J. Phys. Chem. 1995,99, 3815-3822
3815
The Quest for a Metaphosphate Intermediate. The Mechanisms for Hydrolysis of Pyrophosphates with and without Catalysis Buyong Ma, Cynthia Meredith, and Henry F. Schaefer In* Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602 Received: May 30, 1994; In Final Form: December 13, 1994@
Ab initio quantum mechanical methods have been employed to study the mechanisms for the hydrolysis of the pyrophosphate and p-monothiopyrophosphate (MTP) anions at the self-consistent-field (SCF) and secondorder perturbation ( M E ) levels of theory using double zeta plus polarization (DZP) and DZP plus diffuse functions (DZP+diff) basis sets. Metaphosphate is found to be a kinetically important species in the hydrolysis of pyrophosphate for three mechanisms examined in this study ( S N dissociation, ~ acid catalysis, and Mg2+ catalysis). The transition state for the unimolecular reaction of hanion to yield a PO3- anion is dissociative, with the reaction coordinate distance as long as 2.91 8, at the DZP SCF level. This dissociation reaction has a gas phase classical barrier of 25 kcal mol-' (DZP MP2) and 26 kcal mol-' (DZP+diff SCF). For the proton-catalyzed hydrolysis of pyrophosphates, the potential energy surface of the pyrophosphate is dissociative if the bridging oxygen atom is protonated. This dissociation thus yields a metaphosphate and an orthophosphoric acid (H3P04). A hypothesis is formulated to explain the catalytic effect of the Mg2+ cation on the hydrolysis of the pyrophosphate. We predict that one of the P-0 bridging bonds is activated in the Mg2+*H2P2G2-complex. Upon hydrolysis, the Mg2+*H2P2G2-complex may isomerize to the HzFQ-*M~Z+*PO~complex initially; then the H2P04-*Mg2+*P03- complex may be captured by a water molecule to form the H2P04-*Mg2+*H2P04- complex. The classical activation barrier for the isomerization of Mg2+*H2P2072-to H2P04-*Mg2+*P03-is 7.8 kcal mol-' at the DZP MP2 level. The H2P04-*Mg2+*P03-complex lies 8.9 kcal mol-' (DZP SCF) lower in energy than the Mg2+*H2P2072- complex. Therefore, the isomerization of Mg2+*H2P2072-to H2P04-*Mg2+*P03- is both thermochemically and kinetically feasible.
1. Introduction Phosphoryl transfer is very common in biological reactions.' Despite the importance of those reactions, the chemical and biological mechanisms of phosphoryl transfer remain somewhat elusive.2 For example, it is still debated whether a metaphosphate (PO3-) intermediate is involved in phosphoryl The possibility of the involvement of metaphosphate in the hydrolysis of pyrophosphates and ATP was summarized by Westheimer.' Recent studies2V6have indicated that the metaphosphate anion may be a discrete intermediate in the hydrolysis of p-monothiopyrophosphate (MTP). MTP differs from pyrophosphate in that its bridging atom is a sulfur atom instead of an oxygen atom as in pyrophosphate. The P-S-P linkage is too weak to tolerate the electrostatic repulsion forces in the MTP anions; therefore, the breaking of the P-S-P linkage to yield the metaphosphate intermediate is facilitated.2,6 However, since the P-0-P bridging bonds in the pyrophosphate are much stronger than the corresponding P-S-P bonds in MTP, the electrostatic repulsion effect may be less obvious for the hydrolysis of pyrophosphate than that for the hydrolysis of MTP. However, the possible involvement of a metaphosphate intermediate in the hydrolysis of phosphate needs to be investigated. It was well-known that the hydrolysis rates of pyrophosphates (in the absence of divalent cations) decrease with increasing pH.5,7 Pyrophosphate is extremely inert at neutral pH under laboratory condition^;^ however, divalent metal cations and enzymes accelerate its hydrolysis sufficiently for it to participate in and hydrolysis is fastest at neutral pH in the presence of divalent c a t i o n ~ . l , Numerous ~*~ experimental studies have investigated these phenomena, yet there is no clear and simple e~planation.~ In aqueous solution, with so many species involved in the hydrolysis reaction and with the richness of the @Abstractpublished in Advance ACS Abstracts, February 15, 1995.
0022-365419512099-38 15$09.0010
possible hydrolysis mechanisms, the experimental limitations are easy to understand. Consequently, an ab initio quantum mechanical study could provide insight into the mechanism for the hydrolysis of pyrophosphate. In a previous paper? we have demonstrated that electrostatic effects are important for the structures and the thermochemistry of the hydrolysis reactions of pyrophosphates. However, electrostatic repulsion is subject to the influence of both cations and solvation. Augmented with those results, this study addresses the mechanisms for the hydrolysis of the pyrophosphates, which are of fundamental importance in energy conversion in biological systems. We will focus our attention on two questions: the involvement of a metaphosphate intermediate and the catalytic effect of the Mg2+ cation. We selected Mg2+ as the catalytic agent because it is the cation that living systems employ in phosphate metabolism. It was concluded from experimental observations that any theoretical consideration of the mechanism for the hydrolysis of pyrophosphate (or ATP) must account for the observation that the substrate is an Mg2+pyrophosphate ~ o m p l e x . ~
2. Theoretical Methods The Hartree-Fock self-consistent-field (SCF) approach has been used to locate stationary points via analytic energy first derivative techniques. Subsequently, analytic energy second derivative techniques were used to determine harmonic vibrational frequencies when necessary. The effects of electron correlation on total energies were evaluated using second-order Moller-Plesset perturbationlo (MP2) theory. For the MP2 calculations no core electrons were frozen, and geometries were optimized at the DZP SCF level. All computations were performed using the program TURBOMOLE of Ahlrichs and co-workers. The basis sets employed here include double zeta plus polarization (DZP)12a-cfor the H, P, and 0 atoms and are the 0 1995 American Chemical Society
3816 J. Phys. Chem., Vol. 99,No. 11, 1995
Ma et al.
TABLE 1. Exponents (a)and Contraction Coefficients (c) of the (lls7p/7s4p) Basis Set for Me
P
S
a 20050.658 3032.1 175 703.46530 202.44638 67.051978 24.957500 9.9991499 2.8865634 0.98260981 0.11696893 0.04631753
C
0.001011159 0.007639352 0.037498441 0.13592739 0.3332544 1.0 1.0 1.0 1.0 1.0 1.0
a 98.017627 22.628868 6.8714539 2.2520752 0.72246001 0.233 0.075
C
0.014474438 0.095122167 0.30577266 0.4981464 1.0 1.o 1.o
same as those used in our previous work.13 Diffuse functions are added to the phosphorus and oxygen atoms, and the resulting basis set is designated DZP+diff. The diffuse functions include both s and p functions on the heavy atoms and have orbital exponents a,(O) = 0.0845, a,,(O) = 0.0845, a,(P) = 0.0348, and ap(P) = 0.0348. For sulfur atom the basis set is S (1 ls7pld 6s4pld),12with Q(S) = 0.5. For the magnesium atom the basis set is Mg (lls5p/7s2p), plus two sets of even-tempered p functions used as polarization functions [a,(Mg) = 0.233, 0.0751. The exponents and contraction coefficients are taken from the atomic SCF calculations of Huzinaga,12d and are displayed in Table 1. Previous work has shown that the basis sets and correlated level employed here are sufficient to give quite accurate thermochemical properties for phosphates?J3J4 and the present results also suggest the same conclusion. For example, the dissociation energies and activation energies of H2P2072- at the DZP SCF, DZP+diff SCF, and DZP MP2 levels are generally quite close (Table 3). Even though our results are strictly applicable to the gas phase only, they may nevertheless provide insight into these reactions in aqueous solution.
3. Results and Discussion A. Structures and Potential Energy Surface for p-Monothiopyrophosphate (MTP) Anions. The structures of the H3MTP- monoanion, H2MTP2- dianion, and HMTP3- trianion are illustrated in Figure 1. Clearly the increase in electrostatic repulsion increases the P-S-P bond angle from 96.0" in the monoanion to 112.3" in the trianion. HMTP3- trianion is expected to be unstable in the gas phase because as many as eight occupied molecular orbitals have positive orbital energies for the HMTP3- trianion at the DZP SCF level (Table 2). The equilibrium geometry for the HMTP3- trianion (Figure IC) shows a strong hydrogen bond between the proton and the two phosphate groups. This hydrogen bond is !te key structural feature that decreases electrostatic repulsion in the HMTP3trianion. Thus, if we impose a C, symmetry constraint that prevents intramolecular hydrogen bonding (Figure Id), the potential energy surface of the C, symmetry conformation is dissociative-that is, the Hh4TP3- trianion will dissociate into Po3- and HSP032- anions, at DZP SCF levels. This means that the P-S-P bridging bonds are too weak to tolerate the electrostatic repulsion within the HMTP3- trianion. In aqueous solution, the electrostatic repulsion within the HMTP3- trianion will decrease. However, the intramolecular hydrogen bond will be weakened or not present. The above observation lends credence to the experimental hypothesis that the hydrolysis of MTPs may involve a discrete Po3- anion.2q6 B. Gas Phase Dissociation Reaction of Pyrophosphate Anions. I. Geometry of the H P 2 0 9 - Trianion. Although we
have discussed other pyrophosphate anions in the earlier paper? we report our results for the HPz07,- trianion here for comparison with the HMTP3- trianion, which dissociates to yield a metaphosphate intermediate. As expected, there is a strong electrostatic repulsion effect on the structure of the H P z O ~ ~trianion. Its equilibrium geometry is shown in Figure 2a. In this structure one of the P-0 bridging bonds is elongated to 1.706 A, and the P-0-P bond angle is 139.2", which is significantly larger than that in the equilibrium structure for the H z P ~ 0 7 ~dianion. There is a strong intramolecular hydrogen bond between two phosphate groups, with the 0-H distance as short as 1.663 A. A constrained C,symmetry conformation (Figure 2b), without the intramolecular hydrogen bond, has a P-0-P bond angle of 156.9", and one P-0 bridging bond is elongated further to 1.764 A. However, unlike the HMTP3- trianion, the C, conformation potential energy surface for the trianion is not dissociative, apparently because the P-0 bridging bonds in the trianion are significantly stronger than the P-s bridging bonds in the HMTP3- trianion. II. The Electronic Structure of the H P 2 0 J - Trianion and HPOd2- Dianion. There is a question of whether the DZP basis set is adequate for the proper characterization of the anions under consideration here. In general, diffuse functions are necessary to describe anions. However, it has been noted that diffuse functions do not significantly improve the results for phosp h a t e ~ . For ~ ~ the HP042- dianion there are two occupied molecular orbitals that have positive orbital energies, and for the H P z O ~ trianion ~there are there are nine such orbitals (DZP SCF; Table 2). These results suggest that the electrons are held loosely for those multicharged anions. Thus, an examination of the effects of adding diffuse functions was necessary. We have performed calculations on the HP04'- dianion and H p ~ 0 7 ~trianion at both the DZP SCF and the DZP+diff SCF levels. With diffuse functions added to the basis sets, there is still one occupied molecular orbital that has a positive orbital energy (Table 2). The equilibrium geometries for the HP042dianion are almost the same at the DZP SCF and DZP+diff SCF levels (Figure 3). This holds true for the H P z O ~ trianion ~at the DZPfdiff SCF level (Figure 2). There are still seven occupied molecular orbitals that have positive orbital energies. III. Thermochemistry and Transition State for the Gas Phase Dissociation of the H P 2 0 9 - Trianion. Even though the potential energy surface for the ~ ~ ~ trianion 0 ~ 3is -not dissociative, its dissociation reaction is thermochemically feasible in the gas phase (Table 3), as indicated by reactions 1, 2, and 3:
AE, = 50.7 kcal mol-' H,P20,2-
-
"0:-
AE, = -86.0 kcal mol-'
+ diff SCF)
+ PO,(DZP + diff SCF) + PO,(DZP+ diff SCF)
H2P04-
AE, = -17.5 kcal mol-' HP20,3-
(DZP
(2)
(3)
Clearly, the driving force for these dissociation reactions is electrostatic repulsion; with increasing total negative charge, the dissociation reaction becomes more exothermic. Here, the examination of the barrier for the isomerization reaction 3 is in order. We have studied the transition state
Hydrolysis of Pyrophosphates
J. Phys. Chem., Vol. 99, No. 11, 1995 3817
c.
1.894A
....................
c1
0.958A
5.453A
(3
1.502A
d. C, Figure 1. Equilibrium geometries. a. p-Monothiopyrophosphoricmonoanion H3MTP- at the DZP SCF level. b. p-Monothiopyrophosphoricdianion H&lTP2- at the DZP SCF level. c. p-Monothiopyrophosphoric trianion €IMP3- at the DZP SCF level. d. One point on the dissociative potential energy surface of the p-monothiopyrophosphoric trianion HMTP3- with constrained C, symmetry at the DZP SCF level.
a. C1 0.0 kca~mor1
4.2'63 0.948A DZPSCF 0.949A DZP+diN SCF
2.846A
0
1.471A 1.473A
..............................
z.wA
2.869A
1471A I:472A
--.
*..**-.
149.2'
............. n
--..
b. C, 20.5 kcal mol-' DZP SCF
c.
l.52lA 1.522A
1.512A 1.516A
0
c,
25.8 kcal mol-' DZP SCF 25.4 kcal mol-' DZP+diff SCF 24.4 kcal mol" DZP MP2
Figure 2. a. The equilibrium structure for the trianion at the DZP SCF and DZPi-diff SCF levels. b. A stationary point for the trianion with constrained C, symmetry at the DZP SCF level. c. The geometry of the transition state for the dissociation of the pyrophosphate
trianion H P 2 0 7 3 - at the DZP SCF and DZP+diff SCF levels. (Figure 2c) for the dissociation of the H P z O ~ ~trianion, for which the probability of dissociating to yield metaphosphate should be highest due to the repulsive effects of three negative charges. The classical barrier height for reaction 3 is predicted to be 25.4 kcal mol-' (DZP+diff SCF) and 24.8 kcal mol-' (DZP MP2; Table 3). However, we expect this unimolecular dissociation to have a higher barrier in aqueous solution, where the electrostatic repulsion is decreased by solvation and the presence of cations. We would like to focus attention on the structure of the transition state. The structure of the transition state for reaction
3 is indicated in Figure 2c. The striking feature of this transition state is that the reaction coordinate p.0 distance reaches a maximum of 2.899 A (DZP SCF). The corresponding imaginary vibrational frequency is only 83i cm-' (DZP SCF), indicating a very flat reaction coordinate. The significance of these results extends beyond the dissociation of the pyrophosphate; it illuminates numerous experimental observations concerning the phosphoryl transfer reaction involving the breaking of a P-0 bond.z-6 Much experimental effort has been expended toward demonstrating the possibility of the involvement of metaphosphate in the phosphoryl transfer reactions.z-6 It was frequently concluded that the transition state may involve
Ma et al.
3818 J. Phys. Chem., Vol. 99, No. 11, 1995 TABLE 2. Selected Occupied Molecular Orbital Energies for Several Anions (hartreep MO 1 (HOMO) 2 (SHOMO) 3 4 5 6 7 8 9 10
H2MTP2-
HMTP3-
HZP207'-
DZPSCF -0.068 -0.105 -0.106 -0.133 -0.134 -0.158 -0.164 -0.180 -0.185 -0.205
DZPSCF 0.120 0.093 0.064 0.061 0.041 0.025 0.014 0.008 -0.013 -0.014
DZP SCF - 0.112 - 0.117 - 0.130 - 0.131 - 0.148 - 0.165 - 0.172 - 0.183 - 0.203 - 0.204
HP04'-
DZP SCF 0.028 0.001 -0.002
HP04'-
DZP+diff SCF 0.003 -0.023
HP207)-
DZP SCF 0.101 0.084 0.063 0.063 0.049 0.029 0.024
HP2073DZP+diff SCF 0.080 0.062 0.041 0.041 0.028 0.007 0.003
0.020
-0.00&
0.002 - 0.015
-0.190 -0.037
MTP = PzO~S.
\\
n
0.944A DZPSCF 0.944A DZP+diff SCF
C1
W
Figure 3. The equilibrium geometry for the orthophosphoricdianion mod2-at the DZP SCF and DZP+diff SCF levels. a dissociative metaphosphate-i.e., there is essentially no bond between the metaphosphate and the other leaving group in the transition state, regardless of whether the metaphosphate could be a free intermediate beyond the transition state.2-6 Therefore, our theoretical results support the experimental conclusion concerning the case of the dephosphorylation reaction of the pyrophosphate. C. Pyrophosphate Hydrolysis in Acid Media. The hydrolysis rate of pyrophosphates in the absence of divalent cations decreases with increasing P H . ~At a given pH, the hydrolysis is first order in the pyrophosphate c~ncentration.~ Therefore, it was concluded that the stability of pyrophosphates increases in the order H & 0 7 H3P207H2P~07~- HP2073P ~ 0 7 ~ most - , likely due to increasing electrostatic repulsion between the pyrophosphate and the nucleophile (H20).7 However, there was an alternative explanation, namely that the hydrolysis reaction is catalyzed by protons or, more strictly, by H30+, H502+, etc. in aqueous s ~ l u t i o n . ~ Considering the P-0-P linkage in the pyrophosphate, we suppose that the rate-controlling step for the acid-catalyzed mechanism should be the electrophilic attack, i.e., the protonation of the bridging oxygen atom. To test this hypothesis, we studied a possible structure of an isomer of H&O7 with a protonated bridging oxygen atom, as indicated in Figure 4. When we attempted to minimize the energy of this isomer of H&O7, we discovered that the potential energy surface in this region is dissociative. Specifically, the P-0-P bridging bond breaks upon protonation, resulting in discrete HPO3 and H3P04 molecules. Because HPO3 is extremely reactive in aqueous solution, it will rapidly react with a water molecule to yield H3P04. This result supports Westheimer's postulation' that the acid-catalyzed chemical hydrolysis of ADP involves monomeric metaphosphate. This dissociative potential energy surface enables us to understand the pH-rate profile (in the absence of divalent cations) for the hydrolysis of both pyrophosphate7 and MTP.2*6 There are two reasons for the decrease in the hydrolysis rate for those species with increasing pH. First, the hydrolysis rate
Figure 4. Schematicrepresentation of proton-catalyzedhydrolysis of pyrophosphate via a metaphosphate intermediate. The relative energies are at the DZP SCF level of theory. obviously will decrease with decreasing proton concentration. Second, with increasing pH, more oxygen atoms (except the bridging one) will be fully negatively charged. Because those negatively charged oxygens are more attractive to protons than are the bridging atoms (0 or S), it becomes more difficult to protonate the bridging atom, resulting in a decreasing hydrolysis rate. D. The Mg2+*H&0?- Complexes and Their Reactions. I. Geometries and Potential Energy Suflaces for the Mg2+H2P203- Complexes. We have examined two configurations of the Mg2+*H2P~072complex, as indicated in Figure 5 . The global minimum geometry for the complex is shown in Figure 5a. The Mg2+ cation is three-coordinated and the configuration of the H2P2072- dianion corresponds to two negative charges localized at the same phosphate group. The second configuration is that in Figure 5b, which is 2.9 kcal mol-' higher in energy than the global minimum (Figure 5a). The Mg2+ cation is twocoordinated in this structure. Compared with the global minimum structures for the MH3P207 (M = Li, Na, K) moleculesg and that for the Mg2+*HzP~072complex, we can see one of the unique effects of the divalent cation. For the Mg2+*HzPz072-complex, one of the P-0 bridging bonds is activated, Le., elongated to 1.738 A (Figure 5a), whereas the P-0 bridging bond distances are much shorter for the MH3P207 (M = Li, Na, K) molecules.
Hydrolysis of Pyrophosphates
J. Phys. Chem., Vol. 99, No. 11, 1995 3819 complex-i.e., the isomerization should be thennochemically feasible. Second, the barrier for the isomerization should be reasonably low-Le., the isomerization should be kinetically feasible. Finally, the hydration of H2P04--Mg2+*P03- (reaction 5 ) should be sufficiently fast-Le., it should not be a ratecontrolling step. The latter requirement is clearly satisfied, as the metaphosphate is highly reactive and cannot exist in aqueous ~olution.'-~J3 We have examined the fist and second requirements and found that our theoretical results support these as well, as shown by the following. The structure (Figure 7b) of the H2PO4-a Mg2+*P03-complex is predicted to be 8.9 kcal mol-' lower in energy than the Mg2+*H2Pz072-complex (Figure 5a), meaning that the isomerization reaction
1
a. C1
-.H2P04-*Mg2+*P03-
Mg2+*H2P20,2-
0.0 KcaVmol
o.9soA
AE, = -8.9
b. C1 2.9 KcnVrnol
Figure 5. The equilibrium geometries of the MgZ+*H&072-complex at the DZP SCF level: a. the global minimum (note that one of the P-0 bridging bonds is elongated to 1.738 A); b. a local minimum with no symmetry.
This may be one reason why divalent cations catalyze the hydrolysis of pyrophosphate. ZZ. Catalytic Mechanism of M$+ Cation for the Pyrophosphate Hydrolysis, an Isomerization Pathway. Our hypothetical catalysis mechanism for the role of Mg2+ cation in hydrolysis is illustrated in Figure 6 and involves reactions 4 and 5 : Mg2+-H2P20,2-
+
-
H2P04-*Mg2+*P03- H20
H2P04-*Mg2+*P0,-
-L
(4)
H2P04-*Mg2+*H2P04- ( 5 )
Initially (reaction 4), a metaphosphate intermediate may be formed as part of the H2P04-*Mg2+*P03-complex (Figure 7b) through the isomerization of the Mg2+*H2P2072- complex (Figure 5a). The resulting H2P04-*Mg2+*P03-complex may then be captured by a water molecule to form the final HzP04-.Mg2+-H2P04- complex (Figure 7c; reaction 5). Of course, due to the reactivity of the metapho~phate,'-~,'~ there is a possibility that the metaphosphate might be captured by a water molecule as early as in the transition state (Figure 7a) for the isomerization of Mg2+*HzP2072-(Figure 5a) to H2P04-* Mg2+*P03- (Figure 7b). There are three requirements to ensure the feasibility of this mechanism. First, the H2P04-*Mg2+*P03-species should be energetically lower than or close to the Mg2+*H2P2072-
(4)
kcal mol-'
is thermochemically feasible. The transition state for reaction 4 is shown in Figure 7a. The reaction coordinate involves the attack of Mg2+ at the bridging oxygen atom and the breaking of one P-0 bridging bond. The classical barrier height for this isomerization is only 8.2 kcal mol-' (DZP Mp2; Table 3). By comparison of the barrier for the dissociation of the HP2073- trianion reaction 3, this isomerization barrier is significantly lower, thus manifesting the catalytic effect of the Mg2+ cation. Even though the reaction coordinate distance (2.474 A) for the transition state is significantly shorter for this isomerization reaction than that for the dissociation of the HP2a3 trianion (2.899 A), the transition state is still dissociative, with an imaginary vibrational frequency of 138i cm-'. Unlike the dissociation of the HP2073- txianion reaction 3, the impetus for this isomerization is not electrostatic repulsion; rather, it is driven by the intrinsic coordination requirements of the Mg2+ dication, and therefore, it is still feasible in aqueous solution. There have been many hypotheses concerning the mechanism of the metal ion-promoted dephosphorylation of polyphosphates. Among the possible roles suggested for a metal cation in accelerating depho~phorylation~~~ are (a) charge neutralization or shielding, (b) polarization or electron sink, (c) strain induction, (d) template formation for orienting substrates and enzymatic catalytic groups, (e) coordination to the leaving group, and (0 relatively tight coordination to the transition state. In comparison, our hypothesis in Figure 6 is consistent with the former hypotheses, especially with respect to points c, e, and f above. The strain induction of a divalent cation is manifested by an elongated P-0 bridging bond in the Mg2+*H2P2072-complex (Figure 5a). The Mg2+ dication is strongly coordinated in the transition state of reaction (4) (Figure 7a). The Mg2+ dication is strongly coordinated to the hydrolysis product H2PO4- as well, as indicated in Figure 6d and in the reactions
+
Mg2+*H2P20,2- H 2 0
-
H2P04-*Mg2+*H2P04- ( 5 )
AEe = -52.8 kcal mol-' Mg2+*H2P20:-
+ H 2 0 -H3P04+ Mg2+HP04-
(6)
AE, = 45 kcal mol-' Reactions 5 and 6 indicate that the trend of this coordination will increase the exothermicity of the hydrolysis reaction. This is consistent with the experimental observation that the -AGO
Ma et al.
3820 J. Phys. Chem., Vol. 99, No. 11, 1995
-
bo
transition state H
H
H
+ H2O
C. H2P04- *MgZ'*PO3-
tE
d
H2P04-*Mg2+*H2P04-
b. transition state 11.4 kcalhole (DZP S O , 7.8 kcaVmol (DZPMP2) -9.
.*.
*.-•
.*
.-w
-. -... 8..
e .
a. Mg2'*H2P20:-
-*.
.. -. *.
c. H,PO,-
% -8.9 ...%
*M$*PO~-
kcaVmole (DZP SCF)
I I
0.0 kcaUmole
II
i
+H20
I
i
Figure 6. Schematic representation of Mg2+ cation-catalyzed hydrolysis of pyrophosphate via a metaphosphate complex intermediate.
increases with increasing concentration of Mg2+ cation for the hydrolysis reactions of both ATP and pyr~phosphate.'~
4. Conclusion We have studied the mechanisms of the hydrolysis of pyrophosphates and p-monothiopyrophosphate (MTP) anions, with the emphasis both on the possible involvement of metaphosphate intermediates and on the catalytic effect of the Mg2+ dication. Our theoretical results support the experimental hypothesis that the hydrolysis of MTP involves a discrete metaphosphate anion2*6 because without intramolecular hydrogen bonding, the potential energy surface of the HMTP3- trianion will dictate dissociation into the PO3- and HSP03- anions. The driving force for this dissociation may be electrostatic repulsion. However, because the P-0-P bond in the pyrophosphate is much stronger than the P-S-P bond in the MTP,it is more difficult for the pyrophosphate to dissociate to yield the PO3anion. Even with a strong electrostatic repulsion, the dissociation of the ~ ~ 2 0 trianion 7 ~ - has a gas phase classical barrier of 24 kcal mol-' (DZP MP2). The transition state structure for the dissociation of the H ~ 2 0 7 ~trianion is dissociative, with the reaction coordinate distance reaching a maximum of 2.899
8, (DZP SCF),consistent with previous experimental conclusions concerning phosphoryl transfer.'-6 For the acid-catalyzed hydrolysis of pyrophosphates, the potential energy surface is dissociative if the bridging oxygen atom is protonated. This dissociation thus yields a metaphosphate and orthophosphoric acid (H3P04), and the metaphosphate will be captured by a water molecule to yield orthophosphate. Protonation should be the rate-controlling step. Clearly, the possibility of this protonation will decrease with increasing pH, and therefore the hydrolysis rate will decrease in turn, as has been observed e~perimentally.~ The stability of pyrophosphate in neutral pH aqueous solution may be attributed both to the difficulty of protonation of the bridging oxygen atom and to the fact that the P-0-P bridging bonds are strong enough to tolerate substantialelectrostaticrepulsion. Note that the P-S-P bridging bonds in the MTP are comparatively much weaker, and thus more easily broken by electrostatic repulsion, allowing MTP to be hydrolyzed at an appreciable rate in high pH solution.2S6 A hypothesis is formulated to explain the catalytic effect of the Mg2+ dication on the hydrolysis of the pyrophosphate. We
J. Phys. Chem., Vol. 99, No. 11, 1995 3821
Hydrolysis of Pyrophosphates
TABLE 3. Thermochemical Predictions for the Formation of MetaphosphaW barrier heights for transition states
AE,
-
reaction (1) H3Pz07reaction (2)
51.0 50.7b -21.0 -24.2 (-23.0) (-23.5) - 17.5' -85.1 -86.P
+ Po3-
-
HzPz07'HzP04- -k Po3reaction (3)
-
AEQ
AIP
AG'
AS'
-23.2 (-22.5)
-36.2 (-35.5)
43.6
HPzO~~-HP04'- -k Po3-8.9 reaction (4) MgZ+.H2Pz072- HzP04-.MgZ+*PO3reaction (5) -52.0 MgZ+*HzPz072+ HzO HzP04-*Mg2+*HzP0445.0 reaction (6) Mg2+*HzPz07'- HzO &Po4 + MgZ+HP04-
+
-
AEet
AEot
Wt
AG't
AS"?
25.8 (24.4) 25.4c 11.3 (7.8)
24.3 (22.9)
24.9 (23.5)
23.1 (21.7)
6.0
10.2 (6.6)
10.5 (6.9)
9.3 (6.7)
4.2
The values of AEe, AEo (AEe plus ZPVE correction), AIP,and AGO are in kcal mol-', while ASo is in cal/Kmol. The standard state is 1 atm at 298 K. DZP MP2 energies are in parentheses. Most results are at the DZP SCF level, but critical energies were also evaluated with diffuse functions and via second order Derturbation theorv. These values are at DZP+diff SCF level based on the geometries at the DZP SCF level. The values are at D;
0.948b
a. C1
2'054A/q 1.486A
106.0'
c. C2" Figure 7. a. The geometry of the transition state for the isomerization 2- to HzPO4-.MgZ+*P03at the DZP SCF level. b. The of MgZ+*HzPz07 equilibrium geometry of the H2P04-.Mgz+.P03- complex at the DZP SCF level. c. The equilibrium geometry of the H2P04-*Mgz+*H~P04complex at the DZP SCF level. found that one of the P-0 bridging bonds is activated in the Mg2+-H92e2-complex. Upon hydrolysis, the Mg2+*H2P2072complex might isomerize to the H2P04-*Mg2+*P03-complex initially; then the H2P04--Mg2+*P03- complex may be captured by a water molecule to form the H904-*Mg2+.H2P04- complex. The classical activation barrier for this isomerization is only 8.2 kcal mol-' at the DZP MP2 level. The H2P04-*Mg2+*P03complex is 8.9 kcal mol-' lower in energy than the Mg2+*H2P2072-complex. Therefore, this isomerization is both
thermochemically and kinetically feasible. This catalytic mechanism supports previous hypo these^^,^ concerning the role of metal cations in terms of strain induction, relatively tight coordination to the transition state, and coordination to the leaving group. There are some similarities between the possible catalytic effects of protons and of Mgz+ cations on the hydrolysis of pyrophosphates. Both involve electrophilic attack at the bridging oxygen atom in the pyrophosphate and the formation of a metaphosphate intermediate. However, protonation requires a strongly acidic medium whereas the formation of the Mg2+* H~P207~complex is preferred in the neutral solution, the latter of which is closer to physiological conditions.'6 Finally, we answer the question raised in the title of this paper concerning the quest for a metaphosphate intermediate. Obviously, metaphosphate is a key species in all three mechanisms (sN1 dissociation, acid-catalyzed hydrolysis, and Mg2+ cationcatalyzed hydrolysis) studied here. Therefore, the metaphosphate is a kinetically important3 species in the hydrolysis of pyrophosphate. However, if we broaden the term "intermediate" to refer not only to the involvement in the transition state or to related species on the potential energy surface but also to the ability to be diffusable, as Herschlag and Jencks suggested? then it will be more complex. Whether a metaphosphate intermediate has a lifetime sufficient to allow diffusion depends on the solvation system. In aqueous solution, there is no barrier sufficiently high to prevent the metaphosphate from being captured by water molecules to yield orthoph~sphate.~~
Acknowledgment. This research was supported by the US. Air Force Office of Scientific Research under Grant AFOSR92-J-0047. We appreciate helpful discussions with Dr. Y. Yamaguchi, Dr. Y. Xie, and Mr. P. Schreiner. References and Notes (1) Westheimer, F. H. Chem. Rev. 1981, 81, 313. Westheher, F. H. Science 1987, 235, 1173. (2) Halikides, C. J.; Frey, P. A. J. Am. Chem. SOC. 1991, 113, 9848, and references cited therein. (3) Friedman, J. M.; Freeman, S.; Knowles, J. R. J. Am. Chem. Soc. 1988, 110, 1268. (4) Herschlag, D.; Jencks, W. P. J. Am. Chem. Soc. 1989,111, 7579. Herschlag, D.; Jencks, W. P. J. Am. Chem. Soc. 1989,111,7587.Herschlag, D.; Jencks, W. P. J. Am. Chem. Soc. 1990, 112, 1951. ( 5 ) Hendry, P.; Sargeson, A. M. In Progress in Inorganic Chemistry; Lippard, S. J., Ed.; John Wiley & Sons: New York, 1990; Vol. 38, p 201.
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