Deprotonation of Water in the Presence of Carboxylate and

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6342

J. Phys. Chem. B 1998, 102, 6342-6350

Deprotonation of Water in the Presence of Carboxylate and Magnesium Ions Amy Kaufman Katz,† Jenny P. Glusker,*,† George D. Markham,† and Charles W. Bock†,‡ The Institute for Cancer Research, Fox Chase Cancer Center, Philadelphia, PennsylVania 19111, and The Philadelphia College of Textiles and Science, Philadelphia, PennsylVania 19144 ReceiVed: March 18, 1998; In Final Form: May 13, 1998

The effects of a metal ion-bound carboxylate group on the acidity of a water molecule bound to the same cation have been assessed by ab initio molecular orbital calculations. In the hexahydrate Mg[H2O]62+ the free energy required to deprotonate one coordinated water molecule is only 40% of that required to deprotonate a free water molecule, indicating that the presence of the magnesium ion facilitates the ionization of water. However, if one of the water molecules in this hexahydrate Mg[H2O]62+ is replaced by a carboxylate ligand, the energy required to dissociate a proton from a metal ion-bound water molecule is increased by approximately 80 kcal/mol and is intermediate between the energy required to deprotonate one water molecule in Mg[H2O]62+ and that for a free water molecule. This effect of the carboxylate group on the pKa of metal ionbound water appears to be primarily the result of a reduction of the net positive charge of the overall Mg[H2O]52+-(RCOO-) complex rather than any changes in the electronic structure of the magnesium cation itself, since a Mg2+-coordinated chloride ion has a similar influence on acidity. Two aquated magnesiumcarboxylate motifs have been identified in crystal structures of small molecules and in proteins. One is a magnesium-bound hydrated carboxylate motif with an internal hydrogen bond. Formation of the hydrogen bond within this motif does not appear to appreciably affect the pKa of the metal ion-bound water molecule. A major role of such a motif, found in many protein crystal structures, may be to help align the rather rigid magnesium coordination octahedron, thus positioning appropriate functional groups for efficient catalytic activity. A second motif, which involves a carboxylate group bound to two metal ion-bound water molecules, is also found in several protein crystal structures. It is, however, more flexible in conformation than is the first motif and therefore cannot exert such rigid orientational powers. Thus, metal ion-bound water molecules and carboxylate groups can interact in a synergistic fashion to assist in the catalytic activity of enzymes by altering the pKa of the water molecule and by providing a means for aligning required functional groups in a stereochemically precise manner (“coordination clamping”).

Introduction Enzymes employ metal ions in several ways.1,2 A metal ion can activate a chemical bond and make it more amenable to reaction. Nature has commonly used transition metal ions for such a purpose, although other metal ions are also used. Another use of metal ions in enzymes is to provide structural stability of the active site and a correct geometric orientation of the substrate within it. A further use is to alter the number of electrons in the substrate during conversion to an intermediate or product; this is done by a change in the oxidation state of those metal ions that have redox capability. When a cation is bound to a protein, the common binding groups are side-chain carboxylate, imidazole, hydroxyl, and sulfhydryl groups and main-chain carbonyl groups. Of these, the negative charge on carboxylate ions favors cation binding. The geometry of this binding has been examined in crystal structures, and it is found that metal ions generally bind to isolated carboxylate groups near the plane of the carboxylate group.3,4 Three types of interaction, syn, anti, and bidentate (illustrated in Figure 1), result from the two locations and directions of the lone pairs of electrons on each oxygen atom of the carboxylate ion and on the metal-oxygen distance. The * Corresponding author. E-mail: jp [email protected]. † Fox Chase Cancer Center. ‡ The Philadelphia College of Textiles and Science.

syn

anti

Figure 1. Syn, anti, and bidentate binding of a carboxylate group to a magnesium ion.

most common orientation has been found to be the syn conformation.4 The bidentate conformation is mainly found when the metal-oxygen distance is in the range 2.4-2.6 Å, as is found for calcium ions (Ca2+); magnesium ions (Mg2+), which have shorter metal-oxygen distances, rarely take part in such bidentate binding. Several enzymatic reaction mechanisms involve the dissociation of a metal ion-bound water molecule to give a proton (as hydronium ion) and a metal-bound hydroxyl group. The extent to which this occurs depends on the nature of the metal ion and is presumably modified by other functional groups bound to the metal ion or hydrogen bonded to the water molecule. In this paper we describe investigations of the effect of the introduction of a carboxylate group into the inner coordination sphere of the metal ion on the energetics of such a deprotonation of metal ion-bound water molecules. The carboxylate group was chosen for this study because it is a common magnesium-

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Deprotonation of Water with Carboxylate and Mg Ions binding group in proteins. In a somewhat analogous study, the question of the effect of replacing ammonia ligands by carboxylate groups on the pKa of zinc-bound water has been investigated by Bertini and co-workers.5 We address here the manner in which enzymes bind magnesium ions and the role of specific modes of magnesium binding on subsequent enzymatic reactions. We have concentrated on complexes of magnesium because this metal ion shows a strong preference for octahedral coordination of oxygencontaining ligands and this simplifies the analysis.3,4 The magnesium ion is similar in size to many of the transition metal ions but has a complete outer shell of electrons which provides it with a certain inertness and hardness.2 The common occurrence of the Mg[H2O]62+ unit in many crystal structures, despite the presence of anions which would have been expected to coordinate directly to the magnesium ion,3 highlights the fairly rigid stereochemical requirements of this metal ion. During this study we have identified a common metal ionbinding motif (I) in which the carboxylate ion spans a metal ion-bound water molecule. A hydrogen bond is formed between water and the carboxylate oxygen atom that is not bound to the metal ion. This motif is found in crystal structures of small molecules6 and in protein crystal structures, such as those of D-xylose isomerase7 and mandelate racemase.8 The extent to which this motif affects the pKa of the water molecule within it is investigated here. The methods used in this study include analyses of crystal structures of small magnesium complexes and magnesium-containing enzymes and ab initio molecular orbital calculations which assess the energetics and bonding characteristics of relevant metal-ion complexes.

J. Phys. Chem. B, Vol. 102, No. 33, 1998 6343

Figure 2. Motifs in aquated magnesium carboxylate complexes: (a, left) motif I and (b, right) motif II.

Methods A. Crystal Structural Analyses. The frequency of occurrence of motif I in reported crystal structure analyses was established by investigations of the results of such determinations to be found in certain databases. Three-dimensional atomic coordinates on both small and macromolecular molecules contained in the Cambridge Structural Database (CSD) and Protein Databank (PDB), respectively, were used as a basis for our study.9,10 The CSD was searched by way of the program QUEST3D for all published crystal structures involving a magnesium ion, carboxylate group, and a water molecule; a master file was created of compounds containing these groups. We limited our search to magnesium bound to O (carboxyl group, water molecules, etc.), and to N, S, Cl, and/or Br as the remaining ligands, because we were interested in crystal structures relevant to magnesium-protein and magnesiumnucleic acid interactions and in possible drug binding in an aqueous environment. Some crystal structures were eliminated from this analysis (by use of the program QUEST3D) because there was disorder in the crystal structure and/or the crystallographic R factor was high (greater than 0.10). The crystal structures selected were then examined to determine whether they contained motif I. From this analysis 39 crystal structures containing a magnesium ion, carboxyl group, and water molecule were identified, and six of these contained motif I. The motif geometry is diagrammed in Figure 2a and illustrated, by use of the program ICRVIEW,11 in Figure A of the Supporting Information. It appears that if it is energetically favorable for the magnesium ion to bind a carboxylate group in a syn manner, it is possible to form motif I. Many compounds, however, contain additional groups that also bind the magnesium ion and preclude the formation of motif I.

Figure 3. Motif I in protein crystal structures: C ) carboxyl group; W ) water; X ) substrate. Arrows in motif I point from the carboxylate oxygen to water.

We then examined macromolecular crystal structures in an analogous manner. The PDB was searched for all proteins that contain a magnesium ion bound directly to a carboxylate group (aspartate, or glutamate side chains) and a water molecule. These structures were then viewed by use of the programs ICRVIEW11 and Rasmol.12 It was found that motif I exists in several protein crystal structures, as diagrammed for some in Figure 3. B. Molecular Orbital Studies. The energetics of deprotonation, dehydration, and proton-transfer reactions in the presence of divalent magnesium were determined by performing ab initio molecular orbital calculations on a variety of hydrated magnesium complexes. The GAUSSIAN 94 series of programs13 was used throughout, and the calculations were carried out on the CRAY YMP computer at the National Cancer Institute, Frederick, MD, and several Silicon Graphics and DEC alpha computers. Optimizations were performed in all cases at the restricted Hartree-Fock (RHF) level using the internally

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TABLE 1: Binding of Carboxylate and Water Molecules to Magnesium Ions in Crystal Structures in the CSDa no. of carboxylate groupsb

coord no.

no. of entries

no. of water molecules

1 1 2 2 2 2 2 2 2 3 3 4 4 4 4 6

6 6 5 5 6 6 6 6 6 6 6 6 6 6 7 6

1 4 1 1 4 3 1 1 11 1 1 2 1 4 3 4

5 4 1 1 2 3 4 2 1 2 1

others OH, N O O CdO, N, ClO ClN N O O, ClO N

a Shown are the number of carboxylate groups and the number of water molecules bound to Mg2+, together with information on the coordination number of the Mg2+, the number of entries, and other ligands to the Mg2+. b All carboxylate groups are bound in a monodentate manner to Mg2+.

stored 6-31G* basis set14 and in selected cases using secondorder Møller-Plesset (MP2) perturbation theory15 with the 6-31G* and 6-31+G* basis sets.14,16 The default geometry convergence criterion in GAUSSIAN 94 was used in all cases.13 Vibrational frequencies were obtained from analytical second derivatives calculated at the RHF/6-31G*//RHF/6-31G* level in order to verify that each calculated structure reported here corresponded to a local minimum on the potential energy surface (PES) and to estimate the thermal and entropic corrections required to obtain reaction enthalpies and free energies at 298 K.17-19 No symmetry constraints were imposed during any of the optimizations, and all starting geometries had C1 symmetry. Numerous single-point calculations at the MP2(FULL)/6311++G** level with all orbitals active (FULL)20 were carried out to assess the sensitivity of calculated reaction energies to the use of more complete basis sets and to judge any corrections required for the results of the lower-level calculations. In a few cases, single-point calculations using fourth-order MøllerPlesset (MP4) perturbation theory, including all single, double, and quadruple excitations (S, D, and Q), with the core orbitals frozen (FC) were also performed (MP4SDQ(FC)/6-31G*). Charges and electron configurations on the atoms in the various complexes were calculated from natural population analyses (NPA) using both the RHF and MP2 densities with a variety of basis sets.21-23 Results Motif I. Structural Studies. Our present analysis of crystal structures was confined to those with divalent magnesium directly coordinated to at least one carboxyl group. A water molecule is the most common ligand found in such magnesium carboxylate structures in the CSD (89%), as seen in Table 1. A list of 39 crystal structures from the CSD containing a magnesium ion and a carboxylate group is given in Table A of the Supporting Information, and the bibliographic reference for each is given in Table B of the Supporting Information. The entries were then divided in terms of the number of carboxylate groups bound to the metal ion, as shown in Table 1 and Table

A. A divalent magnesium cation was found to be bound to two different carboxylate groups (related by a center of symmetry in the crystal structure) in 19 entries (22 Mg2+ sites) in the CSD. Three monodentate carboxyl groups were found bound to a single Mg2+ in 2 entries, and four monodentate carboxylate groups to one Mg2+ in 10 entries. No entries were found for five carboxylate groups, and there were only 4 entries that contained six monodentate carboxylate groups around one Mg2+ (see Table 1). Thus, half of the entries involved two metal ion-bound carboxylate groups. Entries in the CSD that contain a carboxylate group and at least one water molecule bound to the metal ion were further analyzed for motifs I and II (Figure 2). Motif I was identified in six entries, FELGUY01, VAXHUX01, YUHJIU, BAWZII, SONPAM, and VAXJAF.24-26 These six structures are shown in Figure A (with journal references in Table B, Supporting Information). The extent to which magnesium binds in the syn and anti conformations (see Figure 1) is listed in Table C (Supporting Information). To form motif I, the metal ion must bind in a syn conformation, while if the metal ion is chelated to other functional groups, the water must lie in the anti position. Of nine compounds with syn binding (see Table C (Supporting Information)), six involve motif I, and in the remaining three, the carboxylate group bridges two metal ion sites. Of the 16 compounds in the CSD with anti binding, the magnesium ion in 13 is chelated to two connected functional groups of a ligand molecule, and in one bridges two carboxylate groups. In addition, 7 structures show a mixture of syn and anti binding. The occurrence of motif I in macromolecular structures stored in the PDB10 was then investigated. A set of 50 magnesium binding proteins was studied. Motif I has been identified in 11 crystal structures in the PDB: bacterial luciferase,27 catechol O-methyltransferase,28 CheY,29 3′,5′-exonuclease E. coli DNA polymerase,30 EcoRV endonuclease,31 enolase,32 avian sarcoma virus integrase,33 mandelate racemase,8 tumor necrosis factor (extracellular domain),34 RNaseH from bacteriophage T4,35 and D-xylose isomerase.7 Motif II. Another motif, II, shown in Figure 2b, was identified in nine structures in the CSD. In this motif the oxygen atoms of the carboxyl group bridge the hydrogen atoms of two metal ion-bound water molecules. Motif II is also found in several protein crystal structures in the PDB: elongation factor EF-Tu from E. coli,36 the R subunit of the G protein Gi1,37 ras p21,38 the R subunit of integrin CR3,39 and transducin-R complexed with GTPγS.40 II. Molecular Orbital Studies. a. Structures and Charge Distribution in Aquated Magnesium Complexes. The optimized RHF/6-31G* and, where available, the MP2(FULL)/6-31G* and MP2(FC)/6-31+G* structures of six-coordinate divalent magnesium complexes Mg[H2O]62+, Mg[H2O]52+-OH-, Mg[H2O]52+-HCOO-, Mg[H2O]42+-OH--HCOO-, and Mg[H2O]42+-OH--HCOOH are shown in Figure 4, and atomic coordinates are listed in Table D of the Supporting Information. Total molecular energies, thermal corrections, and entropies of all the structures in Figure 4 are listed in Table E of the Supporting Information. The octahedral (Th) magnesium complex Mg[H2O]62+, structure 1 in Figure 4, has been investigated by several other authors, and our geometrical parameters are in good agreement with those reported previously using calculations at different levels.41-44 The metal-oxygen bonding is predominantly electrostatic in this complex, although some charge has been transferred from

Deprotonation of Water with Carboxylate and Mg Ions J. Phys. Chem. B, Vol. 102, No. 33, 1998 6345

Figure 4. The structures of Mg[H2O]62+ (1), Mg[H2O]52+-OH- (2), Mg[H2O]52+-HCOO- (3, 4), Mg[H2O]42+-OH--HCOO- (5-8), Mg[H2O]52+-Cl- (9), Mg[H2O]42+-OH--Cl- (10), Mg[H2O]42+OH--HCOOH (11), Mg[H2O]52+ (12), Mg[H2O]42+-HCOO- (13, 14), Mg[H2O]52+-NH2COO- (15), Mg[H2O]42+-OH--NH2COOH (16), and Mg[H2O]52+-NCCOO- (17, 18). Structural parameters and charges at a variety of computational levels can be found in Supporting Information Figures.

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TABLE 2: NPA Charge and Natural Electron Configuration for Selected Magnesium Complexes Calculated at the MP2(FULL)/6-311++G**//MP2(FC)/6-31+G* Computational Level structure (cn ) 6)a

magnesium

NPA charge on oxygen

natural electron confign

Mg[H2O]62+ Mg[H2O]52+-OH-

1 2

+1.799 +1.786

Mg[H2O]52+-HCOOMg[H2O]42+-OH--HCOO-

3 5

+1.765 +1.762

9 14

+1.711 +1.800

-1.005b -1.366c -0.976 f -1.020b -0.977 f -1.015b -1.350c -0.952 f -1.028b -0.979 f -0.993b -0.994 f -1.079b

Mg: [core]3s[0.17]3p[0.02]3d[0.01]4p[0.01]; sp0.118 Mg: [core]3s[0.18]3p[0.02]3d[0.02]4p[0.01]; sp0.111 O: [core]2s[1.82]2p[5.46]3s[0.01]3p[0.05]3d[0.02]d Mg: [core]3s[0.19]3p[0.02]3d[0.02]4p[0.01]; sp0.105 Mg: [core]3s[0.19]3p[0.02]3d[0.02]4p[0.01]; sp0.105 O: [core]2s[1.82]2p[5.44]3s[0.01]3p[0.05]3d[0.02]d Mg: [core]3s[0.22]3p[0.04]3d[0.03]4p[0.01]; sp0.182 Mg: [core]3s[0.17]3p[0.02]3d[0.01]4p[0.01]; sp0.118

Mg[H2O]52+-ClMg[H2O]42+-HCOO- (unidentate) a

cn ) coordination number. b Water oxygen atom charges. c Hydroxyl oxygen atom charges. d Hydroxyl oxygen atom configuration.

the water ligands to the magnesium ion, as can be seen from the populations of the 3s, 3p, 3d, and 4p natural atomic orbitals listed in Table 2.23 Removal of a proton from one of the water molecules in Mg[H2O]62+ and subsequent reoptimization yields structure 2 shown in Figure 4. At all the computational levels we employed, the Mg‚‚‚O (water) distances for the five water molecules in Mg[H2O]52+-OH- (in 2) are greater than those in the parent complex 1. (The Mg‚‚‚O distances in Mg[H2O]62+ are all 2.11 Å, and the average Mg‚‚‚O (water) distance in Mg[H2O]52+OH- is 2.13 Å at the MP2(FC)/6-31+G* level.) As might be expected, the Mg‚‚‚O (hydroxyl ion) distance (1.96 Å), with its greater negative charge on the oxygen atom, is significantly smaller than the Mg‚‚‚O distance for any of the five water molecules. The shortest of the Mg‚‚‚O (water) distances (2.11 Å) involves the water molecule directly opposite the hydroxyl group. It should be noted that two of the water molecules in Mg[H2O]52+-OH- are directly involved in hydrogen bonding interactions with the hydroxyl group, although the O‚‚‚H distances are not the same; see Figure 4. The magnesiumoxygen bonding remains primarily electrostatic in Mg[H2O]52+OH-; the NPA charge on the magnesium ion and the natural electron configurations are nearly the same for Mg[H2O]62+ and Mg[H2O]52+-OH- despite the difference in the net charge on these two complexes; see Table 2. This is consistent with the results of Bertini and co-workers who have shown that the Mulliken charges on the divalent zinc ions in Zn[NH3]52+H2O and Zn[NH3]52+-OH- are very similar.5 In searching for stable forms of Mg[H2O]52+-HCOO-, only one local minimum on the PES could be identified at the RHF/ 6-31G* level, and in this case the carboxylate oxygen atom that is not bound to the magnesium ion interacts with two hydrogen atoms from distinct water molecules; see structure 3 in Figure 4. The magnesium ion in this complex ion is in a syn orientation relative to the carboxylate group.4 This complex, initialized in an anti orientation, isomerized to the syn form, 3, during the optimization, in agreement with results reported by Deerfield et al.45 At the MP2(FC)/6-31+G* computational level conformer 3 of Mg[H2O]52+-HCOO- was also found, but, in a search of the PES, a second local minimum was identified in which a carboxylate oxygen atom interacts with only one water hydrogen atom; see structure 4 in Figure 4.46 In this conformer the metal ion is also in a syn orientation relative to the carboxylate group. The O‚‚‚H distance is over 0.25 Å shorter than either of the two O‚‚‚H distances in structure 3. At the MP2(FULL)/6-311++G**//MP2(FC)/6-31+G* level, conformer 3 (with two internal hydrogen bonds) is approximately 0.6 kcal/mol lower in energy than conformer 4 (with one internal hydrogen bond). Only slightly more charge is transferred to the magnesium ion from the ligands in complex 3 than in Mg[H2O]62+ and Mg[H2O]52+-OH-, and the natural electron configuration is nearly the same in each; see Table 2. It should

be noted, however, that while the carboxylate-water interaction motif in structure 4 is found in a variety of crystal structures in the current versions of the CSD and PDB,9,10 no entries containing the motif in 3 are found. The average Mg‚‚‚OH2 distances in structures 3 and 4 from the MP2(FC)/6-31+G* optimizations are 2.118 and 2.116 Å, respectively, similar to the value of 2.110 Å observed for Mg[H2O]62+; the Mg‚‚‚ carboxylate O distances are shorter, 2.033 and 2.017 Å, respectively. Several local minima of the Mg[H2O]42+-OH--HCOOcomplex were identified on the PES at the RHF/6-31G* computational level and are shown as structures 5-8 in Figure 4. In all these complexes the magnesium ion is in a syn orientation relative to the carboxylate group; no attempt was made to find anti structures corresponding to structures 5-8. The initial geometries for these optimizations were obtained from Mg[H2O]52+-HCOO- by removing selected protons. The total molecular energies of all four of these complexes are quite similar, differing by less than 2 kcal/mol at the MP2(FULL)/ 6-311++G**//RHF/6-31G* level. In the three lowest energy forms, 5-7, a carboxylate oxygen atom forms a hydrogen bond with only one water molecule, whereas in the highest energy form, 8, this oxygen atom is hydrogen-bonded to two distinct water molecules. All four of these complexes have intramolecular interactions between water molecules and the hydroxyl group; see Figure 4. The RHF/6-31G* optimized form of Mg[H2O]42+-OH-HCOOH is shown as structure 11 in Figure 4. This complex has a relatively short O‚‚‚H hydrogen bond between the hydroxyl oxygen atom and the acidic hydrogen atom in formic acid. The complex Mg[H2O]42+-OH--HCOOH is approximately 4.9 kcal/mol higher in energy than conformer 3 of Mg[H2O]52+-HCOO- at the MP2(FULL)6-311++G**//RHF/631G* computational level. Interestingly, several attempts to find a local minima of Mg[H2O]42+-OH--HCOOH failed at the MP2(FC)/6-31+G* level, and each attempt reverted to Mg[H2O]52+-HCOO-. b. Energetics of Ionization and Proton Transfer in Magnesium-Bound Water. Two reactions of aquated magnesium complexes were studied. In the first, one of the water molecules in the octahedral environment of Mg[H2O]62+ or Mg[H2O]52+-HCOO- ionizes, i.e., deprotonation reactions.

Mg[H2O]62+ f Mg[H2O]52+-OH- + H+

(1)

Mg[H2O]52+-HCOO- f Mg[H2O]42+-OH--HCOO- + H+ (2)

Deprotonation of Water with Carboxylate and Mg Ions

J. Phys. Chem. B, Vol. 102, No. 33, 1998 6347

TABLE 3: Enthalpy Changes, ∆H298° (kcal/mol), and Free Energy Changes, ∆G298° (kcal/mol), for Deprotonation Reactions RHF/6-31G* Geometry MP2(FC)/ 6-31G*

MP4SDQ(FC)/ 6-31G*

MP2(FC)/6-31+G* Geometry MP2(FULL)/ 6-311++G**

MP2(FC)/ 6-31+G*

MP2(FULL)/ 6-311++G**

∆H298°

∆G298°

∆H298°

∆G298°

∆H298°

∆G298°

∆H298°

∆G298°

∆H298°

∆G298°

H2O f OH- + H+

419.9

413.3

421.3

414.7

389.4

382.8

Mg[H2O]62+ f Mg[H2O]52+-OH- + H+ Mg[H2O]52+-HCOO2- f Mg[H2O]42+-OH--HCOO2- + H+

165.6 246.7 247.6 247.0 247.8

156.9 239.7 240.7 240.6 241.6

168.0 241.4 242.2 241.6

159.4 234.4 235.2 235.2

165.0 246.1 247.0 246.9 247.9 245.5d

156.3 239.2 240.1 240.4 241.7 239.8

381.2a [382.2]b 158.3a 238.2a c c c c

374.6a [375.6]b 149.6a 231.2a c c c c

389.5a [390.5]b 164.6a 245.5a c c c c

382.9a [383.9]b 155.9a 238.5a c c c c

reaction

Mg[H2O]52+-Cl- f Mg[H2O]42+-OH--Cl- + H+

a Thermal corrections and entropies were obtained from RHF/6-31G* frequency analyses. b Thermal corrections and entropies were obtained from MP2(FC)/6-31+G* frequency analyses. c An MP2(FC)/6-31+G* optimization was not attempted. d At the MP4SDTQ(FC)/6-31G*//RHF/631G* level, ∆H298° ) 245.3 kcal/mol.

TABLE 4: Enthalpy Changes, ∆H298° (kcal/mol), and Free Energy Changes, ∆G298° (kcal/mol), for Proton-Transfer Reactions RHF/6-31G* geometry MP2(FC)/ 6-31G*

MP4SDQ(FC)/ 6-31G*

MP2(FC)/6-31+G* geometry MP2(FULL)/ 6-311++G**

MP2(FC)/ 6-31+G*

MP2(FULL)/ 6-311++G**

∆H298°

∆G298°

∆H298°

∆G298°

∆H298°

∆G298°

∆H298°

∆G298°

∆H298°

∆G298°

H2O + H2O f OH- + H3O+

253.6

254.4

254.1

254.9

224.6

225.5

Mg[H2O]62+ + H2O f Mg[H2O]52+-OH- + H3O+ Mg[H2O]52+HCOO- + H2O f Mg[H2O]42+-OH--HCOO- + H3O+

-0.7

-2.0

+0.9

-0.4

+0.2

-1.1

221.1a [221.8]b -1.8a

221.9a [222.0]b -3.1a

224.8a [225.6]b -0.1a

225.6a [225.8]b -1.3a

80.4 81.3 80.7 81.5

80.8 81.8 81.7 82.7

74.3 75.0 74.5

74.7 75.7 75.4

81.3 82.2 82.1 83.1

81.8 82.7 83.0 84.3

78.1a c c c

78.6a c c c

80.8a c c c

81.3a c c c

reaction

a Thermal corrections and entropies were obtained from RHF/6-31G* frequency analyses. b Thermal corrections and entropies were obtained from MP2(FC)/6-31+G* frequency analyses. c An MP2(FC)/6-31+G* optimization was not attempted.

In the second, a proton is transferred from one of these magnesium-bound water molecules to a free water molecule giving the hydronium ion, i.e., proton-transfer reactions.

Mg[H2O]62+ + H2O f Mg[H2O]52+-OH- + H3O+

(3)

Mg[H2O]52+-HCOO- + H2O f Mg[H2O]42+-OH--HCOO- + H3O+ (4) In Table 3 we list the values of ∆H298° and ∆G298° for the deprotonation of the Mg[H2O]62+ at a variety of computational levels. Since there are no experimental energy data available for this process, we also list in this table the calculated enthalpy and free energy changes for the deprotonation of an isolated water molecule at 298 K using the same computational levels. It would appear that the 6-31G* basis set is too restrictive to allow an adequate description of the deprotonation of water. The inclusion of diffuse functions, providing additional flexibility in the valence shell, and p-functions on the hydrogen atoms reduce the calculated deprotonation enthalpy by some 30 kcal/mol to approximately 390 kcal/mol, which is in good accord with the experimental gas-phase measurements by Kebarle, which give a proton affinity of 390 kcal/mol.47 Higherlevel MP2(FULL)/6-311++G(2df,2pd) and MP4SDTQ(FULL)/ 6-311++G(2df,2pd) calculations using the MP2(FC)/6-31+G* geometries find values for ∆H298° of 390.6 and 392.3 kcal/mol, respectively, suggesting that multiple polarization functions and higher-order perturbation corrections are not critical in describing such processes. Furthermore, the calculated values of ∆H298° and ∆G298° for the deprotonation of water do not depend significantly on whether the thermal corrections and entropies are calculated at the RHF/6-31G* or MP2(FC)/6-31+G* level.

As can be seen from Table 3, it requires substantially less energy (approximately 60% less) to deprotonate one of the water molecules in the inner hydration sphere of a divalent magnesium ion than it requires to deprotonate an isolated water molecule.48 Nevertheless, the calculated values of ∆G298° for the deprotonation of Mg[H2O]62+ are extremely high, +156-157 kcal/mol, which is in accord with the low solution acidity of Mg[H2O]62+.3 It may be noted that the basis set dependencies of the deprotonation enthalpies and free energies for Mg[H2O]62+ are smaller than those for isolated water (approximately 30 kcal/ mol for water compared with 10 kcal/mol for the magnesium complex; see Table 3). In Table 4 we list the calculated values of ∆H298° and ∆G298° for the proton-transfer reaction 3. The analogous reaction involving two isolated water molecules, 2H2O f OH- + H3O+, is well-known to be highly endothermic, the calculated value of ∆H298° being nearly 225 kcal/mol at the MP2(FULL)/6311++G**//MP2(FC)/6-31G* computational level. In the presence of a divalent magnesium ion, however, the value of ∆H298° for reaction 3 is nearly zero at this computational level, while the value of ∆G298° is slightly negative, showing that such a proton-transfer reaction is energetically feasible, at least in the gas phase. The deprotonation process in Mg[H2O]52+-HCOO- is complicated by the presence of a variety of unique proton environments. We initially determined the energy required to remove various protons without reoptimizing the resulting hydroxide complexes. The results obtained at the MP2(FULL)/6311++G** level are shown in Figure 5. Interestingly, the lowest ionization energy is associated with the removal of a proton from the water molecule directly opposite the carboxylate group. On the basis of these results, four of the hydroxide

6348 J. Phys. Chem. B, Vol. 102, No. 33, 1998

Figure 5. Energetics involved in removing selected protons from Mg2+bound water molecules. The numbers (5-8) that appear on four specific hydrogen atoms in this figure indicate conformers of Mg[H2O]42+OH--HCOO- which result when that proton is removed and the remaining structure reoptimized. The energies (kcal/mol) given next to selected hydrogen atoms in the figure indicate the energy required to remove that proton with no reoptimization of the structure.

complexes were selected and optimized; the results are shown as structures 5-8 in Figure 4. As noted previously, all four of these complexes have very similar energies. Calculated values of ∆H298° and ∆G298° for these deprotonation processes are listed in Table 3. At each of our computational levels there is approximately an 80 kcal/mol increase in the endothermicity for the deprotonation compared to that in Mg[H2O]62+. This is in line with the results of Bertini et al.5 who reported an 82 kcal/mol increase in the energy required to deprotonate Zn[NH3]22+-HCOO--H2O compared to Zn[NH3]32+-H2O. There is, of course, an analogous increase in the energy required for the corresponding proton-transfer reaction, and the value of ∆G298° in this case is approximately +81 kcal/mol; see Table 4. Thus, the presence of a carboxylate group in the place of a water molecule in the first coordination shell of magnesium effectively blocks this proton-transfer reaction in the gas phase. To a large extent, the increase in the enthalpy required for the deprotonation of (or proton transfer from) Mg[H2O]52+HCOO- is a direct result of the reduced charge on the overall complex. This can be demonstrated by calculating the deprotonation enthalpy for Mg[H2O]52+-Cl-, which has a chloride ion in place of the carboxylate group. The optimized structures of Mg[H2O]52+-Cl-, 9, and Mg[H2O]42+-OH--Cl-, 10, are shown in Figure 4, where only one conformer of Mg[H2O]42+OH--Cl- was considered. As can be seen from Table 2, slightly more charge has been transferred to the magnesium ion in Mg[H2O]52+-Cl- than in Mg[H2O]52+-HCOO-, but the values of ∆H298° for the deprotonation reactions, 245.5 and 246.1 kcal/mol at the MP2(FULL)/6-311++G**//RHF/6-31G* level, are nearly identical. Thus, the net charge on the complex plays a dominant role in the energetics of these deprotonation and proton-transfer reactions, whereas small differences in the charge or electron configuration on the magnesium ion play a relatively minor role. It would therefore appear that a variety of negatively charged ligands will effectively inhibit such proton-transfer reactions from divalent magnesium complexes in the gas phase. An alternative process that produces a magnesium-hydroxyl group is an intramolecular proton transfer from one of the water molecules in Mg[H2O]52+-HCOO- to the carboxylate group giving Mg[H2O]42+-OH--HCOOH. As noted previously, no local minimum corresponding to Mg[H2O]42+-OH--HCOOH could be found at the MP2(FC)/6-31+G* computational level, but, at the MP2(FULL)/6-311++G**//RHF/6-31G* level, this intramolecular transfer only requires approximately 5 kcal/mol.

Katz et al. We then investigated the effect of replacing the hydrogen atom in the HCOO- ligand by the electron-donating group -NH2. The RHF/6-31G* optimized structures of Mg[H2O]52+-NH2COO-, 15, and Mg[H2O]42+-OH--NH2COOH, 16, are shown in Figure 4. Comparing the NPA charges on Mg[H2O]52+HCOO-, 3, and Mg[H2O]52+-NH2COO-, 15, clearly shows that the carboxylate oxygen atoms carry more negative charge in Mg[H2O]52+-NH2COO-, which results in shorter Mg2+‚‚‚ O and O‚‚‚H distances for carbon atom-bound oxygen atoms in this complex. Furthermore, the energy required to transfer a proton from water to the carboxyl group is reduced to only 3 kcal/mol at the MP2(FULL)/6-311++G**//RHF/6-31G* computational level. At the MP2(FC)/6-31+G* level, Mg[H2O]42+OH--NH2COOH is also found to be a local minimum on the PES; see Figure 4. Replacing the hydrogen atom in HCOOin 3 by the electron-withdrawing group NtC- results in structure 17, shown in Figure 4. As expected, the charges on the carboxylate oxygen atoms in Mg[H2O]52+-NCCOO- (17) are less negative than those in Mg[H2O]52+-HCOO- (3), and this apparently results in longer Mg2+‚‚‚O and O‚‚‚H distances. No local minimum of the form Mg[H2O]42+-OH--NCCOOH could be found at the RHF/6-31G* level. The optimization gave instead structure 18, a second conformer of Mg[H2O]52+NCCOO- with only a single hydrogen bond, which is approximately 0.8 kcal/mol higher in energy than the doubly hydrogen bonded conformer 17. It is thus clear that the nature of R in Mg[H2O]52+-RCOO- plays an important role in such intramolecular proton-transfer processes. c. Effects of Second-Sphere Water Molecules. To investigate the effects of water molecules in the second shell around the magnesium ion on the deprotonation and proton-transfer reactions, calculations were carried out on one conformer42 of Mg2+‚6H2O‚2H2O in the following schemes:

Mg[H2O]62+‚2H2O f Mg[H2O]52+-OH-‚2H2O + H+ (5) Mg[H2O]62+‚2H2O f Mg[H2O]52+-OH-‚H2O + H3O+

(6)

Mg[H2O]62+‚2H2O + H2O f Mg[H2O]52+-OH-‚2H2O + H3O+ (7) Equation 5 represents deprotonation of an inner-sphere (metal ion-bound) water molecule. The value of ∆G298° is 170.1 kcal/ mol [at the MP2(FULL)/6-311++G**//RHF/6-31G* level], which is some 13.8 kcal/mol higher than the corresponding value we obtained with no second-sphere water molecules. Thus, a few second-sphere water molecules apparently impede deprotonation of an inner-sphere water molecule. Reactions 6 and 7 represent proton-transfer processes, and the energetics were calculated at the same level used for reaction 5. In both cases an inner-sphere water molecule loses a proton, but in (5) the proton is lost in conjunction with a second-sphere water molecule and released as H3O+, while in (6) the proton is transferred to an isolated water molecule. Calculated values of ∆G298° were 18.7 and 12.7 kcal/mol for reactions 6 and 7, respectively. The energy for (7) is slightly higher (by about 14 kcal/mol) than that found when there was only inner-sphere water around the magnesium ion, again suggesting that a few isolated second-sphere water molecules impede proton transfer. It will be interesting to see what effect a completed second-shell around Mg2+ has on the values of ∆G298° for these processes as it becomes possible to include more water molecules in these calculations.

Deprotonation of Water with Carboxylate and Mg Ions

J. Phys. Chem. B, Vol. 102, No. 33, 1998 6349

TABLE 5: Enthalpy Changes, ∆H298° (kcal/mol), and Free Energy Changes, ∆G298° (kcal/mol), for Water Dissociation Reactions RHF/6-31G* geometry MP2(FC)/6-31G*

MP4SDQ(FC)/6-31G*

reaction

∆H298°

∆G298°

∆H298°

∆G298°

∆H298°

∆G298°

Mg[H2O]62+ a f Mg[H2O]52+ b + H2O Mg[H2O]52+-HCO2- a,c f Mg[H2O]42+-HCO2- a,d + H2O

34.0 20.4

21.4 9.4

33.7

21.1

31.9 16.7

19.3 5.7

a

MP2(FULL)/6-311++G**

Coordination number: 6. b Coordination number: 5. c Monodentate. d Bidentate.

d. Dehydration of Mg[H2O]62+ and Mg[H2O]52+-HCOO-. Optimized structures of Mg[H2O]52+, 12, and Mg[H2O]42+HCOO-, 13 (bidentate) and 14 (unidentate), are shown in Figure 4. In Table 5 we compare the energy requirements for removing one water molecule from Mg[H2O]62+ and Mg[H2O]52+HCOO-. The values of ∆G298° are +19.3 and +5.7 kcal/mol, respectively, where we have used the lower-energy bidentate form of Mg[H2O]42+-HCOO- for the calculations. As expected, both values are positive, but the value for Mg[H2O]52+HCOO- is significantly smaller. One source of this difference in free energies can be found in the structure of Mg[H2O]42+HCOO-. When a water molecule is removed from Mg[H2O]52+-HCOO- and the structure reoptimized, the carboxylate group goes from a monodentate configuration to a bidentate configuration. Thus, water removal from Mg[H2O]52+HCOO- can occur with no change in the coordination number of magnesium. A unidentate form of the Mg[H2O]42+-HCOOcomplex 14 is also a local minimum on the PES, but this form is more than 6 kcal/mol higher in energy than the bidentate form. Discussion a. Facilitation of the Deprotonation of Water. The ab initio molecular orbital calculations, described here, show that the energy required to deprotonate one of the magnesium-bound water molecules in a gas-phase Mg[H2O]62+ complex is only about 40% of that required to deprotonate an isolated water molecule. This implies that binding to a magnesium ion activates a water molecule bound to it so that deprotonation occurs more readily. This leads to slightly negative values of ∆G298° for the proton-transfer reaction Mg[H2O]62+ + H2O f Mg[H2O]52+-OH- + H3O+, thus providing a plausible mechanism for the formation of a magnesium-bound hydroxyl group. Replacing one of the water molecules in Mg[H2O]62+ with a carboxylate group to form Mg[H2O]52+-HCOO- results in an approximately 80 kcal/mol increase in the energy required to deprotonate any of the remaining magnesium-bound water molecules, effectively increasing their pKa value and making the analogous proton-transfer reaction, Mg[H2O]52+-HCOO+ H2O f Mg[H2O]42+-OH--HCOO- + H3O+, a less likely mechanism for the formation of a magnesium-bound hydroxide group in biological systems. This effect of a metal-bound carboxylate group on the deprotonation of water appears to be primarily electrostatic in nature. The calculated values of ∆G298° for the deprotonation of Mg[H2O]52+-Cl- and Mg[H2O]52+-HCOO-, 239.8 and 239.2 kcal/mol, respectively, are nearly identical. A negatively charged ligand in the inner coordination sphere lowers the net charge on the magnesium complex and thus lessens its ability to dissociate a proton. On the other hand, the presence of a carboxylate group in place of a water molecule in the inner coordination sphere around magnesium allows for the formation of a hydroxyl group

by means of the intramolecular proton-transfer process, Mg[H2O]52+-RCOO- f Mg[H2O]42+-OH--RCOOH. Although an MP2(FC)/6-31+G* optimization was unable to identify Mg[H2O]42+-OH--HCOOH as a local minimum on the PES, Mg[H2O]42+-OH--NH2COOH is a local minimum at this computational level and the proton transfer requires only about 3 kcal/mol. b. Role of Motif I in Enzymes. Our analysis of the crystal structures of small magnesium complexes and magnesiumcontaining enzymes has shown that this metal ion binds oxygen atoms in as near an octahedral manner as possible. It binds a carboxylate in a monodentate manner and in a variety of structures often forms motif I. The ab initio molecular orbital calculations indicate that the deprotonation of a water molecule in motif I is not significantly different in energy from the deprotonation of an independent water molecule bound to the metal ion. This means that formation of motif I does not significantly affect the pKa of metal-bound water molecules. This then raises the question of the utility of motif I, which is common in protein structures. When magnesium is the metal ion in an enzyme, then the coordination around the metal ion is a fairly rigid octahedron.2 If motif I is formed by a water molecule and a carboxylate ligand, then the positions and orientations of the remaining four ligand-binding positions will be predetermined and this may aid in orienting enzyme side chains and functional groups on the protein. The common occurrence of this motif I in protein crystal structures (see Figure 3) suggests that it serves to align the rather rigid magnesium octahedron so that other ligands in the reaction to be catalyzed are correctly oriented for chemical reaction. Information on the local charges around magnesium ions in some protein crystal structures presently available in the PDB are diagrammed in Figure 3. The 2+ charge of magnesium is locally neutralized by two inner-sphere-bound carboxylate groups in motif I because one oxygen atom interacts directly with the metal ion while the other takes part in a hydrogen bond to a water molecule. Each carboxylate oxygen atom can, however, bind more than one group or ion, so that its single negative charge may be neutralized to some extent by more distant groups (presumably positively charged). Mandelate racemase8 is the only example in Figure 3 of three bound carboxylate groups; when substrate binds, the number is 4. In the vicinity of the substrate are the active site catalytic groups, a histidine and a lysine residue. Two carboxylate groups bind in catechol O-methyltransferase,28 CheY,29 avian sarcoma virus integrase,33 and bacterial luciferase.27 If there is just one example of motif I around the magnesium ion, four binding positions remain available. If, however, there are two such motifs, there are only two possibilities. Only one carboxylate group binds to the magnesium ion in T4 RNaseH35 (and tumor necrosis factor34) so that the net charge is +1 and negatively charged groups such as phosphate groups can bind nearby. It will be of interest to learn of the effect of modifying the local charge on enzyme-bound Mg2+ on the catalytic activities of the enzymes.

6350 J. Phys. Chem. B, Vol. 102, No. 33, 1998 Motif I has the function of orienting specific functional groups in the active site of the enzyme and in controlling, by the overall charge, the nature of the functional groups attracted to the magnesium ion in the active site of an enzyme. Thus motif I has both a structural effect, rigidly defining the orientation of groups that bind to the magnesium ion (coordination clamping), and an electronic effect of modifying the pKa of a magnesiumbound water molecule. This “coordination clamping” is more rigid than the “latching” (described for enolase49), which involves a more flexible motif. Motif II is also more flexible than motif I and therefore is unable to perform this orientational function in as rigid a manner. Acknowledgment. Helpful discussions with Professors Philip George and Albert S. Mildvan are gratefully acknowledged. We thank the Advanced Scientific Computing Laboratory, NCI-FCRF, for providing time on the CRAY YMP supercomputer. This work was supported by Grants CA10925 (to J.P.G.), GM31186 (to G.D.M.), and CA06927 (to FCCC) from the National Institutes of Health and by an appropriation from the Commonwealth of Pennsylvania (to FCCC). Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the National Cancer Institute. Supporting Information Available: Tables listing crystallographic data, bibliography of compounds, syn/anti conformations, structure coordinates, and molecular energies and figures showing details of motifs I and II and geometry of the complexes (42 pages). Ordering information is given on any current masthead page. References and Notes (1) Frau´sto da Silva, J. J. R.; Williams, R. J. P. The Biological Chemistry of the Elements. The Inorganic Chemistry of Life, Clarendon Press: Oxford, England, 1991. (2) Douglas, B. E.; McDaniel, D. H.; Alexander, J. J. Concepts and Models of Inorganic Chemistry; Wiley: New York, 1994. (3) Bock, C. W.; Kaufman, A.; Glusker, J. P. J. Am. Chem. Soc. 1995, 117, 3754-3765. (4) Carrell, C. J.; Carrell, H. L.; Erlebacher, J.; Glusker, J. P. J. Am. Chem. Soc. 1988, 110, 8651-8656. (5) Bertini, I.; Luchinat, C.; Rosi, M.; Sgamellotti, A.; Tarantelli, F. Inorg. Chem. 1990, 29, 1460-1463. (6) Kaufman, A.; Afshar, C.; Rossi, M.; Zacharias, D. E.; Glusker, J. P. Struct. Chem. 1993, 4, 191-198. (7) Carrell, H. L.; Glusker, J. P.; Burger, V.; Manfre, F.; Tritsch, D.; Biellmann, J. F. Proc. Natl. Acad. Sci. U.S.A. 1989, 86, 4440-4444. (8) Neidhart, D. J.; Howell, P. L.; Petsko, G. A.; Powers, V. M.; Li, R.; Kenyon, G. L.; Gerlt, J. A. Biochemistry 1991, 30, 9264-9273. (9) Allen, F. H.; Bellard, S.; Brice, M. D.; Cartwright, B. A.; Doubleday: A.; Higgs, H.; Hummelink, T.; Hummelink-Peters, G. G.; Kennard, O.; Motherwell, W. D. S.; Rodgers, J. R.; Watson, D. G. The Cambridge Crystallographic Data Centre: Computer-based search, retrieval, analysis and display of information. Acta Crystallogr. 1979, B35, 23312339. (10) Bernstein, F. C.; Koetzle, T. F.; Williams, G. J. B.; Meyer, E. F., Jr.; Brice, M. D.; Rogers, J. R.; Kennard, O.; Shimanouchi, T.; Tasumi, M. J. Mol. Biol. 1977, 112, 535-542. (11) Erlebacher, J.; Carrell, H. L. ICRVIEW-Graphics program for use on Silicon Graphics computers from The Institute for Cancer Research; Fox Chase Cancer Center: Philadelphia, PA, 1992. (12) Sayle, R. RasMol, v2.5, a molecular visualization program; Glaxo Research and Development: Middlesex, U.K., October 1994. (13) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T. A.; Peterson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski,

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