9198
Interactions of Divalent Metal Ions with Inorganic and Nucleoside Phosphates. 11. Kinetics of Magnesium(I1) with HP3oIo4--, ATP, CTP, HP2073-,ADP, and CDP' Cheryl Miller Frey, Joseph L. Banyasz, and John E. Stuehr**
Contribution f r o m the Department of Chemistry, Case Western Reserve Unicersity, Cleveland, Ohio 44106. Received November 22, 1971 Abstract: Kinetic data are reported a t 15" for the interaction of Mg2+ with six inorganic and nucleoside phosphates : H P 3 0 1 ~ 4 -ATP, , CTP, HP,0i3-, ADP, and CDP. Complexation of magnesium with tripolyphosphate and pyrophosphate yields kinetic results consistent with a single rate-determining step involving the expulsion of water molecule(s) from the inner hydration shell of the magnesium ion. Reaction with the nucleotides yields the following results. First, the adenine and cytosine nucleotides of a given charge type exhibit the same kinetic behavior with magnesium. Second, the mechanism which quantitatively fits the data for all Mg-nucleotide systems involves the formation of a 1 :1 complex (ML) coupled t o 2 : 1 complex (M2L). Finally, the rate-determining step in the formation of both complexes is the expulsion of water molecule(s) from the inner hydration shell of the magnesium ion.
A
number of temperature-jump kinetic investigations of complex f o r m a t i o n with various metal ions and ATP, 3 , 4 ADP,j and the corresponding inorganic phosphates (HP30104-,H P z 0 7 3 - ) 6 have indicated that the mechanism of c o m p l e x a t i o n involves f o r m a t i o n of a n ion pair (solvent separated) followed by the ratedetermining dissociation of one or more water molecules from the inner hydration shell of the metal ion. The rate constants characterizing the dissociation of water molecules from the completely aquated m e t a l ion h a v e been found to be essentially independent of the particular ligand. That is, t h e kinetics of t h e interactions of various metal ions with these ligands seemed to be merely a reflection of t h e charge type of the ligand and the w a t e r exchange rate of the particular metal i o n . U p until this time, however, there has been no comparison of the influence of different ring systems (purine CS. pyrimidine) on metal c o m p l e x a t i o n kinetics. This p a p e r describes a systematic study of the kinetics of MgY-with six di- and triphosphates (HP30104-,HP2073--, ATP, CTP, ADP, and C D P ) . By studying these six particular ligands we sought to indentify and systematically characterize t h e effects of (1) metal-phosphate interactions (the inorganic p h o s p h a t e s ) ; (2) the l e n g t h of t h e p h o s p h a t e backbone and charge ( d i p h o s p h a t e s cs. t r i p h o s p h a t e s ) ; and (3) the influence of two differe n t ring systems (adenine and cytosine, Figure 1). In addition kinetic e x p e r i m e n t s were carried out over a wide range of c o n c e n t r a t i o n s to -IO-' M). Experimental Section Materials. Nucleoside phosphates were purchased principally from the Sigma Chemical Co. and were used without further purification. These compounds were stored as solids in a desiccator below 0 '. For kinetic experiments, solutions were prepared daily by dissolving carefully weighed amounts of material in 0.1 M (1) A preliminary account of this work was presented at the North East Regional Meeting of the American Chemical Society, BuRalo, New York, Oct 1971. ( 2 ) NIH Career Development Awardee (17834). (3) H . Diebler, M. Eigen, and G. Hammes, 2. ,Varurfoorsch. B, 15, 554 (1 960). (4) M. Eigen and G. Hammes, J . Amer. Chem. Soc., 83,2786 (1961). 15) M. Eigen and G. Hammes, ibid., 82, 5951 (1960). (6) G. Hammes a n d M. Morrell, ibid., 86, 1497 (1964).
Journui o f t h e American Chemical Society
1 94.26
K N 0 3 in a volumetric flask and adding the desired amount of stock metal solution. Tripolyphosphate (NajPaOio)was prepared by column fractionation.? Contamination by orthophosphate and pyrophosphate was not detectable by thin-layer chromatography.8 Concentrations were verified by titration with standardized KOH. Pyrophosphate (Na4P20,) was purified by the method of Q ~ i m b y . ~ The metal salts KNOBand Mg(NO& were obtained from Fisher Scientific. Stock solutions of Mg(NO& were standardized volumetrically with EDTA and the indicator Eriochrome Black T. Chlorophenol Red (CPR) and Phenol Red (PR) were used as rapid pH indicators in the kinetic experiments. All solutions were prepared in triply distilled water. Methods. All kinetic data were obtained at 15" on a temperature jump spectrometer (Messanlagen Studiengesellschaft). Concentration changes following the temperature jump were monitored by transmittance at 500-570 mp, depending on the indicator used. Prior to a kinetic determination, the temperature jump cell compartment was equilibrated at 10" for at least 2 hr, and the thermostated cell of a pH meter adjusted to 15". The pH cf the experimenial solution was adjusted by dropwise addition of solutions of KOH and/or H N 0 3 . The pH was measured at 15" on a Sargent digital or Beckman pH meter and the solution then transferred to the T-jump cell. After about 30 min, the solution was jumped 5 i 0.3" by means of a calibrated high voltage discharge (35 kV) and the resultant relaxation trace photographed. At least 20 min were allowed between jumps to ensure thermal equilibrium. The pH of the solution was checked after jumping to ensure that there had been no change. Subsequent solutions were dilutions of a stock metalligand solution, rather than the initial solution, to guard against decomposition by repeated electrical discharge. All solutions were free of turbidity. In all cases metal-indicator and ligand-indicator systems were tested independently to be sure that metal-ligand interactions were being measured. Proton transfer reactions of the various ligand and indicator systems were observed a t 20-50 psec, but were not studied. Treatment of Data. The relaxation times were computed from at least three oscilloscope tracts, photographed with a Polaroid camera, All traces were enlarged on graph paper and then plotted on semilog paper to determine the relaxation times. Table I lists the equilibrium constants. Equilibrium concentrations of all species, as well as various concentration functions, were calculated from the constants and overall metal ion and ligand concentrations and pH by means of a Univac 1108 computer. I n the interpretation of data we will have need for the outersphere equilibrium constant ( K d , which describes the complex or ion pair in which the reacting species are separated by a solvent molecule. The value of KO, depends on interacting charge types (7) R. H. I 5 X l e 4 M ) , however, the graphs for the nucleotide systems deviate substantially from linearity. It is thus apparent that (1) there are additional interactions with the metal ion when a nucleoside is present; (2) these interactions do not distinguish between an adenosine or cytosine moiety; ( 3 ) no effect is seen on the values of the complexation and dissociation rate constants, which are identical to those for the corresponding inorganic phosphates. Any postulated mechanism must be consistent with these observations. An interpretation of the kinetic results must take into account all species which are known to exist in aqueous solution. The nucleotide itself can exist in various protonated states (L, HL, HzL)l 4 and conformational states (syn and anti). l 5 The purines can readily adopt both syn and anti conformations whereas the pyrimidines exist predominantly in the anti form. It is also
+
(14) R. Izatt, J. Christensen, and J. Rytting, Chem. Rel;., 71, 439 (1971), and references therein. (15) L. Rhodes and P. Schimmel, Biochemistry, 10, 4426 (1971). and references therein.
MgHP30io
107 107y
8 . 7 X 108
8 . 5 X 106
lo2
7.8 X 102
8.5 X 102
80 1 . 1 x 105
80 1 . 1 x 105
103~
106
59
6 X 105 1 x 104 8.7 1 . 4 x 105
Data taken at 25",0.1 M KNOs, ref 5.
+ B)
Triphosphates-------MgCTP
MgATP
59
1 x 106 1 x 104 2.0 1 . 1 x lo"
Q=
=
3.85 X 106
9
where
a!
7
MgHP207
~
H
6 X lo5 1 x 104
8.1
1 . 4 x 105
(exp) ~ O
-
lo5, ref 26.
possible for the free nucleotide to self-associate or base-stack, l6 especially in concentrated solutions. There are a number of metal-nucleotide complexes possible: (1) outer- and inner-sphere complexes with the phosphate portion of the ligand (ML) as well as the protonated ligand (MHL); l 4 ( 2 ) interaction of some metal ions with sites on the ring as well as the phosphates; l 4 and (3) higher order complexes (e.g., M2L)due to the availability of multiple binding sites. 17, Detailed consideration of all these facts leads to the conclusion that there might be a number of mechanistic possibilities which could explain the deviations from linearity seen in the metal-nucleotide systems. Several, however, could be immediately discarded. First, we tested for the contributions of a kinetic pathway involving the protonated ligand via MHL. Analysis in detail of such mechanisms by the CastellanIg determinantal technique clearly showed that they made negligible contributions at the pH's and concentrations employed for all systems. This is in agreement with all previous investigators, who concluded that above pH -6, the MHL species could be neglected kinetically for metal-nucleotide systems. 3 , 4 Second, the effect of base stacking of the nucleotides alone as a rapid preequilibrium was considered (2L = Lz). The inclusion of this preequilibrium with any reasonable value of the stacking equilibrium constant (K 5-10 M-l)*O had virtually no effect 011 the data displayed in Figure 3. Third, the effect of the existence of two different forms of the nucleotide, i.e., syn and anti,15 was tested. Such a preequilibrium (L = L') would change the observed forward rate constant for the magnesium-nucleotide systems, but not the functional dependence (Le., curvature at high concentrations). It should be pointed out here that the Eigen-Tamm mechanism itself (C) (see Discussion) predicts deviations from linearity at sufficiently high concentrations. The relaxation time for (C) is given by
-
(16) M. Schweizer, A. Broom, P. 0. P. Ts'o, and D. Hollis, J . Amer. Chem. Soc., 90, 1042 (1968), and references therein. (17) C. Liebecq and M. Jacquemotte-Louis, Bull. SOC.Chim. Bid., 40, 67 (1958). (18) M. Mohan and G. Rechnitz, J . Amer. Chem. Soc., 94, 1714 (1972). (19) G. Castellan, Ber. Bunsenges. Phys. Chem., 67, 898 (1963). (20) A. Broom, M. Schweizer, and P . 0. P. Ts'o, J . Amer. Chem. SOC.,89, 3612 (1967).
Frey, Banyasz, Stuehr
Interactions of Diualent Metal Ions
9202
With the outer-sphere equilibrium constants applicable to the present work, the denominator in eq 4 is never larger than about 1.1 for the triphosphates or 1.04 for the diphosphates. Thus, unless KO*'values were more than an order of magnitude larger than estimated for both diphosphates and triphosphates, eq 4 cannot account for the curvature in Figure 3. Increasing Kos' by an order of magnitude however would yield anomalously low values of k H I O for all systems. Finally, no such curvature is found in the inorganic phosphates, which have the same charge as the corresponding nucleotides. We conclude therefore that the denominator in eq 4 cannot account for the observed curvature in the nucleotide systems. Another possibility is that the concentration functions were in error because of significant amounts of KOH that were needed to adjust the pH at the higher nucleotide concentrations. This will affect the total potassium concentration (and hence the amount of K-ATP3-) as well as the ionic strength. This was tested by an interative computer program which explicitly took into account the increased concentrations of K+ and the accompanying ionic strength dependence of the rate and equilibrium constants. Only an approximate treatment was possible because the variation of activity coefficients with ionic strength for high charge types is difficult to assess. Nevertheless, we were able to show that if there were any changes in the p) E , they were shifted slightly values of Z / ( l to higher values. We concluded therefore that the curvatures observed at high concentrations are not due to medium effects of this type. On the other hand, there is now considerable evidence that both Ca2+ and MgzAform MzL complexes with ATP. The species MgzATP has been implicated in certain enzymatic transphosphorylation reactions. Kuby, Noda, and LardyZ1found that the initial velocity of the forward reaction catalyzed by creatine kinase is dependent on the ratio Mgt/ATPt. Maximum relative initial velocity is reached when the ratio is about unity and decreases asymptotically to about 75 of the maximum when the ratio is increased above unity. The authors interpreted this result to indicate that the species M g A T P is forming at high Mgt/ATPt ratios and that it is less reactive than the normal substrate MgATP. The same authors,22in a study of the equilibrium constant of the creatine kinase reaction, concluded that MgzATP is necessary to account for the magnesium dependence of the apparent equilibrium constant. More recently, Noat, et U I . , ~observed ~ that high Mg2+ concentrations have an inhibitory effect on the forward reaction of yeast hexokinase. Since the free Mg2+ion has no affinity for the enzyme, they concluded that the inhibition could only be accounted for by the formation of an inactive MgzATP complex. From their kinetic data the authors estimated the value of the ~ be about 40 M-I at I = 0.1 stability constant K M 2 to M . Rechnitz and coworkersz4recently determined the value of K ~ I by ~ La direct potentiometric method using
+
+
(21) S . Kuby, L. Noda, and H. Lardy, J . B i d . Chem., 210, 65 (1954). (22) L. Xoda, S . Kuby, and H. Lardy, ibid., 210, 83 (1954). (23) G. Noat, J. Ricard, M. Borel, and C. Got, Eur. J . Biochem., 13,
347 (1970). (24) G. A . Rechnitz, et al., in preparation, private communication to J. L. B.
Journal of the American Chemical Society 1 94:26
divalent specific ion electrodes. They obtained a value of K M =~405 ~ M-' for the Mg2ATP system at 25" and zero ionic strength. We found that the addition of the M2L complex formation to the normal complexation mechanism resulted in a quantitative fit to our kinetic data. We used the extended Debye-Huckel equation to adjust Rechnitz' value of KM*Lto 59 M-' at 0.1 M ionic strength. The data for metal ion-nucleotide complexation are completely consistent with a two-step mechanism involving the formation of a 1 : l Mg-nucleotide complex coupled to a 2 : 1 complex as follows. 2M
+
H f
kif
ML
+M
k2r
ML
(B)
HL K I ~ e In + H
HIn
The two slow relaxation times for (B) are given by the following determinental equation
all -
1
-
7
1 azl
j
a12
a22
-
1
=o
(5)
-
r
where
H
=
K, + E/(1
+ a)
and
-I _- - '/Z[(Ull
+ azz)
T*
V(aii
+
~ z z )-~
4(aiiazz - aizazi)] (6)
The two relaxation times have the following properties. The positive root ( ~ + - 1 ) begins at a rather high value, and curves upward (see dotted line in Figure 3). The negative root (T-- l ) at low concentrations has the form
(7) That is, it varies linearly with the concentration function for a simple complexation reaction. At high concentrations, the predicted behavior of r--I is to deviate downward from the linear initial slope, eventually transferring to a smaller slope corresponding to the concentration function for aZ2. Since the value of K ~ I is~ available L experimentally, we were able to carry out a rigorous analysis for the MgATP system. The solid curve in Figure 3 is the predicted behavior of T - - ~ with JT/(1 6) 1 for mechanism B. The values of klf and klr were obtained from the linear initial portion of the curve. These values, as stated
December 27, 1972
+
+
9203
earlier, are the same as for the inorganic tripolyphosphate system. Since K M 2is~estimated to be 59 M-l at I = 0.1, the rate constant k2f can be obtained as the only variable in the high concentration region of Figure 3. The result is klf = 8.7 X lo6 and k2f = 6 X IO5 M-1 sec-1. The last column in Table I1 shows the relaxation times calculated for this mechanism as compared to the experimental values. The interpretation of the MgCTP system was analogous. The values for klt and klr were obtained from the linear portion of the curve. Since k2f for the MgATP system appeared to be the "normal" constant for the Eigen-Tamm mechanism (see Discussion) for the charge type involved, k2f was set equal to 6 X 10; M-' sec-1 for the MgCTP system as well. The value of KMIL was adjusted until a fit was obtained to the data. The value of kzr was obtained from the relationship kPr = k2f/KhIZL.The value obtained for KM?L for MgCTP was identical to that for Mg-ATP within experimental error. Figure 3 shows that the two systems indeed superimpose. The diphosphate nucleotides were analyzed in the same manner as Mg-CTP. The values of kPf were computed on the basis of electrostatic considerations to adjusted be 1 X 105 h 4 - I sec-I and the values of K>I?L until a fit was obtained. Table IV shows that the L also identical values of the rate constants and K M ~are for the two Mg?+diphosphate systems. A kinetic study of the MgATP system has also been carried out by Mg'j nmr spectroscopy. By studying the line broadening of the Mg2j resonance as a function of temperature, Bryant?; was able to obtain an exchange rate of 2 X lo4 sec-' at pH 7.9 and ionic strength 4.5 (1.5 M MgCIz, 2 X lo-* M ATP) and 25", which he attributed to the dissociation of the MgATP (1 : 1) complex. Bryant noted that this dissociation rate constant was a factor of 10 larger than the value of 1.3 X I O 3 sec-I obtained in an e a ~ - l i e rT-jump ~ > ~ study at I = 0.1. He attributed the difference to differences in ionic strength and pH between the two investigations. The dissociation of MgATP however is a (pseudo-) first-order process and consequently should not be so strongly ionic strength sensitive as would be required, nor should the pH be a factor at all if a true rate constant is involved. A far more likely explanation is that Bryant was observing the dissociation of the Mg2ATP species. Under his experimental conditions (large excess of Mg?+), one may show that the predominant coniplexed species is in fact Mg,ATP, constituting about 98z of all the complexes in the system. Our own kinetic study shows the dissociation rate constant to be k2r = 1.0 X IO4 sec-I at 15". A value of 2 X lo4 sec-I at 25" is completely consistent with this result.
Discussion The usual formulation of the Eigen-Tamm mechanism for complex formation uiu an outer-sphere complex (MWL) may be represented by the following reactionz6
(25) R. Bryant, J . Magn. Resonance, 6 , 159 (1972). (26) M. Eigen and I
