Ab Initio Calculations of Proton Dissociation Energies of Zinc

Despite intensive studies of zinc's role in proteins and recent growing appreciation ..... Matsukura, T. Crystalline l-carnosine zinc complex and prod...
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J. Phys. Chem. B 1999, 103, 8773-8779

8773

Ab Initio Calculations of Proton Dissociation Energies of Zinc Ligands: Hypothesis of Imidazolate as Zinc Ligand in Proteins Jamal El Yazal and Yuan-Ping Pang* Mayo Clinic Cancer Center, Tumor Biology Program, Department of Pharmacology, Mayo Foundation for Medical Education and Research, 200 First Street SW, Rochester, Minnesota 55905 ReceiVed: June 2, 1999; In Final Form: July 27, 1999

Despite intensive studies of zinc’s role in proteins and recent growing appreciation of zinc in modern biology, the knowledge of the protonation state of common zinc ligands in proteins remains controversial. Water, the side chains of Glu, Asp, and Cys residues, and even the peptide nitrogen atom are treated as a deprotonated, negatively charged ligand in the zinc complexes in proteins, whereas the side chain of His residue is treated as a neutral ligand in the zinc complexes regardless of the common knowledge that the imidazole nitrogen proton is more acidic than the peptide nitrogen proton. In an attempt to resolve this controversy, we performed large basis set DFT calculations of proton dissociation energies of common zinc ligands in the presence and absence of Zn2+. Herein, we report the results of our calculations revealing that the proton dissociation energies of H2O, MeOH, MeSH, imidazole, and N-methylacetamide are dramatically reduced when they coordinate to Zn2+ and that the proton dissociation energy of the zinc-bound imidazole is 4 kcal/mol lower than that of the zinc-bound N-methylacetamide that is known to be deprotonated according to the X-ray and NMR studies. The result thus suggests further investigations of the possibility of imidazolate as a zinc ligand in proteins.

Introduction The important role of zinc in antiproliferation and antiangiogenesis for cancer treatments and its role in zinc fingerprotein mediated protein-protein and protein-nucleic acid interactions prompted us to investigate the nature of coordination between the zinc divalent cation and its ligands in proteins.1-3 In particular, we looked for the reasons why water, the side chains of Glu, Asp, and Cys residues, and even the peptide nitrogen atom4,5 are treated as deprotonated, negatively charged in the zinc complexes whereas the side chain of His residue is treated as neutral in the zinc complexes. According to the acidities of the peptide nitrogen proton (pKa ) 17) and the imidazole nitrogen proton (pKa ) 14),6 it seems counterintuitive to deprotonate the peptide nitrogen atom and protonate the imidazolate when they interact with Zn2+, which has a profound effect on lowering the pKa values of zinc ligands.6 It is perhaps that Zn2+ would lower the pKa value of the peptide nitrogen proton much more than that of the nitrogen proton of imidazole. Ab initio calculations of proton dissociation energies of zinc ligands in the absence and presence of Zn2+ should offer insights into the protonation state of imidazole as a zinc ligand. Although improvements in computing power and numerical computer programs have made ab initio calculations feasible for medium and even moderately large molecules,7 no comprehensive ab initio calculations of the proton dissociation energies of zinc ligands in the presence and absence of Zn2+ have been reported so far.8 We have therefore performed ab initio calculations in vacuo to study the effect of Zn2+ on proton dissociation energies of common zinc ligands in proteins.9 We first examined the accuracy of a number of ab initio methods and basis sets implemented in the Gaussian 94 program by comparing the calculated proton dissociation energies with the experimental * To whom correspondence should be addressed. E-mail: [email protected].

values and then used the B3LYP method with the 6-311+G(2d,2p) basis set to calculate the difference of proton dissociation energy between imidazole and N-methylacetamide. Here, we report the results of our calculations which offer a new insight into the protonation state of imidazole as a zinc ligand in proteins. Methods General Description. The ab initio calculations were carried out by using the Gaussian 94 program10 running on a SGI Origin 2000 (8 × 195 MHz, 2.0 GB memory and 70 GB disk) and four Origin 200s (8 × 180 MHz, 1.2 GB memory and 16 GB disk). Three ab initio methods in combination with three basis sets available in the Gaussian 94 program were used. The first method used was the Hartree-Fock (HF) method that is useful for providing initial, first-level predictions and yet insufficient for accurate modeling of the energetics of reactions and bond dissociation because of its neglect of electron correlation.11-13 The second method was the second-order Møller-Plesset (MP2) method which adds electron correlation corrections to the HF method.14-19 This method can successfully model a wide variety of systems and yield accurate geometries. However, it sometimes overcorrects the HF results and requires excessive computing time and computer disk space. The third method was Becke’s three-parameter formulation (B3LYP) density functional theory method.20,21 The density functional theory method computes electron correlation through functions of the electron density which itself is a function of coordinates in real space. Such functions partition the electronic energy into several components which are computed separately: the kinetic energy, the electron-nuclear interaction, the Coulomb repulsion, and exchange and correlation. The last two functions are used to account for the remainder of the electron-electron interaction. The exchange function is defined as a linear combination of Hartree-Fock, local, and gradient-corrected exchange terms and

10.1021/jp991787m CCC: $18.00 © 1999 American Chemical Society Published on Web 09/18/1999

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El Yazal and Pang

TABLE 1: Proton Dissociation Energies (kcal/mol) in the Absence of the Zinc Divalent Cation ab initio method

H2O

MeOH

MeCO2H

EtOH

HCO2H

MP2/LANL2DZ//MP2/LANL2DZ B3LYP/LANL2DZ//B3LYP/LANL2DZ HF/LANL2DZ//HF/LANL2DZ MP2/6-311+G(d,p)//MP2/6-311+G(d,p) B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p) HF/6-311+G(d,p)//HF/6-311+G(d,p) MP2/6-311+G(2d,2p)//MP2/6-311+G(2d,2p) B3LYP/6-311+G(2d,2p)//B3LYP/6-311+G(2d,2p) HF/6-311+G(2d,2p)//HF/6-311+G(2d,2p) MP2/6-311+G(2d,2p)// MP2/LANL2DZ B3LYP/6-311+G(2d,2p)// B3LYP/LANL2DZ HF/6-311+G(2d,2p)// HF/LANL2DZ calculated by others experimental

404 408 406 391 388 398 389 390 399 389 389 399 406,8 39231 370-392,29 39030

390 391 395 383 379 390 381 380 390 381 380 391 38132 379,37 38338

345 348 350 347 345 353 346 346 354 346 346 353 35232 348,37 34438

386 386 392 379 376 388 378 377 388 378 377 389 37832 376,37 38038

343 344 346 342 340 348 342 342 349 342 342 349 34632 345,37 34338

ab initio method

HCOH

C2H6

MeSH

imidazole

MeCONHMe

MP2/LANL2DZ//MP2/LANL2DZ B3LYP/LANL2DZ//B3LYP/LANL2DZ HF/LANL2DZ//HF/LANL2DZ MP2/6-311+G(d,p)//MP2/6-311+G(d,p) B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p) HF/6-311+G(d,p)//HF/6-311+G(d,p) MP2/6-311+G(2d,2p)//MP2/6-311+G(2d,2p) B3LYP/6-311+G(2d,2p)//B3LYP/6-311+G(2d,2p) HF/6-311+G(2d,2p)//HF/6-311+G(2d,2p) MP2/6-311+G(2d,2p)// MP2/LANL2DZ B3LYP/6-311+G(2d,2p)// B3LYP/LANL2DZ HF/6-311+G(2d,2p)//HF/LANL2DZ calculated by others experimental

404 404 401 397 392 399 396 393 399 397 394 400 NAa 39240

435 437 438 420 419 428 419 419 428 419 419 428 NA 42141

357 358 353 360 355 357 357 356 359 357 356 359 362 ( 2.139 359 ( 239

352 356 359 346 349 355 346 350 355 346 350 356 36931 NA

367 371 375 360 362 371 360 362 371 360 362 371 NA NA

a

NA, not available.

TABLE 2: Proton Dissociation Energies (kcal/mol) in the Presence of the Zinc Divalent Cation ab initio method

H2O

MeOH

MeSH

imidazole

MeCONHMe

B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p) B3LYP/6-311+G(2d,2p)//B3LYP/6-311+G(2d,2p) B3LYP/6-311+G(2d,2p)//B3LYP/LANL2DZ calculated by others experimental

56 55 55 102,8 108,8 and 8531 NA

69 68 68 NA NA

68 70 69 NA NA

117 118 121 16331 NA

121 122 122 NA NA

is then combined with a local and/or gradient-corrected correlation function. The B3LYP method has gained steadily in popularity for its greater accuracy than the HF method at only a modest increase in computing time and disk space but far less than the needs by the MP2 method. The first basis used set was LANL2DZ. This simplified basis set is developed to handle heavy atoms after the third row of the periodic table and treat the electrons near the nucleus in an approximate way via effective core potentials.22 The second basis set was 6-311+G(d,p). This set adds the d functions as polarization functions to heavy atoms (labeled with “d”) and the p functions as polarization functions to hydrogen atoms (marked with “p”) in order to allow orbitals to change size and shape. The p functions for the hydrogen atoms are important for calculations when the hydrogen atoms are the sites of interest as in our study of proton dissociation. It also adds the largesize versions of the s- and p-type functions as diffuse functions (noted with “+”) to heavy atoms to allow orbitals to occupy a larger region of space. The diffuse functions are necessary for molecules in our study with electrons relatively far from the nucleus, molecules with lone electron pairs, and molecules with significant negative charges. Furthermore, it adds extra three sizes of s and p functions to heavy atoms in order to model heavy atoms such as zinc. The third basis set was 6-311+G(2d,2p). This set is the same as the second except that it adds 2d functions to the heavy atoms and 2p functions to the hydrogen atoms to count the polarization effect. All the three

basis sets have reportedly been used to successfully describe the hydration energy of the zinc divalent cation.23 The structures of the zinc ligands and the zinc-ligand complexes were first generated with the Quanta program and optimized by energy minimization with the CHARMm force field.24 The structures generated by molecular mechanics calculations were then optimized with the above-mentioned electron correlation methods and basis sets employing the Gaussian 94 program. The quadratic convergence method (SCF)QC)25 was used to solve the numerous convergence problems encountered in energy minimizations. Proton dissociation energy was computed as the energy difference between the molecule of interest and the same molecule that was deprotonated. Both singlet- and triplet-state energies of each molecule in Tables 1 and 2 were taken into account. Only the lower energy of the two was used in calculation of proton dissociation energy. The energy of each molecule was corrected with the thermal energy that was calculated by running a frequency job at the optimized geometry using the same method and basis set. In the calculations of the N-methylacetamide containing complexes, different positions of the zinc divalent cation relative to N-methylacetamide in the protonated and deprotonated forms were systematically examined by energy minimizations with the ab initio method in order to find the complexes with minimal energy. Justification for Study of Proton Dissociation Energy. The objective of the present study was to investigate the protonation

Proton Dissociation Energies of Zinc Ligands

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TABLE 3: Effect of the Presence of Zinc and Its Ligands on Proton Dissociation Energy (PDE) Difference ∆PDE ) PDEN-methylacetamide - PDEimidazole (kcal/mol) ab initio method

Zn2+

Zn2+(HO-)3

Zn2+(H2O)3

B3LYP/6-311+G(d,p)// B3LYP/6-311+G(d,p)

4

2

3

state of imidazole as a zinc ligand similar to those found in zinc proteins. To achieve this goal, one could use the calculated Brønsted acidities of zinc ligands to deduce the protonation state. The justification for use of proton dissociation energy is due to the following reasons. First, the Brønsted acidity of a compound is defined as the free energy change for the deprotonation reaction eq 1.

ROH + H2O h RO- + H3O+

(1)

However, because the entropic term (mainly due to the H3O+) cancels out in a comparison of the relative Brønsted acidities, we could then use proton dissociation energy, the enthalpy term, as a measure of ligand’s relatiVe acidity. Second, in the definition of the Brønsted acidity, the proton as the product of a deprotonation is associated with water or other solvents. In proteins, the proton is not solvated but associated with a nearby basic residue, which can affect the protonation state of zinc ligands in proteins. Therefore, just like the calculated proton dissociation energy in vacuo, the Brønsted acidity describes nothing more than the intrinsic tendency of deprotonation of a compound. There are technical advantages to use of proton dissociation energy. First, proton dissociation energy can be readily computed with the well-tested and widely used Gaussian 94 program. Second, the calculated proton dissociation energies can be compared directly with experimentally determined enthalpies. The conceptual advantage to use proton dissociation energy is that it allowed us to take an indirect approach that makes use of the experimental evidence for the existence of the amidate as a zinc ligand in peptides.4,5 The NMR and X-ray crystallographic experiments have revealed that the amide group is deprotonated when it coordinates to zinc.4,5 It is possible that the imidazole group is deprotonated as well when coordinating to zinc if the imidazole proton is more or as acidic as the amide proton in the presence of zinc. The objective of our calculations was therefore to calculate the relatiVe, intrinsic acidities of the imidazole proton and the amide proton in the presence of zinc divalent cation, and not the absolute acidity of the imidazole or amide proton in a four-ligand zinc complex of a specific protein. For the relative acitidies, it is not necessary to consider the influence on proton dissociation energy of imidazole by the presence of other zinc ligands, the residues on the second and third zinc coordination shells, and the electrostatic field of the entire protein. The proton dissociation energy based indirect approach thus simplifies theoretical calculations. To ensure that the influence on proton dissociation energy difference between imidazole and N-methylacetamide by other factors in proteins can be canceled out, we carried out proton dissociation energies of imidazole and N-methylacetamide in the presence of a zinc divalent cation coordinated to three hydroxide molecules and in the presence of a zinc divalent cation coordinated to three water molecules. As is apparent in Table 3, other factors in proteins do not significantly change the proton dissociation energy difference between imidazole and N-methylacetamide.

Results Proton Dissociation Energy with Zn2+ Absent. We first calculated the proton dissociation energies of a number of small molecules in the absence of Zn2+ with three common ab initio methods (HF, MP2, and B3LYP) in combination with three basis sets [LANL2DZ, 6-311+G(d,p), and 6-311+G(2d,2p)] (see Methods) and compared the calculated results with the experimental values. To balance accuracy and computing time, we also explored the possibility of optimizing structures with the LANL2DZ basis set followed by a single-point energy calculation with a larger basis set of 6-311+G(2d,2p). In addition to water, methanol, ethanol, methanethiol, acetic acid, imidazole, and N-methylacetamide that represent the zinc ligands in proteins, we included formaldehyde, formic acid, and ethane in the present study to increase the acidity range of our investigation. As indicated in Table 1, for all the three ab initio methods, the proton dissociation energies calculated with the LANL2DZ basis set for water, methanol, ethanol, aldehyde, and ethane are about 10 kcal/mol higher than the experimental values. However, for formic acid, acetic acid, and methanethiol, the values derived with the LANL2DZ basis set are identical, within the so-called chemical accuracy (ca. 2 kcal/mol),26 to the experimental values no matter which of the three methods was used. The discrepancies between the calculated and experimental values are probably due to the fact that the LANL2DZ basis set is developed for atoms after the third row of the periodic table (see Methods). It is therefore inappropriate to use the LANL2DZ basis set to estimate the effect of Zn2+ on the proton dissociation energies of the selected zinc ligands. For the two larger basis sets, both the MP2 and B3LYP methods gave proton dissociation energies identical, within the chemical accuracy, to the experimental values for all the molecules, whereas the HF method yielded values that are about 5-10 kcal/mol higher than the experimental ones. Considering several orders of magnitude more computing time and disk space required for the MP2 method than the B3LYP method and the deviations of the reported experimental values, it is advantageous to use the B3LYP method with the 6-311+G(2d,2p) basis set to estimate the effect of Zn2+ on the proton dissociation energies of the selected zinc ligands. Interestingly, as apparent in Table 1, with both the MP2 and B3LYP methods, single-point energy calculations with the 6-311+G(2d,2p) basis set at the structures that were optimized with the LANL2DZ basis set (abbreviated as B3LYP/6-311+G(2d,2p)//B3LYP/LANL2DZ, and MP2/6-311+G(2d,2p)//MP2/ LANL2DZ, respectively) were nearly as good as the calculations at the structures optimized with the 6-311+G(2d,2p) basis set (abbreviated as B3LYP/6-311+G(2d,2p)//B3LYP/6-311+G(2d,2p) and MP2/6-311+G(2d,2p)//MP2/6-311+G(2d,2p), respectively). It seems acceptable to use the B3LYP/6-311+G(2d,2p)// B3LYP/LANL2DZ method to approximately estimate the effect of Zn2+ on the proton dissociation energies of the selected zinc ligands when there is a restraint on computing resource. Proton Dissociation Energy with Zn2+ Present. We calculated the proton dissociation energies of water, methanol, methanethiol, imidazole, and N-methylacetamide in the presence of Zn2+ employing the B3LYP/6-311+G(2d,2p)//B3LYP/ LANL2DZ method (Table 2). As expected, the proton dissociation energies of water, methanethiol, and N-methylacetamide in the presence of Zn2+ are reduced to 55, 70, and 122 kcal/ mol, respectively, compared to those in the absence of Zn2+, which range from 356 to 390 kcal/mol (Table 1). These results are consistent with the experimental observations that Zn2+

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Figure 1. Geometries of the zinc-ligand complexes optimized by the ab initio calculations with the B3LYP/6-311+G(2d,2p)//B3LYP/6-311+G(2d,2p) method and definitions of distance (D), angle (A), and torsion (T) used in Table 4.

reduces the pKa values of water, methanethiol, and N-methylacetamide and causes these ligands to be deprotonated and negatively charged in the zinc complexes in proteins.4,27,28 Interestingly, we found that the proton dissociation energy in the presence of Zn2+ for imidazole is smaller than that of N-methylacetamide. To confirm this finding, we repeated the calculations employing the more accurate methods of B3LYP/ 6-311+G(d,p)//B3LYP/6-311+G(d,p) and B3LYP/6-311+G-

(2d,2p)//B3LYP/6-311+G(2d,2p) and found that the proton dissociation energy of imidazole is indeed 4 kcal/mol smaller than that of N-methylacetamide (Table 2). This result suggests that, in the presence of Zn2+, the imidazole nitrogen proton is more or at least as acidic as the peptide nitrogen proton. Geometries of the Zinc-Ligand Complexes. We also examined the geometries of all the zinc-ligand complexes optimized by ab initio calculations in order to ensure that our

Proton Dissociation Energies of Zinc Ligands

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TABLE 4: Distances, Angles, and Torsions of the Zinc Divalent Cation and Its Ligands Calculated from the Structures Optimized by ab Initio Methods (see Figure 1 for Definitions of D, A, and T) optimization method B3LYP/6-311+G(d,p) ligand H2O HOMeOH MeOMeSH MeSimidazole imidazolate MeCONHMe MeCON-Me

B3LYP/6-311+G(2d,2p)

distance angle torsion distance angle torsion (D, Å) (A, deg.) (T, deg.) (D, Å) (A, deg.) (T, deg.) 1.883 1.777 1.858 1.802 2.346 2.196 1.881 2.068 1.821 1.867

125.4 114.2 131.8 126.6 109.8 105.9 125.2 127.6 131.6 121.2

180.0 NA -180.0 180.0 -99.1 180.0 180.0 -180.0 -160.4 -178.5

1.875 1.769 1.860 1.794 2.340 2.190 1.888 2.059 1.814 1.862

125.1 113.3 129.8 125.1 109.3 105.7 125.7 127.6 129.2 121.0

180.0 NA 157.2 -180.0 -98.2 180.0 170.2 -180.0 -163.1 -178.3

computational results are not artifacts of incorrect chemical structures occasionally caused by energy minimization. As apparent in Figure 1 and Table 4, all the optimized structures of the zinc complexes (Table 4) are consistent with the corresponding structures found in the crystal structures of zinc proteins.9 In the imidazole and imidazolate complexes, the distances between the zinc ion and the nitrogen atom in both complexes agree with the average Zn-N distance of 2.1 ( 0.1 Å obtained from the X-ray structures of zinc proteins;1 the zinc ion is in the plane of the imidazolate ring and near the plane of imidazole ring and forms angles of 128° and 125° of arc with the nitrogen atom and its covalently bonded carbon atom in imidazoleate and imidazole, respectively (Figure 1). In the N-methylacetamide and N-methylacetamide anion complexes, the Zn-N distances agree with the same experimental average Zn-N distance; the zinc ion is in the plane of the peptide anion and about 30° of arc off the plane of the peptide, and forms an angle of 121° and 129° of arc with the nitrogen atom and its covalently bonded carbon atom in the charged and neutral forms, respectively (Figure 1). These geometries reveal that the nitrogen atom is ligated to Zn2+ with its sp2 lone electron pair occupied in one of zinc’s four vacant orbitals (4s, 4px, 4py, 4pz), and clearly exclude the possibility of being computational artifacts. Discussion Comparison to Other Computations. The comparison to experimental data has confirmed the accuracy of method as described above. Comparison to other calculations is to determine which method is more accurate. The proton dissociation energy of water calculated with the HF method in the absence of Zn2+ was reportedly 406 kcal/mol,8 which was justified by a misquoted “experimental value” of 410 kcal/mol.8 This calculated value is not accurate because of the use of the insufficient HF method and the oversight of the thermal energy correction, which is about 7.4 kcal/mol according to our calculations. The correct experimental value of proton dissociation energy of water was reported first to be 372-392 kcal/ mol29 and later to be 390 kcal/mol,30 which is in excellent agreement with our calculated value of 390 kcal/mol (Table 1). Our proton dissociation energy of water is in excellent agreement with another reported value of 392 kcal/mol31 calculated by an ab initio method. On the other hand, in ref 31 the proton dissociation energies of 369 and 163 kcal/mol for imidazole in the absence and presence of Zn2+ were also reported and are significantly different from our values of 350

and 118 kcal/mol, respectively. Despite the fortuitous match between the calculated water proton dissociation energy and the experimental value, the calculated values in ref 31 are not reliable because the structures of the zinc-water and the zincimidazole complexes were not optimized in the calculations of ref 31. Other proton dissociation energies in the absence of Zn2+ reported in the literature include those of methanol, ethanol, formic acid, and acetic acid that were calculated with the GVB+CI wave function32 (Table 1). This method gave equally good predictions of the proton dissociation energies as the methods used in the present study. These comparisons indicate that, with the current available computing resource, the ab initio method that we used in the present study is comparable to or better than the other ab initio methods reported in the literature. Proton Acceptors in Proteins. The results of our proton dissociation energy calculations suggest that imidazole may serve as a proton donor when it coordinates to Zn2+ in proteins. However, the results would not be biochemically relevant if appropriate proton acceptors were absent in proteins. To address this issue, we examined the possibility that the carboxylate group of Glu and Asp may serve as a proton acceptor for the zinccoordinated imidazole in proteins, since the carboxylate group surrounds the zinc-imidazole complex in the vicinity of up to 8 Å away from the imidazole ring in 93% of the proteins containing the zinc-imidazole complex according to our recent survey of the zinc protein crystal structures in the PDB (unpublished work). We calculated the energy of a system in which an imidazole is close to a carboxylate group that does not form a hydrogen bond with the imidazole and coordinate to the zinc ion (Figure 2) and the energy of the same system except that the zinc coordination ligand is deprotonated and the surrounding molecule is protonated (Figure 2). The total energies of these systems are listed in Table 5. In the absence of the zinc ion, the energy of the system in which the proton of the imidazole is transferred to its surrounding molecule is at least 13 kcal/mol higher than that of the system with a neutral imidazole. In the presence of the zinc ion, the system with an imidazolate is at least 17 kcal/mol lower than that with an imidazole, suggesting that the carboxylate group can be a proton acceptor for the zinc-coordinated imidazole in proteins and that our calculations are biochemically relevant. Imidazolate in the Zinc Complex. The histidine side chain is reportedly found in proteins as an imidazolium, imidazole, or occasionally imidazolate.6,33,34 In 1981, it was suggested, on the basis of molecular orbital calculations, that a system in which a deprotonated carboxylate forms a hydrogen bond to a histidine side chain which, in turn, coordinates to a zinc ion is isoenergic with a system in which the carboxylate is protonated and the histidine side chain is negatively charged.35 In other words, it was suggested that both imidazole and imidazolate could be in equilibrium in the zinc complexes in proteins. In addition, resonance Raman spectroscopic experiments suggest the presence of both carboxylate-histidine-iron and carboxylic acidhistidinate-iron forms in the active site of cytochrome c peroxidase.36 These results had led to the expectation that imidazolate exists in the zinc complexes in proteins in 1995.33,6,34 On the basis of the findings of the present study, we suggest a further investigation of the possibility that the presence of imidazolate in the zinc complexes in proteins might be independent of the hydrogen bonding interaction between the imidazole and the carboxylate group.

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Figure 2. The carboxylate group serves as a proton acceptor for the zinc-coordinated imidazole. The geometries of imidazole, imidazolate, zinccoordinated imidazole, zinc-coordinated imidazolate, MeCO2-, and MeCO2H were optimized individually with the B3LYP/6-311+G(2d,2p) method.

Conclusion On the basis of large basis set DFT calculations of proton dissociation energies of common zinc ligands in the presence and absence of Zn2+, we have found that the proton dissociation energies of H2O, MeOH, MeSH, imidazole, and N-methylacetamide are dramatically reduced when they coordinate to Zn2+.

Furthermore, we have found that the proton dissociation energy of the zinc-bound imidazole is 4 kcal/mol lower than that of the zinc-bound N-methylacetamide that is known to be deprotonated according to the X-ray and NMR studies. The result thus suggests further investigations of the possibility of imidazolate as a zinc ligand in proteins.

Proton Dissociation Energies of Zinc Ligands

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TABLE 5: Total Energies (kcal/mol) of the Systems Depicted in Figure 2 B3LYP/LANL2DZ system -

imidazole-MeCO2 imidazolate-MeCO2H Zn2+-imidazole-MeCO2Zn2+-imidazolate-MeCO2H

D)5Å

D)8Å

-285307.9 -285291.1 -326216.4 -326233.8

-285303.2 -285290.7 -326087.9 -326234.1

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