1144
L. B. NANNINGA
respective of whether the CMD show hypercoiling or simply coiling, in NaCl solutions there are strong attractive forces present to collapse the molecules. I n acid solutions, on the other hand, the molecules contain no bound ions and are subject to no electrostatic attractions. Their viscosities should therefore reflect greater hydrodynamic volumes unless changes in the solvent environment on the addition of HC1 favor tightly coiled units. The addition of electrolytes to solutions of the CMD may well make the solvent poorer with respect t o the polyelectrolyte molecules. This would lead to a salting out of the CMD. In addition, the absence of ionic groups reduces the penetration of solvent molecules into the polymer m.olecules. As long as electrostatic repulsions do not prevent the coiling of the molecules, whether through the neutralization postulated by Fuoss and Strausss in salt solutions or through the discharge of the carboxylate groups by the common hydronium ions, the salting out leads to the most tightly coiled configuration for the CMD. The poorness of the solvent is the chief factor in governing the ultimate configuration of the molecules, since HC1 and NaCl solutions of equal concentrations are probably quite similar in their solvent efficiency whereas the mechanism of ion neutralixation apparently is not important. This explanation requires, however, that the ex-
Vol. 61
panded, charged form of the polyelectrolyte molecules are in a relatively better solvent environment than are the collapsed molecules in either HCl or NaCl solution. Consequently, experiments with polyelectro!ytes under these conditions do not give information about uncharged analogs to the expanded, charged molecules. The intrinsic viscosities resulting from such measurements therefore cannot be taken as measures of the configuration of the molecules in the absence of electrostatic repulsions since solvent effects must be considered as well. Conclusions The addition of HC1 reduces the viscosities of solutions of CMD to the same extent as, though by a different mechanism from the addition of salts. The added acid not only discharges the bound carboxylate groups but also leaves the uncharged polymer molecules in a poorer solvent environment, so that they tend to coil closely. The addition of salts also leads to a partial salting out, and therefore to identical polymer configurations. Acknowledgments.-The authors are greatly indebted to the Research Corporation, New York, whose financial support made this work possible. They are grateful to the Dextran Corporation for a gift of dextran. They thank Mr. Robert C. Lange for help with some of the measurements.
FORMATION CONSTANTS AND HYDROLYSIS AT 100' OF CALCIUM AND MAGNESIUM COMPLEXES OF ADENOSINETRI-, DI- 'AND MONOPHOSPHATE1 BY L. B. NANNINGA~ From The Institute.for Muscle Research, Woods Hole, Mass., and National Institute of Arthritis and Metabolic Diseases, National Institutes of Health, Public Health Seruice, U.S. Department of Health, Education and Welfare, Bethesda, Maryland Received January 8, 1967
The formation constant of complexes between ATP and Mg or Ca was studied a# a function of p H , temperature, ionic strength and Na concentration. Free energy, enthalpy and entropy are derived; the last two are positive for the formation. The constant for MgATP*- is about three times that of CaATP*-. Data about the activity coefficient are derived for the ATP4- ion from the dependence of the formation constant of RSgATP on the ionic strength. Heat hydrolysis was Rtudied a t pH 8.8 and velocity constants are calculated. Ca accelerates ATP splitting by heat, while Mg inhibits it. Formation constants and heat hydrolysis were also studied for ADP and AMP. It is concluded that the different effects of Ca and Mg in t,he.ATP splitting by myosin are caused by interaction of these ions with the ATP rather than by their interaction with the myosin.
Introduction useful to elucidate the binding of these ions to the A study of the binding of magnesium and cal- ATP as a first approach to an understanding of their cium to adenosine triphosphate (ATP) and adeno- antagonistic behavior in the ATP splitting by myosine diphosphate (ADP) was started as an exten- sin. I n the literature before 1956, only two data on sion of the knowledge of the binding of these ions to these formation constants could be found: Burton the meromyosins. As no differences in binding be- and Krebs4a reported in 1953, 830 for MgATP2tween Mg and Ca could be found,8it was considered at ionic strength ( p ) 0.2, while DiStefano and Neuman4bin the same year published the value 11,500 (1) This work waa done during the tenure of a Research Fellowship for CaATP2- a t p = 0.1 and p H 7.4, stating also from the American Heart Association and as a Visiting Scientist a t the that one Ca is bound to one ATP. Both values are National Institutes of Health. Presented partly a t the 40th Annual Meeting of the Federation of American Societies for Experimental in I./mole; the equationis (MgATP2-) = kt(Mg*+) Biology, Atlantio City, April, 1956. (ATP4-). Hers,6 Kielley,Ba and Kuby, Noda and (2) University of California Medical Center, UCLA, Los Angeles 24, California. (3) L. B. Nanninga, Circulation, 14, 976 (1956); Biophghya., in grese,
(4) (a) K. Burton and H. Krebs., Biochsm. J . , 64, 94 (1953);
Arch. Bioehen.
03) V. DiStefano and W. F. Neuman, J . B i d . Chsm., 200, 759 (1953). (5) R,G. Hem, Biochim. st Biophys. Acta, 8, 424 (1952).
.
Sept., 1957
FORMATION CONSTANTS OF CALCIUM AND MAGNESIUM COMPLEXES OF ATP
1145
Lardy,Eb concluded from enzymatic studies, in = (HZ)/(H)(Z) and KFIMZ= (HMZ)/(H)(MZ); ATP4-: HZ = ATPH*-; MZ = ATPMg2-; which maximal activity was obtained a t the pro- Z portion of one Mg to one ATP, that MgATP is the MHZ = ATPH Mg-. When K H Zis not equd to formula of the complex. KHMZ,[(ZH) (MHZ)I/[(H)(Z MZ)I is not Spicer' reported in 1952 that Mg gives a larger constant. As ~ K R M = Z 4.5 for Mg and ATPg decrease in pH when added to an ATP solution (5.0 according to Smith and AlbertylO), while than Ca does in the same concentration, which p K ~ = z 6.9," this quotient, however, is not conmeans that Mg is more strongly bound than Ca. stant, which invalidates this derivation. This observation, confirmed by Schiffman and Experimental MacLaughlin,*means that a t least one of the two The formation constants were measured according to a published values must be in error to a considerable method given by Schubert1*J3 in 1952. This method uses extent as the value for Ca is about 14 times the the competition of a basic resin, Dowex-1, mesh 200-400'* value for Mg, while it should be smaller than the Mg and Mg for the ATP. A series of mixtures was made with M) value according to the pH experiment^.^ This large 'the same amount of ATP (final concentration 1 X and with increasing amounts of Mg (0-2 X 10-8 M ) . The uncertainty and the importance of knowing the amount of resin (50 mg.), buffer (0.02 M ) and NaCl(0.1M) right values for these complexes which are of con- was the same in all cases. Acetate and tris-(hydroxymethy1)siderable physiological significance were the rea- aminomethane buffers were used. The total volume was sons to start this investigation. At that time the 12.5 ml. After equilibration by shaking for 4 hours and centrifugation, free ATP plus complexed ATP were detervalues of Martell and Schwar~enbach,~ and Smith mined in the supernatant after tenfold dilution by means and Alberty'o (see below) were not yet known. of the extinction a t 260 mfi. According to Bock, et al.,j6 HersKconcluded from titration curves that espe- and confirmed here, Beer's law is valid below concentracially the terminal phosphate group is involved in tions of lo-' M ATP. It was confirmed that addition of Mg Ca does not change the extinction of ATP at 260 mp, the binding. This was confirmed by experiments or as was mentioned by Blum.16 This means that these ions on titration curves of ATP by Schiffman and Mac- probably do not bind to the adenine ring. The same conLaughlin,* who concluded that only the terminal clugion was drawn from the negative effect on the pK of the phosphate group is binding Mg. Burton and amino g r o ~ p . ~ , * i ~ The determinations were made against a blank with the Krebs4"found that the pK of the amino group is not same amount of buffer, resin and NaC1, so that the effect changed in the presence of Mg, which means that of the buffer on the extinction was taken into account. The Mg is probably not bound to this group. This was resin alone does not bring anything in the supernatant which recently confirmed by Martell and Schwar~enbach.~influences this extinction. The extinction caused by the The association constants calculated by them,g buffers was very small compared to that caused by ATP. Knowing ATP plus complexed ATP in the soluwhen corrected for Na binding, will increase twofold (see below) and are tabulated together with .tion (centrifugate),the amount of ATP on the resin the recent values of Smith and Alberty,lo which is found by subtracting the first amount from the are deduced from titration curves and have been total amount of ATP present. The amount of ATP on the resin divided by the remainder of the ATP is corrected for Na binding. Their values are considerably nearer to the values called the distribution coefficient K d . The apparfound here than the other reported values (Table I). ent formation constant Icf of the Mg ATP complex The experimental error given by Smith and Alberty and its stoichiometry can be calculated in the folwas 230 for MgATP while the error here is about lowing way : the same (see below). kr apparent formation constant of ATP Mg complex in 1./
+
TABLE I Association constant of MartellSohwarsenbach" p = 0.1 200 Smith-Alberty p 0.2 25O This paper p = 0.1 23' Burton-Krebsa I* 0.2 DiStefanoNeumana p = 0.1
-
-
MgATPB-
CaATPs-
MgADP- MgAMP
20,000
12,000
...
..
3,000
2,000
1,000
50
4,070
1,380
1,070
100
2,490
..
..
..
..
23,000
..
..
+
mole Kd distribution coefficient of ATP between resin and soln. in presence of Mg the same in absence of Mg (AM,,) complex concn. in mole/l. (AR) ATP bound to resin ZM total Mg concn. in mole/l. (A) free ATP concn. in mole/l. (M) free Mg concn. i? mole/l. u vol. of soln. in ml. m mass of resin present in g. n number of Mg per ATP in complex (AM,) = ki(A)(M)"
Corrected for Na binding by multiplication of the published values with 1 10(Na) as mentioned below.
+
It is implied in the derivation of Martell and From (2) and (3) SchwarzenbachBthat K H Z= K H M Zin, which KHZ (11) N. Melchior, J . Biol. Chem., 208, 615 (1954). (6) (a) W. W. Kielley and R. K. Kielley, J . Biol. Chsm., 200, 213 (1953); (b) S. A. Kuby, L. Noda and H. A. Lardy. ibid., 210, 65 (1954). (7) 9. S. Spioer, ibid., 199, 301 (1952). (8) J. Schiffman and J. A. MaoLaughlin, personal communication. (9) A. E. Martell and G. Schwarsenbaoh, Helu. Chim. Acta, 89, 653 (1956). (10) R. M. Smith and R. A. Alberty, J . A m . Chsm. SOC..7 8 , 2376 (1956).
(12) J. Schubert, THISJOURNAL, 88, 113 (1952). (13) J. Schubert, E.R. Russell and L. 8. Myers, J . B i d . Chsm., 186, 387 (1950). (14) The resin was equilibrated with 0.1 M NaCl after several CI--OH- cycles; the p H of an unbuffered supernatant was not changed by the resin. (15) R. M. Bock. N. Ling. S. A. Morel1 and S. H. Lipton, Arch. Biochsm. Biophys., 62, 253 (1956). (16) J. J. Blum, ibid., 56, 486 (1955).
L. B. NANNINQA
1146 I
I
I
.I
I
'
I
,
I
I
20
0
i
16 l8
x
Vol. 61
The amount of ATPMgz- adsorbed on the resin must be small compared with ATP4- adsorbed as the slope in the 1/& versus (M) plots is constant and extrapolates into l/Kd,. Otherwise, the slope would decrease with increasing (M) for, in that case, Kdo RAM/A has to be put instead of Kd, in (6) as can be derived from
+
t
10
3
4
5
6
8
7
9
PH. Fig. 1.-Formation constant of MgATP and CaATP versus pH. The values are "apparent" values and have to be corrected for Na binding by multiplication of 1.85 (see text). The shape and the dzerences between Ca and Mg are not influenced by this. (4)
From (2) and (1) (5)
From (5) and (4) When is plotted against total Mg concentration, linear proportionality is obtained in all cases, which means that n = 1. This confirms the conclusions about the one Mg to one ATP proportion in the literature. The apparent formation constant is found from the slope divided by the intercept. However, total M is different from the free M concentration, which should have been used in the plot according to equation 6. One can correct for this by calculating AM from the quadratic equation AM = k(M)(A) = kf(ZM - AM)(AM A AM) in which ZM is total Mg and A AM is total ATP in the supernatant. As only one value for AM is smaller than A AM, only this value is real. Deduction of AM from total M gives free M. The corrected k is found by re-plotting 1/Kd versus free M. It was ascertained that ATP4- has a true ionexchange reaction with the C1- in this resin: &, is independent of v/m. Over an eightfold change of v/m, Kdoremained constant within 6%) as appears from this table. Total ATP concentration = 1 X lopaM , NaCl = 0.1 M , pH 8.6. After addition of resin the mixture is shaken for 4 hours a t 23".
+
+
+
Resin, mg.
(ATP) in iupernat. X 10-4,M
ATP-R
ATPsup.
12.5 5.92 0.69 4.55 1.20 25 2.92 2.42 50 I .56 5.40 100 The av, value of K d is 642 f 40
v/m
Kda
1000 500 250 125
690 600 605 675
Also, by comparing ATPMg2- with AMP2-, it is probable that ATPMg2- is bound much less to the resin that ATP4-, for the Kdo value of AMP2- is about 10% of the Kdo value of ATP4- In the following it has been assumed that the binding of the complex to the resin can be neglected. Phosphate Determination (for Bydrolysis at looo) according to Youngburn and Y~ungburn.~~-To5 ml. PO4 (below 12 y P)-containing solution, 4 ml. of molybdate sulfuric acid is added. On addition of 1 ml. of diluted SnClz solution, the blue color develops immediately and is read a t 610 mp after a few minutes. 10 y P gives an extinction of 0.55. The extinction is proportional to the concentration of P. The molybdate sulfuric acid was made from 9.38 g. of Na molybdate $250 ml. of 5 N Has04 HeO to 500 ml. The solution has to be exactly 2.50 N . The diluted SnCL solution is prepared by 200-fold dilution of a stock solution of 10 g. of SnClr in 25 ml.of 35% HC1 which is kept a t 0". Results pH Dependence.-In Fig. 1, kf values are plotted versus pH for Mg and Ca complexes of ATP at 23", 0.085 M NaCl and total ionic strength 0.0960.116. Above pH 8, a plateau is reached for MgATP, while kf drops considerably at lower pH. This is not found for CaATP. Above pH 8, Mg reacts only with the ATP4-ion, forming MgATP2-. The apparent uncorrected formation constant is 2000 1.7mole. The binding of Mg2+ and Ca2+ to OH- can be neglected, f o r the second dissociation constant of Mg(OH)Pis2.6 X 10a3andthat of Ca(OH)1198.6X therefore
+
(Mg2+)(OH-).= 2.6 10-8 (MgOH+); (MgZ+) = 260 (MgOHf) at pH 9 (CaOH+); (Ca*+) = 8600 (Caa+)(OH-) = 8.6 (CaOH+) at pH 9
*
The binding of Mg2+and Ca2+to the amino group of tris-(hydroxymethy1)-aminomethane can be neglected too, assuming that this binding is comparfor, acable to the binding of these ions t o "3, cording to BjerrumZ0
.
( MgNHa2+) = 0.25(Mgz+)( NHa) and
(CaNHZ2+)= 0,12(Ca*+)(NHs)
hence Mg bound to tris = 0.005 (Mg2+) and Ca M. bound to tris is 0.0025 (Ca2+)for tris 2 X At the low pH side the curve levels off to about 300 a t p R 3.7 for MgATP. (17) G . E. Youngburn and M. V. Youngburn, J . Lab. CEin. Med., 16, 158 (1930). (18) D. I. Stock and C. W. Daviea, Trans. Faraday Soc., 44, 856
(1948).
(19) I. M. Kolthoff,Rec. Irav. Chim. Pays Bas, 42, 977 (1923). (20) J. Bjerrum, Chern. Rea., 46, 381 (1950).
1147
FORMATION CONSTANTS OF CALCIUM AND MAGNESIUM COMPLEXES OF ATP
Sept., 1957
Effect of Na Concentration.-The apparent formation constants found, 2000 l./mole for MgATP2- and 750 ]./mole for CaATP2-, have to be corrected for the binding of Na+ by the ATP4-, & which competes with the binding of Mg2+or Ca2+. p4 4 Melchior" reported in 1954 that one Na+ is bound to one ATPQ- and that the formation constant of NaATPa- is 10 l./mole at p = 0.2-0.3. From the shift of the titration curves of the terminal phos0.1 0.2 0.3 0.4 0.5 phate it is clear that Na+ is bound to this terminal 4 . phosphate group, liberating E+, SO that Na+ cornfor MgATp2- (corFig. 2,-LOg of formation Pete8 with Mg2+for the same site. Melchiorl' de- rected for Na effect) versus square root of ionic strength. rived the kf value for Na+ obviously as follows: Dotted line is theoretical limiting slope, which has to be -8 = 10'.gO(H+) (ATP4-) = 106S60(H+). (see text). (ATP'-) [(ATP'-) (ATPNaa-)I, as the pK = 6.90 in absence of Na+ and 6.50 in 0.15 M NaC1. both at la5 the same ionic strength with tetraethylammonium bromide. Therefore (NaATp8-) (Na+)( ATP")
*
'
+
106.90-6.60
=
0.15
-1
= 10 l./mole
1.o
Assuming that the same value holds for p = 0.1 (compare below on influence of ionic strength), then the apparent kf values are transformed into the real ones (k*J for the same ionic strength as (MgATPa-) = k*r(Mg2+)(ATP4-) = kr(Mga+)(ATP4NaATPa-) (NaATP3-) = 10(Na+)(ATP4-) 10(Na+)] k*f = k f [ l
+
+
While the Na concentration varied from 0.004 to 0.085 M , the ionic strength was kept to 0.1 with tetraethylammonium bromide, whose cation is not bound. 11,21 The values corrected for Na binding are k f in I./mole
PIC
4070 =k 250 3 . 6 1 & 0.03 MgATP21380 3.14 CaATP23.04 MgADP-" 1070 690 2.84 CaADP-" 2.0 MgAMP" 100 a The association constant for NaADP = 5 according to Melchiorll and that for NaAMP = 2.5 according to Smith and Alberty.*2
Effect of Ionic Strength.-The formation constants were measured for MgATP2- at pH 8.8 a t different ionic strengths, obtained with tetraethylammonium bromide. The const.ants were corrected for the effect of Na+. The log h values are plotted against the square root of the ionic strength (Fig. 2). The limiting slope of this curve, i.e., the slope at zero ionic strength, has to be -8 according to the limiting law of Debye-Huckel. If kf, is the formation constant at infinite dilution log k t = log kro $. log fATP4-
0.1
0.2
0.3
0.4
4;.
Fig. 3.-Negative log of activity coefficient versus square root ionic strength. Dotted line is theoretical limiting slope ( = 8) for ATP4-. Lines a, b and c are for tri-, diand monovalent anions, taken from Kielland23 (see text).
experimental points and this theoretical limiting slope, kt, is found to be 57,500 (log kf, = 4.76 f 0.05). From kf and h,,10gfATP4- can be calculated as function of di (Fig. 3). Here again, the limiting slope should be 8 and -log f = 0 for dji = 0. In the same plot, values for activity coefficients of other ions are given, taken from KiellandZs: Pod3and citrate3- follow curve a ; S042- and C2042curve b; and C1-; Br- and I- curve e. The free energy change at infinite dilution, AFa = -2.303RT log kr, = -6580 cal./mole at 25". At p = 0.15, A F = -4920 cal./mole at 25" and AF,] = -2.3RT log fATP4- = 4-1660 cal./mole at 25" or 1730 cal./mole a t 37". This value agrees within 5% with the value 1820 (7120 - 5300),calculated by Hillz4for the salt correction of the electrostatic free energy of ATP4- at p = 0.15 and 37". Effect of Temperature ; Entropy and Enthalpy.The following data were obtained for the apparent formation constants in 0.085 M Na, p = 0.15, pH 8.8: Temp., "C.
1000/T log kf MgATP
1
3.65 3.06 log kt CaATP 2.65 In the experiments a t 43' it was
23
43a
3.38 3.34 2.87
3.16 3.50 3.12
checked that after 4 for low ionic strength as the activity coefficients hours no ATP was hydrolyzed in absence or presence of Mg (f) for the 2- and the 2+ ions cancel at low ionic or Ca. strength. In Fig. 4 log kt is plotted versus 1000/T. The LOgfATP4- = -0.519dG = - 8 4 G at high dilution (approaching zero ionic strength). From the change in enthalpy is calculated from A H = -R [d(ln kf)/d(l/T)]. The log kf values are increased (21) J. R. Van Wazer and D. A. Campanella, J . A m . Chem. Soc., 7 2 , 655 (1950). (22) R. M. Smith and R. A. Alberty, THISJOURNAL, 60,180 (1956).
(23) J. Kielland, J . Am. Chem. Soc., 59, 1675 (1939). (24) T.L.Hill, Arch. Biochem. Biophys., 57, 229 (1955).
Vol. 61
L. B. NANNINGA
1148
I\
100' incubation was measured after different times (Fig. 5).26 From Fig. 5 it is evident that Ca accelerates the hydrolysis and Mg inhibits it. The last fact is contrary to Spicer's statement.' I n order to arrive a t a first-order reaction constant (kl) for the ATP splitting, it has to be considered that a t the same time part of the ADP formed is hydrolyzed into AMP. AMP does not split into adenosine and P under these conditions, at least not within two 3.1 3.2 3.3 3.4 3.5 3.6 3.7 hours, as experiments with AMP showed under the 1000/T. Fig. 4.-Logarithm of apparent formation constant of same conditions. ADP splits according to a firstMgATPP- (0) and CaATP2- ( 0 ) as function of 1000/T. (k0.2) min.-', order reaction, with k = 2.8 X as experiments with ADP showed under the same conditions. This constant will be called ICz. The 16 I I reaction constant of the ATP splitting, kl, can be calculated from the initial slope of (P) as function of t (Fig. 5 ) as is derived in the following. The initial ATP concentration is a = equiv./l. 3.5
(ATP) = x = ae-tlt (ADP) = y (AMP) = a - X - v (P) = ( a x) ( a - x
- +
4 t
dy = k1x
///
dt
10 20
30 40 50 60 70 80 Minutes. Fig. 5.-Hydrolysis of ATP at looo, pH 8.8 in absence and resence of Ca and Mg. Liberated phoephate ( P ) in y / m f against time ( t ) . For t 03, P is 62 y/ml,, see text.
by log 1.85 = 0.27 in order to correct for Na+ binding as mentioned above. This implies that the AH for Na binding is assumed to be zero. The resulting values for change in free energy ( A F ) , change in enthalpy (AH) and in entropy ( A s ) are for 25" AF
cal./m'ole
MgATP CaATP
-4560 -4000
AS
AH cal./dole
cd./mol'e/oC.
+4120 4560
+29.1 +28.7
+
The positive AH and large and positive A S are probably caused by the dehydration of Mg2+ and ATP4- ions, which has to occur before a complex can be formed. The increase in entropy because of the liberated water molecules is larger than the heat of dehydration minus the heat liberated in the complex formation causing the reaction to proceed towards complex formation. Clarke, Cusworth and DattaZ6found analogous, but somewhat lower data for Mg-glycerol 2-phosphate, Mg-glucose 1-phosphate and MgHP04: A S is equal to 4-21 to +23 cal./mole; AH is equal to +2900 to +3400 cal./mole and AF is equal to --3300 to -3700 cal./mole. Hydrolysis at 100' of ATP4-, CaATP2- and M ATPNa4, lo-* M MgATP2-.-Mixtures of CaC12or MgCL, NaClO.1 M and tris buffer 0.02 M , pH 8.8 (all final concentrations) were compared with the same mixture without Ca or Mg. The liberated orthophosphate expressed as y P/ml. at (26) H. E. Clarke, D. C. Cusworth and S. P. Datta, Biochsm. J . , 58,
146 (1954).
- y ) = 2(a - x) - y
-k2~
Insert 9 = ue-katin (3). This gives (4)
Integration gives and therefore (5)
Fort=O: y = 0
c 3 - -k,a k2
This is 0 for t (P)
=
- ki
0 and 2a for t,.
For klt and k,t
