,June, 1963
BINDING OF
CALCIUM
the expansion of the radial function of the partly filled 4f-shell by covalent bonding retains its validity. In general, a similar effect was observed in the present investigation, particularly with the light lanthanides. I n the heavy half of the series, a comparison of the spectra of the aquo ion with that in the anhydrous molten nitrate frequently revealed little or no definite change in the energy of the band maxima. I n this connection the spectrum of Er+3 proved to be an ex-
IONS TO
SERUM A L B U M I N
1211
ception, exhibiting in general a small shift toward higher energies. This is in the same direction as the shift observed for many solid anhydrous lanthanide fluorides. Acknowledgment.-The author wishes to acknowledge numerous helpful discussions with D. M. Gruen and P. R. Fields during the course of this work. The assistance of R. In. McBeth in obtaining the experimental data is also gratefully acknowledged.
THE BINDING OF CALCIUM IONS TO SERUM ALBUMIN BY H. A. SAROFF AND M. S. LEWIS Xational Institute of Arthritis and Metabolic Diseases, h'ational Institutes of Health, Public Health Service, U . S. Depurtment of Health, Education, and Welfare, Bethesda, Maryland, and National Institute of Dental Research, National Institutes of Health Received November 9, 1968 The binding of C a t + , OH-, and C1- to deionized serum albumin was studied in the pH region of 5 to 10.5. Known constants and simple electrostatic contribution of the charge of the albumin molecule predicted binding in excess by a factor of four over that found experimentally. The interpretation of the data offered in this communication is one involving a carboxylate ion-amino or imidazole chelate aEi the principal binding site for calcium ions.
A number of studies have been reported on calcium binding to serum a1bumin.l-7 The increase in binding with increased pH has generally been attributed to In order to examine more electrostatic effect^.^ carefully the binding of calcium ion, simultaneous measurements were made on (1) the binding of Ca++, ( 2 ) the binding of OH-, and (3) the binding of C1in solutions of deionized human serum albumin containing oiily added calcium hydroxide and calcium chloride. The results of these measurements and their interpretation in light of existing theory are reported in this communication. Materials and Methods Human serum albumin was a sample of Fraction V, lot, number 752, obtained from the American Red Cross. This sample of albumin, on analysis by velocity ultracentrifugation, was found to be as homogeneous as crystalline preparations used in this Laboratory and was considered adequate for this study. A molecular weight of 68,000 g. was employed in the calculations. The albumin was deionized on a mixed bed resin column according to the procedure of The water used in preparing solutions for binding measurements was boiled to remove dissolved COZ. Protein solutions were adjusted to the required pH with calcium hydroxide and the remainder of the required total calcium was added as calcium chloride. All solutions were measured within a period of 24 hours of their preparation and were prepared and kept under nitrogen. Measurements were made a t 25 f 1'. pH measurements were made on a Beckman model G pH meter. Calcium and chloride ion concentrations were measured by the method previously describedQJOin a cell equipped with both negative (sulfonic acid resin) and positive (quaternary amine resin) permselective membranes. The membranes were supplied by the National Aluminate Corporation, Chicago, Illinois. The cell consisted of three lucite blocksl drilled and clamped together to form three compartments with connecting holes to (1) F. C. MoLean and A. B. Hastings, J. B i d . Chen., 108,285 (1935). (2) E. G. Weir and A. B. Hastings, ibid., 114, 397 (1936). (3) J . C. Abels, J Am. Chem. Soc., 68, 260 (1936). (4) J. T. Edsall, H. Edelhooh, R. Lontie, and 1'. R. Morrison, i b i d . , 72, 4641 (1950). ( 5 ) C. W. Carr, Arch. Biochem. Biophys., 48, 147 (1953). (6) S. Katz and I. M. Klotz, ibid., 44, 351 (1953). (7) L. I. Irons and D. J. Perkins, Biochem. J., 84, 152 (8) H. Dintzis, Ph.D. Thesis. Harvard University, 1952. (9) M. 6. Lewis and H. A. Saroff, J . Am. Chem. SOC.,79, 2112 (10) H. A. Saroff and J. W. Healy, J. P h y s . Chen., 63, 1178
(1962).
(1957). (1959).
the sample and solution reservoirs and to the stopcocks in which liquid junctions were made to calomel electrodes. The middle compartment was separated from the compartment on one side by a negative permselective membrane and from the compartment on the other side by a, positive permselective membrane. Protein solutions were placed in the center compartment and calcium chloride solutions of known concentrations were placed in the two side compartments allowing for measurement of potentials to determine both Ca++ and C1- activities.
Results The experimental results are summarized in Table I and the experimental points of Fig. 1. Although little drift occurred in the measurements of both the calcium and chloride ions the chloride ion measurements became unreliable above pII 9. The cause of this unreliability was probably the biionic potential'l resulting from the presence of the hydroxyl ion. The value of FCL was taken as zero a t pH values above 9. When the hydroxyl, chloride, and calcium binding data are summed to calculate the net charge on the protein molecule it becomes obvious that electrostatic factors in the binding are not d primary importance for the p H dependence of the binding. Thus, from pH 5.3 to 7 the net charge on the albumin increases from -4 to -13 and the binding of calcium ion increases from 0 to 2 ions per mole of albumin, while in the pH region from 7 to 10, the net charge increases from -13 to -20 and the binding increases from 2 to 10 calcium ions per mole. The electrostatic effect may be evaluated by defining an apparent intrinsic constant, ICfca,for the binding of calcium ion to serum albumin as (1) where kc, is the intrinsic association constant and e-2zpw'ca is the electrostatic factor.I2 The symbols xp and zca represent the charge on the protein molecule and the calcium ion, respectively, and w has its usual meaning in the Debye-Huckel theory. For application of the simple electrostatic theory, the following JCICa
(11) (12)
= JCcae-2'l~W'ca
S.Dray and K. Sollner, Biochina. Bzophys. Acta, 22,213 (1956). G.Soatchard and E. S. Black, J . Phys. Colloid Chem., 63,88(1949).
H, A. SAROFF AND If. S.LEVIS
1212
SUMMARY OF BINDING OF Ca++, OH-, Alb. ooncn.,
x 104 8.12 5.07 8.14 8.14 8.16 8.15 6.74 6.74 8.16 5.07 8.17 5.07 8.15 8.12 6.76 6.76 6.76 8.16 6.76
N
PH
5.84 6.10 6.11 6.13 7.03 7.13 7.30 7.55 7.92 8.20 8.55 9.07 9.11 9.75 9.89 10.12 10.13 10.16 10.55
Total
Total
Ca++,
OH -, ,M x 103
Total c1, M X 108
0.00 3.52 5.50 5.53 10.98 10.91 14.46 12.74 16.20 11.20 17.85 13.12 21.95 25.78 27.44 29.34 29.10 31.21 32.76
20.00 20,oo 15.09 15.09 11.14 11.93 13.60 13.60 9.55 16.80 7.97 18.87 11.93 19.80 9.08 9.20 9.08 9.55 9.08
x loa 10.00 11.76 10.29 10.31 11.05 11.42 13.03 13.17 12.87 14.00 12.91 15.99 16.94 22.79 18.26 19.27 19.09 20.38 20.92
IM
Vol. 67
TABLE I C1- TO DEIONIZED HUMAN SERUMALBUMIN
AND
CCs. ++,
x IO! 10.56 11.74 10.33 10.33 9.77 10.38 10.85 11.90 10.09 12.00 9.53 13.18 12.54 18.11 11.24 11.87 11.78 12.13 11.90
M
cc1-,
x 103 16.60 17.79 12.45 12.48 9.24 9.91 12.81 10.59 8.21 16.80 6.98 17.80 11.17 19.56 9.96 9.39 10.59 8.53 10.47
M
BCa
0.00 0.04 0.00 0.00 1.57 1.28 3.24 3.13 3.42 3.94 4.14 5.56 5.40 5.76 10.4 11.0 10.8 10.1 13.3
BOH
0.0 6.94 6.76 6.79 13.4 13.4 21.5 19.0 19.8 22.1 21.9 25.9 26.9 31.7 40.5 43.2 41.5 38.1 48.0
BCI
4.19 4.36 3.24 3.21 2.33 2.48 1.19 0.60 1.64 2.50 1.21 2.11 0.93 0.30 ( -1.30) (-0.28) ( -2.23) 1.25 (-2.06)
ZP
- 4.19
-11.2 -10.0 -10.0 -12.5 -13.4 -16.2 -13.3 -14.6 -16.7 -14.8 -14.8 -16.1 -20.2 -19.7 -21.2 -19.9 -17.9 -21.4
where cca is the coiicentration of free calcium ions in solution and n' is the apparent maximum number of sites to which the calcium ions are bound. If it is assumed that n' is constant between pH 7 and 10 or that binding of calcium ion is to the carboxylate ion of serum albumiii and that all of the carboxyl groups are ionized a t pH 7 and above, then the following expression follows from equations 1 and 2.
PH * Fig. 1.-pH dependence of the binding of calcium ions t o serum albumin. Curve 1, predicted binding of calcium ions to the carboxylate ions of serum albumin calculated with equation 4 and k~ = lo5,kce. = 1, n = 100, and w = 0.045. Curve 2, predicted binding of calcium ions to the imidazole and amino groups of serum albumin calculated with equation 4 and k~ = 107,koa = 2.0,n = 16, and w = 0.045 for the imidazole groups and k~ = 109.6,kca = 0.6,n = 56,and w = 0.045 for the amino groups. Curve 3, predicted binding of calcium ions to serum albumin calculated with equation 10,and the values of Table IV. Electrostatic effects were applied using expressions similar to equation 1 with w = 0.015. Curve 4, same as curve 3 except changed from 107 to 108J. Curve 5, predicted binding of calcium ions to serum albumin calculated with equation 15 and the same values as those for curve 4 except (kCa)oh
=
20.
expression for the average number of calcium ions bound, B C ~ per , mole of albumin may be written
where the values of xp a t pH 10 and pH 7 are -20 and - 13, respectively, and the concentration, CC., is 0.011 M . The experimentalvalue of the ratio ( B C ~ ) ~JH (FCa)pH7 was found to be about 6. Calculated values for the ratio ( B C ~ ) ~l oH/ ( i i c a ) p ~ 7 are given in Table I1 for values of w = 0.065,0.045, and 0.015 with values of kc, varying from 0.1 to 10. The value of w = 0.045 is consistent with that employed by Scatchardla in applying electrostatic theory to anion binding to serum albumin. The value of 0.015 is consistent with that employed by Saroff14 in analyzing proton and anion binding to serum albumin. The value w = 0.065 is simply that value of w required to give the ratio 5.2. These calculations demonstrate that in order to explain calcium ion binding to serum albumin with the electrostatic theory explaining the primary effect of pH, a value of w of about 0.065 must be coupled with an intrinsic constant of about 0.1 for the binding of calcium ions to serum albumin. Both of these values are inconsistent with existiiig data and interpretations of protein interactions. Some reported values for the complexation constants for Ca++ and various ligands are collected in Table 111. The sites available'b for the binding of Ca++ to serum albumin include 16 imidazole groups (complexation constant, 2 ) and 56 amino groups (complexation constant, 0.6) as well as approximately one hundred carboxylate ions (complexation constant, 1 to 6). (13) G. Soatchard, J. 9. Coleman, and A. L. Shen, J . Am. Chem. SOC.,79, 12 (1957). (14) H. A. Saroff, J. Phus. Chem., 61,1364 (1957). (15) E. Brand, Ann. N . Y.Acad. Sci., 47, 187 (1946); W. H. Stein and S. Moore, J . Bid. Chem,, 178, 79 (1948).
E ~ N D I N GOF CALCIUM Ioxs
June, 1963
VALUESOF
THE
EQUATION
TABLE I1 RATIO (jCa)pH ~o/($,),E CALCULATED FROM 3 FOR DIFFERENT VALUESOF kca’ AND %u
k’Ca
W
0.1
0.065 0.045 0.015
5.2 3.4 1.5
1.0
0.065 0.045 0.015
2.7 2.8 1.5
0.065 0.045 0.015
1.2 1.6 1.4
10
( h d p H I O / ( ~ C d p H7
TABLE I11 REPORTED FOR C a t f AND VARIOUS TJNI- AND BIDEKTATE LIGANDS” The value of K1 is that for the ligand in the unprotonated form. COMPLEXATION CONSTAXTS
K1 0.6 2.0b
Ligan(1
Ammonia Imidazole Formic acid Acetic acid Propionic acid n-Valeric acid
1.0to 6 . 3
Hippuric acid 2.7 Succinic acid 10 to 100 Glycollic acid 13 t o 39 Glycine 22 to 27 Maleic acid 12 to 270 Oxalic acid 1000 a J. Bjerrum, G. Schwarzenbach, and L. G. Sill&, “Stability Corrected Constants,” The Chemical Society, London, 1957. for the pK of imidazole.
Interpretation of the Binding Data Imidazole and Amino Groups.-It is obvious that the p K of the imidazole and amino groups control the binding of Ca++ to serum It is also clear from the data presented above that the control of calcium binding by the imidazole and amino groups is not a direct function of the change in charge of these groups. It is possible to explain the experimental data in Table I on the basis of binding to imidazole and amino groups with the constants of Table III. (The guanidin0 groups of arginine may be ignored since no measurements above pH 10.5 were made.) For calculating the binding of C a t + to the imidazole and amino groups of serum albumin the following expression for competitive binding is applicableg
where k‘ca is defined in equation 1 and k ‘ is~ similarly defined as kfH=
~ H ~ - 2 z ~ w r H
(5)
I n equation 4 k~ refers to the intrinsic association constant for the binding of hydrogen ion to the same site for which the constant for the binding of calcium ion is kea. I n this and the following calculations the activity coefficients of hydrogen and calcium ions are assumed to be unity. Equation 4 was used to calculate curve 2 in Fig. 1 with the constants JCH = lo’, JGca =
TO
SERUM ALETJMIN
1213
2.0, and n = 16 for the imidazole group, and the constants k~ = 1 O 9 a 5 , kcB = 0.6, and n = 56 for the amino group. The value of w was takeii as 0.045. Curve 2 demoiistrates a satisfactory fit with the data for the binding of calcium ions to serum albumin. Although the calculated curve is satisfactory, the imidazole and amino groups cannot be designated as the sole sites of binding without postulating some restrictive behavior for the carboxylate ions. Carboxyl Groups.-A partial treatment of the binding of calcium ions to the carboxyl groups of serum albumin was presented above with the comparison of the ratio of equation 3 with that of the experimental data. Since reasonable binding constants for the imidazole and amino groups can explain the binding of calcium ions to serum albumin it is of interest to apply an equivalent set of constants to the 100 carboxyl groups. Equation 4 with the constants k~ = lo”, ikca = 1, n = 100, and w = 0.045 was employed to calculate curve 1 of Fig. 1. Examination of curve 1 and its comparison with curve 2 demonstrates clearly that neither the imidazole and amino groups nor the carboxylate ions can be designated as the sole sites for the binding of calcium ions to serum albumin because of the unusual restrictions required in either case. Carboxylate Ion-Imidazole or Amino Chelate.-A combination of (1) pH control by the imidazole and amino groups, (2) the unrestricted binding of Ca+f to carboxylate ions, imidazole, and amino groups, and (3) the restriction on the activity of both the carboxylate ion and nitrogen groupsinay be achieved by a structural pairing14of the hundred carboxyl groups of serum albumin with the hundred nitrogen centers of serum albumin. When this is done the reaction of a carboxylate ion with its paired imidazoliuni, ammonium, or guanidinium ion results in a hydrogen bond or “salt linkage.” This same structural pairingwill also allow the reaction of a calcium ion with the carboxylate ion and the uncharged nitrogen center to form a bidentate chelate with the binding site. To the reactijons previously applied in the case of the carboxyl, imidazole, and amino groups /-COOH
/=SH+
+ Cat+ + Cad++
= =
/-COOCaf /=NCa++
+ H+ + H+
(6)
(7)
is now added the reaction /-COO-.
. . H + . . . NE/ + Ca++ = /-COO-. . . Ca++ . . . N e /
+ H+
(8)
The symbols, /--COO-. . . H + . , . P F , f and /-COO-. . .Ca++. . , x=/, represent a single pair of carboxyl and nitrogenous groups in the hydrogen bonded form and calcium chelated form, respectively. When reaction 8 is added to reactions 6 and 7 , binding of Ca++ to all of the carboxyl, imidazole, and amino groups does not become excessive because of the competition imposed by the hydrogen bond and the restriction imposed on both the carboxylate ion and the nitrogen center by the formation of the bidentate chelate. T o derive the expressions representing reactions 6, 7, and 8 coiisider the following competitive reactions in which each carboxyl group is paired with one basic nitrogen group.
H. A. S-4ROFF A S D M.
12 14
+ H + = (-COOH
(B) (-COO-
H+N=,f
(D) J-COO-
Ca++ i Y ~ , f
(H) (-COOH
H+Sr/
(L) (---COO-
H+N=/.
+ H + = (-COO13
H+iY=(
+ A-
=
(-COOH
A”=/.
+ Ca++ = /-COOCa+
AHK=(
(K) (-COO-
Ca++N=/
kH1 =
Ca++Sz(.
+ Ca++ = /-COOCaf
(M) (-COO-
s. LEWIS
VOl. 67
p ( C O 0 H . H +N)
Ppoo-, H +N)CH
P(CO0H. Ce++N) ~ C H =~P ( C O O - , C a + + K ) C H
k ~ =,
p ( C O O H , AHN) ~ ( C O O HH , +N)CA
H+?J=(. kcel
P ( C O O C a + , H+N)
=
p ( C O O - . H+N)CCa P ( c O o c a + , AHN)
AH;?I’=/. kca1 =
+ Ca++ = /-COOCa+
p ( C O 0 -, AHN)CCa
Ca++S=/. kcal =
P C O O C a + . Ca++N)
P(COO -, C a + + K ) C C ~ (0) (-COOH (PI (-COO(Q)
(-COOCa+
s=/ + Ca++ = (-COOH
+ Ca++ = (-COOS=(
~ ( C O O HC, a + + S )
Ca++K=/. kCaz= Ca++K=(. kea,
+ Ca++ = /-COOCa+
p ( C O O H , N)CCa
COO-, C a + + N ) =
p ( C O O - . N)CCa
Ca++N=/. kcaz =
I n the above reactions, for a single carboxyl group matched to a single basic nitrogenous group, the symbol P ( c o o - , N) represents the fraction of that single site of the protein molecule in the form represented by the species described in the parentheses. The symbol COO- represents a carboxylate ion and N is taken to mean an uncharged, imidazole, amino, or guanidino group. The symbols, k ~ , ,kca1, k ~ k c~a z , , and k~~ represent the intrinsic association constants for the binding of H+ to the carboxylate ion, Ca++ to the
P(COOCa+. Ca++N) P(COOCa+, N ) C C ~
carboxylate ion, H + nitrogen-containing group, C a s + to the nitrogen-containing group, and anion to the positively charged nitrogen group, respectively. The symbol k ~ refers , to the association constant for the hydrogen bonding reaction between the carboxylate ion and the positively charged nitrogen ion with the constant k ~ The ~ . symbol ( k ~ ~ refers ) ~ h to the association constant for the formation of the bidentate chelate from a carboxylate ion and its paired, uncharged nitrogen group.
~BINDIXGOF CALCIUM Ioxs
June, 1963
The symbols CH, CA, and cca refer to the concentrations of the free hydrogen ions, anions, and calcium ions, respectively. The quantity ?ca is defined by the equation
+
f P(COOCa+, ANN) COO-, c ~ + + N ) PCOOH, c~++N) ~ ~ ' ( c o o c ~ + , c ~ + + N ) COO-.. . c ~ + + . . . N ) ] (9)
k a = n [ P ( C O O C a + , N)
+
P(COOCa+, H+N)
+
+
+
and the following expression for vca may be derived.
Electrostatic Effects.-Equation 10 contains no electrostatic correction factors. To add an approximation of the electrostatic effect which is a function of the net charge of the protein molecule each k is replstced by its appropriate k' as defined in equation 1. Pairing of the carboxylate and ammonium ions introduces an additional, localized electrostatic effect of the charge of a grouping within a given pair, Thus, the same I C H ~was applied to reactions (A), (B), (C), and (D). From the standpoint of the effect of the charge of the paired nitrogen group, the observed value of k~~ for reactions (A) and (C) would be the same but the observed value of I C H ~ for reactions (B)and (D) would be smaller than that of (A) and (C) because of the electrostatic repulsion of H+ by the charged nitrogen of the pair. The relationships between the constants for reactions (A), (B), (C), and (D) may be formulated as (kHl)reaction ( A ) = (JCIlJreaction (c) = eH(/CHl)reaction (B) = eH2(kfi1)reaotion (D)
(11)
where k~~ is the unperturbed intrinsic association constant and eH represents the localized electrostatic correction factor resulting from a single positive charge of the nitrogen of a given pair. Similarly
TO
SERUMALBUMIN
The value of k ~ =~ 8'was taken from the chloride ion binding treatment14 and includes the localized electrostatic effect ( k ~ , '= lCDaeH = @.le Equation 10 allows for a distribution of the bound calcium between carboxylate ion-calcium complexes, nitrogen-calcium complexes, and the carboxylate-calcium-nitrogen chelate. The calculated distribution is given in Table V aJnd the total calcium bound is illustrated by curve 3 in Fig. 1. Curve 4 was calculated with the same constants as those used for curve 3 except
that the value of k ~was , changed from lo7to 1Va5. CONSTANTS FOR
- (kAz)reaotion (J) eA
(13)
where eA represents the localized electrostatic correction factor for the association constant of the anion. Curve 3 of Fig. 1 was calculated from equation 10. Electrostatic effectsof the net charge were applied by equations similar to equation 1 with w = 0.015. The localized electrostatic effect of the pairing was held to a minimum and applied only to the value of k ~ , . Table IV summarizes the values used in applying equa1,ion 10. These values are consistent with both the chloride binding in the acid region and observed constants for the binding of Ca++.
THE
TABLE IV BIKDINCOF CALCIUM Iox TO HUMAN SERUM ALBUMIN Carboxyl-imidazole pair
Carboxyl-amino pair"
2 2 2 0.6 kHi 106 106 kHa 107 109.6 kDzeEo 8 8 (kc%)& 10 10 n 4 12 56 kA2 2500 50 1 a The contribution of the carboxyl-guanidino pair varies from 0.1 for the value of i b at pH 5.5 to 0.2 for the value of i c a at pH 10.5 and may be ignored. The values of k ~ =, 0.8 and ea = 10 such that k D a e E = 8 t o be consistent with chloride ion binding data in the acid region.18 kca1
kC*2
TABLE V DISTRIBUTION OF THE SPECIFIC SITESOF BINDINQ OF CALCIUM IONS TO SERUM ALBUMIN,CALCULATED WITH EQUATION 10 AND CONSTANTS OF TABLE IV The value of w was taken as 0.015 and zp at each pH from Table I. Number of C a + + bound t o sites on one mole of albumin Carboxylate ionCarboxylate Imidazole and imidazole and Total ion amino groups amino chelate (i&)
PH
5.5 6.0 7.0 8.0 9.0 10.0 10.5
1
1215
0.23 0.55 0.71 0.93 1.2 2.0 2.7
< 0.01
