic pressure across the membrane. The distinction between these two kinds depends on the nature of the ions to which the membrane remains permeable. It follows from the nature of water as an ionizing solvent that H + and OH- ions can effectively permeate any water-permeable membrane provided only that one other ion, either anion or cation, is also permeable, since changes in H+ and OH- concentrations can be produced by combination of the permeable ion with the solvent. Hydrogen and hydroxyl ions are, however, never present in sufficient concentration at physiological pH to affect the chemical potential of the solvent and hence the osmotic pressure. Osmotically significant Donnan distributions are therefore always due to the other permeable ions present. In the first type of Donnan equilibrium the membrane is impermeable to protein ions but the remaining permeable ions include both cations (in addition to the hydrogen ion) and anions (in addition to the hydroxyl ion). When the protein is, confined to one side of the membrane, there is a difference of osmotic pressure across the membrane partly due to the impermeable protein ions and partly due to the unequal distribution of the permeable ions. There is also a difference of electrical potential and of pH. Such a system can be maintained in equilibrium only if a hydrostatic pressure is applied to the solution containing the impermeable ion. Such conditions obtain in the capillary membrane as was demonstrated by the

OSMOTIC PROPERTIES O F L I V I N G CELLS

397

observations of Landis (1927), who confirmed the theory of Starling ( 18%). In the second type of Donnan equilibrium the membrane is effectively impermeable to protein and to either anions or cations. Thus the remaining permeable ions consist only of either anions or cations (in addition to hydrogen or hydroxyl ions), so that in order to preserve electrical neutrality no net passage of electrolytes across the membrane is permitted. Even if the protein is confined to one side of the membrane, provided there is initially some impermeable ion on both sides, an equilibrium can be attained in which there is no difference of osmotic pressure across the membrane. There is therefore no difference of hydrostatic pressure. Nevertheless a distribution of the permeable ions (anions or cations) takes place which obeys the Donnan rule. Thus with a membrane permeable only to anions and hydrogen and hydroxyl ions

[XI1 where

[x,],

[y;],

[ x c ] , [ Y c ] , and

and

[z;]

[ZB]

are the external concentrations;

are the internal concentrations of the an-

ions; and [H:] and [Hz] are the external and internal hydrogen ion concentrations. There is therefore a difference of p H and of electrical potential across the membrane. These conditions have been shown to obtain in several types of cells (see Table 11). Although fluxes of cations across the cell membrane can occur, efflux always equals influx, so that no net transfer of cations occurs ; i.e., there is a net or effective impermeability to cations and permeability only to water and anions (evidence reviewed by Caldwell, 1956; see particularly Van Slyke et al., 1923; also recent work by Swan et al., 1956). Indeed, as shown in the erythrocyte by Davson (1936), effective impermeability to electrolytes (caused by the effective impermeability of either cation or anion) is an essential condition for survival of all cells, since in its absence the unbalanced internal colloid osmotic pressure will cause swelling and disruption of the cell (see also Wilbrandt, 1948). In these circumstances the internal osmotic pressure of the cell may be considered as made up of the partial osmotic pressures due to the protein and electrolyte components separately (allowance has to be made, however, for the effects of ion binding by the protein), and no Donnan term appears in considering the effect of the protein, account being taken only

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D. A. T. DICK

of the presence in the cell of an equivalent amount of ion of the opposite charge (gegenion) to maintain electrical neutrality. This applies particularly to the calculation of the osmotic coefficient of the cell protein. The osmotic coefficient used in this case is that derived from the partial osmotic pressure of the protein after calculating and subtracting the Donnan element from the total osmotic pressure observed in an osmometer which normally employs a collodion membrane, freely permeable to electrolytes. The Donnan effect as applied to biological phenomena has been reviewed by Henderson ( 1928), Bolam ( 1932), Overbeek ( 1956), and Harris (1956), and in some aspects affecting intracellular p H by Caldwell (1956).

B. Ion Binding by Proteins It is well known that proteins are capable of binding small ions, particularly organic anions and cations and transition metal and alkaline earth cations (for review see Klotz, 1953). These ions are not, however, present in sufficient concentration in biological fluids to make the binding effect of osmotic significance. I t is only recently that binding of any of the ions commonly present in high concentration, e.g., C1-, Na+, and K + , has been demonstrated to an extent sufficient to affect the total osmotic pressure of the protein-salt mixture. Evidence for the binding of C1- ions to bovine plasma albumin was first obtained during osmotic pressure studies by Scatchard et al. (1946). They concluded that each albumin molecule bound about six ions within a certain range of conditions-albumin concentration 1 to 676, to sodium chloride concentration 0.05 to 0.2 M , and p H 4.2 to 8.2. More recent estimates of the ion binding of isoionic serum albumin are those of Scatchard et al. (1950), who found 11 C1- ions bound per molecule of human serum albumin, and of Scatchard et al. (1957), who found an average of 9.16 C1- ions bound per molecule of bovine serum mercaptalbumin in 0.1 M sodium chloride solution. Lindenbaum and Schubert (1956) concluded from investigations of the binding of a variety of organic anions to serum albumin that important causes of binding were low reactivity of the bound ion with the solvent water, attraction of the anion by cationic centers in the protein, and van der Waals forces between the protein and alkyl side chains and aromatic rings in the organic anion. Lewis and Saroff ( 1957), using electrodes which were selectively permeable to cations, claim to have found evidence of binding of Na and K to the muscle proteins myosin A and myosin B. The effect of ion binding is greatly to reduce the net osmotic effect of the pF6tein in a multi-component solution.

OSMOTIC PROPERTIES OF L IVI N G CELLS

399

C. Hydration of Proteins in Solution Hydration as it affects the osmotic properties of proteins denotes no more than an association of the protein with the water fraction of a multicomponent solvent which is closer than its association with any of the other solvent components such as electrolyte ions. This kind of hydration, which has been recognized for a long time, has been named selective solvation by Ogston (1956) ; the definition is similar to that used for “free” and “bound” water by Hill (1930). It may be measured by comparing the concentrations of a solvent component in a protein solution and in an ultrafiltrate or diffusate in equilibrium with it. Although hydration has an influence on the osmotic pressure of the protein, it cannot easily be measured by osmotic methods, since it is extremely difficult to distinguish its effects from those of other factors such as the anomalous entropy of mixing. Selective solvation must be clearly distinguished from total solvation which is calculated from hydrodynamic measurements on the basis of various assumptions as to the shape and structure of the protein molecule (Ogston, 1956). Comparison of the water and salt contents of protein crystals formed from saline solutions with the composition of the solution leads to a further value for the hydration, but this is based on an analogy between the state of the protein in the crystal and in the solution which may be unjustified. This estimate is therefore of doubtful relevance to dissolved proteins. McMeekin et al. (1954) give values for the selective solvation of various proteins in ammonium sulfate solution ranging from 0.24 to 0.31 g. of H 2 0 per gram of protein. Drabkin (1950), in a study of hemoglobin crystals, gives the hydration of hemoglobin as 0.339 g. of H20per gram of protein. Edsall (1953) indicates that the most probable values for hydration of many proteins in solution lie in the range 0.1 to 0.3 g. of H 2 0 per gram of protein, but these estimates are based for the most part on hydrodynamic measurements. Since hydration is no more than a theoretical concept used to account for experimental results in witro, the use of the concept to account for experimental results in vivo results in a circular argument. All that is being done is to use experimental data obtained in vitro to account for observations on cells in vivo, and the concept of hydration appears only as an unnecessary intermediary. I n this comparison it is sometimes best to use the osmotic coefficient, which is an empirical quantity that does not depend on any particular theory of the mechanism involved.

D. Entropy of Mixing of Protein Solutions The expression (given in equation 1 ) for the change in chemical potential of the solvent on mixing with a solute is derived from a theoretical con-

400

D. A. T. DICK

sideration of the entropy change on mixing. That a change of energy (or, strictly, of free energy) takes place during the process of mixing, even when there is no change of temperature, hydrostatic pressure, or volume of the mixture, is due to a change in the entropy or heat capacity of the system. The entropy is related to the degree of randomness or thermodynamic probability of the system. By the methods of statistical mechanics based on the consideration of the number of possible ways of arranging the solute and solvent molecules in the rnixture4.e.) on the probability of any one arrangement-the total change of entropy or heat capacity of the system on mixing solvent and solute may be calculated (for a simple derivation see Butler, 1946), and the result for an ideal solution is

The partial molal entropy of mixing of the solvent alone is AS1

= -R

In

nl

nl

+ nz

But the partial entropy of mixing of the solvent is related to the chemical potential or free energy change thus : Ap1

=

AH1 -

ThSl

( 16)

whereH1 is the change of heat content of the system. If there is no volume or temperature change on mixing, then the heat content remains unchanged, and therefore

=0

(17) On substituting in equation 16 by means of equations 15 and 17, equation 1 results : AH1

Apl

= RT In

nl

nl

+

n2

It is, however, a basic assumption of the derivation of equation 14 that the molecules of solvent and solute should be interchangeable in the solution, i.e., should be of the same order of size. When this condition is not fulfilled, a very different estimate of the partial molar entropy of mixing of the solvent results. Theoretical expressions for the partial molar entropy of mixing of solvent with a macromolecular solute were first obtained by Huggins ( 1942) and Flory ( 1942). Of expressions suitable for application to solutions with a nonuniform distribution of macromolecular segments and solvent molecules such as protein solutions in the range of concentrations present in living cells, the two simplest are those of Flory (1945) and Schulz (1947). Flory used a lattice model for the solution and considered

401

OSMOTIC PROPERTIES OF LIVING CELLS

the possible distributions on the lattice points of solvent molecules or of segments of the macromolecule equivalent in size to solvent molecules, the macromolecule being supposed to consist of a long chain of such segments. The resulting expression was

+

Here vz is the volume fraction of the solute [Let v2 = V 2 / ( V 1 V 2 ) , where V l and V 2 are the volumes of the solvent and solute, respectively, in the solution] ; x is the number of segments in the macromolecule (i.e., 8 2 / P 1 , where P 1 and 8, are the volumes of the molecules of solvent and solute) ; s is the swelling factor

(

i.e, the ratio

gross hydrated volume of solute molecule volume of solid in molecule

)

and f = f(x/s), which equals 1.0 when x / s is very large, as is normally the case with protein solutions. When the swelling factor is taken as unity (i.e., the molecule is considered unhydrated) , Flory’s expres-:on reduces to Rv~ AS1 = -(X 1 4v2 21.3~2~) (19)

+

+

Schulz (1947) employed the model of a rigid spherical solute molecule and in estimating the number of possible configurations took account of the excluded volume surrounding the actual molecule itself into which the center of another solute molecule cannot penetrate ; his equation was

This is equivalent to

since V1 = nlV1 and V 2 = nzVz and therefore v2

=

n2 8

+

2

%Vl n2v2 Thus if terms in vZ2are neglected, Schulz’ and Flory’s expressions give the same result: Rv, AS1 = - ( 1 4~2) (22) X

+

The applicability of these theoretical expressions for the entropy of mixing to real solutions of proteins may be judged by using them to calculate

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D. A. T. DICK

predicted values of the osmotic coefficient. When equations 18 and 21 are used to calculate the osmotic pressure in a protein solution of given concentration, the values of the entropy of mixing which they give are inserted into an equation relating the osmotic pressure to the entropy of mixing of the solvent, which is obtained by combining equations 4, 5, 16, and 17, thus: -IIB1 = -TAS1 (23) When the substitution is made, we obtain from equation 18 II = RTm' (1 4sk2 2 1 . 3 3 f 2 ~ ~ ~ ) (24)

+

+

where m' is the molar concentration ; i.e., m'

=

+

-

n2

nlBl

n2P2

v2 -x

. -1

PI

By comparison with equation 13, it is seen that the value of the molar osmotic coefficient, is 4' = 1 4sU2 Z1.3S2~2~ (25) (taking f = 1.0)

+',

+

+'

+

since is defined by the equation - n = 4' RTm'. Similarly from equation 21 we obtain 4' = 1 4 ~ 2- 8.06~2~ (26) I n a solution containing 10 g. of protein per 100 ml. of solution, if the partial specific volume of the protein is 0.75, then v2 = 0.075. Thus the predicted molar osmotic coefficient is 1.42 from equation 25, if the swelling factor, s, is taken as 1.0 (i.e., the solute molecule is considered to be unhydrated). If s = 1.3 (if we assume a hydration of 0.3 g. of H 2 0 per gram of protein), then the predicted molar osmotic coefficient is 1.59. The prediction from equation 26 (derived from Schulz' formula) is 1.25, and that from equation 22 is 1.30. These predictions may be compared with molar osmotic coefficients calculated from available experimental data for various proteins and shown in Table I. These values have been calculated from the experimental data by correcting molal to molar concentrations when necessary and by interpolation or short extrapolation from the experimental points. It must be emphasized that the possible effects of the heat of mixing, hydration, and ion binding by the protein have been ignored in these calculations, although allowance has been made for the influence of the Donnan effect where the protein solution observed was not at isoelectric point. Nevertheless it may be concluded that a considerable part of the nonideality of the behavior of proteins in aqueous solutions may be accounted for by the nonideal entropy of mixing which results from the great difference in the size of the solvent and solute molecules.

+

403

OSMOTIC PROPERTIES OF LIVING CELLS

Other possible expressions for the entropy of mixing of macromolecular solutions are contained in a review by Flory and Krigbaum (1951) and are discussed by Hildebrand and Scott ( 1950), Mark and Tobolsky ( 1950), Guggenheim ( 1952), and Flory ( 1953). TABLE I OSMOTICCOEFFICIENTS OF VARIOUSPROTEINS

Protein

Human Human Human Human Human Human Human

al-lipoprotein a,-globulin &-globulin y-globulin y-globulin y-globulin y-globulin

Observed molar osmotic coefficient (in soln. of conc. Molecular 10 g./100 ml. weight soln.)

78,000 600,000 93,000 140,000 200,000 155,000 156,000

0.76 8.64 1.71 1.08 1.37 1.18 1.12

References

. Oncley et al.

(1947)

A correction was made in this case for the effect of ion binding to the isoionic protein.

E. S u m w y Although the Donnan distribution of electrolyte increases the osmotic pressure exerted by a protein across a membrane permeable to electrolyte, no such effect occurs when the membrane is effectively impermeable to electrolyte as is the cell membrane; the osmotic pressure exerted in this case is the partial osmotic pressure of the protein ion alone. The net osmotic pressure of the protein may, however, be affected by ion binding. Hydration of proteins in solution is not to be regarded necessarily as a mechanical reality but as a theoretical concept used t o account for experimental

404

D. A.

T.

DICK

results in vitro ; use of the concept to account for observations on cells in vivo results in a circular argument, since all that is being done is to compare physicochemical observations in vivo and in vitro. By statistical mechanical methods it is shown that, when there is a great difference between the size of solute and solvent molecules, an abnormally large entropy of mixing is to be expected, which in turn produces a large osmotic coefficient. It is shown that this theory is capable of accounting at least in part for the osmotic coefficients of proteins which are actually observed. IV.

THERELATIONSHIP BETWEEN VOLUME A N D OSMOTIC PRESSURE AT EQUILIBRIUM I N LIVING CELLS A . Theory

Volume-osmotic pressure relationships in living cells have conventionally been analyzed by means of the simple Boyle-van’t Hoff law given by Luck6 and McCutcheon (1932) in their classic review:

I I ( Y - b ) = IIo(V0 - b ) = K (27) where and Vo are the original or isotonic osmotic pressure and total cell volume. Ponder ( 1948) expressed volume-osmotic pressure relations in the erythrocyte in terms of the equation

+

Y = W(l/T - 1) 100 (28) where V = total cell volume, W = isotonic water content, and T = relative tonicity. This equation is another expression of the simple Boyle-van’t Hoff law and may be easily derived from equation 27 if W is equated to ( V O- b ) , T to IT/&, and it is remembered that Ponder expressed water and solid concentrations not as fractions in accordance with conventional practice but as percentages ( V o = 100%). Ponder’s equation has two nonessential but inconvenient disadvantages : ( 1) Its form obscures the fact that it is derived from the simple Boyle-van’t Hoff law, and (2) the unorthodox symbols employed lead to confusion with those of standard thermodynamic terminology ; e.g., T is conventionally used for absolute temperature. The original expression used by Luck6 and McCutcheon (1932), or a more accurate modification of it, is thus to be preferred to Ponder’s equation. The fact that the erythrocyte does not obey the simple Boyle-van’t Hoff law was first clearly demonstrated by Ponder (see Table 111) ; swelling in hypotonic and shrinkage in hypertonic solutions is always less than that predicted by the law. Thus if equation 28 is used in calculations from experimental data, the value of W obtained is always less than the true isotonic water content of the cell as measured by direct methods. Ponder

OSMOTIC PROPERTIES OF L IVI N G CELLS

405

(1933a, b) expressed the discrepancy between theory and observation by multiplying W by an empirical factor R (normally less than 1.0) before insertion in the equation, thus obtaining the apparent isotonic water content, R W ( R has been represented here by a bold-faced R to distinguish it from the gas constant). Equation 28 thus becomes

+

V = R W ( l / T - 1) 100 (29) For the reasons given above, further description of the theory of the osmotic behavior of living cells will be based on Luck6 and McCutcheon’s (1932) equation. Thus if equation 27 is differentiated and the osmotic pressure is expressed in units of the isotonic osmotic pressure SO that no= 1.0, the result is dV = Vo - b = K = Wo ( 30) d ( l/W where W Ois the apparent isotonic water content of the cell. But it has been shown (Dick and Lowenstein, 1958; see also below) that equation 27 is an approximation, so that the equalities expressed in it are not exact. In consequence, Wo # Vo - b as is otherwise suggested by equations 27 and 30; i.e., W o is only the apparent and not the true isotonic water content of the cell; it is actually only an empirical expression of dV/d( l/lT), i.e. dV W (31) - d ( l / n ) ( = Ponder’s R W ) If W,, the true isotonic water content of the cell, is defined as W , = Vo - b ( = Ponder’s W ) (32) then Ponder’s R in this terminology is WO dV . -1 R== Wm d(l/n) W, The correct value of W oand hence a theoretical expression for Ponder’s R has been obtained by using a more accurate form of the Boyle-van’t Hoff law (Dick, 1958b). It has already been shown (from equations 11 and 12 above) that this is lT(V - b ) = 9 RTn2 (33)

+

Equation 27 is true only if remains constant throughout the range of concentrations produced in osmotic experiments. Since this condition is not fulfilled, owing to the large and concentration-dependent osmotic coefficients of the proteins, a more accurate value of Wo is obtained by differentiating equation 33 correctly, i.e, treating 9 as a function of n (since

406

D. A. T. DICK

the molar concentration of intracellular solute and hence external osmotic pressure, n) ; thus

+ depends on the

O n inserting values at the isotonic osmotic pressure, there results

W o = +oRTn2-

(2)

n = 1

-

RTn2

(35)

since IIo = 1.0, and with (p = +o at isotonic osmotic pressure. But from equations 32 and 33, on inserting values at the isotonic osmotic pressure,

= doRTn2

(36)

-

(37)

since IIo = 1.0. From equations 35 and 36,

wo = w, -

(g)

n = 1

RTn2

but d+/dn is in general positive, owing to the increase of the osmotic coefficient of the protein fraction of the cell solute with concentration (and hence osmotic pressure), and therefore and

wo < w m <

1.0

Since this equation is derived from basic thermodynamic principles, it is of general validity for all cells, provided the assumptions on which it is based (see Dick, 1958b) are fulfilled. It has been used to calculate a predicted value of R for the erythrocyte which is in agreement with the experimental results (Dick, 1958b) and also with the results of previous numerical calculations (Dick and Lowenstein, 1958). This prediction of course applies only to physiologically normal erythrocytes, e.g., in defibrinated or heparinized blood samples. Other values of R are found in abnormal states of the erythrocyte or after the use of certain anticoagulants, and it has been suggested that these are due to an alteration in the physical state of the internal protoplasmic solution (Ponder, 1948). In accordance with equations 27 and 30, volume-osmotic pressure data

OSMOTIC PROPERTIES OF LIVING CELLS

407

are best interpreted by plotting cell volume against the reciprocal of osmotic pressure (Ponder, 1955) or by calculating the resulting relationship by regression analysis (Dick and Lowenstein, 1958). Methods employing the direct relationship between volume and osmotic pressure involve unnecessarily cumbersome mathematics which necessitate crude approximations (eg., Cristol and Benezech, 1946a; Hamburger and MathC, 1952, P. 46).

B. Assumptions Underlying Theoretical Treatment At least three assumptions underly the present theoretical treatment of volume-osmotic pressure relationships described in the preceding section : 1. That the intracellular osmotic pressure with which the equation deals can be taken to be equal to the osmotic pressure of the external medium. 2. That there is no net passage of solute across the cell membrane during the attainment of osmotic equilibrium between the cell and its environment. 3. That the protein component of the cell is in true solution or at least is capable of osmotic behavior as if it were in solution.

1. Although the assumption of osmotic equality between the cell interior and the environment was long tacitly accepted, it has recently been challenged. It has been observed that mammalian tissue slices immersed in isotonic saline solutions swell by imbibition of fluid when their metabolism is impaired by low temperatures, anoxia, or metabolic inhibitors, and that this swelling can be prevented by immersion in strongly hypertonic solutions (Stern et al., 1949; Opie, 1949; Opie and Rothbard, 1953 ; Robinson, 1950, 1953; Aebi, 1952; Adolph and Richmond, 1956; Riecker et al., 1957). Similar swelling of tissues in vivo by hypothermia or anoxemia has been shown by D’Amato (1954) and Hamburger and MathC (1951). If the tissue is reincubated aerobically at 37°C. in the presence of a suitable substrate, swelling is much less and fluid may be re-expelled from tissue which has already swelled (Stern, et al., 1949; Robinson, 1950, 1952a; Aebi, 1952). These observations have been interpreted by Robinson (1953), Opie (1954), and Bartley et al. ( 1954) as evidence that the cell interior is normally hypertonic to its environment and that a steady state is maintained only by continuous active expulsion of water. It has, however, been clearly shown that the fluid which enters the cells in conditions of impaired metabolism is not pure water but water plus sodium and chloride ions in a mixture approximately isotonic with the immersion medium (Mudge, 1951 ; Conway and Geoghegan, 1955 ; Leaf, 1956; Whittam, 1956; Gaudino, 1956) (although Schwartz and Opie, 1954, claimed

408

D. A. T. DICK

that sodium entered only the extracellular space during equilibration of tissue slices in saline) ; thus, whatever other evidence may be produced in favor of the theory of normal intracellular hypertonicity, the interpretation of tissue swelling by impaired metabolism as evidence for the theory is certainly not valid. Conway and McCormack (1953) attempted to settle the question by direct measurement of the intracellular osmotic pressure. They measured the freezing-point depression of tissues frozen and pulverized in liquid oxygen and then mixed with 0.95% saline at 0°C. It was found that the freezing-point depression increased rapidly with time even at 0°C.) and this was shown to be due to autolytic changes (Conway et al., 1955). To obtain the true osmotic pressure of the tissue in vivo, freezing-point depressions were measured at different times and extrapolated to zero time. It was concluded that the osmotic pressures of the tissues examined did not differ significantly from that of homologous serum. Brodsky et al. (1956) have criticized the method of Conway and his colleagues on the grounds that delay in equilibrating the tissue-saline mixture may occur and that the osmotic pressure measured is therefore that of the isotonic saline and not that of the tissue. Brodsky et al. obtained evidence of delay in mixing of about 10 minutes in liver samples mixed with hypertonic saline but not in those mixed with distilled water. After this interval tissue-saline mixtures showed a steady increase in freezing-point depression similar to that found by Conway and McCormack (1953). Brodsky et al., however, have extrapolated osmotic pressure to zero time only from data obtained in the first 10 minutes of the experiment, when mixing is probably incomplete ; and statistical methods of regression analysis were apparently not used. But after the first 10 minutes diffusion equilibrium has almost certainly been attained whether or not the tissue has been completely disrupted, and thereafter the variation in osmotic pressure is almost certainly due to autolysis. Thus, extrapolation to zero time of data obtained during the first 10 minutes is not equivalent to Conway and McCormack’s procedure ; significant comparisons can be made only by extrapolating from data obtained after the first 10 minutes. Such extrapolations have been performed on the data of Brodsky et al. by the present author using regression analysis. The results for the tissue osmotic pressure of liver so obtained are different from those given by Brodsky et al. in their paper-i.e., from isotonic saline mixtures 378 m-osm. (S.E. 17.4) instead of 317 to 340 m-osm. ; from hypertonic saline mixtures 324 m-osm. (S.E. 20.0) instead of zero ; and from distilled water mixtures 31 1 m-osm. (S.E. 10.1) instead of 300 to 305 m-osm. Thus in contrast with Conway and McCormack’s results hypertonic saline and distilled water mixtures

OSMOTIC PROPERTlES OF L I VI N G CELLS

409

gave a tissue osmotic pressure similar to that of plasma, and only isotonic saline mixtures gave an extrapolated osmotic pressure significantly different from the plasma osmotic pressure of 300 m-osm. Brodsky et al. have also given estimates of the osmotic pressure of many different undiluted tissue samples ; values ranged from 286 m-osm. to 827 m-osm., but it was suggested that the high values may be due to keeping the tissue at 0°C. for several hours, which from the findings of Conway et al. (1955) would be expected to result in a considerable degree of autolysis. Data of Brodsky et al. on the variation with time of tissue osmotic pressure measured without admixture of saline further suggest a hypertonic tissue ; however, the difficulties of measurement of accurate freezing points in viscous tissue homogenates must be very great as, unless equilibrium is rapidly attained, too low values (and thus high osmotic pressure estimates) result (see Dick and Lowenstein, 1958). Values of freezing-point determinations obtained on undiluted homogenates must therefore be treated with reserve. The definite conclusion that “the freezing point depression of freshly excised frozen tissues . . . is greater than that of plasma” does not appear to be justified by the rather inconsistent results presented in the paper of Brodsky et al. (1956). Appelboom ( 1957) has recently found from freezing-point determinations on boiled tissues that the intracellular osmotic pressure is not significantly different from that of plasma. Maffly and Leaf (1959) have reached a similar conclusion from melting-point determinations on frozen tissues. The finding of Robinson (1952b) that the base content of kidney cortex cells is higher than that of the extracellular phase does not necessarily imply a higher intracellular osmotic pressure, since some of the base may be present in an osmotically inactive state, e.g., bound to protein molecules (see Section 111. B above), or, as suggested by Mudge (1953), the excess of base may be needed to offset the osmotic deficiency due to polyvalent anions in the cell. Nichols and Nichols (1953) calculated from the concentrations of the known constituents of the erythrocyte and plasma that the total osmotic pressure within the erythrocytes of patients recovering from acidosis is only 274 m-osm. as compared with 302 m-osm. in the plasma. They concluded that the discrepancy was only apparent and was probably due to the presence of unknown solutes in the cell which had not been taken into account. However, the authors calculated the osmotic contribution of the hemoglobin without taking account of its large osmotic coefficient, so that the calculated value was only 4.5 m-osm. instead of the correct value of 16 m-osm. When this correction is made, a large part of the observed discrepancy is accounted for.

410

D. A. T. DICK

The assumption of osmotic equality does not seem to be unequivocally contradicted by any evidence so far available; as suggested by Darrow and Hellerstein (1958), it appears to be at least permissible to continue to make it. As indicated by Manery (1954),the success of theories based on this assumption in accounting for the osmotic behavior of living cells is itself a point in its favor. Theoretical treatments of cellular osmotic phenomena may be considered as dependent on proof of this assumption. This is not yet available. It must be noted, however, that most osmotic theories will be disturbed only when it is shown not only that osmotic equality does not occur between cells and environment but that there is not even a linear relationship between the intracellular and extracellular osmotic pressures, since even this modified condition would satisfy the requirements of the theories. 2. In a discussion of the relation between cell volume at osmotic equilibrium and electrolyte movements across the cell membrane, two points must be noted. First, the attainment of osmotic equilibrium is rapid, owing to the high permeability of the cell to water ; therefore since osmotic experiments, for the determination both of equilibrium and of kinetics, are of short duration-usually less than one hour-only electrolyte movements occurring within a period of a few hours need be considered. Second, it is necessary to discuss only the actual distribution of solute which occurs in cells and determines osmotic phenomena ; discussion of the mechanism which produces that distribution is not directly relevant to the problem. Also, since obviously only net transfers of solute and not actual effluxes or influxes determine over-all solute distributions, only net transfers are significant from the osmotic point of view. Available data on net cation transfers in various cells and tissues under physiological conditions are given in Table 11. It is seen that losses of potassium from individual cells and portions of undamaged rat diaphragm into media containing mostly sodium with small quantities of potassium are very small within the first few hours. There is some indication that they may be balanced (or even outweighed) by gains of sodium. On the other hand, in tissue slices of kidney cortex and guinea pig brain, the movements of ions are different; in the first there is a gain instead of a loss of potassium, and in the second the loss of potassium is much more rapid than in isolated cells. These differences may be associated with tissue damage during the preparation of the slice or with uptake of an actively transported anion, e.g., a-ketoglutarate. The evidence demonstrates that net cation transfer across the membranes of erythrocytes, leukocytes, and muscle cells is negligible within the first few hours of immersion in saline solutions. Since net anion transfer is dictated by cation

411

OSMOTIC PROPERTIES OF L I V I N G CELLS

transfer, owing to the necessity for preserving electrostatic neutrality, the assumption that no net transfer of solute across the cell membrane occurs during the attainment of osmotic equilibrium appears to be justified by TABLE I1 NET CATIONMOVEMENT I N CELLSIMMERSED I N PLASMA OR PHYSIOL~CICAL SALINE

Cell

Temperature (C.1

Human erythrocyte

25

K loss Time (% of interval initial (hours) conc.)

1 3

5

20 Human erythrocyte

Human erythrocyte Human erythrocyte Chicken erythrocyte Duck erythrocyte Rabbit leukocyte Rat muscle Rat muscle Guinea pig brain Kidney cortex

Na gain (% of initial conc.)

1.1 2.3 3.3 6.0

Ponder (1947a)

2 3 5 12

0.8 1.3

1.3 2.1

3.2 5.4

4.7

5 40

1 1

1.5 4.5

-

37

6

1.3

0.4 (loss)

25

7.9

-1 ,

0.5 5.0 (approx.) (approx.)

37

3

37

Several

Nil

Nil

37 38 37

6 12 4

Nil 2.0 Nil

Nil

40

1

5.2(gain)

-

37

10min.

6.5

References

1

Na

1

+ K)

Ponder (1947b) (immersed in 0.1 M NaCl) Davson (1937)

[

Maizels (1954)

(% of total initial

+

Na K) Hunter et a/. (1956) Tosteson and Robertson (1956) Hempling (1954) Creese (1954) Calkins et al. (1954)

-

-

21.0

(% of total initial

Terner et al. (1950)

{

(% of total initial

+

Na K) Whittam and Davies

the limited evidence available. Transfers of certain nonelectrolytes such as glucose or urea may of course occur, but these substances are not present in sufficient concentration to be of osmotic significance. It may be noted that, since the cell membrane appears to present no

412

D. A . T. DICK

distinct barrier to the passage of anions as it does to cations, an exchange of anions may readily occur. Thus if erythrocytes are placed in a solution containing a divalent anion, a two-for-one exchange with intracellular univalent anions may occur, resulting in diminution of the intracellular osmolarity and hence shrinkage of the cell (Parpart, 1940). A similar phenomenon has recently been demonstrated in Ehrlich mouse ascites tumor cells (Hempling, 1958). Conway ( 1957) has reviewed evidence that, contrary to previous opinion, the muscle cell is permeable to C1- ions. Ponder (1953) found that the concentrations of solutions of the alkaline earth chlorides needed to maintain erythrocytes at the same volume as in 1.0% sodium chloride were 0.105 M BaC12, 0.1 10 M MgC12, 0.130 M SrC12, and 0.10M CaC12. Since the respective osmotic coefficients are NaCl 0.928, BaC12 0.843, MgC12 0.861, SrC12 0.850, and CaCl2 0.854 (Robinson and Stokes, 1955), and thus the corresponding osmotic pressures are NaCl 317 m-osm., BaC12 266 m-osm., MgCl2 284 m-osm., SrC12 332 m-osm., and CaC12 256 m-osm., it is seen that, with the exception of SrC12, a lower concentration of divalent ion is needed to maintain the isotonic volume in saline solution ; a possible interpretation of the phenomenon might be that a limited two-for-one exchange of divalent for univalent cations takes place similar to that found for anions. Heilbrunn (1952, p. 127) reported similar findings in sea urchin eggs immersed in calcium chloride solutions. Grim (1953) has provided a theoretical treatment for predicting the osmotic properties of a membrane which is permeable to both water and solutes. This treatment is applicable, however, only when the permeability of the solutes is comparable with that of the solvent. 3. The evidence bearing on the physicochemical organization of solute and solvent in the cell interior is very unsatisfactory. Ponder (1948, 1949, 1955) has brought forward some indirect evidence for the conclusion that the erythrocyte possesses an internal structure formed either by an unidentified nonhemoglobin component or by interaction or orientation between the hemoglobin molecules themselves. Ponder has also suggested that the osmotic behavior of abnormal erythrocytes, e.g., crenated forms in oxalated blood or the paracrystalline rat red cell, is due to gelation in the cell interior. Dervichian et al. (1947) have concluded from comparative X-ray diffraction studies of erythrocytes, hemoglobin solutions, and hemoglobin crystals that the arrangement of the hemoglobin molecules in the erythrocyte is intermediate between the order present in a crystal and the disorder of a dilute solution. Frey-Wyssling (1953) has suggested that the protein molecules in the cell interior are connected by various types of junction or chemical bond. These junctions are considered to be highly labile, and

OSMOTIC PROPERTIES OF L IVI N G CELLS

413

changes in them produce gel-sol transitions in the protoplasm which are responsible for protoplasmic flow. Further evidence on the viscosity and elasticity of the protoplasm is interpreted as demonstrating a state intermediate between that of sol and gel. The bearing of electron-microscope evidence on the physicochemical state of the living protoplasm, though apparently direct, depends largely on assumptions about the relation of the fixed tissue to the living state. Frey-Wyssling ( 1955, 1957) has described four types of organization in the ground structure of the cytoplasm-reticular, granular, fibrillar, and lamellar. Palade ( 1955, 1956) has described an endoplasmic reticulum in the cytoplasm of a great variety of cells (Frey-Wyssling suggests that this may be equated to his lamellar organization). The reticulum has been found to be highly labile in character and is to this extent consistent with Frey-Wyssling’s views. The only cell type in which the endoplasmic reticulum has not so far been found is the mature erythrocyte, but this may be due to the extreme difficulty of preparing adequate thin sections of the erythrocyte. Thus it appears to be equally unlikely either that the protein component of the cell interior is in simple solution or that it is merely an insoluble structural framework. It must be remembered that so far as the osmotic properties of the cell are concerned this is a quantitative and not a qualitative question. What matters is not the mere fact that a structural component influences the osmotic behavior of the cell but the degree of that influence. It is equally possible that an apparently solid morphological structure may have a comparatively small quantitative effect on the solute properties of the protein composing it or, on the other hand, that the solute properties of the intracellular protein may be affected to a large extent by ultramicroscopic intermolecular chemical bonds which are revealed only by indirect evidence. It will be seen later that volume-osmotic pressure relationships in living cells may be interpreted so as to have a bearing on this question.

C . Techniques of Volume Measurement The difficulty of investigating volume-osmotic pressure relationships in living cells lies mainly in the measurement of cell volume. It is necessary, however, to measure only the relative and not the absolute cell volume. A great number of techniques have been used for this purpose, and these may be listed as follows.

1. Direct measurement of diameter of spherical cells. 2. Hematocrit methods. 3. Measurement of concentration of nonpenetrating solute.

414

D. A. T. DICK

4. Angular diffraction of light by cell suspensions (halometry). 5. Measurement of conductivity of cell suspensions. 6. Measurement of opacity of cell suspensions. 7. Measurement of changes in the solid and water contents of the cell. In a restricted compass it is possible only to outline the methods and to indicate, where appropriate, the scope and accuracy of the technique. 1. Direct Mearurement of Diameter of Spherical Cells. This method has been used extensively in measurements on marine invertebrate eggs (see Table IV). I t suffers only from the disadvantage that, since the calculated volume is proportional to the cube of the diameter, the percentage error of volume is three times the percentage error of the linear measurement. The absolute size of the cell is thus an important factor in the application of this technique, since as the diameter of the cell increases the percentage error falls ; the technique is thus more suitable for large cells such as sea urchin eggs rather than small ones such as leukocytes or sphered red cells. 2. Hematocrit Methods. The hematocrit technique involves centrifuging suspended cells at high speed and measuring the volume of packed cells. The application of the method to measurements of erythrocyte volume has been extensively reviewed by Ponder (1948). Recent determinations of the amount of trapped plasma in the packed cell column after centrifugation have shown that considerable errors can arise from this source (Leeson and Reeve, 1951 ; Chaplin and Mollison, 1952 ; Bernstein, 1955 ; Ebaugh et al., 1955). The extent of this effect in cells at other than isotonic osmotic pressures has been described by grskov (1946). Parpart and Ballantine (1943) used very high speeds of centrifugation and suggested that packing was practically complete after centrifugation at 30,000g for 5 minutes. Workers using the high-speed hematocrit at 10,OOO to 12,000 r.p.m. (grskov, 1946 ; Ponder, 1950) have obtained relative volurnes which give R values comparable with those resulting from methods of entirely different kinds (see Table 111). The modified van Allen dilution method, centrifuging at 2500 to 3000 r.p.m. (Guest and Wing, 1942), has given similar results (Guest, 1948). Side1 and Solomon ( 1957), however, who centrifuged at 7800s for 30 minutes obtained an R value of 0.64, and Ponder and Barreto (1957), who centrifuged at 20,OOOg for 90 minutes, an R value of 0.78. Hendry ( 1954) has criticized the hematocrit technique for measuring the relative volume of swollen erythrocytes in hypotonic solutions. H e claimed that such cells are more sensitive to compression during centrifugation than are cells in isotonic solution. This criticism, if valid, implies that the hematocrit is unreliable even if the duration and force of centrif-

OSMOTIC PROPERTIES OF LIVING CELLS

415

ugation are carefully standardized ; it cannot be expected to estimate accurately even relative volume changes. The hematocrit method has also been applied to measuring the volume of sea urchin eggs (Shapiro, 1935). The values obtained were on an average 2.5% greater than those given by the combination of hemocytometer count and measurement of diameter, but the range of the discrepancy was high (from +28.2% to -15.5%). Using the same material Clowes and Krahl (1936) found that the hematocrit results were on average 8% higher than the hemocytometer values. The discrepancy appears to be due to the presence of jelly adhering to the egg surface. Since the amount of jelly is very variable (Shapiro, 1935), the hematocrit appears to be unreliable for this purpose. 3. Measurement of Concentration of Nonpenetrating Solute. This method has been applied to the erythrocyte. The concentration of some substance in the plasma or suspending fluid either added artificially or naturally present is measured before and after osmotic volume changes in the erythrocytes. From the concentrations the volumes of the plasma and hence the volumes of the cells are easily measured. Substances measured have been artificially added hemoglobin (Ponder and Saslow, 1930), the dye Evans’ blue (Shohl and Hunter, 1941; Ponder, 1944), and the plasma proteins (Hendry, 1954). Provided the basic assumptions-that the measured substance is truly nonpenetrating and is not adsorbed on the erythrocyte surface-are satisfied, the method appears to be reliable, since it gives results consistent with values of R obtained by other methods (see Table 111). 4. Angular Diffraction of Light by Cell Suspensions (Halometry). The history and technique of this method have been fully reviewed by Ponder (1948, 1950). When a narrow beam of light is passed through a suspension of fine spherical articles, it becomes surrounded by bright and dark rings due to scattering of the original straight beam of light. The angular distance of the rings of scattered light from the source beam depends on the diameter of the particles which cause the scattering. From measurements of the angle the diameter of the particles can be calculated. This method has chiefly been applied to erythrocytes. Thus use of it involves two difficulties: (e) Before the method is applied to measuring the volume of erythrocytes, they must first be turned into spheres ; Ponder ( 1929) claimed that disc-sphere transformation can be produced without change of cell volume, but unpublished observations of Lowenstein and Dick (1958) show that, although in the first stage of the transformation a crenated sphere is produced which has a diminished diameter but the same volume as the original erythrocytes, this crenated sphere rapidly

416

D. A. T. DICK

increases in diameter and volume with disappearance of the original crenations. ( b ) Since the method involves the calculation of volume from diameter, it necessitates the inevitable trebling of the percentage error which has already been mentioned. 5. Measurement of Conductivity of Cell Suspensions. From measurements of the conductivity of a suspension of cells and of the suspending medium, the volume fraction of cells in the suspension can be calculated. Although the theoretical foundation of the method is sound, the equation used in the calculation contains a “form factor” which depends on the shape of the cell used. The “form factor” can be accurately calculated for a sphere or a spheroid, but for an irregular cell such as the erythrocyte it must be determined empirically by means of suspensions of known concentration calibrated by another method (eg., the hematocrit) . In addition to this source of uncertainty the conductivity of a suspension is liable to wide variations if it is stirred, due to formation of eddy currents. The method is therefore only of limited value. The application of the method to erythrocytes has been reviewed by Ponder (1948). 6. Measurement of Opacity of Cell Suspensions. The use of this technique for the measurement of red cell volume has been reviewed by Ponder (1948). The method has been applied to leukocytes by Shapiro and Parpart ( 1937), by Luck6 and Parpart (1954), by Luck6 et al. (1956), and by LeFevre and LeFevre ( 1952). The opacity of a suspension is expressed by the fraction Intensity of transmitted light Intensity of incident light The opacity of a suspension of cells depends on the amount of light lost by absorption and scattering. Neither of these quantities is amenable to accurate theoretical treatment. Besides the number and size of cells, absorption depends on the concentration of absorbing material in the cells, and the distribution of the cells. Scattering depends on the difference of refractive index between cell and immersion medium. Thus changes in the opacity of a cell suspension depend on a number of variables. Nevertheless it has been found experimentally in many cases that an approximately linear relationship exists between the opacity of the suspension and the total volume fraction of cells in the suspension. I t must be emphasized, however, that this relationship is purely empirical and has no satisfactory theoretical foundation. Although the method therefore cannot be used for measuring absolute cell volumes, it provides a useful method of measuring relative volume changes, particularly if these are rapid. The accuracy of the method is limited, however, to the accuracy of the volume-

OSMOTIC PROPERTIES O F L I VI N G CELLS

417

measuring method, usually the hematocrit, which is used in the calibration and the accuracy of the calibration technique itself. Relative cell volume has recently been measured by a variation of the opacimetric technique (Side1 and Solomon, 1957). Instead of measuring the transmitted light, the light scattered by a red cell suspension at right angles to the incident beam is measured. An empirical linear relation is found between the scattered light and the volume fraction of cells in the suspension. The method is subject to the same limitations as the opacimetric technique. 7. Measurement of Changes in the Solid and Water Contents of the Cell. From changes in the solid and water contents of the cell, relative changes in volume due to osmotic conditions can be calculated, provided it is assumed that volume changes are due solely to water transfer ; as seen in Section IV. B. 2, this assumption appears to be substantially justified by the evidence available. Methods of measuring the solid and water contents of the erythrocyte are reviewed by Ponder (1948). The density of the erythrocyte can be measured by various methods ; the hemoglobin content of cells is measured by centrifuging, lysing the packed cells, and estimating the hemoglobin present colorimetrically ; the erythrocyte water content is determined directly by centrifuging the cells at high speed and drying a weighed sample to constant weight. The estimations of hemoglobin and water content are of course dependent on the efficiency of centrifuging. The most recent technique applied for this purpose is that of immersion refractometry (Barer and Joseph, 1954, 1955a, b ; Barer, 1956). The refractive index of the cell cytoplasm is determined by immersing the cell in solutions of bovine plasma albumin of different refractive index until a condition of zero contrast is obtained between the cell and the background as seen in the phase-contrast microscope. The refractive index of the cell is then the same as that of the immersing medium, and from it the solid concentration of the cytoplasm may be directly calculated from the equation n

=

n,

+ aC

where n = the refractive index of the cytoplasmic colloidal solution.

nzo = the refractive index of the pure solvent, i.e., water. a = the average specific refraction increment of the cell solute. C = the solid concentration of the cell expressed as weight/volume of solution. For cells other than erythrocytes, a is taken as 0.0018, a value slightly less than the average for most proteins, to allow for the presence of lipoprotein in the cell (it is considered that the amount of the nonprotein

418

D. A. T. DICK

constituents of the cell is so small that it does not affect the value significantly). For the erythrocyte a is taken as 0.0019, which is again slightly less than the accepted value for hemoglobin. This method has been applied to erythrocytes (Dick and Lowenstein, 1958; Gaffney, 1958) and to chick heart fibroblasts in tissue culture (Dick, 1958a). The results obtained are consistent with recent values obtained by other methods (see Tables I11 and I V ) . Particular advantages of the refractometric technique for the measurement of volume-osmotic pressure relationships are its applicability to irregular cells and the fact that besides relative volume there is obtained at the same time a determination of the isotonic water content of cell which is needed in the calculation of Ponder’s R.

D. Volume-Osmotic Pressure Relatwnships in Erythrocytes Owing to its easy availability in quantity, the osmotic properties of the erythrocyte have been more extensively studied than those of any other kind of cell. The subject has been reviewed by Luck6 and McCutcheon (1932) and by Ponder (1933a, b, 1940, 1948, 1955). It is now well established that when the total cell volume is plotted against the reciprocal of osmotic pressure a linear relationship is obtained within certain limits of hypotonicity and hypertonicity (e.g., Dick and Lowenstein, 1958). Beyond the hypotonic limit the cell fails to increase in volume as expected, probably owing to the prehemolytic loss of ions from the cell. That the linearity found is more apparent than real is demonstrated by equation 34, but by means of the treatment described in Section IV. A it may be used to calculate the value of R for the erythrocyte. Data available from the literature are shown in Table 111. Observations made on cells from defibrinated or heparinized blood are shown first; these cells may be presumed to have been in a physiologically normal condition. I t is seen that the values of Ponder’s R are highly variable, especially in the earlier measurements. With improved techniques, however, values obtained from cells in hypotonic saline appear to lie for the most part in the range of 0.90 to 1.0. On the other hand, values from cells in hypertonic saline are much lower. This is in accordance with the theory presented in Section IV. A, since the osmotic coefficient of hemoglobin changes ever more rapidly with concentration at the high concentrations produced by hypertonic osmotic pressures, i.e., the value of d+/dII is greatly increased and a low value of R results. Part A of Table I11 shows R values obtained from cells in oxalated blood; it is seen that the majority of values lie in the range 0.5 to 0.8 and are thus much lower than those of cells from defibrinated or heparinized blood. This difference was first described by Ponder and Robinson (1934a). Since the enzyme mechanisms of cells in oxalated

OSMOTIC PROPERTIES OF LIVING CELLS

419

blood samples are grossly dislocated, some alteration in the osmotic properties of the cell is to be expected. Table 111, part C, shows one low R value for citrated blood, but the method used was unreliable. Several theories have been put forward to account for the value of R. T o avoid confusion these must be divided into two groups:

1. Theories applicable to the physiologically normal erythrocyte. a. Binding of water of solvation to the erythrocyte proteins (Jdrskov, 1946; Cristol and Benezech, 1946a; Ponder, 1948). It has been shown in Section 111. C that the status of water of solvation is rather nebulous and that it is in many cases merely a hypothetical concept used to interpret observed results. Cristol and Benezech (1948) have used the binding of water of solvation as an explanation of the fact that the chloride content of the erythrocyte is less than that of the plasma; such an interpretation ignores the effect of the electrical charge on the hemoglobin in producing an unequal Donnan distribution of the electrolyte. b. Increase of osmotic activity of salts in concentrated hemoglobin solutions (e)rskov, 1946). This possibility is very improbable, as protein-salt interactions in concentrated hemoglobin solutions are more likely to diminish than to increase the osmotic activity of the salt. c. Elasticity and resistance to shrinkage of hemoglobin molecules in concentrated solutions (Jdrskov, 1946). This theory is open to criticism on the ground that the elasticity of a true aqueous solution is so small as to be negligible. It is, however, possible that the partially gel-like properties of the intracellular solution of the erythrocyte (see Section IV. B. 3) confer some elasticity on it. d. An internal nonhemoglobin framework in the cell resists shrinking (Jdrskov, 1946; Ponder, 1940). Evidence for such an internal framework at least in the region close to the erythrocyte membrane has been put forward by Mitchison (1953) and Ponder (1949, 1951b), although the electron microscope has not so far confirmed it. e. Tension in the cell membrane (Cristol and Benezech, 1946b). A similar mechanism was proposed for the erythrocyte ghost by Teorell (1952). There is no evidence that the intact red cell membrane is capable of withstanding pressures of significant degree in relation to the large osmotic pressures involved (the isotonic osmotic pressure is 7 atmospheres). The prehemolytic failure of the erythrocyte to increase its volume proportionately to the fall of osmotic pressure is more likely to be due to leakage of solute than

n.

420

A. T. nrcK

TABLE I11 VALUESOF PONDER'S R I N ERYTHROCYTES Range of relative osmotic Ponder's Technique pressure R A . Defibrinated or Heparinked Blood Hematocrit (dilution) 1 - 1.5 0.66 Colorimetric Hypotonic 0.5 (approx. 1 Vapor pressure measurement 1-2.0 0.97 Hematocrit 1 - 0.65 0.85-0.98 Density measurement 1 - 0.65 Diffraction 1- 0.5 0.65-1.00

Animal Horse Rabbit Ox

Rabbit

Man Rabbit

ox

Sheep Rabbit Rabbit Man

zL

Rabbit Dog Rabbit

1

Diffraction Diffraction Diffraction Diffraction Measurement of diameter

1- 0.41 1- 0.47 1 - 0.50 1 - 0.58 1-0.5

0.79

Conductivity Conductivity

1- 1.5 1- 1.5

0.72-0.95 0.73-0.96

0.69 - 2.0

0.58-0.81 0.58-0.91 0.6 -0.8

Hematocrit

Man

Water concentration 1- 2.56 1- 0.68 measurement Hematocrit (van Allen) 1-0.425

Man Man

Colorimetric Not stated

Man Man Man Man Man Man Chicken

Hematocrit 1 - 0.62 Hematocrit 1 2.39 Hematocrit (van Allen) 1 - 0.425 Not stated Hypertonic Hematocrit (dilution) 1 - 0.2 1- 0.45 Diff ractometry Hematocrit 1 - 2.0 1-0.7 Opacimetry 1- 2.0

1- 0.5 1 - 4.0

-

0.64-0.79

0'7(M'84 0.57-0.90 0.63-0.86

0.6 -0.73 0.5 o.74

I I

1}

0.96-1.05 0.93-0.97 0.70 0.79 0.98 0.79 0.9 0.75-0.85 0.55-0.85

}

References Hamburger (1898) Ponder and Saslow (1930) Hill (1930) Ponder and Robinson (1934a)

Ponder (1935a)

Ponder (193%) Ponder (1935b) Parpart and Shull (1935) Davson (1936) Guest and Wing ( 1942) Ponder (1944) Cristol and Benezech (1946a) grskov (1946) Guest (1948) Giraud ef nl. (1950) Ponder (1950) Ponder (1951a)

42 1

OSMOTIC PROPERTIES O F LIVING CELLS

TABLE I11 (continued) Range of relative osmotic pressure

Ponder’s R

Animal Man

Technique Plasma concentration measurement

Man

Hematocrit

Man

Immersion refractometry 1 - 0.62 0.95 (S.E. 0.018)

References

1 - 0.58 0.97 (S.E. 0.011) 0.5- 1.7 0.78

Hendry (1954) Ponder and Barreto

Man Immersion refractometry 1 - 0.56 0.90 (S.E. 0.035) Chicken Immersion refractometry 1-0.56 1.00 (S.E. 0.051)

B. Oxalated Blood Rabbit

Hematocrit (dilution)

1 - 1.5 1 - 0.5

1.06 0.83

Man

Hematocrit

1 - 0.75 1 - 2.9

0.65 0.54

Man

Hematocrit (dilution)

1-0.6 1 - 1.25

0.76 0.68

1-3.0 Sheep Rabbit

Diffraction Hematocrit (dilution)

Man Rabbit

Hematocrit (dilution) Density measurement H b concentration measurement Water concentration measurement

1 - 0.46 1-2.0 1 - 0.56 1-0.5 1-0.65

0.47-0.59 0.15 0.58-0.73 0.63 0.55-0.72

1 - 0.65

0.53-0.69

1 - 0.65

0.6

Rabbit

Hematocrit Density measurement Diffraction Hematocrit

1 - 0.65 1 - 0.65 1-0.75 1 - 0.68

Man

Hematocrit

1 - 0.6

Rabbit

0.6

(approx. 1

}

1

(1957) Dick and Lowenstein

(1958) Gaffney (1958)

Ege (1922) Gough (1924) Christensen and Warburg (1929) Krevisky (1930) Ponder and Saslow

(1931)

Schi@dt (1932)

Macleod and Ponder

(1933)

(approx.)

0.71-0.85 0.54-0.72 0.65 0.77-0.89 0.71

Ponder and Robinson (1934a) Ponder and Robinson (193413) Castle and Daland

(1937)

C. Citrated Blood

Horse

0.56

Slawinski (1936)

422

D. A. T. DICK

to the membrane tension of 0.75 atmosphere suggested by Cristol and Benezech. f. As discussed in Section IV. B. 3, it is possible that some degree of intermolecular linkage modifies the osmotic properties of the hemoglobin, e.g., makes the osmotic coefficient considerably greater than that of a corresponding solution in vitro. g . Anomalous molal osmotic coefficient of hemoglobin in solution. This was used to account for the difference in vapor pressure and freezing-point depression between whole and laked blood (Roepke and Baldes, 1942; Williams et al., 1955). It has been used to account quantitatively for R values (Dick and Lowenstein, 1958 ; Dick, 1958b) (see Section IV. A ) . It may be noted that this explanation merely interprets the osmotic behavior of the erythrocyte in terms of that of hemoglobin solutions in vitro. Discussion of the actual mechanism involved is avoided, although as has been rioted in Section 111. D the large partial molal entropy of dilution of hemoglobin in solution due to the large size of its molecule plays a most important part in causing the large osmotic coefficient. 2. Theories applicable to the abnormal erythrocyte. a. Gelatin of the corpuscle interior (Ponder, 1940, 1948). This is associated with crenation which is produced by the action of oxalate (Ponder, 1944) or of citrate at low temperature (Ponder, 1945). It is supposed that elastic forces resist swelling in the gelated corpuscle and produce a low R value. b. Leakage of solute from the cell (Ponder and Robinson, 1934b). As has been seen above (Section IV. B. 2 ) , this does not occur in cells kept under good physiological conditions but can be expected to occur whenever the conditions are disturbed. Although ion leakage may contribute to the effects, losses actually measured are insufficient to account for the entire depression of the R value which is found (Davson, 1936, 1937). Agna and Knowles (1955), Streeten and Thorn (1957), and Riecker (1957) have shown from studies of the effect of change of plasma osmotic pressure by water injection, drinking, or abnormal pathological states that the erythrocyte in vivo undergoes shrinking and swelling in response to external osmotic changes similar to that observed in vitro.

E.

Volume-Osmotic Pressure Relationships in Cells Other Than Erythrocytes As described in Section IV. A, a graphical plot of total cell volume against the reciprocal of the osmotic pressure may be used to find the

OSMOTIC PROPERTIES OF L I V I N G CELLS

423

value of Wo,the apparent isotonic water content of the cell. The apparent nonsolvent volume, b', may be defined by the equation

Wo = Vo - b'

(39) Emphasis in the interpretation of osmotic experiments in all cells except the erythrocyte has hitherto been placed on the calculation of b'. This emphasis appears, however, to be misplaced ; it is much more important to calculate the value of Wo, the apparent isotonic water content, and to compare it with W,, the true water content obtained by direct methods, and thus obtain the value of Ponder's R as in the erythrocyte. This aspect of experiments on marine invertebrate eggs and leukocytes has been neglected. Owing to this neglect, the actual water content of cells used in osmotic experiments has in many cases not been given. Table IV has been constructed from values for the actual water content, W,, which are calculated by applying to the dry weight the average specific volume of 0.75; but the dry weight employed in the calculation has often 'been obtained from a different source so that it need not necessarily apply to the cells actually used in the osmotic experiment. This is particularly the case with Arbacia eggs, whose dry weight may be increased by the presence of a layer of jelly on the surface of the egg (Shapiro, 1935). This may account for the high R values shown for Arbacia in' Table IV. Hamburger and Math6 (1952, p. 46) obtained volume-osmotic pressure data on leukocytes and claimed to find a direct linear relationship between the volume and the applied osmotic pressure; in view of the other evidence and the sound theoretical basis available which predicts a hyperbolic relationship in this case, Hamburger and MathC's interpretation of their results is improbable. Ross ( 1953), in experiments on snail spermatocytes, claimed that the cells suffered no change in volume between osmotic pressures corresponding to 0.5% and 0.8% NaCl; however, the scatter of his observations is so high that no conclusion regarding constancy or change of volume can safely be drawn, and the claim made seems unjustified. The interpretation of R values in other cells may be considered by using the hypotheses which have already been applied to the erythrocyte. Some modifications must be made, however, particularly to take account of the lower concentration of protein in such cells. Thus it has been shown that a n osmotic coefficient for the cytoplasmic proteins comparable with that of a similar protein solution in vitro is probably insufficient to account for the observed R value in chick heart fibroblasts (Dick, 1958a). The difference may be accounted for by a modification of the osmotic properties of the protein due to intermolecular bond formation.

TABLE IV NONSOLVENT VOLUME A N D PONDER’S R IN CELLSOTHER THANERYTHROCYTES

Species

Technique

Range of relative osmotic pressure

b

wo a

(see text)

W,

R0

References Lillie (1916) F a d - F r e m i e t (1924) Skowron and Skowron (1926) Ephrussi and Neukomm (1927)

A . Eggs of Marine and Aquatic Invertebrates (Unfertilized) Arbacia punctulata Sabellaria alveolata Sphuerechinus granularis

Measurement of diameter Measurement of diameter Measurement of diameter

1-0.4

0.370

0.63

0.80a

0.79

2.24-0.25

0.31~

0.69

0.750

0.92

1-0.43

0.330

0.67

-

-

Paracentrotus lividus

Measurement of diameter

1.16-0.36

0.46c

0.54

0.740

0.73

d r b a c k punctulata

Measurement of diameter

1-0.5

0.07 0.13 0.14 0.09 0.12 0.39 0.44 0.320 0.57

0.93 0.87 0.86 0.91

0.80b 0.80b 0.80b 0.80b 0.80b

%

1.08 1.14 1.11

0.61 0.56 0.68 0.43

-

0.85 0.50

0.08 0.21 0.21 0.28

0.92 0.79 0.79 0.72

0.80b 0.800 (approx. ) 0.80b 0.740

Luck6 (1932) Luck6 et al. (1935) Shapiro (1941) Luck6 and Ricca (1941) Churney (1942) Raven and Klomp (1946)

1.16 1.07

Shapiro (1948) Mettetal (1948)

Arbacia punctulata (fragments) ArbacM punctulata Chaetopterk pergamentaceous Ostrea virginica Arbacia punctulata Limnea stagnalis

Measurement Diffraction Measurement Diffraction Measurement Measurement

of diameter of diameter

1-0.6 1-0.6 1-0.4 1-0.4 1.134.5 1.5-0.5

Arbacia punctulata Paracentrotus lividus Strongylocentrotus interrnedius Strongylocentrotus nudus

Measurement Measurement Measurement Measurement

of of of of

1-0.6 Hypotonic 1-0.6 1-0.5

of diameter of diameter

diameter diameter diameter diameter

0.88

-

-

}

-

-

}

McCutcheon et al. (1931)

Shinozaki (1951)

p ? +I

:

U

TABLE I V (continued)

Species

Technique

Range of relative osmotic pressure

WO a

b

(see text)

W,,,

Ra

-

-

References

B. Other Cells Egg of Murphysa gruvelyi Rat lymphocyte (Lewis strain) Rat lymphocyte (Wistar strain) Mouse lymphdcyte (C3H strain) Gardner mouse ascites tumor Lewis rat lymphoma Murphy-Sturm rat lymphosarcoma Mouse sarcoma cell Chick heart fibroblast (plasma clot culture) Chick heart fibroblast (fluid plasma culture) Chick heart fibroblast (saline culture)

Measurement of diameter Opacimetry Opacimetry Opacimetry Opacimetry Opacimetry

1-0.45 1-20 1-2.0 1-2.0 1-2.0 1-20

0.670 0.36 0.26 0.21 0.31 0.40

0.33 0.64 0.74 0.79 0.69 0.60

0.89 0.89a 0.89 0.86e

Opacimetr y

1-20

0.36

0.64

-

0.74 0.78

-

0.87a

0.82

0.87

0.90 I 0.94 1

0.87

1.15

Measurement of linear dimensions Immersion refractometry Immersion refractometry

1.78-0.39 1-0.58

0.18

0.00

1.00

0.886

0.72 0.83 0.89 0.80 0.68

-1 -

1 *

Krishnamoorthi (1951)

i Luck6 et a!. (1956)

30 $

T:u

}

1

M

-

v)

Brues and Masters (19364 Dick (1958a)

Calculated by the present author. Calculated by the present author from data of Hutchens et ul. (1942). 0 Calculated by Luck6 and McCutcheon (1932). d Calculated by the present author from data of Joseph (personal communication from the Department of Human Anatomy, Oxford). e Calculated by the present author from data of Hempling (personal communication from Department of Physiology, Cornell University Medical School, New York) .

% E:

s

Z c,

n M r

r

v)

a b

R

VI

426

D. A. T. DICK

The work of McDowell et al. (1955) on the apparent volume of distribution of solutes injected into nephrectomized animals and the clinical water and salt balance studies of Wynn and Houghton (1957) and Wynn (1957) have shown that cells in vivo shrink and swell in response to changes of external osmotic pressure less than would be expected on the basis of the simple Boyle-van? Hoff law. This finding is in accordance with the accumulated observations on individual cells. McDowell et d. considered that the effect was due to “an idiogenic increase of osmotic pressure in proportion to applied osmotic stresses tending to dehydrate cells”; but it is probably to be at least partly explained by the osmotic properties of the intracellular proteins. An exception to the normal osmotic behavior of cells is the egg of teleost fishes. There is evidence that the egg of Salmo does not change its volume with variation in the external osmotic pressure (Gray, 1932) and that this is due to an almost complete impermeability to water (Prescott, 1955). In the activated egg of Fundulus immersed in hypertonic solution or sea water a hydrostatic pressure develops within the chorion which is produced by colloids in the perivitelline space. This pressure in turn tends to compress the egg itself so that its volume diminishes (Kao et al., 1954; Kao, 1956). F. Osmotic Behavior of the Nucleus Most of the observations recorded in Table IV refer to volume changes in the whole cell. A few observations are available relating to the volume changes in the nucleus and other inclusions. Beck and Shapiro (1936) found that in starfish eggs the nucleus swells in hypotonic solutions as the whole cell does but proportionately to a slightly greater extent than the whole cell. Similar swelling was noted by Kamada (1936). Churney (1942) measured the volume of the nucleus and of, the whole cell at different osmotic pressures and found also slightly greater relative swelling in the nucleus. By the use of an inappropriate method of statistical analysis, however, he reached the erroneous conclusion that the nonsolvent volume of the cell and nucleus is zero at near isotonic osmotic pressures but becomes positive in anisotonic solutions. If a correct method of regression analysis is applied to Churney’s data and the apparent isotonic water content ( W o ) is calculated by equation 31, it is found that W Ofor the nucleus is higher than that for the whole cell; for Arbacla punctulata the values of W o are for the whole cell 0.68 (S.E. 0.02) and for the nucleus 0.84 (S.E. 0.07). This interpretation also provides a reasonable explanation for Beck and Shapiro’s results. The fact that, when the chick heart fibroblast is immersed in a solution of the same refractive index as the cytoplasm, the’ nucleus frequently appears (with positive phase con-

OSMOTIC PROPERTIES O F LIVING CELLS

427

trast) very slightly brighter than either cytoplasm or background also supports the suggestion that the solid concentration of the nucleus is slightly lower than that of the cytoplasm and the water content is correspondingly higher (Barer and Dick, 1957). In contrast with the above results Marshak (1957) found that the nuclei of starfish eggs did not change volume either in hypotonic or hypertonic solutions of polyhydric alcohols or sucrose. Since in these experiments the egg cytoplasm was found to swell in both hypotonic and hypertonic solutions and considerable morphological changes occurred (e.g., nuclear extrusion), it is probable that the physiological state of the cells was considerably altered by the solutions employed. Harris (1943) concluded that the pigment granules of the sea urchin egg swell and shrink along with the cytoplasm in the same way as the nucleus. G . Conclusion Deviation of the osmotic behavior of cells from the conventional Boylevan? Hoff law is expressed by Ponder’s empirical factor R. An equation connecting the average osmotic coefficient of the intracellular protein with the value of Ponder’s R has been given. In consequence R is a much more significant cellular parameter than the apparent nonsolvent volume, b‘, on which osmotic studies have been conventionally based. The value of R may be useful in drawing conclusions concerning the physical state of the intracellular proteins and the possible presence of intermolecular chemical bonds. In order that accurate values of R for different cells may become available, it is essential that in all future osmotic studies the true water content of the cell be determined independently for comparison with the apparent water content. The immersion refractometry technique offers considerable advantages for this purpose. OF OSMOTIC VOLUME CHANGES I N LIVING CELLS V. KINETICS A . Introduction

Because movement of solute across the cell membrane is negligible in physiological saline solutions, the volume changes in cells produced by changes of external osmotic pressure are due almost entirely to the entry or exit of water. A study of the kinetics of such changes is thus equivalent to a study of the permeability of the cell to water. It must be recognized, however, that this is not the only criterion of permeability to water. Permeability may also be studied by measuring the rate of diffusion of isotopically labeled water (HiO, HiO, or H20l8) into or out of the cell. The two methods are not equivalent because the mechanisms of water transport in the two cases are not the same. In the case of osmotic water

428

D. A. T. DICK

transfer a net flow of water occurs across the cell membrane, whereas in the diffusion method there is only an exchange of labeled for unlabeled water molecules without net transfer. The water permeability measured by the osmotic method is always higher than that obtained by the diffusion method (Prescott and Zeuthen, 1953). The reason for this difference will be discussed in Section V. E. It is essential to appreciate the distinction between the two water permeabilities before examining the theory of osmotic water transfer. The subject of water permeability of cells has been reviewed by Luck6 and McCutcheon ( 1932), Luck6 ( 1940), Brooks and Brooks ( 1941), Davson and Danielli (1952), Jacobs (1952), Ussing (1952), and Harris (1956). An extensive introductory account of theoretical aspects of diffusion and permeability processes has been given by Jacobs (1935).

B.

Theory of Osmotic Water Permeability It has been a basic assumption of all measurements of the water permeability of cells that resistance to the passage of water is effectively confined to the membrane of the cell. This assumption has been made more because it was considered essential to the mathematical treatment of the problem than because it was supported by evidence (this question is fully discussed in Section V. F), but it has nevertheless become implicit in the technical use of the term permeability and in the choice of units to measure it. The permeability or volume of water crossing the cell membrane is assumed to depend on ( 1) the area of the membrane, (2) the time of permeation, and (3) the difference of osmotic pressure between the two sides of the membrane. The conventional unit of water permeability is thus the number of cubic microns of water crossing one square micron of the cell membrane in one minute in response to a difference of osmotic pressure of one atmosphere, or p3/p2/min./atm. If the dimensions of this unit are reduced to the simplest form, it may be expressed with no ambiguity as p min.-' atm.-l. The osmotic water permeability unit described above may be converted into what may be called a concentration permeability unit by expressing the difference of osmotic pressure which appears in it as a difference of water concentration. The method of this calculation has been described by Frey-Wyssling (1946) and LZvtrup and Pigon (1951) and the transformation has been employed by Prescott and Zeuthen (1953) and Harris (1956). The resulting concentration permeability unit when reduced to its lowest dimensions is expressed as p/sec. The basic equation used in the interpretation of the kinetics of osmotic water flow is

OSMOTIC PROPERTIES O F LIVING CELLS

dV = kA(rI - n,)

429

(40)

dt where V is the volume of the cell, t the time of measurement, k the permeability coefficient, A the area of the cell membrane, and rI and He the internal and external osmotic pressures. Two assumptions underlying this equation are (1) that the mechanism of permeation of the cell membrane is one of simple diffusion, i.e. there are no energy barriers requiring activation energies to overcome them and (2) that the resistance of the membrane does not vary during osmotic volume changes. I n order to apply it in practice, equation 40 must be integrated ; several methods have been used for doing this. 1. I n the case of the erythrocyte which has a disc shape, the volume may be greatly increased without significant change in the area of the cell membrane. Jacobs ( 1932) therefore performed the integration by treating A as a constant. By substituting for V , using the simple equation IIV = rIOV0 (Jacobs’ symbols have been altered to conform to present usage), obtained , r10Vo drI - - - -- kA (rI - II,) r12 dt of which the integral form is drI kAt = -rIovo II2 (rI - rIe) or

he

where TIe is the osmotic pressure of the external medium. No allowance is made in this equation for the nonsolvent volume in the erythrocyte. Dick (1959a) used a similar expression in treating kinetics of osmosis in chick heart fibroblasts in a cover slip culture. These cells, being thinly spread out on the cover slip, alter their volume largely by changes of thickness, and the surface area available for water transfer remains practically constant. The substitution for V is performed by using an equation already obtained from equilibrium experiments (Dick, 1958a) : 0.817 I I o V o V = rI + b or dV 0.817rIoV0 (43)

so that the nonsolvent volume is allowed for.

430

D. A. T. DICK

2. I n spherical cells the area of the cell membrane may be expressed in terms of the volume of the cell by the equation A = (36.rr)%V ? S (44) and the integration is performed by treating the area as a function of the volume. The equation so obtained by LuckC et al. ( 1931 ) was

k ( 3 6 ~ ) ~ ~ (Yo f l o - b ) t = (Ye- b) X

where Vo = initial total cell volume. no = initial intracellular osmotic pressure. V, = total cell volume at final equilibrium with external medium. V = total cell volume at time t. This equation has been used in all subsequent studies of spherical cells. Historically, two equations which are now obsolete were used in permeability studies. Lillie ( 1916), in the first mathematical treatment of permeability, used a supposed analogy with monomolecular chemical reactions and obtained the equation

dV- K(II dt

- 11,)

where K is a constant; the surface area has been assumed constant and combined with the permeability coefficient, k, to form a different constant, K . The constant K could not of course be used to compare the permeabilities of cells of different area. The integral form of equation 46 was given by Lillie as 1 V , - Yo K=-ln (47) t - Vt

v,

This equation contains two errors, however : (1) it has not been integrated correctly, and (2) the assumption that the surface area does not alter during volume changes in spherical cells is obviously incorrect and leads to a dependence between the value of the external osmotic pressure and the permeability coefficient obtained by the use of Lillie's equation. LuckC and McCutcheon (1927), who used Lillie's equation, found just such a relationship in the eggs of Arbacia punctulata. Northrop (1927) corrected both of the errors in Lillie's equation. H e

OSMOTIC PROPERTIES OF L IVI N G CELLS

43 1

used a different approach, however, in estimating the effect of cell swelling or shrinking on the resistance of the membrane to the passage of water. His basic equation took account of the thickness as well as the area of the cell membrane (the symbols have been altered to conform) :

where k' is a constant, and h is the thickness of the cell membrane. If the volume of the membrane, m, is assumed to remain constant during changes of cell volume, then, since m is the product of the area and thickness of the membrane,

h = and

m

A

If m is incorporated into the permeability coefficient, the resulting equation is

where k" is a new constant of permeability. A similar equation was also derived by Northrop on the different assumption that water transfer takes place through pores whose diameters change with change of area of the cell membrane. It was shown by .Luck6 et al. (1931) that the course of osmotic changes in the egg of Arbacia punctuhta is described equally well by equations 45 and 50, so that it is not possible to distinguish between them on empirical grounds ; nevertheless equation 45 has been preferred in subsequent studies, e.g., Luckk et al. (1956). C. Methods of Measuring Osmotic Water Permeability

As pointed out in the previous section, this is largely a question of determining the rate of change of cell volume in an anisotonic solution. Many of the methods of measurement of cell volume already described in Section IV. C have therefore been applied to the measurement of cell permeability, particularly diameter measurement, measurement of angular diffraction, measurement of opacity of cell suspensions, and recently immersion refractometry.

432

D. A. T. DICK

Two further methods of measuring cell water permeability of a different type are the hemolytic method of Jacobs applied to erythrocytes and the simultaneous measurement of water and solute permeability. When erythrocytes are hemolyzed in hypotonic solutions, the occurrence of hemolysis is always associated with a definite and constant increase in the volume of the erythrocytes. I n practice, since not all the cells of a given sample hemolyze at once, but the percentage of hemolysis increases with the degree of swelling of the erythrocytes, it is found that when cells are 75% hemolyzed the volume of the erythrocytes has always increased to 1.70 times their isotonic volume (Jacobs, 1934). The degree of hemolysis of the erythrocyte suspension is measured by a simple opacimetric method, and the time required to produce 75% hemolysis is noted; from the known increase in volume associated with this and the corresponding time the permeability coefficient of the erythrocyte is measured (Jacobs, 1932, 1934). I t has been shown, however (Jacobs, 1955), that the accuracy of the hemolytic method may be seriously affected by prehemolytic ion transfers across the cell membrane. When cells are suspended in isotonic saline which has been made hypertonic by the addition of a penetrating solute, they first shrink in response to the hypertonic environment, and then swell as the penetrating solute enters the cell, finally returning to their original volume when the penetrating solute has reached diffusion equilibrium across the cell membrane. I t has been shown by Jacobs and Stewart (1932) and by Jacobs (1933a, b) that, if the size and time of attainment of minimum volume are measured, then the permeability coefficients both of water and of the penetrating solute can be calculated. Methods for calculating the two permeability coefficients from the rate of swelling of cells in a pure solution of a penetrating solute have also been given by Jacobs (1933a, b) and applied to the erythrocyte (Jacobs, 1934). An equation for use when both penetrating and nonpenetrating solutes are present is given by Jacobs (1933~).

D. Osmotu Permeability Coefiicients of Cells Data collected from the literature have been summarized in Table V. Besides the permeability coefficients, there are also shown diffusion COefficients for the rate of water diffusion in the protoplasm. These have been calculated by neglecting the resistance of the cell membrane according to the method discussed in Section V. F. The ratio of surface area to volume is also shown for these cells for which sufficient data are available. It is seen that there is a large variation in the permeability coefficients and that this variation is related to the surface-volume ratio (this relationship is fully discussed in Section V. F).

TABLE V PERMEABILITY COEFFICIENT OF CELL. MEMBRANE AND DIFFUSIONCOEFFICIENT OF WATERIN CYTOPLASM (See Text)

1

Cell Amoeba proteus Amoeba Zebra fish egg Frog egg Xenopus egg Eggs of: Arbacia punctulata Arbacia punctulata Paracentrotus lividus Arbacia punctuluta

Fucus vesiculosis Peritrich Eggs of: Arbacia punctulata Arbacia punctulata Arbacia punctulata

Strongylocentrotus intermedius

2

3

Direction of Technique water flow" Measurement in capillary' Ex tube End Diameter measurement Diameter measurement End End Diameter measurement End Diameter measurement

4

5

6

Permeability Diffusion coefficient coefficient Temperature (p min-1 (cm.Z/sec) ( X 1010) ("C.) atm.-l) 18-25 0.0268 -

-

-

0.017 0.020 0.059 0.072

-

7

Surfacevolume ratio (p2/p3)

0.039

0.009 0.003 0.004

8

1

References Mast and Fowler

(1935) Prescott and Zeuthen

(1953)

Diameter measurement Diffraction Diameter measurement Minimum volume method

End End End Ex

15 22 20-22 21-22

0.05 0.106 0.06-0.16 0.15

0.087

Luck6 et al. (1931) Luck6 et al. (1935) Mettetal (1948) Stewart and Jacobs

Diameter measurement Linear measurement

Ex End

20 14.5-16

0.133-0.187 0.125-0.25

0.086 0.234

Resuhr (1935) Kitching (1938)

Minimum volume method Diffraction (sea water) Diffraction (ethylene glycol solution) Diffraction (diethylene glycol solution) Diameter measurement

Ex End Ex

22-23

0.166 0.14-0.19 0.20

0.079

Ex

-

Ex

End

-

24

22.7

20.2-22.5

-

(1935)

-

0.21

-- 1

0.212 0.197

-

Jacobs (1933a) Luck6 et al. (1951) Luck6 et al. (1951)

} J

Shinozaki (1952)

End - endosmosis ; Ex -exosmosis. This value should probably be doubled since Mast and Fowler assumed the internal osmotic pressure of the Amoeba to be only Sm-osm. instead of l07m-osm. as measured by Lfivtrup and Pigon (1951). 0

b

TABLE V (continued)

1

7 Surfacevolume ratio

8

( X 1010)

(pz/p3)

References

-

0.072

Direction of water flowa End

Temperature

Technique Diameter measurement

("C.) 17-22

Diameter measurement

End

17-22

0.128

0.047

Diameter measurement Diameter measurement Diameter measurement

End End End

17-22 17-22 17-22

0.138 0.206 0.207

0.049 0.033 0.047

Diameter measurement Diameter measurement in penetrating solvent Diameter measurement in penetrating solvent Diameter measurement

End End Ex End Ex End

17-22 22 19 22 22 20

0.409 0.27 0.25 0.45 0.38 0.2

0.035 -

Diameter measurement

End

Ex

24 23

0.25 0.38

-

Arbacia Punctulata

Diffraction

Cumingia tellenoides

Diffraction

Chaetopterus Pergamentaceous Chaetopterus Pergamentaceous

Diffraction

End Ex End Ex End Ex End

22.5 22.5 22.5 22.5 22.5 22.5 21.3-25

0.12 0.17 0.38 0.41 0.44 0.46 0.49

0.078 0.078 0.092 0.092 0.057 0.057 0.060

Diameter measurement

3

6 Diffusion coefficient (cm.Z/sec)

5 Permeability coefficient (p min-1 atm.-1) 0.093

Cell Strongylocentrotus Purpuratus Strongy locentrotus franciscanus Urechis caupo Patiria miniata Dendraster excentricus Pisaster ochraceous Strongy locentrotus intermedius Strongylocentrotus nudus Strongylocentrotus intermedius Strongy locentrotus nudus

2

4

Leitch (1931)

Shinozaki (1951)

LuckC et al. (1939)

LuckC et al. (1939) Shapiro (1941)

P P

C A

1

2

Cell

Technique

TABLE V (continued) 4 5 Permeability coefficient (p min-1 Direction of Temperature atm-1) ("C.) water flowa 0.410 Ex 3

6 Diffusion coefficient (cm.z/sec) ( X 1010)

7 Surfacevolume ratio

8

References

(pZ/p3)

Ex Ex

-

0.470 0.49c

2.8 13 15

0.86 0.90 0.62

Opacimetry

Ex

-

0.490

9.1

0.56

Opacimetry Opacimetry Diameter measurement

Ex Ex End

Room temp.

0.560 0.620 0.7

15 15 -

0.88 0.66 0.55

Opacimetry Opacimetry

End End

20-23 20-23

0.29 1.35

Diameter measurement Diameter measurement Hemolysis (penetrating solute) Hemolysis method Hemolysis method Immersion refractometry

End End End

21-26 21.5

2.2 0.7

Room temp.

2.5

-

End End End

Room temp. Room temp. 38

2.2 3.0

5.0 -

1'75

2.82

6.6

1.37

Dick (1958b)

End and E x

23-26

5.7

-

1.88

Side1 and Solomon (1957)

C3H mouse lymphocyte Wistar rat lymphocyte Murphy-Sturm lymphoma Gardner mouse ascites tumor Lewis rat lymphocyte Lewis rat lymphoma Chick heart fibroblast (plasma clot culture) Rabbit leukocyte Human leukocyte

Opacimetry Opacimetry Opacimetry

Giant axon of Loligo Giant axon of Sepia O x erythrocyte

Ox erythrocyte Human erythrocyte Chick heart fibroblast (fluid plasma culture) Diffraction Human erythrocyte

-

Brues and Masters (1936b) Shapiro and Parpart

-

0.75

(1937)

Hill (1950)

0.02

Jacobs (1931)

1.75

1.88

}

m 4

z

rn

8

c

5 z

0

cl

M F

t:

Jacobs (1932)

Dr. H. G. Hempling of the Department of Physiology, Cornell University Medical College, New York, has corrected an error in the calculation of the published figures and the corrected values are given here by permission of Dr. Hempling. c

M

P

436

D. A. T. DICK

The relation of endosmosis to exosmosis may be seen from the table. Although the data of Luck6 et al. (1939) show that exosmosis is consistently slightly more rapid than endosmosis, the results of Shinozaki (1951) are inconsistent. The values given for the permeability of the erythrocyte are widely different. In view of the possibility of prehemolytic ion movements in the hemolytic method of Jacobs (Jacobs, 1955), the higher value of 5.7 p min.-' atm.-l given by Side1 and Solomon (1957) is to be preferred to those of Jacobs (1932, 1934). The rate of osmotic flow of HZ0 into erythrocytes was studied by Parpart (1935), who found that it was 44% slower than that of HzO. This finding was confirmed by Brooks (1935), but it was explained by the fact that the lower fugacity of Hi0 caused a lower osmotic pressure difference than expected. Luck6 and Harvey (1935), in a similar study on Arbacia eggs, equilibrated the cells first in an isotonic HZO solution before the beginning of the permeability experiment and under these conditions found no difference between the permeabilities of HZO and HzO.

E. Difference between Oslnotic and Diffusion Methods of Measuring Water Permeability It has already been indicated that two difficulties arise in comparing the value of water permeability obtained by measuring the net flow of water through the cell membrane in response to an osmotic gradient with that obtained by measuring the diffusion of labeled water through the membrane. The first difficulty arises from the different mechanisms in the two cases, the one involving net transfer and the other merely exchange of water molecules. The second arises from the impossibility of a strict comparison of the permeability coefficients used and this will be dealt with first. Jacobs (1935) claimed that Fick's law of diffusion is not applicable to substances in high concentration such as the water in biological systems (concentration approximately 55M) and that in consequence it is not possible to compare the permeability of water with that of other substances whose permeability is studied in low concentrations. The modern physico-chemical approach is, however, to regard Fick's law as applicable at all concentrations but to recognize that the value of the diffusion coefficient which is inserted into Fick's equation varies with the concentration. Thus although Jacobs' arguments are not now acceptable, his conclusion that permeability coefficients measured at widely different concentrations are not directly comparable is still valid. If this principle were applied to the comparison of osmotic permeability measurements

437

OSMOTIC PROPERTIES O F LIVING CELLS

with those obtained from the diffusion of isotopic water whose concentration is very low, then it might be expected to introduce into the comparison a further difficulty in addition to the basic difference of mechanism mentioned above In this case, however, since the molecules of normal and isotopic water are physically almost identical, the water concentration involved is the total concentration of normal and isotopic water which is of course similar in osmotic and isotopic experiments. A small difference in the permeability coefficients obtained may be expected analogous to the difference between self-diff usion and diffusion coefficients, but the discrepancy from this source is unlikely to be of practical importance. If the difficulty of comparison of permeability coefficients is ignored and the osmotic water permeability is expressed in terms of concentration difference-i.e., as grams of water passing through one square centimeter of cell membrane in one second with a difference of water concentration of one gram per cubic centimeter (this unit when reduced to its lowest dimensions is cm./sec., or, more conveniently, p/sec.)-then it is found that the osmotic is always greater than the diffusion permeability. This difference was demonstrated for several egg cell membranes and the amoeba by Prescott and Zeuthen (1953) and for the erythrocyte by Sidel and Solomon ( 1957). The available comparative data are summarized TABLE VI COMPARISON OF WATERPERMEABILITY COEFFICIENTS MEASURED BY AND OSMOTIC METHODS

Cell

Diffusion water Osmotic water permeability permeability coefficient coefficient ( d s e c .) (Wsec.1

Xenopus egg Zebra fish egg Amoeba

0.90 0.36 0.23

1.59 0.45 0.37

Human erythrocyte

53

125

THE

DIFFUSION

References

I J

Prescott and Zeuthen (1953)

{

Sidel and Solomon (1957) Paganelli and Solomon (1957)

in Table VI. It seems certain that a difference of this size has some fundamental cause. Koefoed-Johnsen and Ussing (1953) and Ussing and Andersen (1956) have suggested that this big difference is due to bulk flow of water through pores in the cell membrane and that the area and diameter of the pores may be calculated from it. Such calculations have been per-

438

D. A. T. DICK

formed by Paganelli and Solomon ( 1957) and by Nevis (1958). Chinard (1952) has claimed, however, that the conception of osmotic transfer of water through a membrane as a bulk flow is wholly mistaken. O n the other hand, Kuhn (1951), Pappenheinier (1953), and Garby (1955) claim that osmotic and hydrostatic pressures can exert exactly equivalent effects on a membrane, including a bulk flow of solvent through it. Pappenheimer (1953) has further produced evidence that if the radius of the postulated “pores“ in the biological membrane concerned exceeds 20 A. then a large part of any net solvent transfer either under a hydrostatic or under an osmotic pressure gradient consists of a bulk flow. Poiseuille’s law is applicable to such a flow, thus enabling the area and diameter of the pores to be calculated. I t must be noted, however, that none of the evidence produced by Pappenheimer is relevant to membranes having smaller pore radii than 20 A., although Renkin (1954) has produced a modified theory which appears to be applicable down to pore radii of 15 A. Although there is some evidence that Pappenheimer’s theory is applicable to a membrane similar to the capillary membrane (Mauro, 1957) and to frog gastric mucosa (Durbin et ul., 1956), there appears to be no experimental support for its application to the cell membrane. Harris (1956) has put forward an alternative explanation for the difference observed between the osmotic and diffusion permeability coefficients of the cell membrane; it is based on a solution of a similar problem in potassium transfer in nerve axons by Hodgkin and Keynes (1955). If the diffusing water molecules lie in long narrow pores in the cell membrane, then it is to be expected purely on grounds of statistical probability that the net transfer of water molecules, irrespective of label, will greatly exceed the flux of labeled water molecules under similar concentration gradients. Whatever the ultimate explanation may be, it may be concluded that Harris’ theory removes any compulsion to postulate bulk flow through the cell membrane merely on the grounds of the difference between the osmotic and diffusion permeability coefficients.

F.

T h e Rate of Diffusion of Water through the Cell Protoplasm

The almost universal assumption in permeability studies that water transfer under osmotic gradients is significantly resisted only at the cell membrane will now be examined. The diffusion of water both in the internal protoplasm of the cell and in the external medium is considered to take place with such rapidity that the time so occupied is negligible. This assumption has been introduced on grounds of mathematical convenience in order to obtain a numerical expression of the permeability of the cell, but no evidence has been produced to support it. O n the contrary, evidence is available which suggests that it is probably untrue.

OSMOTIC PROPERTIES O F L I V I N G CELLS

439

It has been shown by Kamada (1936) and by Beck and Shapiro ( 1936) that, when an invertebrate egg cell swells in hypotonic solution and the nucleus also swells, the time relations of nuclear swelling are not the same as those of the whole cell; both the onset and the termination of nuclear swelling are delayed. Kamada also noted that on transfer of an egg from tonicity A to a lower tonicity, B, the rate of swelling between the stages corresponding to an intermediate tonicity, C, and the final tonicity, B, was slower than that of an egg transferred to tonicity B after being first equilibrated at tonicity C. These facts point strongly to the conclusion that equilibration within the egg protoplasm is delayed because diffusion of water through the protoplasm requires a significant length of time. A further pointer to the same conclusion is seen by examining the permeability data presented in Table V. An inverse correlation exists between the size of the cell and its permeability coefficient. This may be expressed in the form of a direct correlation between the permeability coefficient and the surface-volume ratio. For spheres this ratio is inversely proportional to the radius, since Surface = 4x1.2

4 3

Volume = -4 and thus

Surface - 3 Volume r

The correlation is best examined by taking logarithms of both permeability coefficient and surface-volume ratio ; the resulting relationship is shown graphically in Fig. 2. The correlation is highly significant ( P < 0.001). (Only two values deviate considerably from the rest, those relating to the giant axons of Loligo and Sepia. It may be shown that the mean of these values deviates significantly ( P < 0.001) from the mean regression line, and thus it may be concluded that some other factor is operating in this case.) It is an obvious interpretation of this correlation that the apparent decrease in the permeability attributed to the cell membrane of the larger cells (which have small surface-volume ratios) is due to the length of time that water takes to diffuse through the proportionately larger volume of the internal protoplasm (see also Dick 1959b). In further investigation of this conclusion, it is useful to examine the consequences of making an opposite assumption regarding the cell, i.e., that the resistance to water entry is uniformly distributed through the protoplasm of the cell, including its membrane. This assumption makes possible an alternative mathematical treatment from which the average

440

D. A. T. DICK

diffusion coefficient of water in the cell protoplasm may be calculated. The equations used are given by Crank (1956) ; for spherical cells

for flat approximately planar cells such as the fibroblast in fluid culture (see Dick, 1959a).

M, = fractional volume increase at time t. Mm = fractional volume increase at equilibrium. a = radius of sphere at mean volume. 1 = thickness of cytoplasm at mean volume. D = diffusion coefficient. t = time of diffusion. ( I n order to simplify the mathematical treatment it is necessary to assume a volume-fixed boundary for diffusion equivalent to the position of the cell membrane when half of the total volume increase in time t has taken place.) The diffusion coefficients of water in the protoplasm calculated by this means are shown in column 6 of Table V. Two points may be noted about them : cm.2/sec. to 5 X 1. The range of values from 1.5 x cm?/sec. is much lower than the comparable diffusion coefficients for protein-water systems in vitro which lie for the most part between and 10-6 cm?/sec. (Edsall, 1953). 2. The diffusion coefficients are inversely correlated with the surfacevolume ratio as illustrated in Fig. 3 ; the correlation is statistically significant ( P < 0.001) . Both facts point to an important contribution by the membrane to the resistance of the cell to water entry. Since both the permeability of the cell membrane and the diffusion coefficient of water in the protoplasm are intrinsic properties of membrane and protoplasm, there is no obvious reason why they should be correlated with the absolute size or surface-volume ratio of the cell. By assuming that water entry into the cell is impeded by a nonuniform resistance, which is most intense in the cell membrane, but is also present in the protoplasm, the correlations which are found may be attributed to error in the calcula-

441

OSMOTIC PROPERTIES OF LIVING CELLS

=

t1.0

I€

c

0

[ a.

.

a

0

8 E 0

-

-1.0

a

m

n

a

0

a

a

0 0

I

I

Loglo (surface-volume ratio)

( @/p3 )

FIG.2. Variation of the apparent permeability coefficient of the cell membrane of isolated cells with the surface-volume ratio. a '8.0

-

@

a

a

a

-d In

2$

--

-85-

a

C

P

.-

5

L

-

0

8

-9.0

.

a

a

c

.-In

a

*

L

.-

a

0

0

m

2

-9.5

a

-

@ a I

-10

I

I

1

-0.5

0

0.5

FIG.3. Variation of the apparent diffusion coefficient of water in the cytoplasm of isolated cells with surface-volume ratio.

442

D. A. T. DICK

tions due to neglecting the role of either protoplasmic or membrane resistance. It is likely that in any given case the true permeability of the cell membrane is higher than the value calculated by neglecting the resistance of the protoplasm, and the true diffusion coefficient of water through the protoplasm is also higher than the value calculated by neglecting the resistance of the cell membrane. By making the further assumption that the permeability coefficient of the cell membrane and the diffusion coefficient of water through the protoplasm are practically uniform in all the cells studied, it would be possible to calculate the values of these quantities. Such a calculation is being attempted (Crank and Dick, 1959). It is of interest that Harris (1957) and Harris and Prankerd (1957) have concluded from a study of the kinetics of permeation that protoplasmic resistance as well as membrane resistance determines the rate of entry of cations into frog muscle and human and dog erythrocytes.

G. Conclusion There are a number of different methods of measuring and expressing the permeability of the cell to water which are based on various assumptions about the cell. The accuracy of these assumptions largely determines the significance of the different permeability values obtained. These methods and the units employed may be summarized as follows. A. Methods assuming instantaneous diffusion within the cell and giving an apparent permeability coefficient of the cell membrane. 1. Osmotic difference method. a. Expressed in osmotic units (p min.-' atm.-l). b. Expressed in concentration units (p sec.-l). 2. Diffusion method using isotopic water (p sec.-l). B. Method assuming uniform distribution of water resistance in both cell membrane and cytoplasm and giving an average diffusion coefficient of water in the protoplasm (cm.2 sec.-l). The simple conversion of osmotic permeability units into concentration permeability units involves theoretical difficulties which may or may not be of practical significance. The diffusion permeability measurement gives lower values than the osmotic one, probably owing to the statistical laws of molecular transfer by random movement in long narrow pores in the cell membrane. The concept of osmotic water movement as a bulk flow is possibly mistaken. Available evidence suggests that the basic assumptions underlying both methods A and B are erroneous. Water movement is probably most strongly impeded at the cell membrane, but the internal protoplasm of the cell also offers significant resistance. Consequently all permeability

OSMOTIC PROPERTIES OF LIVING CELLS

443

coefficients calculated by conventional methods are probably too low. In order to supply more evidence bearing on this conclusion, further studies of the osmotic permeability of isolated cells must include data of the cell dimensions for the calculation of the surface-volume ratio and sufficiently full time-volume data for the calculation of the diffusion coefficient of water in the protoplasm. VI.

ACKNOWLEDGMENTS

Many helpful suggestions and criticisms received from Drs. R. L. Baldwin, R . Barer, J. Crank, E. J. Harris, and A . G. Ogston, F.R.S. are gratefully acknowledged. VII. REFERENCES Adair, G. S. (1929) Proc. Roy. SOC. A M , 16.

Adair, G. S., and Robinson, M. E. (1930) Biochem. J. 24, 1864. Adolph, E. F., and Richmond, J. (1956) A m . J. Physiol. 187, 437. Aebi, H. (1952) Helv. Physiol. Acta 10, 184. Agna, J. W., and Knowles, H. C. (1955) J. Clin. Invest. 34, 919. Appelboom, J. W. (1957) Federatiofi Proc. 16, 278. Babbitt, J. D. (1955) Science 122, 285. Barer, R. (1956) In “Physical Techniques in Biological Research” (G. Oster and A. W. Pollister, eds.), Vol. 111. Academic Press, New York. Barer, R., and Dick, D. A. T. (1957) Exptl. Cell Rcsearch Suppl. 4, 103. Barer, R., and Joseph, S. (1954) Quart. J . Microscop. Sci. 96, 399. Barer, R., and Joseph, S. (1955a) Quart. J. Microscop. Sci. 96, 1. Barer, R., and Joseph, S. (1955b) Quart. J . Microscop. Sci. 96, 423. Bartley, W., Davies, R. E., and Krebs, H. A. (1954) Proc. Roy. SOC.B l a , 187. Beck, L. V., and Shapiro, H. (1936) Proc. SOC.Exptl. Biol. Med. 34, 170. Bernstein, R. E. (1955) I. Clin. Puthol. 8, 225. Bolani, T. R. (1932) “The Donnan Equilibria.” G. Bell and Sons, London. Brodsky, W. A., Appelboom, J. W., Dennis, W. H., Rehm, W. S., Miley, J. F., and Diamond, I. (1956) J. Gen. Physiol. 40, 183. Brooks, S. C. (1935) I. Cellular Comp. Physiol. 7, 163. Brooks, S. C., and Brooks, M. M. (1911) “The Permeability of Living Cells.” Protoplasma-Monographien, Borntrager, Berlin. Brues, A. M., and Masters, C. M. (1936a) A m . J. Cancer 28, 314. Brues, A. M., and Masters, C. M. (1936b) A m . J. Cancer 28, 324. Bull, H. B. (1951) “Physical Biochemistry.” Wiley, New York. Burk, N. F. (1932) J. Biol. Chew. 98, 353. Butler, J. A. V. ( 1946) “Chemical Thermodynamics,” Macmillan, London. Caldwell, P. C. (1956) Intern. Rev. Cytol. 6, 229. Calkins, E., Taylor, I. M., and Hastings, A. B. (1954) A m . J. Physiol., 177, 211. Castle, W. B., and Daland, G. A. (1937) A . M . A . Arch. Internal Med. 60, 949. Chaplin, H., and Mollison, P. L. (1952) Blood 7, 1227. Chinard, F. P. (1952) Ant. J. Physiol. 171, 578. Chinard, F. P., and Ems, T. (1956) Science IN, 472. Christensen, I., and Warburg, E. J. (1929) Actu Med. Scand. 70, 286.

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