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COMPOSITION OF BONE.IX. EQUILIBRATION OF SERUM WITH DICALCIUM PHOSPHATE.*

BY M. J. SHEAR AND BENJAMIN KRAMER.(From the Pediatric Research Laboratory, The Jew ish Hos pital of Brooklyn,

New York.)(Received for publication, January 27, 1930.)

The mechanism of calcification is still obscure. One theory (2)postulates the formation of intermediate calcium-protein andcalcium-protein-phosphate compounds, produced by the inter-action between the cartilage protein and the calcium and phos-phorus of the body fluids; the calcium-protein-phosphate com-pound is supposed to decompose with the formation of calciumphosphate and the release of the protein. The other leadingtheory ascribes calcification to the precipitation of CaS(PO&and CaC03.A number of lines of evidence point to precipitation of calciumphosphate as a likely mechanism. Thus the correlation betweennormal calcification, healing rickets, and active rickets on the onehand, and the empirical Ca X P product of Howland and Kramer(3) on the other, is suggestive of the operation of a solubilityproduct. Furthermore, experiments on calcification in vitro (4, 5)show that calcification may be produced or prevented at willmerely by changing the concentrations of calcium and phosphorusin the inorganic serum solution in which the calcifying tissue isimmersed. Here, too, the occurrence of calcification and theCa X P product are related in such a way as to suggest the pre-cipitation of calcium phosphate. The inhibitory effect of mag-nesium on in vitro calcification (6-8) is overcome by increasedconcentration of phosphate; increase of the ionic strength of thesolutions also inhibits calcification in vitro (7, 9). These factors

* A preliminary report (1) was read before the Society for ExperimentalBiology and Medicine, New York, October 16, 1929.677

byguest,onJanuary21,2012

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678 Composition of Bone. IXaffect calcification in a manner analogous to their effect on theprecipitation of calcium phosphate.

However, physicochemical studies (10-26) have not borne outthe view that calcification is due to the precipitation of Ca3(PO&.Thus, Holt, La Mer, and Chown (10) and Holt (11) were led to theconclusion that even ricketic serum is supersaturated with respectto Ca3(P04)2. Sendroy and Hastings (12) concluded that serumdoes not appear to be supersaturated with respect to Ca3(PO&in the usual sense of the term and that supersaturation cannotbe the sole explanation for the apparently abnormal amounts ofcalcium in serum. Klinkes (13) experiments constitute additionalevidence against the view that serum is supersaturated withrespect to Ca3(POJ2.

It might therefore be concluded that the precipitation theory ofcalcification is untenable. But before abandoning this theory,another alternative remains to be investigated; namely, thepossible bearing of CaHP04 on this problem.We realize, of course, that the presence of CaHP04 in bones hasnever been demonstrated (14, 15). Nevertheless, it is of interestto obtain data on the solubility relations of CaHP04 to see whatlight they can throw on the mechanism of calcification.

Because the proteins present in serum give rise to complications,we studied the solubility equil ibria of CaHP04 in protein-freesolutions first. It was found (15) that solutions with the inorganiccomposition of ricketic blood serum are markedly undersaturatedwith respect to CaHP04 and that it is only solutions which haveCa X P products greater than about 50 which are supersaturatedwith respect to this compound.

It had been pointed out previously (14, 15) that the ion product[Ca+f] X [HPOd=] in a serum with a given calcium and phos-phorus content cannot be greater than the ion product in aninorganic serum solution with the same calcium and phosphoruscontent. If the value of this ion product is different it must beless in serum, since part of the serum calcium appears to be boundto protein, thus making [Ca++] in serum less than [Cal. On thebasis of these considerations it appeared that blood sera withCa x P products of 50 or less are undersaturated with respectto CaHP04.

The present paper is a report of experiments in which bloodsera were shaken with crystalline CaHP04.


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M. J. Shear and B. Kramer 679Methods.

Calcium and phosphorus were determined in duplicate asdescribed previously (15). The CaHP04 used was the sameanalyzed crystalline2 preparation used in the previous experiments(15). The new Hastings hydrogen ion calorimeter (Bauschand Lomb) was employed for the determination of pH. Theequilibration was carried out at 38 f 2. Total nitrogen andnon-protein nitrogen were determined according to the method ofVan Slyke (27).

Calculations.-The calculation of [HPOk=] is the same3 as thatemployed for protein-free solutions (14, 15). [Cal is the totalcalcium as given by analysis; the symbol [Ca++] represents theconcentration of calcium ions.

Calf Serum.Serum from the blood of a 6 months old calf was analyzed induplicate for calcium, phosphorus, and pH. Two 20 cc. aliquots

of the serum were shaken with CaHP04 for 1 hour as previouslydescribed; two other aliquots were shaken for 2 hours. Theresults are given in Table I.

Our previous experiments, in which protein-free serum solutionswere shaken with CaHPO+ showed that equilibrium was attainedafter shaking for only 1 hour; the equilibrium constant obtaineddid not change during the subsequent 3 hours. Serum similarlycomes rapidly into equilibrium with CaHP04.

1 In this paper phosphorus means the inorganic phosphorus of theserum.2 These crystals of CaHPOl had been dried at 110 for 7 hours. Theanalytical data showed that the specimen so prepared contained 1.87molecules of water of crystallization for every molecule of CaHPO4.8 This depends on the assumption that the total inorganic phosphorus asobtained by analysis is present as phosphate ions. This appears to be avalid assumption since numerous investigators have found that the in-organic phosphorus in serum is 100 per cent dialyzable. Grollman (28)found that addition of large amounts of calcium to serum reduced therelative amount of filtrable phosphorus. However, for mammalian serumhe found that the phosphorus begins to be held back only when the empiricalCa X P product exceeds 95. In all of the sera studied here the Ca X Pproducts were less than 90.


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680 Composition of Bone. IXTABLE I.

Sera Equilibrated with CaHP04 at 58.

Specimen.*[Cal [PI [HPOa] Khl x

$12 jlj iT&E

Calf serum.

1 hr. (a)

1 (b)

nu42.642 592.62

Same

2 hrs. (a) Sam e

2 (b) Sam e

?nM 7nM2.52 2.422 52 2 36__-2.52 2.392.42 Same2.442.432.34 Same2.372.362.39 Same2.422.41

x 1065.2

77L.u7L.u rnM ?nMnM ?nM x 1062.87.872.68.682.78.78 7.50 1.982.41 5.2.50 1.982.412.80.802.84.842.82.82 7.53 1.982.50 5.2.53 1.982.50 5.22.93.932.84.842.89.89 7.48 1.982.51 5.2.48 1.982.51 5.22.87.872 80802.84.84 7.49 1.982.47 5.2.49 1.982.47 5.2

-< 106

6.1

6.1

5.9

6.0-Lamb sera equilibrated for 1 hr.?

Serum 1. 2. 3.IL 4.

2.62 2.65 2.29 2.45 7.58 1.902.18 5.0 5.82.34 2.32 2.90 3.00 7.55 2.412.67 5.6 6.22.47 2.44 2.35 2.58 7.57 1.952.29 4.8 5.62.52 2.59 2.35 2.55 7.49 1.952.21 4.9 5.7

Human sera equilibrated for 1 hr.?Cord 1. 2.77 2.87 1.77 2.06 8.4 1.472.02 4.1 5.8

CL 2. 2.87 2.87 1.58 1.84 7.85 1.311.73 3.8 5.0 3. (a) 2.92 2.94 1.94 2.10 7.58 1.611.87 4.7 5.5 3. (b) 2.92 2.87 1.94 2.06 7.63 1.611.85 4.7 5.3

Adult cardiac. (a) 2.42 2.69 1.74 2 .45 8.03 1.442.35 3.5 6.3 (b) 2.42 2.69 1.74 2.32 8.06 1.442.33 3.5 6.0Normal adu lt. (a) 2.50 3.19 1.13 2.16 7.62 0.941.92 2.4 6.1

CL (b) 2.50 3.22 1.13 2 .19 7.53 0.941.93 2.4 6.2* (a) and (b) indicate duplicate experiments.t The values given for calc ium and phosphorus are the averages of two

determinations (cf. calf serum).


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M. J. Shear and B. Kramer 681There is excellent agreement between the duplicate experiments

at 1 hour of equilibration; the same holds true for the duplicateexperiments at 2 hours. Such equilibration experiments withserum are therefore accurately reproducible. There is no appre-ciable change in the [Cal X [HP04=] products after the 1st hour.In all the subsequent experiments, therefore, the sera were shakenfor only 1 hour.

After the serum was shaken for 1 hour the calcium decreasedabout 5 per cent; the phosphorus, however, increased about 16per cent. In the duplicate experiment the calcium decreasedabout 7 per cent while the phosphorus increased about 19 per cent,After the serum was shaken for 2 hours, the calcium decreased 9.5per cent; the phosphorus, however, increased about 22 per cent.The duplicate 2 hour experiment gave results for calcium andphosphorus that were almost identical with those of the duplicate1 hour experiment. Equilibration had resulted in a definiteincrease in the product [Cal X [HPOh=] from 5.2 X 10V6 to(6.0 f 0.1) X 10-6.

Lamb Serum.In this set of experiments the blood sera of four lambs, al l of

them 6 months old, were employed. The results are given inTable I.For the first three sera, the calcium values after equilibrationwere the same, within the analytical error, as the init ial values;in Lamb Serum 4 there was a small but definite increase in calcium.The phosphorus value in each case increased slightly but definitelyas a result of equilibration.

The [Cal X [HP04=] products in the sera as drawn wereunusually high; these sera were obtained from healthy younganimals at an age when calcification is occurring vigorously. Inspite of the high concentrations of calcium and phosphorus presentinitially, these sera were undersaturated with respect to CaHP04.This is shown by the increase in the [Cal X [HPOa=] productsfollowing equilibration.

Human Serum.The first three specimens were taken from the cord at delivery.They show little change in calcium and a definite increase in


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682 Composition of Bone. IXphosphorus as a result of shaking with CaHP04. This increase isalso shown by the increase in the [Cal X [HPOI=] products.(See Table I.)In three cases the equilibration was performed in duplicate;these are indicated by the letters (a) and (b) in Table I. Thesera were analyzed for calcium and phosphorus in duplicate, butonly the mean values are given in Table I; the agreement betweenduplicate analyses of the same serum was the same as that shownin the experiments on calf serum.

Equilibration produced an 11 per cent increase in calcium and a41 per cent increase in phosphorus in the serum of an adult cardiac.The product [Cal X [HP04=] increased markedly from 3.5 X lo- 6to 6.3 X 10-6. A duplicate experiment gave similar results.

The most striking change was obtained with the serum from anormal adult. The final calcium was 28 per cent greater thanthe init ial value, and the final phosphorus was 91 per cent greaterthan in the serum as drawn. The [Cal X [HPOd=] productshowed a striking increase from 2.4 X 10e6 to 6.1 X 10-6. Aduplicate experiment gave similar results.

E$ect of Xhalcing on Inorganic Phosphorus.The question arose as to whether mere shaking for 1 hour at 38,

in the absence of the solid phase, might not produce an increasein the inorganic phosphorus concentration of serum. This ap-peared improbable for many reasons; but even if it did occur, itwould not affect the conclusions drawn. No matter what theorigin of the additional inorganic phosphorus, the fact that thesera were capable of retaining this increased concentration ofphosphorus with an accompanying increase in the value of the[Cal X [HPOd=] product in the presence of the solid phase, showedthat the sera were initially undersaturated with respect to CaHP04.Certainly the calcium cancentrations could not increase, as theydid in the adult human sera, in the face of such marked increasesin phosphorus concentration unless the sera were definitelyundersaturated with respect to CaHPO .

Nevertheless, to rule out whatever doubt remained on thispoint the following experiment was performed. A specimen ofadult human serum was divided into four aliquots. One aliquotwas analyzed for inorganic phosphorus. The other three aliquots


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M. J. Shear and B. Kratier 683were then put into the thermostat. One aliquot was shaken withCaHP04 for 1 hour at 38; another aliquot was shaken for 1 hourat 38 without the addition of the solid phase. A fourth aliquotwas left undisturbed in the thermostat for 1 hour at 38 withoutthe addition of any solid phase and without shaking. They werethen al l analyzed at the same time for calcium and inorganicphosphorus. The results are given in Table II.

TABLE I I .Effect of Shaking on Inorganic Phosphorus.

Adult human Serum 3.Aliquot. Treatment.

-

i

None.

1 hr. at 38. No CaHPO a. No shakin g.

1 I I 38. Shaking.

1 38. Shak ing with CaHPOa.

ng. percent ,nY3.43.23.3

9.8 3.39.9 3.49.9 3.49.8 3.39.8 3.49.8 3.4

11.4 5.211.3 5.011.4 5.1

P

It is seen that standing for 1 hour at 38 does not result in anincrease in the inorganic phosphorus. Neither does shakingwithout the solid phase or 1 hour result in any rise in the inorganicphosphorus concentration. Shaking with CaHP04, however,produces a striking increase in the phosphorus concentration from3.4 mg. per cent to 5.1 mg. per cent. At the same time there is adefinite increase in the calcium content from 9.9 mg. per cent to11.4 mg. per cent.This shows unmistakably that the increase in the phosphorusconcentration, as well as the increase in the calcium concentration,is due to the presence of CaHP04.


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684 Composition of Bone. IXpH Change Produced by Equilibration.

The specimens of blood were obtained under conditions whichrendered it impossible to avoid the loss of some COS. The initialpH was therefore not determined; it was assumed to be 7.35 inall the sera (29).

In a number of instances one aliquot of the serum was stopperedand set aside without the addition of CaHP04. After equilibra-tion of the other aliquot, the pH of the equilibrated and non-equilibrated aliquots were determined at the same time. Table IIIshows that the sera not equilibrated were all somewhat morealkaline than pH 7.35, due in all probability to loss of some COz.

TABLE I I I .pH Change in Serum Produced by Equilibration with CaHPOd for 1 Hour.

SWU IIL Not equilibrated.

Calf. 7.79 7.79Cord 1. 8.08

I 1. 8.08Adult cardiac. 7.66 I 7.66Normal adult. 7.68 I 7.68

* (a) and (b) indicate duplicate experiments.

Equilibrated.*

(a) 7.50(b) 7.53(a) 8.03(b) 8.06(a) 7.58(b) 7.63(a) 7.62(b) 7.53

Equilibration with CaHP04 produced very little change in pH as isseen from Table III; there was in each case a slight change towardsthe acid side. However, in no case was the change sufficient torender the serum more acid than pH 7.50.

The pH values given in Table I are those obtained for the varioussera after equilibration. It will be noted that the pH in no caseis lower than 7.48. Thus after equilibration in no instance is thepH value more acid than normal serum (29). The increasedconcentrations of calcium and phosphorus therefore cannot be dueto an increase in the solvent power of the sera resulting from apH more acid than normal.


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M. J. Shear and B. Kramer 685DISCUSSION.

These experiments were performed to determine whether shakingserum with CaHP04 for brief periods would result in an increaseor a decrease in the concentrations of calcium and phosphorus.Since there resulted in each case an increase in the phosphorusconcentration and in some cases an increase in the calcium con-centration aswell, such that in al l sera the [Cal X [HPOI=] productsincreased as a result of equilibration, it appears evident that serumis undersaturated with respect to CaHP04. Furthermore, thelower the init ial products, the greater is the degree of under-saturation.

Mond and Netter (23) shook bovine serum, containing 9.4 mg.per cent calcium, with CaHPOd. At the end of 1 hour the serumcalcium was unchanged. After the serum was shaken for 3 hoursthe calcium fel l to 8.6 mg. per cent. At the end of 63 hours it hadfallen to 8.1 mg. per cent. These authors concluded that serumwas supersaturated with respect to CaHP04 and that when serumis shaken with solid CaHP04, a small quantity of CaHP04 gradu-ally precipitates out.

It may be pointed out that shaking with CaHP04 can produce adecrease in the calcium concentration without a simultaneousdecrease in phosphorus. In fact the phosphorus may increase sothat the [Cal X [HP04=] product is greater after equilibrationthan in the serum initially. This is shown clearly by the dataon calf serum in Table I.

Calcium values alone, therefore, do not provide sufficientinformation on which to base conclusions regarding the occurrenceof precipitation, or the existence of supersaturation. Sincephosphorus values and pH values are both lacking in the paper ofMond and Netter, [Cal X [HPOI=] cannot be calculated fromtheir data.

Kleinman (25) also equilibrated serum with CaHP04. Heconcluded Tabelle xx zeigt, dass sekundares Calciumphosphat alsBodenkorper wirkungslos ist. However an inspection of hisTable xx shows that although the calcium had not changed, thephosphorus had increased slightly but definitely. Kleinman haddone his four experiments with one serum specimen; apparentlythat particular serum was only very slightly undersaturated withrespect to CaHP04. In the light of our results with Lamb Serum


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686 Composition of Bone. IX2 (Table I), it is readily understood how, if our equilibrationexperiments had al l been performed with that serum alone, wealso might have concluded that CaHPO* is without effect.

Nitschke and Freyschmidt (21) considered serum to be satu-rated with respect to CaHP04. In a later paper, Nitschke (22)concluded from dialysis experiments that, in serum which contains10 mg. per cent calcium and 3.7 mg. per cent phosphorus, about 2mg. per cent calcium is bound to protein, about 5.6 mg. per centis in the form of calcium ions, and that about 2.4 mg. per centcalcium exists as molecular CaHP04. He also concluded Dieauf dieselbe Weise bestimmte Gleichgewichtskonstante fur iiber-sattigte Calciumphosphatlijsungen betragt fiir die Gleichung

[&++I X [HPOa=I = K = 67 X lo-Nitschke did not perform any equilibration experiments withsolid CaHP04. Inspection of his data shows that his solutions

had a composition analogous to those of our solutions which wereundersaturated as evidenced by equilibration with solid CaHP04(15).Peters and Eiserson (30) studied the relative effects of phos-phorus and protein on serum calcium. Following a suggestion ofProfessor A. B. Hastings, these authors attempted to correlatetheir data with the solubility of CaHPOd as follows: If thesolubility product of CaHP04 were the factor responsible for theeffect of P on Ca, then the curve of ionized Ca and HP04 shouldbe a right angle hyperbola and the curve relating their logarithmsshould be a 45 straight line.

It seems to us that this should hold true only if sera were justsaturated with respect to CaHPO*. If sera were exactly saturatedwith respect to CaHP04 then

[Ca++J X [HPOI~ = K'*.p CaHP04Graphically this is given by a rectangular hyperbola since it isof the form xy = constant. However, our experiments show thatserum is undersaturated with respect to CaHP04 and that thedegree of undersaturation varies from serum to serum. The ionproduct [Ca++] x [HPOI=] in serum therefore cannot be aconstant.

Peters and Eiserson applied this criterion and concluded


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M. J. Shear and B. Kramer 687The results were not satisfactory. . . . This does not prove thatthe solubility product of CaHP04 is not the factor responsible forthe effect of P on serum Ca. It may only mean that the calcula-tions involved in the indirect estimation of HP04 were not suffi-ciently accurate.

We wish to point out that even if [HPOd=] were obtainedaccurately from direct determinations of pH, and even if a methodwere available for obtaining [Ca++] accurately, still the curverelating their logarithms should not be a 45 straight line forserum as drawn. This relationship should be expected to holdonly in sera exactly saturated with CaHP04.

Calcium Ion Concentration in Serum.Calcium is essent.ial for calcification. However, the form in

which calcium is present is as important as the total amount ofcalcium given by analysis. Thus Shipley, Kramer, and Howland(5), in their experiments on calcification in vitro, found that whenthe calcium was present as chloride, acetate, or lactate, calcifica-tion was prompt and thorough; when the calcium was present ascitrate no calcification was obtained.

Recent conductivity studies (31, 32) showed that the citrateions combine with the calcium ions to form an unionized complex;the presence of citrate causes a marked diminution in the calciumion concentration. It is thus seen that citrate inhibits calcifica-tion because it decreases the calcium ion concentration; forcalcification to occur, the calcium must be present as calcium ion.

There are no methods in the literature for the accurate deter-mination or calculation of [Ca++] in individual specimens of serum.Until an accurate direct method is devised, the concentration ofionized calcium in serum can be obtained only approximatelyfrom indirect estimations. It is of interest in this connection tonote that the data obtained in the equilibration experiments withCaHP04 may be utilized for calculating the approximate value ofthe ionized and bound calcium in serum. At present we do notknow how valid are the assumptions involved in such a calculation;the values of the calcium ion concentration so obtained are there-fore of undeterminable accuracy. However, the results obtainedwith this new method are in agreement with the values for calciumion concentration obtained by other investigators who used totallydifferent methods.


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688 Composition of Bone. IXAfter inorganic serum solutions were shaken with CaHPOd

for 1 hour at 38, the product [Ca++] X [HPOd=] was a constant(3.4 f 0.1) x 10-C. In serum, similarly shaken with CaHP04,the product [Cal X [HPOd=] was not a constant. Althoughduplicate experiments gave results which were in good agreement,the product varied from serum to serum; the values ranged from5.0 X 1O-6 to 6.3 X 10-6. All the products were greater than3.4 X lO-j, the value for inorganic serum solutions.

Since equilibrium had apparently been established between thesolid CaHP04 and the sera, the ion product [Ca++] X [HPOI=]in the sera should be the same as in inorganic serum solutions inequilibrium with CaHP04; i.e., 3.4 X 10d6. The products[Cal X [HPOI=] were greater than K,,,.CaHP04. Thisindicates that part of the total calcium was bound in a formwhich rendered it unavailable for this ionic equilibrium.

In the equilibrated serum, the calcium ion concentration shouldbe given by

[Ca++l K& CaHPObequil. = [HPOI=l,q,il.and the bound calcium, [CaX], should be given by

(1)

(2)where [CaX] is the concentration of bound calcium and [Cal isthe concentration of total calcium after equilibration.

The assumption is next made that the concentration of boundcalcium is the same before and after equilibration. This wouldappear to be a valid assumption in those cases in which equilibra-tion produces little or no change in the total calcium and in PH.~The concentration of ionized calcium in the serum as drawn canthen be obtained from the expression

where[Ca+l serum = [Cd8erum - lCaXlserum (3)

[Ca++] = concentration of ionized Ca in serum as drawn.[Cal = i tota1 (L I [CaX] = t bound I<

4 In those cas es where there has been a change in pH, the amount ofcalciu m bound at pH 7.4 may be calcula ted from the amount bound at thepH of equilibrated serum by means of an expression derived from Equation72 of Ha sting s, Murray, and Sendroy (24).


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Concentration OfSpecimen.

(1)-

Calf.

Lamb 1.

I 2.

3.

4.

Human cord 1.

C 2

I 3

Adult cardiac.

Normal adult.

1.05 0.0:1.04 0.03__-1.05 0.031.11 0.041.09 0.04--1.10 0.041.21 0.021.18 0.04--1.20 0.031.27 0.021.37 0.02--1.32 0.021.39 0.031.31 0.02__1.35 0.03

1.16 0.041.16 0.04__1.16 0.041.02109 0.051.061.111.13 0.06_1.121.471.45 0.241.461.381.42 0.051.40

-

6.4

6.6

7.3

8.1

8.3

7.0

0 6.3

3 6.6

8 7.6

3-

8.4

TABLE IV.Ionized Calcium in Serum.-I d I Bound Ca:T

mo .Per100 ccno .Pergm .

4.2 6.3 60 0.663.9 6.6 63 0.61

10.5 4

9.4 4

9.9 3

10.1 4.

11.1 4

11.5 3

11.7 (a) 4(b) 4.

3.9 6.6 63 0.59

3.8 5.6 60 0.52

3.5 6.4 65 0.43

4.0 6.1 60 0.48

2.8 8.3 75 0.40

2.8 8.7 75 0.44

4.0 7.7 66 0.613.5 8.2 70 0.53

9.7 (a).5. 3.5 6.2 64 0.46(b) 4. 3.2 6.5 67 0.42

10.0 (a) 5. 4.9 5.1 51 0 .58(b) 5. 5.4 4.6 46 0.64

Average.............................................* (a) and (b) indicate duplica te experiments.

689

6.6 - 63 0.53


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690 Composition of Bone. IXThe results obtained by the aid of such calculations are given in

Table IV. In order to see whether there is any regular relation-ship between the concentration of CaX when calculated in thisway and the serum protein concentration, the sera were analyzedfor total nitrogen and non-protein nitrogen. Column 4 gives theprotein content in gm. per 100 cc. The total calcium in theoriginal sera is given in Column 5. The bound calcium CaX, inthe serum at equilibrium is given in Column 6; the calcium boundat pH 7.4 was calculated from the values in Column 6 by means ofthe expression

[CaXL?,,, = [CaX lequil, X 74 - .OPHepuil. - Owhich was derived from Equation 72 of Hastings, Murray, andSendroy (24). These values are given in Column 7. The calciumion concentrations in the original serum calculated with the aidof these four equations are given in Column 8. Column 9 givesthe per cent of total calcium which is present in the original serain ionized form. All of the concentrations in Table IV are ex-pressed in terms of mg. and gm. per 100 cc.

In order to see what relation exists between the protein con-centration and the concentration of bound calcium, the data inColumn 10 were calculated. This column gives the ratio of mg.of bound Ca per gm. of serum protein.

It will be seen from Table IV that the values for ionized calciumgive an average of 6.6 mg. per 100 cc., and that the average ratioof bound Ca: protein is 0.53 mg. per gm. These results may beformulated as follows:

Ca = 0.53 X protein + 6.6 (5)This is quite similar to the results obtained by other investi-

gators. Hastings, Murray, and Sendroy plotted total calciumagainst protein and obtained an expression which may be written5

Ca = 0.56 X protein + 5.6 (6)Peters and Eiserson, using the same statistical method, obtained

Ca = 0.56 X protein + 6.0 (7)6 See reference (30), footnote on page 158.


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M. J. Shear and B. Kramer 691Marrack and Thacker (19) applied a similar method to data on

various body fluids and obtained three straight lines whose equa-tions may be written

Ca = 0.66 X protein -I- 6.0 (8)Ca = 0.61 X protein + 5.5 (9)Ca = 0.55 X protein + 5.0 (10)It is interesting to note that although the calculation of [Ca++]in serum from [Cal X [HPOd=] involves a number of assumptions,the results obtained are in agreement with those obtained by otherindirect methods. According to Column 9 of Table IV about 60per cent of the calcium in serum is present as calcium ion; thevalues range from 46 per cent to 75 per cent. These valuesare similar to those obtained by numerous investigators whoemployed dialysis and ultrafiltration methods for estimatingthe concentration of diffusible calcium in serum.6

CONCLUSION.These equilibration experiments show that serum is under-saturated with respect to CaHP04. In normal young animals,in whom calcification is proceeding vigorously, the calcium andinorganic phosphorus concentrations in the serum may reach highlevels; such sera are only slightly undersaturated with respect toCaHP04. Sera which contain concentrations of Ca and P such asoccur in normal adult animals or in ricketic young animals aremarkedly undersaturated with respect to CaHP04.It may be remarked here that the concentrations of calciumand of phosphorus in serum are not the only factors which areinvolved in calcification. The conditions existing locally in thetissues must be understood before we can have a complete descrip-tion of the mechanism of calcification.6 These results should not be construed as demonstrating that all of thebound calcium is tied to protein. At, present it is impossible to determinewhat percentage of serum calcium is bound to protein, and how much isbound to other unknown factors. If the values for [Ca++] obtained by theuse of Equations 1 to 4 are correct, then the difference between the total andionized calcium gives the concentration of bound calcium. It, does not,,however, give any information as to the form in which the bound calciumexists. The ratio bound Ca: protein was calculated merely for the sakeof comparison with the results obtained by other investigators who em-ployed entirely different methods in calculating this ratio.


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692 Composition of Bone. IXWith a given state of affairs in the provisional zone of calcifica-

tion, the occurrence of calcification will depend on the chemistryof the serum. On the other hand, with a given state of affairs inthe chemistry of the serum, the occurrence of calcification willdepend on the local factors. When rickets heals, calcificationdoes not occur simultaneously in all regions of the affected areas,this indicates that there may be marked differences in the localfactors in different parts of the same bone. Thus Hess, Wein-stock, Rivkin, and Gross (35) report the experimental productionof a type of rickets which persists in the face of high concentrationsof serum calcium and phosphorus. They attribute this to highlyadverse local conditions.The composition of bone is not known with certainty. On theone hand, the main constituent is generally stated to be Ca3(PO&or a compound with the formula 3Ca3(POd)z.CaC03, analogousto minerals of the apatite group. However, as pointed outpreviously (14, 15), neither of these compounds has as yet beendemonstrated to be present in bone. Furthermore, solubilitystudies have as yet not succeeded n showing that such compoundsmay be obtained by precipitation from body fluids, or that theymay exist in equilibrium with body fluids.On the other hand, neither has the presence of CaHP04 inbones been demonstrated. Furthermore, it is generally statedthat in neutral or alkaline solutions Ca3(PO&, or a still morebasic phosphate, is precipitated and that CaHP04 is obtainableonly from definitely acid solutions. Finally bone analyses givevalues which more nearly fit such formulas as Caa(PO& or3Ca3(P0&CaC03 than CaHP04.Yet, CaHP04 comes rapidly into equilibrium with inorganicserum solutions and with serum. This curious finding raises thequestion as to whether K,.,,CaHP04 is of biological significance.

Miss Dora Luntz and Mr. Jac Siegel gave technical assistancein these experiments.SUMMARY.

1. Blood sera were shaken with crystalline CaHP04 for 1 hourand then analyzed for calcium, phosphorus, and pH.7 Cf . discussion of Local Factors by Shear and Kramer (14) pages139-140. See also Jones (33) and Hess (34) page 138.


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M. J. Shear and B. Kramer2. The product [Cal X [HPOI=] increased in each case as a

result of equilibration.3. The lower the initial value of [Cal X [HPOI=] in the serum

as drawn, the greater was the increase produced by equilibration.4. These experiments show that serum is undersaturated with

respect to CaHP04.BIBLIOGRAPHY

1. Shear, M. J., and Kramer, B., Proc . Sot. Exp. Biol. and Med., 27,46 (1929).

2. Freudenberg, E., and Gyiirgy, P., Bioc hem . Z., 110, 299 (1920); 116,96 (1921); 118, 50 (1921); 124, 299 (1921). Gyiirgy, P., Jahrb. Kinder-heilk., 102, 145 (1923). Brehme , T., and Gyiirgy, P., Bioc hem . Z.,167, 243 (1925). Schwa rz, R., Ede n, R., and Herrmann, E., Bio che m.Z., 149, 100 (1924). Do lhaine , H., Bioc hem . Z., 178, 233 (1926).

3. Howland, J., and Kramer, B., Tr. Am. Pediat. Sot., 34, 204 (1922).4. Shipley, P. G., Bu ll. John s Hopkins Hosp., 36, 304 (1924).5.. Shipley, P. G., Kramer, B., andHowland, ,J., Bioche m. J., 20,379 (1926).6. Kramer, B., She lling, D. H., and Orent, E. It., Bu ll. John s Hopkins

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(1929).16. Kuge lmass, I. N., and Shoh l, A. T., J. Bio l. Chem., 58, 649 (1923-24).17. Behrendt, H., Bioche m. Z., 146,318 (1924).18. Hollo, J., Bioche m. Z., 160, 496 (1924).19. Marrack, J., and Thac ker, G., Bioc hem . J., 20,580 (1926).20. Warburg, E. J., Bioche m. Z., 178,208 (1926).21. Nitschke, A., and Freyschmidt, 11. J., Bioche m. Z., 174,287 (1926).22. Nitschke, A., Bioche m. Z., 192, 123 (1928).23. Mond, R., and Netter, H., Arch. ges . Phy siol., 212, 558 (1926).24. Ha sting s, A. B., Murray, C. D., and Sendroy, J., Jr., J. Bio l. Ch em.,

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