kb...(3) subsequently expressed this proportionality between total calcium and total protein more...

RELATION OF SERUMCALCIUMTO SERUMALBUMINANDGLOBULINS

By ALEXANDERB. GUTMANAND ETHEL BENEDICT GUTMAN(From the Department of Medicine, College of Physicians and Surgeons, Columbia University

and the Presbyterian Hospital, New York City)

(Received for publication July 9, 1937)

In 1923, Salvesen and Linder (1) pointed outthat hypoproteinemia in the nephrotic type ofBright's disease is associated with hypocalcemia,the calcium content of the serum tending to paral-lel the total serum protein level. Marrack andThacker (2) and Hastings, Murray and Sendroy(3) subsequently expressed this proportionalitybetween total calcium and total protein more pre-cisely in the form of an empirical regression equa-tion. By plotting the calcium content of bodyfluids of low or normal protein content as ordi-nates against the respective total protein values,they showed that the points so obtained approxi-mate a straight line which has a positive slope andintersects the " y " (Ca) axis at a point above theorigin. Such a linear relation, since confirmed innephrotic and normal sera by others (4, 5, 6),may be expressed by the general regression equa-tion (5):

Total Ca l mtotal protein + b, I

where m, the slope of the line, is a constant whichdefines the amount of calcium bound per unittotal protein

and b, the intercept on the " y " axis, is a constantwhich defines the amount of calcium not boundto protein.

Though derived from clinical data, and purelyempirical, Equation I is in accord with deductionsdrawn from dialysis and ultrafiltration experi-ments. These indicate that calcium present inserum is partly in a non-diffusible, partly in a dif-fusible state. At physiological concentrations ofCa++, PO4- and H+, the non-diffusible calciumfraction appears to be protein-bound calcium; andvalues obtained for the diffusible calcium fraction,which is composed largely of Ca++ (7, 8), are insatisfactory agreement with values obtained forb. McLean and Hastings (5) have shown, fur-ther, that Equation I may be derived from a gen-eral mass law equation for the dissociation of

calcium proteinate where the protein molecules areassumed to be composed of a series of negativelycharged divalent ions:

[Ca++] [Prot.--] = K[Ca Prot.] II

Substituting [Total Prot.] -[Ca Prot.] for[Prot.-] and simplifying, we obtain:

[Ca++] [Total Prot.] = K + [Ca++].[Ca Prot.)

Substituting [Total Ca] - [Ca+] for [CaProt.] and dividing both sides of the equationby [Ca++], we obtain:

[Total Prot.] KK[Total Ca] - [Ca++] [Ca++]

For the special case where the concentration ofCa++ is constant (and the experimental data usedin deriving Equation I are restricted by definitionto that condition), the constant b may be substi-tuted for [Ca++]. Designating the relation of

constants Kb + 1 by the reciprocal of the constant

m, we obtain:

[Total Prot.] _ 1[Total Ca]-b m

which solved for [Total Ca] gives Equation I.Equation I does not apply if there is a primary

disturbance in calcium metabolism (3) nor in thepresence of hyperphosphatemia (1, 4). But apartfrom these restrictions, this equation seems so wellsupported by both empirical and theoretical evi-dence that it has come to be regarded as a gen-erally valid expression of the relation between to-tal calcium and total serum protein.

For example, it is inferred-as follows fromEquation I-that elevated calcium values are tobe expected in association with hyperproteinemia.Since a significant proportion (almost half) ofthe total calcium in normal serum is bound to

903

ALEXANDERB. GUTMANAND ETHEL BENEDICT GUTMAN

protein, it does seem to follow that with increasedprotein content there would be an increase in cal-cium bound to protein and, consequently, a risein the total calcium content of the serum; hyper-proteinemia being regarded in this sense as "acause of " or "responsible for" hypercalcemia.A number of cases of multiple myeloma havebeen described in which hyperproteinemia was, infact, associated with hypercalcemia. And in suchcases, a definite increase in the non-diffusible (orprotein-bound) calcium fraction could be demon-strated by ultrafiltration-a result in accord withthe implications of Equation I.

Despite this considerable body of supportingevidence, however, empirical equations of the gen-eral form of Equation I should be regarded, asPeters and Van Slyke (9) have pointed out, onlyas " rough first approximations " of the relationof calcium to protein in serum. It has often beennoted that when, as in hepatic cirrhosis (10), de-creased serum albumin is associated with increasedserum globulin, the serum calcium level seems toparallel the albumin rather than the total serumprotein content. Such observations led Schmidtand Greenberg ( 11 ) to conclude that " because theprotein bound calcium probably is very largelyunited to the albumin rather than to the total pro-tein, the total protein content of the serum canonly give an inadequate representation."

Our own data indicate that in a variety of dis-eases presenting hyperglobulinemia, there is a se-rious discrepancy between observed serum cal-cium and that calculated by formulae based uponEquation I (6, 12). It would appear that Equa-tion I in its present form is not generally valid(within the limitations prescribed above), as hasbeen assumed. Analysis of our data suggests fur-ther that a more satisfactory approximation couldbe effected by an expression relating calcium spe-cifically to the several protein fractions of whichthe total serum protein is composed. A definitiveequation of this kind is not attainable for thepresent because of the prevailing uncertainty re-garding the serum protein fractions and their cal-cium-binding properties under the conditions ex-isting in serum. By graphic and statistical analy-sis of our data, however, we derived an equationrelating total calcium to serum albumin and twoarbitrarily defined serum globulin fractions. Thisequation appears to give better agreement between

observed and calculated serum calcium over awide range of variation in serum proteins than doequations relating total calcium to total protein,to albumin and total globulin, or to albumin alone.

MATERIAL ANDMETHODS

Our data (Table I) include 27 observations on 21 casesof the nephrotic syndrome, with low albumin and normalor somewhat decreased globulin levels; 20 observationson 15 normal subjects; 50 observations on 39 cases oflymphogranuloma inguinale, 37 sera containing more than8.0 per cent total protein; 25 observations on 20 miscel-laneous cases with hyperproteinemia not due to lympho-granuloma inguinale, multiple myeloma or hepatic cir-rhosis; and 42 observations on 28 cases of hepatic cir-rhosis, with low or normal albumin and normal or highglobulin levels. With the exception of cases of extremedehydration, which were not available for study, the datamay be regarded as illustrative of the types of changes inserum proteins occurring in disease.

For reasons stated in the text, conditions in which theconcentration of Ca++ per unit serum water could not beassumed to be within normal limits were excluded: Caseswith a primary disturbance in calcium metabolism (in-cluding multiple myeloma); cases with hyperphosphate-mia; and cases with hypoproteinemia due to malnutritionor occurring in terminal stages of wasting diseases.Apart from these restrictions, and the inclusion of only afew representative normal values, the data are unselected.

Serum calcium was determined by the Clark and Collipmodification of the Kramer and Tisdall method (30).Serum protein was determined by difference, total nitro-gen by the Kjeldahl technique, and nonprotein nitrogenby Folin's method with nesslerization (31). Albumin andthe globulin fractions were estimated by Howe's method(32), nitrogen being determined by the micro-Kjeldahltechnique and titration. Inorganic phosphorus was deter-mined by the method of Kuttner and Lichtenstein as mod-ified by A. Bodansky (33). All determinations were car-ried out in duplicate, except some calcium analyses, wheninsufficient serum was available.

In view of the wide range in total protein content ofour sera, the concentrations of all relevant solutes wereexpressed in terms of serum H2O. This involves a cor-rection:

C, -*C.

,100,where

Cw, = concentration of solute per unit weight of serumH20.

Cs = concentration of solute per umit volume of serum.8 = grams of H,0 per 100 cc. serum.

Ws was calculated by the McLean and Hastings' for.-mula (5):

Ws= 99.0- 0.75P8,

904

RELATION OF CALCIUM TO ALBUMIN AND GLOBULINS

where

P. = grams of total protein per 100 cc. serum,

0.75 = the Svedberg and Sjogren factor for specificmolecular volume of serum protein

and 1 per cent of serum volume is assumed to be occupiedby solutes other than protein.

A quotient nomogram (Figure 1), which proved use-

ful for rapid conversion of large groups of data and forchecking values calculated in the usual manner, was con-

structed on the basis of the formula:

wherelog x = log y + colog z

x = Cw as defined above,y = C. as defined above,z = WJ as defined above . 100.

Column P. represents the observed serum protein con-

tent in grams per 100 cc. serum. The columns Cs andC'. represent the observed concentration per 100 cc. serum

of that solute which is to be expressed in terms of serum

water; C8 being scaled to cover the range 1.5 to 3.0 and3.0 to 6.0; the scale of C'. reading from 1.0 to 1.5 andfrom 6.0 to 10.0.1 A straight line connecting the pointon the P. column corresponding to the observed totalprotein content of the serum, with the point on the C.or C',s column corresponding to the observed concentra-tion of solute in serum, will intersect the adjacent Cw,or the respective C' column at a point representing thedesired concentration of solute in serum water.

The nomogram is applicable to sera containing 3.0 to12.0 grams of total protein per 100 cc. serum. It givesresults accurate to the third significant figure over therange of variation in serum electrolytes (expressed inmilligrams respectively grams, or in milliequivalents).

RESULTS

Relation of total serum calcium to total serum

protein in the nephrotic syndrome and in normalsubjects. In Figure 2, we have plotted values fortotal serum calcium against the respective totalprotein content of sera obtained from patientswith the nephrotic syndrome. To show the trendmore clearly, 4 observations on 4 cases of " healednephrosis " and 15 representative results on nor-

mal subjects are included. The points, indicatedby hollow dots, show a positive linear correlationwhich is in good agreement with Equation I. Thestraight line shown in Figure 2 was not drawnthrough our points but represents Equation Iwhere m 0.75 and b 5.6, total protein beingexpressed in grams, total calcium in milligrams

1 To convert solute concentrations greater than 10.0,move the decimal point to conform with scales of the C.or C'. column and the respective Cw or C'w, column.

per 100 grams serum water. These values for mand b are the means of the several constants ob-tained empirically by various investigators, as cal-culated by McLean and Hastings (5).

Our results, therefore, are in accord with thefindings in the literature with respect to the directproportionality between total serum calcium andtotal serum protein in the nephrotic syndrome andin normal subjects. As a corollary, it may be in-ferred that the standard methods employed in de-termining calcium and protein give results in ourhands which are consistent with those obtained byothers; and consequently the discrepancies en-countered in the diseases now to be considered arenot due to differences in technique.

Relation of total serum calcium to total serumprotein in lymphogranuloma inguinale. As waspointed out elsewhere (13, 14), many cases oflymphogranuloma inguinale present hyperpro-teinemia, the total protein reaching levels as highas 11 grams per 100 cc. serum. Hyperproteinemiain lymphogranuloma inguinale is not, however,associated with hypercalcemia (13, 14). Thepoints obtained by plotting total calcium againstthe respective total serum protein in our cases(Figure 2) do not fall along the straight line cor-responding to Equation I. The trend shown bythese points is approximately parallel to the " x "axis. It would appear, therefore, that the linearrelation between total serum calcium and totalserum protein observed in hypoproteinemia doesnot obtain in hyperproteinemia due to lympho-granuloma inguinale.

Relation of total serum calcium to total serumprotein in miscellaneous diseases presenting hy-perproteinemia. This discrepant relation is notpeculiar to hyperproteinemia occurring in lympho-granuloma inguinale. In Figure 3, we illustratethe distribution of points obtained by plotting to-tal calcium against total serum protein in 20 mis-cellaneous cases presenting hyperproteinemia notdue to lymphogranuloma inguinale, multiple mye-loma or hepatic cirrhosis. This group is composedchiefly of various infections. In some instances,no diagnosis could be established. In several in-stances, lymphogranuloma inguinale was suspectedclinically, but the Frei test was negative.

As in lymphogranuloma inguinale, the points donot fall along a straight line corresponding toEquation I but show a trend approximately paral-

905

906 ALEXANDERB. GUTMANAND ETHEL BENEDICT GUTMAN

2.0 B 6 0

.0~~~~~~~~~~~~~

/0

0 .2__ - 2tS S 4d j4

bB i u a

0~~~~~~~~~~~~~

0_

.1o .i- cZko,_ _

10~~~~~~~~~~~. x ,-

8~~~SLT COCNwAINPER 10 GRmCsRmH

FIG1.NOMGRMFR CNVRTIGSLUECNCETRAIOSPR10 C. ERU T

0~~~OUECNETIN E 0 RM EU ,


TOTAL SERUMPROTEIN GMS. PER /00 64#S. H2

FIG. 2. RELATIoN OF TOrAL CALCIUM TO THE RESpEcTIVE TOTAL PROTEIN CONTENTOF SERA IN THENEPHROTICSYNDROMEAND IN NORMALSUBJECTS, SHOWINGA DIRECT PROPORTIONALITYBETWEENTHESETwo CONSTITUENTS

This proportionality does not hold in hyperproteinemia due to lymphogranuloma inguinale.

lel to the " x " axis. Our results (Table I andFigure 3) indicate that, contrary to the implica-tions of Equation I, the total serum calcium doesnot rise in hyperproteinemia but is maintained atnormal levels. (This generalization does not ap-ply to relative increases in serum proteins andother solutes occurring in extreme dehydration;or to conditions like multiple myeloma where thereis a primary disturbance in calcium metabolism.)

Relation of total serum calcium to total serumprotein in hepatic cirrhosis. Figure 3 also showsthe distribution of 42 points obtained by plottingtotal calcium against the respective total serumprotein content in cases of hepatic cirrhosis, inmost instances of the Laennec type. The serumalbumin may be considerably decreased in cirrho-

sis of the liver, as is well known, and some casesalso show varying degrees of hyperglobulinemia(Table I).

The points representing our cases of hepatic cir-rhosis do not fall along the straight line corre-sponding to Equation I. The discrepant relationof the 164 observations plotted in Figure 3 indi-cates that Equation I is not generally valid overthe range of variation in serum proteins, as hasbeen assumed.

Calcium-protein relation in multiple myeloma,hyperphosphatemia and malnutritional hypopro-teinemia; grounds for exclusion of these condi-tions. It has been known for some time (15)that in multiple myeloma hyperproteinemia andhypercalcemia may co-exist. Of 75 published

907


TOTAL SERUMPROTEIN GMS. PER /00 GMS. /QFIG. 3. TOTAL CALCIUM IS PLOTTEDAGAINST TOTAL PROTEIN IN 164 SERA PRESENTINGVARIOUS CHANGES

IN SERUMPROTEINSThere is no linear relation between total calcium and total protein.

cases of multiple myeloma in which both proteinand calcium were determined (including 15 of ourown), hyperproteinemia occurred in 43 of which29 also presented hypercalcemia. The co-exist-ence of hyperproteinemia and hypercalcemia inmultiple myeloma has been regarded as evidencefor the validity of Equation I in hyperproteinemia.But when total calcium is plotted against the re-spective total serum protein found in publishedcases of multiple myeloma (Figure 4), it is evi-dent that the points so obtained do not fall alongthe line corresponding to Equation I. In fact, nolinear relation can be made out between total cal-cium and total serum proteins.

Multiple myeloma is a disease characterized byextensive bone destruction and should be classi-fied with conditions presenting a primary dis-

turbance in calcium metabolism. Since, as statedat the outset, Equation I applies only where thereis no primary disturbance in calcium metabolism,we regard discussion of the conformity or lack ofconformity of such cases to Equation I as irrele-vant; and feel justified in omitting our cases ofmultiple myeloma, by definition, from the datasubjected to analysis.

The hypercalcemia observed in many cases ofmultiple myeloma (18) may well be due, not tohyperproteinemia (which may not be present inassociation with the hypercalcemia), but to thecomplication of co-existent bone destruction byneoplastic tissue; like the hypercalcemia found oc-casionally with metastatic osteolytic carcinoma, inwhich serum proteins are normal or low (18, 19).That the majority of cases of multiple myeloma

908


TABLE I

Total protein, albumin and calcium content of 144 sera obtained from patients with diseases affecting the serum pro-teisw; and of 20 normal sera

Totalprotein Albumin Total

calcium

grams per grams per mgm. per100 cc. 100 cc. 100 cc.serum serum serum

LYMPHOGRANULOMAINGUINALE

11.411.110.710.310.110.1

9.69.59.59.49.49.39.19.19.19.09.09.08.88.88.78.78.78.68.68.58.58.58.48.48.48.48.48.38.28.18.18.07.97.97.97.97.87.87.87.77.67.57.47.3

2.63.32.93.13.53.33.63.43.13.63.43.34.03.53.13.83.63.53.83.23.53.43.04.03.63.83.73.54.24.03.93.22.34.13.83.93.33.64.34.24.13.74.74.73.93.84.33.32.93.1

8.59.69.2

10.610.3

9.19.5

10.710.610.010.710.210.210.8

9.49.9

10.59.3

10.710.810.2

9.39.3

11.310.110.410.2

9.610.810.6

9.810.9

8.910.710.310.3

9.410.610.3

9.810.5

9.810.89.69.8

10.110.410.3

9.110.6

HYPERPROTEINEMIAOF MISCELLANEOUSORIGIN

12.110.3

9.69.59.49.19.08.98.9

2.94.33.73.24.64.23.44.54.3

10.49.99.89.2

10.69.7

11.210.5

9.9


calcium


HYPERPROTEINEMIAOF MISCELLANEOUSORIGlN-COnt.

8.9 4.2 9.78.8 3.6 9.78.8 3.5 9.68.8 3.0 9.18.7 4.6 10.88.7 4.0 10.58.5 4.0 10.08.5 4.0 9.98.3 3.8 9.28.2 4.6 10.48.2 3.3 9.58.0 4.6 9.88.0 4.4 11.18.0 4.3 11.08.0 4.3 9.97.9 3.9 10.8

CIRRHOSIS OF THE LIVER

9.58.78.68.48.28.28.28.18.18.07.97.97.77.67.47.47.47.37.37.27.27.27.16.96.86.66.56.46.36.36.36.16.16.06.05.95.85.75.75.45.35.0

2.22.44.12.43.02.22.03.81.92.92.42.13.13.24.12.11.84.22.44.52.21.71.72.44.21.82.12.93.53.42.23.21.82.01.62.71.83.71.71.92.31.5

9.08.89.79.2

10.58.78.4

10.27.58.68.88.79.79.89.98.89.29.78.7

10.59.38.69.68.7

10.08.48.08.39.49.08.58.78.98.57.38.48.98.67.78.19.08.5

909


TABLE I-Continued


calcium


" HEALED" NEPHROSIS

7.1 4.6 10.16.7 4.4 10.46.5 4.6 10.46.3 3.9 10.4

NEPHROTICSYNDROME

5.85.25.15.05.04.84.74.74.54.54.34.34.13.83.83.83.83.83.33.3

3.23.02.32.81.82.52.52.13.42.42.02.02.21.91.81.71.51.32.01.6

9.89.48.48.88.48.69.58.48.29.58.68.18.18.28.57.98.27.58.98.0


calcium

grams per grams Per maM. per100 cc. 100 cc. 100 cc.serum serum serum

NEPHROTICSYNDROME-Continued

3.3 1.5 8.03.2 1.3 8.13.2 1.1 7.1

NORMALSUBJECTS

7.67.67.67.57.47.47.37.37.37.37.27.27.27.17.06.96.76.66.56.3

4.94.43.85.15.04.55.14.94.84.85.04.94.85.24.74.64.64.54.04.5

10.911.010.210.510.210.611.0

9.911.010.511.310.810.710.110.510.510.9

9.39.9

10.0

presenting hyperproteinemia also exhibit hyper-calcemia may mean only that myelomatosis severeenough to cause hyperproteinemia is likely to beextensive enough to produce widespread skeletaldamage, resulting in hypercalcemia. An absoluteincrease in protein-bound calcium demonstratedby ultrafiltration in some cases of multiple mye-loma occurs, apparently, only in cases presentinghypercalcemia, and then irrespective of whetheror not the serum protein content is increased (6).We have suggested elsewhere (6) that this in-crease in protein-bound calcium is a result, notthe cause of the hypercalcemia; a result of the in-flux of Ca++ caused by bone destruction, with re-establishment of equilibrium between these twofractions at higher levels of both ionized andprotein-bound calcium. Moreover, it seems likelythat, for reasons stated later, most of the increasedprotein-bound calcium in multiple myeloma pre-senting both hyperproteinemia and hypercalcemiais calcium bound by albumin; and little calcium is

bound by the euglobulin increment usually re-sponsible for the hyperproteinemia.

Cases of hyperphosphatemia are excluded be-cause hyperphosphatemia, as is well known, de-presses the total calcium content of the blood bymechanisms not directly dependent upon the se-rum proteins. The presence of hyperphosphate-mia lowers the Ca++ concentration and disturbsthe equilibrium between Ca++ and protein-boundcalcium, apparently in part, at least, through theformation of non-diffusible (colloidal) calciumphosphate complexes. Peters and Eiserson (4)have suggested an empirical equation relatingcalcium to total protein and inorganic phosphorus.Wehave not attempted to formulate such a moregeneral equation from our data, however, buthave included in Table I only sera containing 2.5to 5.0 mgm. inorganic phosphorus per 100 cc.serum.

In our cases of malnutritional hypoproteinemia,points obtained by plotting total calcium against

910


TOTAL PROTEIN - GMS. PER /00 CC. SERUMFIG. 4. RELATION OF TOTAL CALCIUM TO THE RESPECTivE TOTAL PROTEIN CONTENTIN 75 OBSERVATIONSON MUL-

TIPLE MYELOMA,AS REPORTEDIN THE LITERATURE

the respective total protein content fall con-sistently below the straight line corresponding toEquation I, the divergency tending to be moremarked where the total protein content is verylow. Decreased Ca++ may account for this dis-crepancy. It is known that, associated with hypo-proteinemia due to malnutrition, not only the pro-tein-bound but also the Ca++ concentration mayfall-to such low levels that symptoms of tetanymay appear. In a broad sense, this condition con-stitutes a primary disturbance in calcium metabo-lism in that the intake or absorption of calcium is

abnormal. At any rate, the concentration of Ca++cannot be assumed to be within normal limits inmalnutritional hypoproteinemia, and we have ex-cluded our cases from the data subjected to analy-S1S.

Cases with a primary disturbance in calciummetabolism, with hyperphosphatemia and withmalnutritional hypoproteinemia are excluded,then, on the common ground that in these condi-tions, the concentration of Ca++ does not remainwithin normal limits. It is essential that the Ca++concentration remain relatively constant because

911


in this, as in previous empirical attempts to obtaina quantitative expression of the relation of serumcalcium to serum proteins, the effect of varyingserum proteins on the total calcium content of theserum was considered. Since only part of the to-tal serum calcium is bound to protein, this ap-proach is possible only under conditions in whichthat fraction of the total calcium which is notbound to protein (chiefly Ca++) remains constant.Expressed in terms of Equation I, b must remainfixed.

This condition is approximated in normal andnephrotic sera, which have been shown by variousinvestigators to maintain a reasonably constantdiffusible calcium content at a mean level of about5.8 + 0.2 mgm. calcium. This condition obtainsalso in hyperproteinemia due to lymphogranulomainguinale (6) and in other diseases included inour series of cases (34).

In primary disturbances in calcium metabolism,in hyperphosphatemia and in severe malnutrition,however, gross fluctuations in the concentrationof Ca++ occur, for reasons already stated. Suchfluctuations in the concentration of Ca++ affect notonly the level of ionized calcium but also theamount of calcium bound to protein; since thesetwo fractions tend to maintain an equilibrium atlevels which are predictable, as McLean andHastings (5) have shown, from mass law con-siderations. Expressed in terms of Equation I,mbeing a function of b (see derivation from themass law), massumes different values as b varies,and m is fixed only so long as b is fixed. Empiri-cal constants for the calcium-binding propertiesof the serum proteins can be expected to apply,therefore, only under conditions in which the con-centration of Ca++ is the same, i.e., within normallimits.

We have not attempted to estimate protein-bound calcium more directly by ultrafiltration(except in a few instances) or by the McLean andHastings' (16) frog-heart method for direct esti-mation of Ca+. An attempt was made to calcu-late CaProt. and Ca++ from the total calcium andtotal protein (5) or albumin and globulin content(17) of the serum. But this approach was aban-doned when it was found that in sera with markedhyperglobulinemia due to lymphogranuloma in-guinale, calculated values for Ca++ were consid-erably lower than the diffusible calcium (6). In

extreme cases, the calculated Ca++ concentrationwas so low as to be within the range of tetany, ofwhich our cases show no signs clinically. As sug-gested elsewhere (14), constants for B globulinand PKcaProt. derived from normal serum globulinmay not be applicable to globulins occurring inmarked hyperglobulinemia.

DISCUSSION

Our results are in accord with the view that adirect linear proportionality between total serumcalcium and total serum protein, expressed byEquation I, exists in nephrotic and normal sera,from which Equation I was originally derived.When applied to hyperproteinemia, however,Equation I leads to gross discrepancies betweencalculated and observed calcium values (Figures2 and 3); because such application involves extra-polation on the assumption, apparently incorrect,that the straight line relation found in hypopro-teinemia holds at elevated serum protein levels.

In Equation I, the common factor mis used toexpress the amount of calcium bound per gram oftotal serum proteins, although the serum proteinsare known to be composed of several more or lessdiscrete protein fractions. A common factor maybe so employed if the ratio of the respective serumprotein fractions to each other remains fixed indiseases affecting the total protein level of theserum; or, should these ratios vary, if the amountof calcium bound per gram of the several serumproteins is approximately the same.

It is now well established that the ratio albu-min: total globulin does not remain constant asthe total serum protein content rises above orfalls below normal limits. Hypoproteinemia, as iswell known, is due wholly or in large part to de-creased serum albumin; whereas hyperproteinemiaappears to be due invariably to increased serumglobulins (6, 14, 20). Moreover, the severalglobulins present in serum (as defined by frac-tional salting out with sodium sulfate) are them-selves disproportionately affected when the totalglobulin content rises. The euglobulin fraction,as defined by Howe's method, almost invariablyconstitutes most of the globulin increment; oftenin association with a more or less significant risein the pseudoglobulin I fraction, as defined byHowe's method. The pseudoglobulin II fraction,however, so far as we could determine (14, 34),

912


appears to remain within the limits observed innormal serum, despite marked elevations in totalglobulin content. Thus, while the euglobulin frac-tion, as defined by Howe's method, often com-prises 20 per cent or less of the total globulinin normal serum, it may compose 50 per cent ormore of the total globulin in hyperglobulinemia;whereas the pseudoglobulin II fraction, as definedby Howe's method, makes up a third or more ofmost normal serum globulins, but falls to as lowas 15 per cent or less of the total serum globulinsin marked hyperglobulinemia.

As to the amount of calcium bound specificallyto the several serum protein fractions, nothingdefinite is known because the results obtained bydifferent methods are conflicting. The prevailingimpression, derived chiefly from observationsmade in various clinical conditions, appears to bein accord with the view expressed by Schmidt andGreenberg (11) that protein-bound calcium is" very largely united to albumin." Similar con-clusions were reached by Csapo and Faubl (21),who found less calcium carried down by theglobulin fraction precipitated by half-saturatedammonium sulfate than that carried down withthe albumin fraction. The results of ultrafiltra-tion experiments with graded membranes havebeen interpreted (22, 23), in fact, as indicatingthat all protein-bound calcium is bound solely toalbumin. On the other hand, dialysis experimentscarried out with normal serum globulin by Loeb(24) clearly indicate that normal serum globulinbinds calcium. That normal serum globulin bindsa significant amount of calcium was confirmed,among others, by McLean and Hastings (5), whogive the following distribution of calcium frac-tions as typical where the total protein content is7.0 per cent and the A/G ratio is 1.8:

Mgm. per100 gramsserum 120

Total Ca............... 11.60Ca++............... 5.16Ca bound to globulin ....... 1.86 (or 0.744 mgm.TCa per

gram of globulin)Ca bound to albumin ' ...... 3.22 (or 0.716 mgm. Ca per

gram of albumin)Ca unaccounted for 2 ........ 1.36

2 McLean and Hastings point out that serum albumintends to lose some calcium-binding capacity during puri-fication; hence the figure for albumin should be regardedas minimal and that for Ca unaccounted for as maximal.

As will be apparent subsequently, these conflictingresults are not mutually exclusive but may well bedue, in part, to the heterogeneous and varyingcomposition of the total serum globulin fractionin normal serum and in hyperglobulinemia.

So far as our own results are concerned, if theseveral serum protein fractions bound approxi-mately the same amount of calcium per gram,Equation I should give satisfactory agreement be-tween observed and calculated calcium values overthe range of variation in serum proteins; whereasgross discrepancies occur (Figures 2 and 3).Examination of Figure 3 reveals that the dis-crepant points are not erratically distributed but,with few exceptions, lie below the straight linecorresponding to Equation I; i.e., the discordantsera consistently contain less calcium than thatcalculated from their total protein content byEquation I. It is further apparent (Table I,Figures 2 and 3) that the discrepant sera are,with few exceptions, those with increased globu-lin content, irrespective of etiology; i.e., the ob-served calcium content of most sera with markedhyperglobulinemia is significantly lower than thatcalculated from their total protein content. Thisgeneralization appears to hold whether the in-crease in serum globulins results in hyperpro-teinemia (as in lymphogranuloma inguinale) orwhether (as in some cases of hepatic cirrhosis)the total protein remains within normal limits be-cause of very low albumin levels. The serumglobulin content was within normal limits in ourcases with the nephrotic syndrome, in which agree-ment with Equation I was satisfactory.

That the observed calcium in hyperglobulinemiawas lower than predicted was not due to hyper-phosphatemia, which was not present in thesesera; nor to a decrease in the Ca++ fraction, whichwas shown to be within normal limits by ultra-filtration (6) and by the absence of clinical signsof tetany. The discrepancy results because, inhyperglobulinemia, the amount of calcium boundto protein is consistently less than that predictedby Equation I from the total protein content. Weinfer that the total globulin fraction in hyper-globulinemia binds less calcium than indicated bythe several constants proposed in Equation I form (6).

In Figure 5, we have plotted total calciumagainst the respective total globulin content of

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our sera. If the protein-bound calcium content ofthese sera depended chiefly upon their globulincontent, the points would fall along a line havinga definite slope. Wefind, on the contrary, thatthe points fall in a direction approximately paral-lel to the " x " axis-the correlation between to-tal calcium and total globulin appears to bealmost zero. Apart from some low values dueto decreased serum albumin content, the total cal-cium remains within normal limits, irrespectiveof the total globulin level. The graph suggeststhat the amount of calcium bound to globulin iseither insignificant or small and constant through-out. Figure 5 is not wholly satisfactory, however,because though three variables are involved, onlytwo can be plotted; and more precise statisticalanalysis necessitates some modification of thisinitial impression.

In Figure 6, we have plotted total calciumagainst the respective albumin content of our sera.

The points show a definite trend with a sharpslope. The graph indicates that most of the pro-

tein-bound calcium is bound to albumin. That notall the protein-bound calcium is bound to albumin,however, is suggested by the following two ob-servations.

1. It is apparent upon inspection of Figure 6that the intercept on the " y " (Ca) axis of thetrend shown by these points is significantly higherthan 5.8 (the mean of observed values for dif-fusible calcium or Ca++); i.e., a small, constantcalcium fraction is bound to protein but not toalbumin. Since there appears to be no constant,systematic error in determining either calcium or

albumin, and since evidence for a diffusible, non-

ionized calcium fraction in significant amount islacking, we infer that this small, constant calciumfraction is bound to globulin. The amount so

bound was estimated more accurately by derivinga linear equation from our normal and nephrotic

0

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0 NEPHROTICS NDROAOEANDNORMALS

%J O~~~~~~~~~*LYMPHOGRANUL-OMAINGUINAL ExHEPATIC CIRRHOSISsIISCELLANEOUS HIGH PROTEIN SERA

0 1.0 2.0 J.0 4.0 5.0 6.0SERUMALBUM/N GMS. PER /00 GMS. H20

FIG. 6. RELATION OF TOrAL CALCIUM TO ALBUMIN IN 164 SmaThe points show a definite trend with sharp slope, indicating that most of the protein-bound calcium is bound

to albumin.

915


sera by the method of least squares. Calcium isexpressed in milligrams, albumin in grams per 100grams serum water in the equation so obtained:

Total Ca = 0.83 albumin + 7.0. IIIBy subtracting 5.8 from 7.0, the intercept on the" y " axis, we obtain 1.2 as an approximation ofthe mean amount of calcium bound by this globu-lin fraction, designated "globulin fraction II."

2. It is further apparent upon inspection ofFigure 6 that the majority of points correspondingto lymphogranuloma inguinale and other condi-tions with marked hyperglobulinemia fall abovethe general linear trend. Statistical analysis re-veals that this deviation becomes appreciable whenthe total globulin content exceeds approximately4.0 per cent; and that the deviation is roughly pro-portional to the degree of hyperglobulinemia. Weinfer that, in hyperglobulinemia, a small but in-creasingly significant amount of calcium is boundto the globulin increment responsible for the hy-perglobulinemia. This globulin, which we shallrefer to as "globulin fraction I," is presumablychiefly euglobulin, partly pseudoglobulin I, as de-fined by Howe's method. Our calculations indi-cate that this fraction binds approximately 0.1 to0.2 mgm. calcium per gram of globulin.

To sum up then, analysis of our data suggeststhat the total serum calcium is composed of atleast four distinct fractions: 1, Calcium bound toand proportional to the albumin fraction; 2, cal-cium bound to a globulin fraction which remainsrelatively constant in amount irrespective of thetotal globulin level; 3, calcium bound in smallamount to another globulin fraction, increasingwith the total globulin level and becoming signifi-cant in marked hyperglobulinemia; 4, calcium notbound to protein, relatively constant because grossfluctuations are excluded by definition. Thesefractions are represented in the following generalregression equation (12):Total Ca m= * albumin + m2* " globulin

fraction II " + m3" globulinfraction I," + b. IV

Statistical analysis of our own and published datasuggests that these constants have the followinglimiting values: Where b = 5.8 + 0.2 mgm. Caper 100 grams of serum HO, ml is of the order0.7 to 0.9 mgm. Ca per gram of albumin; theproduct mi g" globulin fraction II" is a constant

of the order 1.0 ± 0.5 mgm. Ca per 100 grams ofserum H20; m8 is of the order 0.1 to 0.2 mgm.Ca per gram " globulin fraction I " where " globu-lin fraction I " is defined arbitrarily as all globulinin excess of 3.0 grams of total globulin.

Values calculated for total calcium by EquationIV, using constants within the limits specified,approximate observed total calcium more closelyover the range of variation in serum proteins, thando values calculated by Equation I. This is illus-trated in Figure 7 where we have plotted meanratios, calculated total serum calcium: observed to-tal serum calcium, against the total protein con-tent.8 So plotted, a generally valid equation forcalculating total calcium will yield points whichfall along a straight line at or near 1.00, with zeroslope. Equation IV appears to satisfy these cri-teria. Equation I, on the other hand, yields pointsdiverging progressively upward with increasingtotal protein (globulin) content.

Figure 7 also illustrates the results obtainedwith two other general regression equations sub-jected to statistical analysis (12). In the first ofthese, the term " m-total protein " in Equation Iis expanded to allow for different calcium-bindingproperties of the albumin and total globulin frac-tions:Total Ca= ml albumin + m2*total

globulin + b. VIn the other, all protein-bound calcium is assumedto be bound to albumin, as suggested by Bendienand Snapper (22):

Total Ca m* albumin + b. VIBoth these formulae, like Equation IV, give

predicted total calcium values for nephrotic andnormal sera quite as satisfactory as those obtainedwith Equation I (12). And both formulae, likeEquation IV, may be derived from general mass

8 The ratio, total calcium calculated: total calcium ob-served, was first calculated for each serum, using Equa-tion IV with the constants indicated in the legend of Fig-ure 7. Then the sera were grouped accordinig to totalprotein content, expressed in grams per 100 grams ofserum H,O: 3.1 to 6.0 grams, 28 observations; 6.1 to 8.0grams, 50 observations (20 normal sera, 30 pathologi-cal); 8.1 to 10.0 grams, 68 observations; 10.1 or moregrams, 18 observations. The mean ratio for the sera ineach group was then calculated. The process was re-peated for Equations I, V and VI, using the respectiveconstants indicated in the legend of Figure 7.

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EQUATIONI: TOTAL CA.a0757UALAOTEVN45'|EWA TONM7TAL CA-0.80 ALUIwNf 0.2 lNI'# Z.O

EQATIowN V: oTALCA. 0.5AL/*/N# 025 UN4 6.0

EQATIONWI: TTALCA0.BAL&&IMIN -# 72

1% I 1

|1 1 |I~~~~~~KTOTAL SERUMPROTEIN GM. PER /00 6M. SERUMH2

FIG. 7The mean ratio, calculated total calcium: observed total calcium, is approximately 1.00 throughout the range ofvariation in serum proteins when Equation IV is used. Equation I gives increasingly divergent results in hyper-globulinetnia. Equation V has a positive slope, Equation VI has a negative slope.

law equations by methods analogous to those usedin the derivation of Equation I (see page 903).But as shown in Figure 7, neither Equation V norEquation VI gives as satisfactory agreement be-tween calculated and observed total calcium inboth low and high protein sera as does EquationIV. The points corresponding to Equation Vhave a definite positive slope because of discrep-ancies arising from the heterogeneous compositionof the total globulin fraction, as suggested else-where (6. 12). The points corresponding toEquation VI have a definite negative slope, pre-sumably because the globulin fraction does bindsome calcium.4

4 Of course, the position and slope of the lines cor-responding to these equations depend, in part, upon theconstants employed. For Equation I, means of the pub-lished values for m and b were used as most representa-tive. For Equations V and VI, we used constants givingthe best fit, as determined by the method of least squares.Results obtained by trial of other constants in Equations

"Globulin fraction II," which is relatively con-stant in amount in all sera irrespective of totalglobulin content, resembles in this respect thepseudoglobulin II fraction, as determined byHowe's method. Further, the amount of " globu-lin fraction II" present in serum approximatesthat of pseudoglobulin II, as we could find noevidence of decreased "globulin fraction II " insera containing as little as 1.5 grams total globulin.Since the product mi2 " globulin fraction II " isapproximately 1.0 + 0.5 mgm. Ca, this impliesI, V and VI (12) show that the slopes change in degreebut not in direction.

The dispersion obtained with Equation IV using theconstants indicated in Figure 7 is shown elsewhere bymeans of a scatter diagram (12). The standard errorof estimate is 0.575 mgm. Ca. Sixty-five per cent of theratios are within + 5 per cent of 1.00; in 20 instances theratio exceeded 1.05, of which 5 exceeded 1.10; in 32 in-stances the ratio was less than 0.95, of which 7 were lessthan 0.90.

917

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that "globulin fraction II" binds more calciumper gram than does albumin.

In connection with " globulin fraction I," globu-lins with isoelectric zones at pH approaching thatof serum have been isolated repeatedly from thesera of immunized animals (25, 26, 27, 28). Evi-dence for the existence of such a globulin in hy-perglobulinemia due to kala-azar has been offeredby Chopra and Chaudhury (29). Wehave calledattention elsewhere (14) to certain discrepanciesin the acid-base equivalence of the blood in hyper-globulinemia (of which the discrepancies in cal-cium here described are a special case) as indi-cating the existence of such a globulin fraction.

The inference that the total globulin in normaland pathological sera is composed of varying mix-tures of two or more globulin fractions whichbind different amounts of calcium may explain adiscrepancy already referred to: the apparent con-flict between the view that the protein-bound cal-cium in serum depends chiefly upon the serumalbumin content and the repeatedly demonstratedbinding of considerable amounts of calcium bynormal serum globulin. In hyperglobulinemia,the total globulin fraction appears to be composedlargely of a globulin which binds little calcium("globulin fraction I"); whereas a large pro-portion of normal serum globulin consists of aglobulin (" globulin fraction II ") which bindsappreciable amounts of calcium.

SUMMARY

1. The relation of total serum calcium to totalserum protein and to the several protein fractionswas studied by graphic and statistical analysis of164 observations on 128 cases. The total proteincontent of these sera, expressed in grams per 100grams of serum H2O, was: 3.1 to 6.0 grams, 28observations; 6.1 to 8.0 grams, 50 observations(20 normal, 30 pathological sera); 8.1 to 10.0grams, 68 observations; 10.1 or more grams, 18observations. Cases with a primary disturbancein calcium metabolism (including multiple mye-loma), with hyperphosphatemia or with malnutri-tional hypoproteinemia were excluded.

2. It was found that while total calcium is di-rectly proportional to total protein in nephroticand normal sera, no such relation obtains in hy-perproteinemia. Apart from some cases of multi-ple myeloma, where bone destruction is the prob-

able cause of hypercalcemia, the total serum cal-cium does not rise in hyperproteinemia but ismaintained at normal levels. Equations relatingtotal calcium to total serum protein do not holdwhen hyperglobulinemia is present. This discrep-ancy results, apparently, because the globulin in-crement in hyperglobulinemia binds very littlecalcium.

3. Analysis of our data suggests that the totalserum calcium is composed of at least four frac-tions: 1, Calcium bound to and proportional toalbumin; 2, calcium bound to a globulin fractionwhich remains relatively constant in amount ir-respective of the total globulin level; 3, calciumbound in small amount to another globulin frac-tion, increasing with the total globulin level butbecoming significant only in marked hyperglobu-linemia; 4, calcium not bound to protein, rela-tively constant because cases with gross fluctua-tions are excluded by definition. (Calcium notbound to protein is itself subdivided into anionized and a small non-ionized fraction.)

4. A regression equation relating total calciumto albumin and two arbitrary globulin fractions ispresented in the following general form:

Total Ca - m albumin + m2- " globulinfraction II " + m3* " globulin fraction I " + b.

The several constants in this equation appear tohave the following limiting values: Where b =

5.8 ± 0.2 mgm. Ca per 100 grams serum H20,ml is of the order 0.7 to 0.9 mgm. Ca per gram ofalbumin; the product m,2 " globulin fraction II"is a constant of the order 1.0 + 0.5 mgm. Ca per100 grams of serum H2O; m8 is of the order 0.1to 0.2 mgm. Ca per gram "globulin fraction I,"where " globulin fraction I " is arbitrarily defined

-as all globulin in excess of 3.0 grams of totalglobulin.

5. This equation appears to be more generallyvalid over the range of variation in serum pro-teins (within the limitations prescribed) than are

equations relating total calcium to total protein,to albumin and total globulin, or to albumin alone.

BIBLIOGRAPHY

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the inorganic bases and phosphates in relation to

the protein of blood and other body fluids inBright's disease and in heart failure. J. Biol.Chem., 1923, 58, 617.

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2. Marrack, J., and Thacker, G., The state of calciumin body fluids. Biochem. J., 1926, 20, 580.

3. Hastings, A. B., Murray, C. D., and Sendroy, J., Jr.,Studies of the solubility of calcium salts. I. Thesolubility of calcium carbonate in salt solutions andbiological fluids. J. Biol. Chem., 1927, 71, 723.

4. Peters, J. P., and Eiserson, L., The influence of pro-tein and inorganic phosphorus on serum calcium.J. Biol. Chem., 1929, 84, 155.

5. McLean, F. C., and Hastings, A. B., The state of cal-cium in the fluids of the body. I. The conditionsaffecting the ionization of calcium. J. Biol. Chem.,1935, 108, 285.

6. Gutman, A. B., and Gutman, E. B., Calcium-proteinrelation in hyperproteinemia: Total and diffusibleserum calcium in lymphogranuloma inguinale andmyeloma. Proc. Soc. Exper. Biol. and Med., 1936,35, 511.

7. Greenberg, D. M., and Greenberg, L. D., Is there anunknown compound of the nature of calciumcitrate present in the blood? J. Biol. Chem., 1932,99, 1.

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9. Peters, J. P., and Van Slyke, D. D., QuantitativeClinical Chemistry. Volume I. Interpretations.Williams and Wilkins Co., Baltimore, 1931, p. 814.

10. Flood, C. A., Gutman, E. B., and Gutman, A. B.,Phosphatase activity, inorganic phosphorus and cal-cium of serum in disease of liver and biliary tract.A study of one hundred and twenty-three cases.Arch. Int. Med., 1937, 59, 981.

11. Schmidt, C. L. A., and Greenberg, D. M., Occurrence,transport and regulation of calcium, magnesiumand phosphorus in the animal organism. Physiol.Rev., 1935, 15, 297.

12. Gutman, A. B., and Gutman, E. B., An empirical re-gression equation relating total serum calcium toserum albumin and globulins. Proc. Soc. Exper.Biol. and Med., 1937, 36, 527.

13. Williams, R. D., and Gutman, A. B., Hyperpro-teinemia with reversal of the albumin: globulinratio in lymphogranuloma inguinale. Proc. Soc.Exper. Biol. and Med., 1936, 34, 91.

14. Gutman, A. B., Gutman, E. B., Jillson, R., and Wil-liams, R. D., Acid-base equivalence of the blood indiseases associated with hyperglobulinemia; withspecial reference to lymphogranuloma inguinaleand multiple myeloma. J. Clin. Invest., 1936, 15,475.

15. Perlzweig, W. A., Delrue, G., and Geschickter, C.,Hyperproteinemia associated with multiple mye-lomas. Report of an unusual case. J. A. M. A.,1928, 90, 755.

16. McLean, F. C., and Hastings, A. B., A biologicalmethod for the estimation of calcium ion concentra-tion. J. Biol. Chem., 1934, 107, 337.

17. Weir, E. G., and Hastings, A. B., The ionization con-stants of calcium proteinate determined by the solu-

bility of calcium carbonate. J. Biol. Chem., 1936,114, 397.

18. Gutman, A. B., Tyson, T. L., and Gutman, E. B.,Serum calcium, inorganic phosphorus and phos-phatase activity in hyperparathyroidism, Paget'sdisease, multiple myeloma and neoplastic diseaseof the bones. Arch. Int. Med., 1936, 57, 379.

19. Robbins, C. L., and Kydd, D. M., A note on themetabolic criteria of hyperparathyroidism. J. Clin.Invest., 1935, 14, 220.

20. Wies, C. H., and Peters, J. P., The osmotic pressureof proteins in whole serum. J. Clin. Invest., 1937,16, 93.

21. Csap6, J., and Faubl, J., Calciumgehalt der Serum-eiweissfraktionen. Biochem. Ztschr., 1924, 150,509.

22. Bendien, W. M., and Snapper, I., Untersuchungenuiber die Bindung der Kolloide des Serums mitHilfe von Ultrafiltern erh6hter Durchlassigkeit.Biochem. Ztschr., 1933, 260, 105.

23. Schmitz, J. W., Over Den Toestand Van Het Cal-cium In Bloed En Serum. Jacob Van Campen,Amsterdam, 1937.

24. Loeb, R. F., The effect of pure protein solutions andof blood serum on the diffusibility of calcium. J.Gen. Physiol., 1926, 8, 451.

25. Felton, L. D., and Kauffmann, G., Certain character-istics of the water-insoluble protein of normal ascompared with that of antipneumococcus horse se-rum. J. Immunol., 1933, 25, 165.

26. Reiner, H. K., and Reiner, L., The fractional pre-cipitation of serum globulin at different hydrogenion activities. Experiments with globulin obtainedfrom normal and immune (antipneumococcus)horse serum. J. Biol. Chem., 1932, 95, 345.

27. Liu, S. C., Wu, H., and Chow, B. F., Isolation of abasic globulin fraction from normal and immunehorse sera. Chinese J. Physiol., 1937, 11, 211.

28. Green, A. A., The euglobulins of serum and theircombination with acid and base. J. Biol. Chem.(Proc.), 1937, 119, xxxix.

29. Chopra, R. N., and Chaudhury, S. G., Studies on thephysical properties of different blood sera. V.Buffer action. Indian J. M. Research, 1933, 21,25.

30. Clark, E. P., and Collip, J. B., A study of the Tisdallmethod for the determination of blood serum cal-cium with a suggested modification. J. Biol.Chem., 1925, 63, 461.

31. Folin, O., and Wu, H., A system of blood analysis.J. Biol. Chem., 1919, 38, 87.

32. Howe, P., The determination of proteins in blood-a micro method. J. Biol. Chem., 1921, 49, 109.

33. Bodansky, A., Phosphatase studies: 1. Determinationof inorganic phosphate; Beer's law and interferingsubstances in the Kuttner-Lichtenstein method. J.Biol. Chem., 1932, 99, 197.

34. Gutman, A. B., and Gutman, E. B., Unpublishedstudies.

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kb...(3) subsequently expressed this proportionality between total calcium and total protein more...

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