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CHEMICAL, CLINICAL, AND IMMUNOLOGICAL STUDIES ON THEPRODUCTS OF HUMAN PLASMA FRACTIONATION.

VI. THE OSMOTIC PRESSURE OF PLASMA ANDOF SERUM ALBUMIN" 2

By G. SCATCHARD, A. C. BATCHELDER, AND A. BROWN(From the Research Laboratories of Physical Chemistry, Massachusetts Institute of Technology,

Cambridge, and the Departmen of Physical Chemistry, Harvard Medical School, Boston)

(Received for publication February 17, 1944)

In order to determine the relative dosage ofplasma and of serum albumin in the treatment ofshock and to determine their efficiencies in in-creasing blood volume and other characteristics,we have measured the osmotic pressure ofhuman plasma and serum, of regenerated solu-tions from dried plasma up to four-fold physio-logical concentrations, of human serum albuminsolutions up to 300 grams per liter in 0.15 molarsodium chloride, and of bovine serum albuminover large ranges of pH, albumin concentration,and salt concentration.3 We have not been ableto detect a difference in the osmotic pressures ofhuman and bovine albumin, so we have used themeasurements on bovine albumin to extend therange of those on human albumin.The first function of plasma or serum albumin

in shock is to increase the blood volume byholding water in the blood stream. Parts ofthe water may be injected with the protein, maybe shifted from the extravascular fluids, or maybe drawn from the intestine. This water mustbe held in spite of the excess pressure in thecapillary bed. Most of this retention of wateris not caused by any attraction between theprotein and the water, but arises from the fact

1 This work has been carried out under contract, recom-mended by the Committee on Medical Research, betweenthe Office of Scientific Research and Development andHarvard University.2This paper is Number 16 in the series "Studies on

Plasma Proteins" from the Harvard Medical School,Boston, Massachusetts, on products developed by theDepartment of Physical Chemistry from blood collectedby the American Red Cross.

' All measurements were made with collodion mem-branes, which are impermeable to plasma proteins. Fortechnical reasons, the measurements were made at 250 C.,where the pressure is about 4 per cent less than at 37° C.All concentrations were calculated using the nitrogen fac-tor 6.25 for both albumin and plasma.

that the chemical potential of water is decreasedby the presence of dissolved molecules which arenot water.4A convenient way of measuring the change in

the potential of water produced by the additionof a solute is to measure the decrease in pressurenecessary to maintain equilibrium through amembrane permeable to the water but not to thesolute, and this pressure is called the osmoticpressure of the solution. If the membrane ispermeable to any of the solutes, the pressure issometimes called the colloid osmotic pressure or

"The difference in the potential of any substance attwo different places is the least work necessary to bringunit quantity of that substance from the first place to thesecond if the temperature and total volume of the systemare constant. The substance will shift spontaneously fromthe place of higher potential to that of lower potentialif a path is available, and at equilibrium its -potentialmust be the same throughout the system. The rapiditywith which equilibrium is attained depends upon the na-ture of the available paths as well as upon the differencein potential, but the position of equilibrium depends onlyupon the equality of potential.There may be a difference in gravitational potential due

to different heights in a gravitational field, and this poten-tial is proportional to the difference in height and to theweight of unit quantity. There may be a difference inchemical potential due to different pressures, and thispotential is proportional to the pressure difference and tothe volume of unit quantity. There may also be a differ-ence in chemical potential due to different chemical com-positions. We cannot generalize on the value of thispotential, but in very dilute solutions, the difference inchemical potential of each substance is proportional to thedifference in the logarithm of its mole fraction. Then thedifference in the potential of each solute is proportional tothe difference in the logarithm of its concentration, andthe difference in potential of the solvent is proportionalto the difference in the sum of the concentrations of thesolutes, expressed as moles of solute per unit quantity ofsolvent. These are the three potentials of substanceswhich are physiologically important.

458

OSMOTIC PRESSURE OF PLASMA AND OF SERUM ALBUMIN

the oncotic pressure. Since this is the only typeof membrane across which the pressure is impor-tant, we will use the simpler term.

Van't Hoff pressure

About two-thirds of the osmotic pressure atphysiological concentrations is explained by thesimple theory of Van't Hoff, which says thatthe osmotic pressure is equal to the pressuredifference which would be developed if the sol-vent were removed and the solutes were gases.If the non-diffusible solute is a non-electrolyte,the osmotic pressure should be proportional toits concentration, and the pressure-concentra-tion ratio should be the same for all substancesif the concentration is expressed as moles perunit volume. It is obvious that osmotic pres-sure per unit mass, however, decreases as thesize of the molecule increases. If the concentra-tion is expressed as mass per unit volume, thepressure-concentration ratio is inversely pro-portional to the molecular weight, and onemeasurement of the osmotic pressure and of thecorresponding mass concentration may be usedto determine the molecular weight. The Van'tHoff case is illustrated by curve E in Figures 1and 2. In Figure 1, the osmotic pressure is

Mcss Concentration, C,(gn/AOOc)FIG. 1

C

0

0

I)

(1)

0C.)

co

loo 200Osmotic Pressure, P(mm. Hg)

FIG. 2

plotted against the concentration, and Van'tHoff's theory leads to a straight line whose slopeis inversely proportional to the molecular weight.In Figure 2, the pressure-concentration ratio isplotted against the pressure, and this curve Eis a horizontal line whose ordinate is the slope ofE in Figure 1. The curves A in these figures arethe measured values for serum albumin at pH7.4, and the curves B are for albumin at pH 5.4,both in 0.15 M sodium chloride. At pH 5.4,the albumin is iso-ionic; that is, its average netcharge is zero.

Donnan pressure

The plasma proteins are not neutral non-elec-trolytes, and their ionic charges have an im-portant effect on the osmotic pressure. Theextension of Van't Hoff's theory to this casewas carried out by Donnan. We will limitourselves to the special case of the sodium saltof a non-diffusible protein anion and sodiumchloride, which is a rough approximation ofplasma. The solution must be electrically neu-tral. So, if there is no sodium chloride present,the pressure-concentration ratio corresponds to

459

G. SCATCHARD, A. C. BATCHELDER, AND A. BROWN

the protein ion plus all the sodium ions associatedwith it.

If there is sodium chloride present, its poten-tial must also be the same on the two sides.Since there is more sodium, there will be lesschlorine on the side with the sodium proteinate.So the pressure-concentration ratio is smaller.It corresponds to the protein alone when theratio of protein to chloride is very small, anddepends only upon the protein-chloride ratio.The molecular weight cannot be determinedfrom a single osmotic pressure measurement.However, if a series of measurements is madewith varying protein concentration but constantsalt concentration, the pressure-concentrationratio can be extrapolated to zero protein con-centration, and the molecular weight can bedetermined from this extrapolated value. AtpH 5.4, the Donnan curve is the same as theVan't Hoff curve E. The Donnan curve forpH 7.4, where the measured curve is A, liesclose to the curve B. It is obvious that theDonnan effect increases rapidly with the netcharge of the protein ion. It is, in fact, pro-portional to the square of the net charge.'

5 The statement in mathematical equations is more pre-cise and in some ways simpler. We will let C, C+ and C_be the concentrations in moles per unit volume of protein,sodium ion, and chloride ion within the membrane, andC'+ and C'_ the concentrations of sodium and chlorideions outside: c will be the concentration of the protein ingrams per unit volume, M its molecular weight, which isc/C, z its valence (a negative number for an anion), T willbe the absolute temperature, and R a universal constant.Van't Hoff's law is

P = R[C + C+ + C_- C'+- C'_]

P RT +C++ c-- C/+-C'_]The law of electroneutrality requires that

zC-C_ + C+ = 0and

C'+-C'_ = O

The law of equilibrium, or equality of the potential ofsodium chloride, requires that

C'+C'_ = C+C_

Combination of the last three equations yields

C'_= C_ 1 -C.

Pressure of real solutions

The Van't Hoff theory assumes that each indi-vidual water molecule in a protein solution be-haves like a water molecule in pure water andthat the decrease in potential of the water which

Combination with Van't Hoff's law yields

P _ RT 2C_-zC-2CC _

= M[+ (2 C_]

M [2- + 2-(l- lC

It is clear from the last equation that the expression insquare brackets depends only on zC/C_ for a given valueof z, but it is not clear how it approaches unity as zC/C_approaches zero or even that it does so. To answer thesequestions, we expand the radical in a Taylor's series to give

P zC zC zC2C91 ~C =1~ 2C 8.

c M [ 4C-RT RT(z/M)'c RT M(z/M)'PM 4C_ M 4C_

For a neutral molecule, z is equal to zero, and P/c = RT/Mat all concentrations. For an ion z2C/4C_ is zero onlywhen C is zero, and in dilute solutions P/c increases as alinear function of c when C_ is constant.For a real solution we may also write

P RT- = M~ + bc + dc2 + * -

or

P RT + BP + DP' + ...c M

in which b and d or B and D are constants. The latterform is more useful for our purposes because

1 RTc MP-

In many cases, D is so small that the term DP may beneglected. Then tIX volume of solution per gram ofprotein is equal to the ideal term which is iniversely pro-portional to the pressure plus a term which is independentof the pressure.B will be composed in general of the Donnan term which

is M(z/M)2P/4C_ plus a term arising from the differencebetween the force between two protein molecules and thatbetween one of the molecules and the water displaced bythe other.

460

OSMOTIC PRESSURE OF PLASMA AND OF SERUM ALBUMIN

accounts for the osmotic pressure is solely astatistical effect, due to the fact that a certainfraction of the molecules are not water. Thisis equivalent to assuming that each individualprotein molecule in a concentrated solution be-haves like a protein molecule in an extremelydilute solution, or that the activity of the proteinis proportional to its concentration, and thislatter assumption is easier to consider. TheDonnan extension considers the macroscopic ef-fect of the charge on the protein ion, but stillassumes that the activity of each species is pro-portional to its concentration.

Real protein solutions are not this simple.6For iso-ionic albumin, the osmotic pressure ismuch larger than that calculated by the Van'tHoff theory. At other values of pH, however,the increase over the iso-ionic value is much lessthan predicted by Donnan, so that at pH 7.4, themeasured value does not differ greatly from thatcalculated by his theory, and at still highervalues of the pH, the measured pressures are lessthan those calculated. Real solutions do re-semble the Donnan solutions in that the molecu-lar weight can be determined by extrapolatingthe pressure-concentration ratio to zero concen-tration or pressure.

Figure 1 shows the curves for osmotic pressureversus mass concentration for serum albumin atpH 7.4 (A) and pH 5.4 (B), for human plasma atpH 7.4 (C), and for an ideal Van't Hoff solutewhose molecular weight is 69,000, which is thesame as that of albumin (E). The curves all

6 The ionic charges on proteins cause deviations fromrandom distribution on the microscopic scale as well asthose considered by Donnan, and differences in potentialproportional to the square of the net ionic charge. Evenin iso-ionic albumin, where the average of the charge iszero, the average of the square of the charge is 6, andat pH 7.4 it is 300. In either solution, the total charge isalmost 200, and it is not evenly distributed through themolecule. The resultant electrical field leads to attractionbetween a protein molecule and a simple ion, or between2 protein molecules, which is large compared to the effectof the net charges. Moreover, the rotein molecule whichbears these charges behaves more like an equal volume ofa normal organic liquid than an equal volume of water.This molecular framework tends to repel the electricalfields but to attract another framework. The resultant ofall these forces leads to effects upon the potential of thewater and the resultant osmotic pressure which vary greatlywith the ionic charge.

start at zero concentration and pressure, andcurves A, B, and E, all have the same initialslope. The value for the molecular weight ofserum albumin calculated from these osmoticpressure measurements, 69,000, is in good agree-ment with that obtained from sedimentationand diffusion measurements reported in the firstpaper of this series (1). The plasma curve (C)has a smaller initial slope which corresponds to alarger molecular weight, 93,000. All the experi-mental curves become steeper at higher concen-trations. The difference between A and C isproportional to the concentration.

In Figure 2 is shown the pressure-concentra-tion ratio, P/c, versus the pressure.7 The idealVan't Hoff curve, E, is here a horizontal linewhose ordinate is the slope of E in Figure 1.A and B intercept E at zero pressure, correspond-ing to the same initial slopes in Figure 1, butthey deviate sharply at higher pressures. Theplasma curve, C, has a lower intercept, corre-sponding to the larger average molecular weightof plasma proteins, and the difference betweenA and C is here independent of the pressure.If 60 grams per cent of the plasma protein isalbumin (1), curve C as drawn would give anaverage molecular weight of 194,000 for theremaining 40 per cent. However, our measure-ments do not preclude drawing the intercept at2.1 rather than 2.0, which would correspond to anaverage molecular weight of 88,000, and amolecular weight of 150,000 for the 40 grams percent which are not albumin. The probable valuefor the average molecular weight of plasmaglobulins is 170,000.

Osmotic effiiencyWe are particularly interested in the volume

of solution per gram of protein, 1/c, at a given7 The.experimental points are shown in Figure 2, whose

scale is larger than that of Figure 1. The measurementson plasma are indicated by crosses, those on human al-bumin by open circles, and those on bovine albumin byfilled circles. The measurements at pH 5.4 have a per-pendicular line through the circles.The measurements on albumin at pH 5.4 are carried to

dilute enough solutions so that there is little uncertaintyabout the extrapolation to zero concentration and theresultant molecular weight. The measurements on plasmahave not been carried to such dilution, so the curve hasbeen drawn parallel to that for albumin.

461

G. SCATCHARD, A. C. BATCHELDER, AND A. BROWN

0

I

I.

_~~~~~~_-

I

40 soOsmotic Pressure, P. (m Hg)

FIG. 3

120

3

40

10 (Au)

:9

S 251 _-

0

X--U10'

.I0%

aIt

20

osmotic pressure. This is shown in Figure 3 forthe same measurements.8 As in the previous

figures, curves A and B refer to albumin at pH7.4 and 5.4, respectively, and curve C to plasmaat pH 7.4. The curve for an ideal Van't Hoffsolute corresponding to E of Figures and 2 isomitted. It would lie about 5 cc. below curve B,or about 7 cc. below A at all values of the pres-

sure, as these three curves are nearly parallel.The difference between A and C is almost in-versely proportional to the pressure.

Figure 4 shows the volume of solution per

gram of protein at 25 mm. pressure as a func-tion of the pH. The curve E represents as

before the ideal Van't Hoff solute, with a molecu-lar weight of 69,000, and the curve D representsan ideal Donnan solute with the same molecularweight and the net charge of albumin.9 Al-though the difference between these curves andthe experimental values is not very great at thephysiological pH, it is evident that this is largelya coincidence, for the experimental and idealcurves cross at large angles.

Figure 3 is constructed from the same data as Figures 1

and 2 except that the measurements at very high and very

low pressures are both omitted to permit a larger scale.The individual points are again omitted.

The titration curve for human albumin lies somewhat tothe left of the curve for bovine albumin, used in estimatingnet charge for these calculations.

5.0 60 7.0 8.0

pH

FIG. 4

0*

58N.)

6. eIC

3i

V)

The experimental values of the volume per

gram of protein, 1/c, between pH 6 and 8 maybe expressed by the straight line

1/c = 11.1 + 0.9 pH

Since the difference between 1/c and the Van'tHoff value RT/MP is nearly independent of thepressure, a good approximation for 1/c at any

small pressure is

1/c = 268/P + 0.4 + 0.9 pH

This corresponds to

P/c=268+(0.4+0.9 pH)P= 268

1+(0.4+0.9 pH)c

COMMENT

The chief uncertainty in determining theefficiency of albumin in increasing blood volumelies in the uncertainty of the osmotic pressure ofnormal plasma, which goes back to the uncer-

tainty as to the normal concentration of plasmaproteins. The composition of the proteins ap-

pears to be very constant in physiological plasma(1),1o but the total concentrations quoted by

"IWies and Peters (2) have studied the effect on theosmotic pressure of varying composition of the protein inpathological plasma. Their results cannot be comparedwith ours directly because they determine proteins byHowe's precipitation method and our compositions are de-termined by electrophoresis. If we assume with them that

8 30

20

Ia(I1)-6 tO

4

.I /I /

/00 * cP *. .7

S -

- ' S --

*1'* -E.

I I I

462

15

OSMOTIC PRESSURE OF PLASMA AND OF SERUM ALBUMIN

various observers show variations. Gutmanand his coworkers (3) quote protein concentra-tions in serum for normal adults ranging from6.5 to 7.9 and averaging 7.2 grams per cent.Perera and Berliner (4) quote concentrationsfrom 6.2 to 7.3, averaging 6.8 for normal ambu-latory adults, and from 5.4 to 7.0, averaging 6.0for the same individuals recumbent. The re-

sults for plasma should be 0.4 per cent higherthan for serum. So we must consider the range

from 6 to 8 grams per cent. Since the recipientof a blood substitute will probably be resting,the lower part of the range is probably more im-portant than the higher.

If c is 6 grams per cent, 1/c is 16.7 cc. per

gram. From curve C, Figure 3, we find thecorresponding pressure to be 20 mm., and fromcurve A we find that at 20 mm. pressure, eachgram of albumin retains 20 cc. of solution. If c

is 8 grams per cent, l/c is 12.5 cc. per gram.

The corresponding pressure is 32 mm., and atthat pressure, each gram of albumin retains 15cc. of solution. If the pressure is 25 mm., eachgram of albumin retains 18 cc. of solution, andeach gram of average plasma protein retains15 cc., or the concentration of plasma proteinis 6.67 grams per cent. This is the value whichwe have taken as the norm, with the realizationthat it may vary more than 10 per cent innormal individuals. This corresponds closelyto the average of 17.4 cc. per gram of albumin,given for the increase in blood volume per gram

of added albumin by Heyl, Gibson, and Jane-way (5, 6). This average corresponds to 6.9per cent protein. Their extreme values of 13.2and 24 cc. per gram correspond to 5.1 and 8.8per cent protein. Probably part of this varia-tion corresponds to the inevitable errors ofmeasurements of total blood volumes.

If the increase of blood volume on the addi-

the pressure is a linear function of the ratio of globulin tototal protein, g, at all small pressures and pH's between 6and 8, we may determine the effect of globulin from ourmeasurements on normal plasma, which gives

P/c = 268(1- 0.42 g)1+ (0.4+0.9pH)c

For normal plasma this equation gives a limiting value atzero concentration which is too large, but it should give a

fair representation of the results in undiluted plasma or

serum.

tion of protein is to equal the volume of solutionretained by the protein, the osmotic pressure ofthe plasma must be the same after the additionof the protein as before. It is probable thatthis condition is nearly fulfilled in hemorrhagicshock and also in traumatic shock. Any errorin this assumption will be in the direction ofincreasing the pressure during the infusion andthus giving a smaller increase in blood volume.It is possible, however, that there are cases inwhich the assumption is so greatly in error thatit is more accurate to assume that the bloodvolume is constant, and to determine the in-crease in osmotic pressure per gram of proteinat constant plasma volume. Thus, an increasein osmotic pressure per gram of protein at con-stant volume becomes of interest. This will,of course, depend upon the total plasma volume,of which we have no measure here. Our meas-urements do show the change in pressure forunit change in concentration, and most clearlyin Figure 1. This change, dP/dc, for albuminis 2.7 at zero concentration, 3.9 when c is 2, 5.1when c is 4, 6.3 when c is 6, and 8.4 when c is 8grams per cent. The values of dP/dc for aver-age plasma protein at the same concentrationsare 2.0, 2.8, 3.8, 4.0, and 6.4. For albumin orfor plasma, the change in pressure with changingconcentration increases rapidly as the concen-tration increases.The comparison of the relative efficiencies of

serum albumin and of plasma is more certain.Within the accuracy with which we read ourcurves, the relative efficiencies are independentof the pressure. There is a slight increase inthe relative efficiency of albumin as the pressuredecreases, but we may take, for all physiologicalpressures, our result that each gram of albuminretains as much fluid as 1.2 grams of averageplasma protein. The pooling of plasma fromseveral donors and the relative constancy ofconditions of collecting blood reduce the fluctua-tions in the concentration of plasma. At pres-ent, the Red Cross pooled citrated plasma con-tains 6 grams per cent of protein (1). So eachgram of albumin corresponds to 20 cc. of citratedplasma and 25 grams of albumin corresponds to500 cc. of citrated plasma. This relationship isthe basis for the present containers used by ourarmed forces,-500 cc. of citrated plasma for the

463

G. SCATCHARD, A. C. BATCHELDER, AND A. BROWN

dried plasma container or 100 cc. of 25 per centalbumin.

SUMMARY

The osmotic pressures of plasma and of serumalbumin at 250 have been measured over rangesof concentration and pH, much wider than thephysiological ranges. The extrapolation of theosmotic pressure-concentration ratios to zeroconcentration yields a molecular weight of69,000 for albumin. A similar extrapolation forplasma yields an average molecular weight ofabout 90,000. This corresponds to an averageweight of about 170,000 for the 40 per cent ofthe protein which is not albumin. The osmoticpressure-concentration ratios increase rapidlywith increasing concentration. At pH 7.4, thisincrease corresponds to the Donnan effect of theionic charges, but measurements over a pH rangeshow this to be a coincidence.The volume of fluid held in the blood stream

by each gram of albumin should be about 18 cc.but should vary with the protein concentrationof the plasma. Each gram of albumin is equiva-lent to 1.2 grams of plasma protein or 20 cc. ofthe current Red Cross citrated, pooled plasma.

BIBLIOGRAPHY

1. Cohn, E. J., OncIey, J. L., Strong, L. E., Hughes, W.L., Jr., and Armstrong, S. H., Jr., Chemical, clinical,and immunological studies on the products of humanplasma fractionation. I. The characterization ofthe protein fractions of human plasma. J. Clin.Invest., 1944, 23, 417.

2. Wies, C. H., and Peters, J. P., Osmotic pressure of pro-teins in whole serum. J. Clin. Invest., 1937, 16, 93.

3. Gutman, A. B., Moore, D. H., Gutman, E. B., Mc-Clellan, V., and Kabat, E. A., Fractionation ofserum proteins in hyperproteinemia, with specialreference to multiple myeloma. J. Clin. Invest.,1941, 20, 765.

4. Perera, G. A., and Berliner, R. W., The relation ofpostural hemodilution to paroxysmal dyspnea.J. Clin. Invest., 1943, 22, 25.

5. Heyl, J. T., Gibson, J. G., 2nd, and Janeway, C. A.,Studies on the plasma proteins. V. The effect ofconcentrated solutions of human and bovine serumalbumin on blood volume after acute blood loss inman. J. Clin. Invest., 1943, 22, 763.

6. Janeway, C. A., Gibson, S. T., Woodruff, L. M., Heyl,J. T., Bailey, 0. T., and Newhouser, L. R., Chem-ical, clinical, and immunological studies on theproducts of human plasma fractionation. VII.Concentrated human serum albumin. J. Clin.Invest., 1944, 23, 465.

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