A FORMULAAND NOMOGRAMFOR THE ESTIMATION OFTHE OSMOTIC PRESSUREOF COLLOIDS FROM THE

ALBUMINANDTOTAL PROTEIN CONCENTRATIONSOF HUMANBLOODSERA

By HERBERTS. WELLS, JOHN B. YOUMANS,AND DAVID G. MILLER, JR.

(From the Departments of Physiology and Medicine, Vanderbilt University Medical School,Nashville)

(Received for publication July 31, 1933)

In connection with investigations to be reported subsequently theosmotic pressure of colloids and the albumin and total protein concen-trations of 128 samples of human blood serum were determined. Fromthese data, which cover a wide range of values, an empirical formulahas been evolved which, it is believed, will enable the osmotic pressureto be more accurately estimated from the protein analyses of humansera than is the case with formulae now employed for this purpose (1, 2).A nomogram has been constructed to facilitate such computations. Thesimple, definitely linear relation found to exist between the albuminconcentration and the specific osmotic pressure would indicate that thealbumin: globulin ratio is not as reliable an index of the osmotic prop-erties of serum as is at present often assumed.

It may justly be contended-at least on theoretical grounds-thatthe accuracy of most of the colloid osmotic pressure measurementspreviously carried out on human blood sera is open to serious question,either for the reason that the authors have failed to recognize the funda-mental criteria of equilibrium upon which any good physical chemistwould insist (3) or because of the failure to describe the methods em-ployed in sufficient detail to enable one to judge as to whether suchcriteria have actually been fulfilled.

In a recent communication (4) it was emphasized that, for theaccurate determination of the osmotic pressure of colloids, it is essentialto observe certain rigid criteria of an osmotic equilibrium. Procedureswere described by which these criteria of accuracy might be fulfilled,and a detailed description of the apparatus and methods has recentlybeen published (5). By a strict adherence to such standards it hasbeen possible, during the present investigation, to obtain from duplicatedeterminations on each serum pressure values which, in 95 per cent ofthe cases, do not differ by more than 12 mm. of water. No pressurereading has been considered to be accurate unless it has been possibleto maintain the volume of the serum at a constant value, at this pressure

1103

COLLOID OSMOTIC PRESSURE

and at constant temperature, for a period of at least two hours-a periodof observation sufficient, according to our tests, to insure the attainmentof a definite equilibrium when the membranes are of the standard selectedpermeability. Consequently, it is believed that our figures actually referto equilibrium pressures. The fact that the standard per cent deviationof the calculated from the observed values of the osmotic pressure isonly i4 5 per cent leads us to believe, furthermore, that for routineclinical purposes, the method of calculation, which avoids the manydifficulties inherent in the usual methods of direct determination, willprovide a sufficiently reliable index of the water-retaining power of theserum. Such a conclusion is, however, to be considered as subject to thesame qualifications as apply to all cases of indirect measurements, as forexample, the estimation of the basal metabolic rate from the oxygenconsumption. The possibilities of error in the use of the calculatedfigures will be discussed in later paragraphs.

METHODS

Protein analyses were carried out in duplicate by the macro-Kjeldahlmethod on samples drawn under oil without stasis. Globulin was sepa-rated by precipitation at 380 C. with 22.5 per cent sodium sulphateaccording to the method of Howe (6). Nonprotein nitrogen was esti-mated by the micro-Kjeldahl-Nesslerization method, on oxalated plasma.The usual factor, 6.25, was used to convert protein nitrogen values toprotein concentrations.

The osmotic pressure determinations were carried out in a constanttemperature room at 20° to 220 C. Duplicate determinations were donein all but four instances. The collodion membranes used were stand-ardized to a specific permeability (4) range of 20 X 10-8 to 40 X 10-8.Equilibrium was usually attained in 1 to 3 hours, but a somewhat longertime was occasionally required. The details of the method and thecriteria of osmotic equilibrium have been described elsewhere (4, 5). Oc-casional lapses of the vigilant attention to detail which is necessary forsuccess in carrying out such determinations invariably led to gross errorswhich necessitated discarding the results. On the other hand, all datahave been included for which definite evidence of gross errors of technicwas lacking, regardless of the degree of variation between the duplicatedeterminations.

DATA

The blood samples were taken from 53 individuals, from 1 to 10determinations being carried out on each person, often over periods ofseveral months. Of these 53 persons 14 were laboratory workers, stu-dents, and other volunteers, all apparently in good health; 20 presented,at one time or another, and to various degrees, evidences of nutritionaledema; 12 had heart disease; and 1 each suffered from the following

1104

H. S. WELLS, J. B. YOUMANSAND D. G. MILLER, JR.

pathological conditions: multiple xanthomatosis, chronic diarrhea, aplas-tic anemia, pellagra with chronic colitis, Banti's disease, nephrosis,syphilitic cirrhosis of the liver.

The data are presented in Table I, arranged in order of increasingalbumin concentrations. The 10 lowest albumin, total protein andosmotic pressure figures were obtained from a single individual, over aperiod of 5 months during the gradual decline associated with an ad-vanced nephrosis. The 13 highest values were obtained from blood whichhad been concentrated by causing the subjects to stand in the erectposture for one hour or longer, in connection with experiments whichare to be described elsewhere. The extreme range of the values en-countered may be indicated by the following figures: albumin, per cent,0.89 to 6.62; globulin, 1.66 to 6.48; total protein, 2.99 to 9.64; albumin:globulin ratio, 0.42 to 2.80; osmotic pressure of colloids, 76 to 583 mm.water; and specific osmotic pressure, 25.4 to 59.2 mm. water. Thefigures for the albumin concentrations probably furnish the best indexas to the distribution of the values. There were 10 albumin values below2.5; 13 between 2.5 and 3.5; 50 between 3.51 and 4.5; 48 between 4.51and 5.5; and 7 above 5.5.

ANALYSIS OF THE DATA

The specific osmotic pressure, S, was calculated for each case bydividing the value of the total osmotic pressure, P, measured in mm. ofwater, by the concentration of total proteins, C, measured in grams per100 cc. Values for the specific pressures were plotted on a three-dimensional graph against the corresponding values of the albuminand of the globulin concentrations. This was done by driving wires,sharpened at one end, into the drawing board on which the axes ofalbumin and globulin concentrations (A and G) were laid off on cross-section paper. Each value of S was thus represented by the height ofa wire and the point through which the wire was driven represented thecorresponding A and G values. The surface produced by the tips ofthe wires was seen to be fairly regular, but contrary to our earlier expec-tations it did not show any obvious relation between the specific osmoticpressure and the globulin concentration or A/G ratio. The formula ofGovaerts (1) implies the assumption that the specific pressure is deter-mined primarily by the A/G ratio. According to his concept the valueof S will fall with increasing values of G for sera having a constant valueof A. Govaerts also assumes that the total protein concentration, C,is without effect on the value of S in the case of sera which have the sameA/G ratio. In our series there is an obvious and regular relation betweenC and S and it was apparent, from inspection of the wire model, that theincreasing values of S, as C increased, were due entirely to the increasein A. The relation between the specific pressure and the albumin was

1105

COLLOID OSMOTIC PRESSURE

TABLE I

Data arranged in ascending order of albumin concentrations

Varia-Specific Osmotic tion of Maxi- Unex-

Case Specific pressure, Total Osmotic pressure calcu- mumex- plainednumber Albumin pressure, calcu- protein pressure, calcu- lated perimen- vari-observed lated observed lated from tal error ations

observedpressure

m m m mm.

3737373737373737373735262036494747474949474932493149314731234938323252233342482238231010

gramsPer

100 cc.0.891.251.461.751.931.931.942.282.412.442.572.672.802.873.113.193.193.203.303.303.343.463.493.523.603.613.623.673.673.703.703.733.733.803.823.833.943.984.014.034.044.044.054.10

mm.H20

25.430.929.330.131.230.431.338.634.632.234.139.543.641.540.939.741.039.043.439.640.839.842.747.643.445.743.736.337.541.342.144.646.342.643.046.443.345.944.945.043.845.747.649.1

mm.H20

26.728.830.031.732.832.832.834.935.635.836.637.237.938.339.740.240.240.340.940.941.141.842.042.242.642.742.843.143.143.243.243.443.443.843.944.044.644.945.145.245.245.245.345.6

gramsper

100 cc.

2.993.103.353.563.593.713.894.094.164.284.365.925.929.354.885.745.685.844.985.105.645.187.615.156.386.106.586.716.336.275.257.158.097.446.456.666.506.996.826.716.987.126.496.38

H20

769698

107112113122158144138149234258388199228233228216202230206325245277279288244237259221319375317277309281321306302306325309313

mm.H20

8089

101113118122128143148153159220224358194231228235204208232217320217272260281289273271227310351326283293290314307303316322294291

mm.H20

+ 4- 7+ 3+ 6+ 6+ 9+ 6-15+ 4+15+10-14-34-30- 5+ 3- 5+ 7-12+ 6+ 2+11- 5-28- 5-19- 7+45+36+12+ 6- 9-24+ 9+ 6-16+ 9- 7+ 1+ 1+10- 3-15-22

mm.H20

±t214-224-22±-234±234±234-234±24±t244±24±t25±t27±i27±t31±t26±t27±t27--27±-26±426±t27±427±t30--27±-28±-28±-28-±29±t28±t28--27±-29±-31±t30±t29±429-±29±-29-±29--29±-30±-30±-29--29

mm.H20

- 7

- 1

+16+ 8

1106

H. S. WELLS, J. B. YOUMANSAND D. G. MILLER, JR.

TABLE I (continued)

Varia-CeSpecific Specific Osmotic tion of Maxi- Unex-

Case Specific pressure, Total Osmotic pressure, calcu- mumex- plainednumber Albumin pressure, calcu- protein pressure, calcu- lated penmen- vari-observed lated observed lated from tal error ationsobserved

pressure

_~~~~m mm mm mm.

712163323

4311717172824

350

329

625

4179

1682

30154443

929

82429

517

35121

830303039

815

41

gramsper

100 cc.

4.114.134.144.164.194.224.224.234.254.274.274.304.334.334.364.374.384.394.394.404.414.424.424.434.444.464.464.484.494.504.504.524.524.524.534.544.554.574.594.594.604.624.624.624.634.64

mm.H20

44.247.144.144.344.246.449.245.849.447.748.649.147.245.548.748.045.445.048.047.747.346.447.242.847.049.848.451.248.945.751.046.344.949.847.248.352.849.246.849.648.844.848.648.251.251.5

mm.Hs045.645.845.845.946.146.346.346.446.546.646.646.846.946.947.147.247.247.347.347.447.447.547.547.547.647.747.747.847.948.048.048.148.148.148.148.248.248.448.548.548.548.748.748.748.748.8

gramsper

100 cc.

7.956.337.016.776.927.067.547.086.826.675.996.496.658.186.477.067.117.257.116.647.066.706.806.487.106.266.926.646.997.107.126.787.076.337.446.636.356.696.726.867.277.126.856.916.536.87

mm.H20

352298309300306328371324337318291319314372315339323326341316334311321277334312335340342325363314317315351320335329314340355319333333334354

H20

363290321311319327349328317311279304312384305333336343336314335318323308338299330318335340341326340304358319306324326333353346333336318335

mm.H20

+11- 8+12+11+13- 1-22+ 4-20- 7-12-15-2+12-10- 6+13+17- 5-2+ 1+ 7+ 2+31+ 4-13- 5-22- 7+15-22+12+23-11+ 7- 1-29- 5+12- 7-2+27

0+ 3-16-19

MM.

H204-314-294-304-294-304-30±t304-304±30--294294294±294-31--29±-30-30-1-30±-30±t30±-30±-30±-30±-30±-29±-29±t29-30-±30±t30±-30-±30±t30±-30±t29-±31±t30±t29±30±30±t30±t31±30±30±30430430

mm.H2

+ 2

1107

COLLOID OSMOTIC PRESSURE

TABLE I (continued)

Varia-Specific Osmotic tion of Maxi- Unex-

Case Specific pressure, Total Osmotic pressure calcu- mumex- plainednumber Albumin pressure, calcu- protein pressure, calcu- lated penmen- vari-

observed lated observed lated from tal error ationsobservedpressure

mm mm mm mm mm.

624182434461124131953271215142424

8451240

12129

43419133

531724192113531534

gramsper

100 cc.

4.684.684.694.724.724.774.774.784.784.784.794.814.844.904.914.914.924.925.015.025.035.065.165.185.225.325.365.445.455.485.495.555.605.935.946.086.146.62

mm.H20

47.651.650.548.950.550.350.053.350.449.151.951.451.449.348.549.249.155.751.249.051.652.353.053.649.854.057.952.255.254.254.652.154.856.249.657.456.959.2

MM.

H20

49.049.049.149.249.249.549.549.649.649.649.749.850.050.350.450.450.450.451.051.051.151.351.852.052.252.853.053.553.653.753.854.154.456.456.457.357.660.5

gramsper

100 cc.

6.747.027.927.126.877.517.136.646.917.037.147.027.506.787.586.957.077.956.867.707.036.867.558.267.727.967.728.077.927.828.548.118.308.668.709.058.689.64

mm.H20

321362400348347378357354348345371361385334368342348443351377363359400443384430447421437424467423455487432519494571

mm.HsO

330344389351338372353329343349355349375341382350357401350393359352391429403420409432424420459439452488491518500583

mm.H20

+ 9-18-11+ 3- 9- 6- 4-25- 5+ 4-16-12-10+ 7+14+ 8+ 9-42- 1+16- 4- 7- 9-14+19-10-38+11-13- 4- 8+16- 3+ 1+59- 1+ 6+12

mm.H20

430±430±314±314±304±31±31±30430±31+314±31431±30--31±t31±31±32-±31±32±31±31±32±32±t32±32432±-33±32±32±33±33±33±34±34±t34±-34±36

mm.H20

-10

+25

seen to be quite definitely linear, this fact being indicated clearly by thegeneral appearance of the surface produced by the tips of the wires,which lay, in general, in a plane which was parallel to the G-axis andinclined to the A-axis. These characteristics of the relationships arebrought out in Figure 1, which shows the total lack of correlation betweenS and G and in Figure 2, which shows the high degree of correlation

1108

H. S. WELLS, J. B. YOUMANSAND D. G. MILLER, JR.

TABLE II

Tabulation of errors of calculation and experimental errors

Total Specific TotalAlbumin protein osmotic osmoticpressure pressure

Variations of calculated from observed valuesAbsolute variations

mm. H20 mm. H20Standard error . 2.23Average variation i4 1.74 :4:11.56Maximum variations + 6.8 +59.0

- 5.7 -42.0Per cent variations

per cent per cent

Standard deviation. 5.05 41 5.05Average per cent variation ... 3.87 -+- 3.89Maximum per cent variations + 18.7 + 18.4

-13.1 -13.2

Experimental errorsgrams per grams per mm. H20

100 cc. 100 cc.Differences in values of duplicate deter-minations

Average difference ................ 0.08 0.09 5.1Maximum differences ........... . 0.39 0.66 19.0

601a:w

50

UJ 40-

cr 30

a.

0

02 20

C.)

- 10a.(Q I

1 2 3 4GLOBULIN PER CENT

5 6 7

FIG. 1. Showing complete lack of correlation between specific osmoticpressure and globulin concentration. Higher values of S correspond to highvalues of A, only; and lower values of S correspond to lower values of A,only, regardless of values of G.

* a

3 S

* 3 a A

* .

* *A 0

0*

ALBUMIN ABOVE 441

* ALBUMIN BELOW4.40

0

1109

COLLOID OSMOTIC PRESSURE

O 1 2 3 4 5 6 7ALBUMI N PER CENT

FIG. 2. Showing the linear relation of specific osmotic pressure to albuminconcentration, as a straight line, fitted by the method of least squares. Cor-relation coefficient of S and A is 0.93. Standard error of calculation, indicatedby dotted lines, is 2.2 mm.

between S and A. The Pearson coefficient of correlation between S andA was found to be 0.93, which indicates a high degree of relationshipbetween the variables. The heavy line drawn through the points onthe S-A graph is a straight line fitted to the data by the method of leastsquares. The equation of this line, S = 5.9A + 21.4 is corrected bymeans of the dotted lines on either side for the "standard error" of thecalculated as compared to the observed values. The standard errorbeing -4 2.2 mm. of water, it may be prophesied on grounds of probabilitythat, in any other similar series of measurements, the observed values ofS will, in 68 per cent of the cases, fall within the range of values calculatedfrom the formula S = 5.9A + 21.4 i 2.2. Similarly, if the correctionbe doubled (twice the standard error being i: 4.4) the range will include95 per cent of observed values; while if the correction be trebled 99.7 percent of cases should be included. Actually, in our series the percentageof cases included by the corrections corresponding respectively to thestandard error, to twice the standard error, and to three times the stand-ard error, are 72.6, 93, and 98.5. The frequency distribution of the errorsis therefore quite according to the "normal distribution." The average

1110

H. S. WELLS, J. B. YOUMANSAND D. G. MILLER, JR.

zLUIU

LUIa.

m-j

8 -

7 -

6-

5-

4

2 -

I -

0-i

-70

-60

-50

-40

-30

-25

*21.4

I

Li

J

(17

n

liia:

0n

U

LLUla.C,)

STANDARDERROROFSPECIFIC PRESSURECALCULATION IS

A 2.2 MM.

- 700

.- 600

- 5000N

.- 400 I

22-300L

t

* D- 200

LJii

0-100 2

0

I.

0"a

- 50

-10

-8

L7

-6

-5

-4

-3

-2

I-zLi

C-)LU(I

Lii

0

0H-

FIG. 3. Nomogram. A straight line drawn through the proper points onthe albumin and total protein scales will intersect the middle scale at thevalue of the total osmotic pressure calculated from the formula, P = C(21.4+ 5.9 A).

error of calculation of S was :1 1.74 mm. and the maximum errorsencountered were + 6.8 and -5.7 mm.

The complete independence of the specific osmotic pressure from anyeffect of varying concentrations of globulin is exemplified by the findingson a sample of serum from the patient (Case Number 36) who sufferedfrom Banti's disease. The albumin concentration was 2.87 per cent andthe globulin concentration was 6.48 per cent, giving an A/G ratio of 0.44.The observed specific osmotic pressure was 41.5 mm. of water, while thevalue of S calculated from the albumin concentration is 38.3. On theassumption that the globulin fraction of serum exerts, universally, alower osmotic pressure, gram for gram, than the albumin fraction, one

1111

COLLOID OSMOTIC PRESSURE

should expect the value of S of a serum having such an unusually highglobulin content to be lower than that calculated by our formula. Thefact that it was actually higher, by nearly 8 per cent, indicates clearly theunreliability of the A/G ratio as an index of the specific osmotic pressure,and confirms the idea that it is the albumin concentration which deter-mines the specific osmotic properties of the serum.

The total osmotic pressure, P, is calculated from the formulaP = C(5.9A + 21.4). The nomogram, reproduced in Figure 3, may beused to facilitate the calculations. The absolute error of the calculationof P is equal to the error of S multiplied by the concentration of totalprotein, C. The average error for our series was 41 11.6 mm., themaximum errors being + 59 and - 42 mm. It is the percentage errorof calculation of the total osmotic pressure, however, which will be mostsignificant in practice. The percentage error will, in general, be thesame for S as for P, and for our series the average per cent error is slightlyless than + 3.9, the maximum errors being + 18.7 and - 13.2 per cent.The standard deviation of the per cent errors about their mean (whichis - 0.1) is 41 5.05, which signifies that 68 out of every 100 values of Sor P, calculated by the given formulae, will correspond to the observedvalues within approximately i 5 per cent, and similarly 99.7 out ofevery 100 calculated values should check the observed values within4t 15 per cent. Actually, errors lying within the ranges i 5 per centand i 15 per cent occurred in 77 and 99 per cent of cases, respectively.The per cent errors of calculation may therefore be considered as being

normally " distributed.Sources of error

The term "observed value," as used in the last paragraph, refers,in each case, to the average of the two values obtained from duplicateosmotic pressure determinations. However, in 4 instances, due to ascarcity of serum, only a single determination was run; but in only 1 ofthese cases was the variation between the observed and calculated valuesas great as 5 per cent. The greatest variation between the two valuesobtained from duplicate determinations was 19 mm. The average varia-tion was 5.1 mm. and 95 per cent of the cases showed variations whichwere not greater than 12 mm. In general there was no relation betweenthe closeness of the check of the duplicate osmotic pressure determinationsand the degree of variation of the observed mean pressure from thepressure calculated from the protein analyses.

The question naturally arises as to what extent the variations of thecalculated from the observed pressures may be accounted for on the basisof experimental errors and to what extent they must be considered asdue to unknown factors. Weshould like to be able to decide to whatextent the osmotic pressure of colloids of serum is due to the proteinconcentrations as we have measured them and to what extent it is due

1112

H. S. WELLS, J. B. YOUMANSAND D. G. MILLER, JR.

to other factors that were not measured during these investigations.The average variation of calculated from observed values was +4 11.5 mm.while the average variation of duplicate osmotic pressure determinationswas only 5.1 mm., or :1: 2.55 mm. when related to the means of the pairsof values. Unfortunately the variation of duplicate determinations isnot always a measure of the error of a method. "Good checks," whilereassuring, do not exclude the possibility that systematic errors mayhave affected both values to the same extent and in the same direction.Allowing for the possibility that systematic errors were present of atype which could affect our pairs of observations now in one direction,now in another, at random, we should be fairly safe in assuming, arbi-trarily, that the "maximum expected error" will not be greater thani 12 mm., which is twice the variation from the mean of duplicatedeterminations in 95 per cent of our cases. Wecan neglect the possi-bility that systematic errors may operate in one direction for the wholeseries of cases for they could not be responsible for variations of observedvalues from values calculated by a formula based on the same series ofobservations.

The error of the chemical anialysis of the albumin and total proteinconcentrations will contribute its share to the total error of the calculatedvalue of the osmotic pressure. In 93 per cent of the cases the variationsbetween duplicate determinations of these quantities were not greaterthan 0.2 gram per 100 cc. Assuming that the maximum expected erroris 4- 0.2 gram per 100 cc. for albumin and also for total protein, themaximum, additive error of both analyses will be responsible for apossible error of from i 10 to 4- 20 mm. in the calculation of the osmoticpressure. By the method of differentials, where the pressure is calculatedby the formula P = C(21.4 + 5.9A), the total error is the total differ-ential, dP. Now, dP = 21.4dC + 5.9A dC + 5.9CdA. Since dA anddC, the errors of the analyses, are both considered as i 0.2, we havedP = i [1.2(A + C) + 4.3]. The maximum error of analysis was cal-culated in this way for each case, and the maximum experimental errorfound by adding the maximum error of the osmotic pressure determina-tion, which is considered to be 4 12 mm. The figures are given in thelast column of Table I. Even with so great an allowance for errors ofmeasurement, there were 6 instances in which the errors of calculationcould not be accounted for. It is therefore necessary to assume thatother factors, which were not measured, have a determining influenceupon the osmotic pressure exerted by a given sample of serum. Wemay conclude that, whereas in a series of cases the errors due to theunknown factor or factors will not seriously affect the reliability of thecalculation of the osmotic pressure from the albumin and total proteinconcentration, in any single instance the calculated value may possiblybe in error by an amount which is much greater than the sum of the

1113

COLLOID OSMOTIC PRESSURE

experimental errors of the methods employed. The unknown factordoes not seem to be referable to individual ("personal") peculiarities ofthe blood, for in no instance did a large error occur more than once in theseries of determinations carried out on blood samples from individualsubjects. It may be assumed that the method of calculation will givereliable results when applied to a series of determinations on the sameindividual as well as when applied to single determinations on a series ofseveral individuals. As a matter of fact, the greatest error so far en-countered, 19 per cent, is not so great as to discourage the employmentof the method, for most clinical purposes, for single determinations onsingle individuals. In this respect the method cannot be consideredto be less accurate than the usual determination of the basal metabolicrate, for which an error of 41 15 per cent is ordinarily allowed.

The significance of the relation between the specific osmotic pressure andthe total protein and albumin concentrations. It has been pointed out byMarrack and Hewitt (7) that the "Donnan pressure" due to the excessof diffusible ions in a protein solution over that in the outside solutionwill be proportional to the square of the protein concentration and mustbe added to the osmotic pressure of the protein alone in calculating thetotal osmotic pressure of an ideal protein solution. Theoretically, there-fore, P = aC + bC2, where a is the constant of proportionality relatingthe pressure due to the protein alone to the concentration, and where bis a constant relating to the Donnan pressure at constant pH. Theequation, of course, will be expected to hold for a series of blood seraonly if they contain the same proportions of the two protein fractions,albumin and globulin: that is to say, when A/G remains constant. Butwhen A/G is constant, C is directly proportional to A, so that our equa-tion for the total osmotic pressure, P = 21.4C + 5.9AC, may be writtenP = 21.4C + 5.9bC2, where b is the constant of proportionality betweenC and A for a constant value of A/G. This is the theoretical form ofequation for the Donnan effect. Now S = P/C, so that the theoreticalformula reduces to S = a + bC. For constant values of A/G our equa-tion may be reduced to the identical form, S = 21.4 + 5.9bC.

Interesting though these comparisons of our empirical equations withthe theoretical Donnan equations may be, however, they do not com-pletely explain the peculiar relations which we have found to exist. Itis difficult to understand, on any theoretical basis which is not entirelyspeculative, why the specific pressure should be so completely independentof the globulin concentration and hence of the A/G ratio. The relationwould seem to imply that the specific pressure of globulin in any serumis the same as that of the albumin with which it is associated, and thatit has a value which is directly determined by the concentration of thealbumin. On the other hand, globulin does not appear to have anyeffect on the specific pressure of albumin. It should be emphasized that

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H. S. WELLS, J. B. YOUMANSAND D. G. MILLER, JR.

the term "specific pressure" refers not to the total osmotic pressure, butto the average pressure per gram per cent of total protein. The globulincontent of a given serum appears to contribute gram for gram exactlyas much to the total pressure as does the albumin. Consequently ourdata offer no justification for the assumption that albumin (in serum)has an effective molecular weight which is much less than that of globulin.The actual molecular weights of the two substances may, of course, bewidely different: but if they are, the fact is not reflected in our dataand we must assume that other factors enter in to mask the effects of adifference in molecular weight. Whatever the explanation of this pe-culiar situation may be, the existence of the relation indicates the needfor an experimental study of the osmotic properties of both the separateand the mixed solutions of purified serum albumin and serum globulin.

The finding that the albumin concentration determines the specificosmotic pressure, not only of the albumin itself but also of the accom-panying globulin (regardless of the concentration of the globulin) is ofsome significance in relation to the clinical correlation of edema withlow serum albumin concentrations: for it becomes clear that a progressivelowering of the albumin content of a patient's serum entails a simul-taneous lowering of the specific osmotic properties of the accompanyingglobulin fractions, even if the globulin concentration is not lowered.

The significance of the A/G ratio as an index of the osmotic propertiesof serum depends, apparently, on the clinical fact that changes in thisratio are most often due to changes in the albumin fraction-the globulinchanging relatively less, in most instances. However, in cases where theglobulin undergoes marked variations from the normal value the A/Gratio becomes totally unreliable as an index. In our series as a wholethere is a fair degree of correlation between the specific pressure and theA/G ratio, but this must be attributed solely to the particular selectionof cases. In individual cases the correlation was often very poor indeed.

The fact that the specific pressure increases with increasing totalprotein concentration (except when this increase is due to an increasein G alone) is in accord with the findings of many other investigators:for serum, (8, 9, 10), for serum albumin (11), for other pure proteinsolutions (12, 13) and for all types of concentrated solutions of crystalloidsso far studied, of which the classical example is sucrose (14). Conse-quently it would appear that the contention of Govaerts that the totalprotein concentration is without influence on the specific osmotic pressureis without justification except from his own data.

The apparent unreliability of the formulae of Govaerts and of von Farkas.In general the values obtained by Govaerts for the osmotic pressure ofserum tend to be higher than those obtained by others. Further evidencethat the values upon which Govaerts' formula is based are unreliable isgiven by the fact that Verney (8), employing cellophane membranes

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furnished by Govaerts, obtained values which were lower in relation tothe protein concentrations than those of Govaerts, but of the same orderof magnitude as those of most other workers.

We have used the formula of Govaerts, P = 75.4A + 19.5G, tocalculate the osmotic pressures of our sera and find that these calculatedvalues are, on the average, 18.4 per cent higher than the values whichwe observed, with a range of variation of - 3 to + 59 per cent. Sincethe formula of Govaerts fits his own data very well, we may concludefrom the degree of variability found by the above-mentioned calculationsthat his observed pressures, mostly higher than ours, are not higher inany definite proportion but in a totally irregular manner. If our deter-minations are correct, as we believe them to be, it follows that Govaerts'formula cannot be relied upon to give calculated values which are evenrelatively accurate. The same criticism may be applied to the formulaof von Farkas, P = 68A + 25.1G, for the application of this formulato our data provides values which are, on the average, 13.4 per cent higherthan the values observed by us, the range of variation being - 8 to + 56per cent.

SUMMARY

1. The osmotic pressure of colloids and the total protein, albumin andglobulin concentrations of 128 samples of human serum were determined.The samples were obtained from 53 individuals.

2. Analysis of the data, which cover a relatively wide range of values,indicates that the relation between the total protein and albumin concen-trations and the osmotic pressure is sufficiently regular and definite toallow the use of an empirical formula, derived from the data, for the calcu-lation of the osmotic pressure. The formula is: P = C (21.4 + 5.9A),where P is the osmotic pressure in millimeters of water, C is the totalprotein concentration and A is the albumin concentration, in grams per100 cc. The standard error of calculation is i 5 per cent.

3. A nomogram has been constructed to facilitate calculations.4. The specific osmotic pressure of serum appears to be a linear

function of the albumin concentration. Variations in the globulin con-centration over a wide range produce no effect on the specific pressureat constant values of A. Consequently the A/G ratio is a poor index ofthe osmotic properties of serum. The specific pressure increases forincreasing values of the total protein concentration, but only in so faras these increases are not due to increases in the globulin. The theo-retical significance of these relations is discussed.

5. The formulae of Govaerts and of von Farkas, which have beenused to calculate the osmotic pressure, appear to be totally unreliable.The reasons for this conclusion are discussed.

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H. S. WELLS, J. B. YOUMANSAND D. G. MILLER, JR.

BIBLIOGRAPHY

1. Govaerts, M. P., Bull. Acad. roy. de m6d. de Belgique, 1927, xiii, 356.Influence de la teneur du s6rum en albumines et en globulines sur lapression osmotique des prot6ines et sur la formation des oedemes.

2. v. Farkas, G., Ztschr. f. d. ges. exper. Med., 1927, liii, 666. Studien uiberden kolloidosmotischen Druck des Serums.

3. Burk, N. F. and Greenberg, D. M., J. Biol. Chem., 1930, lxxxvii, 197.The physical chemistry of the proteins in non-aqueous and mixedsolvents. I. The state of aggregation of certain proteins in urea-watersolutions.

4. Wells, H. S., Am. J. Physiol., 1932, ci, 409. Some criteria of accuracyfor the measurement of the osmotic pressure of colloids in biologicalfluids.

5. Wells, H. S., J. Tenn. Acad. Sci., 1933, viii, 102. A modified KroghOsmometer for the determination of the osmotic pressure of colloidsin biological fluids (with directions for its use).

6. Howe, P. E., J. Biol. Chem., 1921, xlix, 109. The determination ofproteins in blood-a micro method.

7. Marrack, J. and Hewitt, L. F., Biochem. J., 1927, xxi, 1129. The effectof hydrogen ion concentration and protein concentration on the osmoticpressure of serum-proteins.

8. Verney, E. B., J. Physiol., 1926, lxi, 319. The osmotic pressure of theproteins of human serum and plasma.

9. Krogh, A. and Nakazawa, F., Biochem. Ztschr., 1927, clxxxviii, 241.Beitrage zur Messung des kolloid-osmotischen Druckes in biologischenFlussigkeiten.

10. Fishberg, E. H., J. Biol. Chem., 1929, lxxxi, 205. The relations of theserum proteins and lipids to the osmotic pressure.

11. Burk, N. F., J. Biol. Chem., (Proc.) 1931, xcii, xl. The molecular weightof serum albumin estimated by osmotic pressure measurements.

12. Kunitz, M., J. Gen. Physiol., 1926-27, x, 811. Hydration of gelatin insolution.

13. Adair, G. S., Proc. Roy. Soc. London, Series A, 1925, cix, 292. Theosmotic pressure of hemoglobin in the absence of salts.

14. Porter, A. W., Tr. Faraday Soc., 1917, xiii, 123. The kinetic theory ofosmotic pressure.

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