Metal Selectivity in Metalloproteins: Zn2+ vs Mg2+ - The Journal of

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J. Phys. Chem. B 2001, 105, 4446-4452

Metal Selectivity in Metalloproteins: Zn2+ vs Mg2+ Todor Dudev† and Carmay Lim*,†,‡ Institute of Biomedical Sciences, Academia Sinica, Taipei 11529, Taiwan, R.O.C., and Department of Chemistry, National Tsing Hua UniVersity, Hsinchu 300, Taiwan, R.O.C. ReceiVed: December 31, 2000; In Final Form: February 8, 2001

To elucidate the factors governing metal cation selectivity by proteins, density functional theory (DFT) and continuum dielectric methods (CDM) were used to evaluate the free energy of metal exchange in model binding sites. We studied Mg2+TZn2+ exchange in rigid sites, where the incoming metal retains the coordination geometry of the outgoing metal, as well as in flexible sites that can accommodate some reorganization of the protein ligands upon metal substitution. The results predict that Zn2+ can dislodge Mg2+ from its octahedral binding site. On the other hand, Mg2+ cannot displace Zn2+ from its tetrahedral binding site, unless a nearby negatively charged side chain can coordinate directly to Mg2+ in an octahedral geometry. The combination of available experimental data with our results suggest that some proteins may have chosen Mg2+ as a natural cofactor due mainly to its natural abundance in living cells. In such cases, it is not the protein that has evolved to select Mg2+ from other cations; instead, it is the cell machinery, which governs metal selectivity by regulating appropriate concentrations of Mg2+ and other cations (Zn2+ in particular) in various biological compartments. In contrast, Zn2+-binding sites appear to be more selective than Mg2+-binding sites. Hence, the protein can select Zn2+ against the background of a higher Mg2+ concentration.

Introduction Although a wealth of information has been accumulated on the biochemical and physiological significance of various metals, some aspects of metal binding to proteins remain poorly understood. A particularly intriguing question is how a protein selects a specific metal cation from the mixture of ions in the surrounding fluids. Is this selectivity due to (i) the natural abundance of the metal in the biological locality, (ii) properties of the metal (e.g., its stereochemical and charge to size requirements), or (iii) properties of the protein (e.g., its unique set of amino acid residues forming the metal-binding pocket and the stereochemistry of this pocket)? Another interesting question is why some proteins (like those with the EF-hand motif) bind only a specific metal, while others (like CheY) bind several ions with similar affinity.1,2 In the latter case, it is not clear if the various metals bind to the same protein cavity or to nearby different sites in the protein. It is also not clear if metalbinding sites in proteins are generally rigid or flexible, and the extent to which the protein can adjust to the stereochemical requirements of the incoming metal ion or conversely, the metal ion can comply with the constraints of the protein matrix. Elucidating the factors that govern the substitution of one metal for another (which dictates metal selectivity) in metalloproteins is of great importance. It can help to shed light on the mechanism(s) of metalloenzyme inhibition. It can also help to elucidate the mechanism of heavy metal poisoning in living cells, which, in many cases, is considered to be closely related to the exchange of a metal for a heaVy metal in the respective protein-binding sites.3,4 Furthermore, it may be useful in structural studies on metalloproteins as metal-binding sites are often probed with different metal cations. For example, Mg2+ is usually substituted with the heavier Mn2+ possessing the same coordination geometry,5 while Zn2+ is often replaced by Co2+, † ‡

Academia Sinica. National Tsing Hua University.

which permits easy monitoring of biochemical processes by absorption electron spectroscopy.6 In proteins, Mg2+ and Zn2+ appear to compete for the same binding site(s). This is evidenced by several X-ray structures showing Mg2+ and Zn2+ to occupy the same binding site upon substitution, for example, Mg2+- and Zn2+-bound enolase (PDB entries 1EBH and 4ENL, respectively), Mg2+- and Zn2+-bound xylose isomerase (1XYA and 1XLL), Mg2+- and Zn2+-bound leucine aminopeptidase (1BPM and 1LAM). Moreover, a number of in vitro experiments have shown that both metals can bind the same protein albeit with different affinities.4,7-9 Magnesium and zinc share certain similarities. They are among the most abundant divalent metals in living organisms (42 g of Mg2+ and 2.3 g of Zn2+ for an average person8,10). They have similar ionic radii (0.65 Å for Mg2+ and 0.74 Å for Zn2+ 11) and completed valence electron shells so they do not participate in redox reactions. Both play a structural and/or a catalytic role in proteins. They prefer to bind to protein ligands situated in cavities where a shell of polar, hydrophilic residues is surrounded by a shell of nonpolar, hydrophobic groups.12 However, the two metals also possess distinct properties. Mg2+ is a “hard” cation that prefers “hard” oxygen-containing ligands, while Zn2+ lies on the borderline between “hard” and “soft” cations and prefers nitrogen or sulfur containing ligands. They also differ in their stereochemical preference: the most common coordination number (CN) of Mg2+ and Zn2+ in metalloproteins is six and four, respectively. Recently, we have carried out a series of systematic studies aimed at elucidating the factors governing metal binding in proteins using a combined DFT/CDM approach (see below) and Protein Data Bank (PDB) surveys of metal-binding sites in proteins. Our previous works addressed the following three aspects of metalloprotein chemistry: (1) Why do metal ions tend to bind to proteins directly (in an “inner-sphere” mode) at centers of high hydrophobic contrast? (2) What is the most thermodynamically preferable set of inner-sphere ligands for a

10.1021/jp004602g CCC: $20.00 © 2001 American Chemical Society Published on Web 04/19/2001

Metal Selectivity in Metalloproteins given metal ion (e.g., Mg2+) in proteins? (3) What is the most thermodynamically preferable coordination geometry of a given metal ion (e.g., Zn2+) in proteins? The calculations showed that a low dielectric medium favors the inner-sphere binding of protein ligands to the metal (Mg2+, Ca2+ and Zn2+).13 Using Mg2+ as an example, we delineated its most preferable set of inner-sphere ligands and suggested an explanation for its role as a carrier of water molecules that mediate enzymatic hydrolysis.14 Furthermore, using Zn2+ as an example, we elucidated its most preferable coordination geometry in a protein environment.15 The calculations showed that hydrated Zn2+ changes its CN from six to four upon binding to the first or second amino acid residue. The decrease in the CN was attributed primarily to the requirements of the metal and ligands, rather than the constraints of the protein matrix on the metal. The aim here is to elucidate the factors that govern metal exchange, specifically, the interchange between Mg2+ and Zn2+, in protein-binding sites. To this end a combined DFT/CDM approach was employed to evaluate the free energy of Mg2+TZn2+ exchange in model binding sites. The metal and ligands forming its first and, in some cases, second coordination shell were treated quantum mechanically using DFT to account for electronic effects such as charge transfer from the ligands to the metal, which has been shown to play a crucial role in determining the metal complex properties.15,16 The rest of the protein was treated as a dielectric continuum using CDM to assess its effect on the free energy of metal exchange (see Methods). Two cases were considered. In the first case, the metal exchange reactions occur in rigid binding sites, where the incoming metal retains the coordination geometry of the outgoing metal. In the second case, the reactions occur in flexible binding sites that can accommodate some reorganization of the protein ligands upon metal substitution. The amino acid residues most commonly found coordinated to Zn2+ and Mg2+ in proteins were modeled by simple organic molecules. These are (i) imidazole (for the neutral histidine side chain), (ii) methanethiolate (for deprotonated cysteine), (iii) formate and formic acid (for deprotonated and protonated aspartic or glutamic acid side chains), and (iv) formamide (for backbone carbonyl groups or asparagine and glutamine side chains). The systems studied and details of the methods used are outlined in the next section. The free energies for replacing Mg2+ with Zn2+ in magnesiumbinding sites and Zn2+ with Mg2+ in zinc-binding sites are presented in the Results section. The errors in the computed free energies are assessed, and the computational results are validated by comparison with available experimental data in the Discussion section. By combining the results from this work with available experimental data, the factors governing Mg2+ and Zn2+ selectivity in proteins (see above) are discussed in the final section. Methods Systems Studied. We modeled several Mg2+ and Zn2+ binding sites that are often found in proteins. The first- and, in some cases, second-coordination layers of the metal were taken into account explicitly. Binding sites comprising of more than one metal and many heavy ligands were excluded from study as they are computationally prohibitive. The following model Mg2+- and Zn2+-binding sites were examined. Octahedral Magnesium-Binding Sites. Types of octahedral magnesium-binding sites are (1) a binding site consisting of five waters and one formate, modeling sites in inorganic pyrophosphatase (Site I, PDB entry 1OBW), parvalbumin (Site I, 4PAL), and arystolochene synthetase (Site I, 5EAS); (2) a binding site consisting of four waters and two formates,

J. Phys. Chem. B, Vol. 105, No. 19, 2001 4447 modeling sites in β-galactosidase (Site I; 1BGL), phosphorybosyltransferase (1DBR), phenylalanyl-tRNA synthetase (1PYS) and ASV integrase (1VSD); and (3) a binding site consisting of three waters, two formates, and one formamide, modeling sites in CheY (1CHN) and E. Coli ribonuclease HI (1RDD). Tetrahedral Zinc-Binding Sites. Types of tetrahedral zincbinding sites are (1) a binding site consisting of two imidazoles and two methanethiolates. This is a typical His-His-Cys-Cys binding site found in “classical” zinc-finger proteins.17 Also, it has been discovered in some enzymes such as galactose-1phosphate uridylyltransferase (1GUQ) and HIV-1 integrase (1WJC); (2) a binding site consisting of one water and three imidazoles, modeling sites in metallo-β-lactamase (1A7T), adamalysin II (1IAG), leishmanolysin (1LML), stromelysin-1 (1SLM), carbonic anhydrase II (2CBA), acutolysin A,18 and colicin E7;19 and (3) a binding site consisting of three waters and an imidazole in the first coordination layer and a formate or formamide in the second coordination sphere, which is hydrogen bonded to an imidazole. These second-layer ligands were included since a PDB survey of Zn-binding sites showed that a histidine side chain from the first coordination shell is often hydrogen bonded either to a backbone carbonyl or an acidic residue from the second coordination layer.20-22 These two-coordination-shell models allow us to study the effects of the second coordination layer upon metal substitution. Binding Site Flexibility Calculations. These employ the thermal B-factors determined for each atom in the protein X-ray structures. For each protein an average atomic B-factor (Bav) was calculated and used to evaluate normalized atomic B-factors, defined as Bnormi ) Bi/Bav. Thus, the mean of Bnormi is unity. Residues with average Bnorm higher than 1.0 were considered to be flexible, while those with average Bnorm lower than 1.0 were considered to be rigid.23 DFT Calculations. These employed Becke’s three-parameter hybrid method24 in conjunction with the Lee, Yang, and Parr correlation functional.25 Two basis sets were used: 6-31+G* (for complexes containing two or more heavy ligands) and 6-31++G(2d,2p) (for structures containing water and a single heavy ligand). The two basis sets were tested on a representative reaction from the series; viz., [Zn‚(H2O)3‚imidazole]‚(H2O)2 + Mg(H2O)6 f [Mg‚(H2O)3‚imidazole]‚(H2O)2 + Zn(H2O)6. They produced exchange free energies that differ by only 0.5 kcal/ mol: ∆Gex ) 16.1 kcal/mol using 6-31+G* and 15.6 kcal/mol with 6-31++G(2d,2p). Thus, the difference in basis sets used is not expected to change the conclusions of this work. Both basis sets have been calibrated with respect to experimental free energies of Mg2+ and Zn2+ binding to simple ligands. They reproduce the experimental observables to within 1 kcal/mol.14,15 Full geometry optimization for the entire series of complexes was carried out using the Gaussian 98 program.26 Vibrational frequencies were then computed at the same level of theory to verify that each complex was at the minimum of its potential energy surface. No imaginary frequency was found in any of the complexes. After the frequencies were scaled by an empirical factor of 0.9613,27 the zero-point energy (ZPE), thermal energy (ET), and entropy (S) corrections were evaluated using standard statistical mechanical formulas.28 The differences ∆Eelec, ∆ZPE, ∆ET, and ∆S between the products and reactants were employed to compute the exchange free energy at room temperature, T ) 298.15 K, according to the following expression:

∆Gex1 ) ∆Eelec + ∆ZPE + ∆ET - T∆S

(1)

Equation 1 was also used to compute the free energy for M2+

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SCHEME 1

TABLE 1: Calculated and Experimental Hydration Free Energies (in kcal/mol) for Zn2+, Mg2+, and Model Amino Acid Ligands species

+ Ln f [ML]2+n, where M ) Zn2+ or Mg2+; L ) H2O, HCONH2, imidazole, imidazolate-, H2PO4-, HCOO-, CH3S-, OH-, and HPO42-. These formation energies were not corrected for basis set superposition error (BSSE) since previous works showed that the dominant effect of the BSSE is not on the total energy, but on properties such as the dipole moment and the polarizability.29 Also, BSSE corrections did not improve the accuracy of the results.14,30 Continuum Dielectric Calculations. The reaction free energy in a given environment characterized by a dielectric constant  ) x can be calculated according to the thermodynamic cycle shown in Scheme 1. ∆Gex1 is the gas-phase free energy computed using eq 1. ∆Gsolvx is the free energy for transferring a molecule in the gas phase to a continuous solvent medium characterized by a dielectric constant, x. By solving Poisson’s equation using finite difference methods31,32 to estimate ∆Gsolvx (see below), the reaction free energy in an environment modeled by dielectric constant x, ∆Gexx, can be computed from

∆Gexx ) ∆Gex1 + ∆Gsolvx(products) - ∆Gsolvx(reactants)

(2)

The continuum dielectric calculations employed a 71 Å × 71 Å × 71 Å lattice centered on the metal cation with a grid spacing of 0.25 Å, ab initio geometries and natural bond orbital (NBO) atomic charges.33 The low-dielectric region of the solute was defined as the region inaccessible to contact by a 1.4 Å-radius sphere rolling over the molecular surface. This region was assigned a dielectric constant of two (in ) 2) to account for the electronic polarizability of the solute. The molecular surface was defined by effective solute radii, which were obtained by adjusting the CHARMM (version 22)34 van der Waals radii to reproduce the experimental hydration free energies of the metal cations and ligands as well as the solution free energies of water f chloride substitution reactions.15 The optimized radii depend on the charge set used. For the 6-31++G(2d,2p) NBO charges, the radii (in angstroms) employed in the study are RZn ) 1.4, RMg ) 1.5, RH(H2O) ) 1.0, RH(C,N) ) 1.468, RO(HCOO-) ) 1.65, RO(H2O) ) 1.69, RO(HCONH2) ) 1.79, RN ) 1.7, RC ) 1.9, and RS ) 2.0. These radii could also be used for the 6-31+G* NBO charges, except that RO(HCOO-) and RN had to be slightly lengthened to 1.67 and 1.77 Å, respectively. The free energies computed with the 6-31+G* and 6-31++G(2d,2p) geometries, NBO charges, and radii for Mg2+, Zn2+, HCOO-, CH3S-, HCONH2 and imidazole agree with the respective experimental values to within 2.5% (Table 1). Buried or partially buried metal-binding sites were characterized by an external dielectric constant out equal to 2 or 4,31,35 whereas fully solvent-exposed sites were modeled by an out equal to 80. Thus, Poisson’s equation was solved with out equal to 1, 2, 4, or 80 and in ) 2. The difference between the computed electrostatic potentials in a given dielectric medium ( ) x) and in the gas phase ( ) 1) yielded the solvation free energy ∆Gsolvx of the metal complex.

Zn2+ Mg2+ HCOOCH3SHCONH2 imidazole HCOOH

∆Gsolv ∆Gsolva 6-31+G* ∆Gsolva 6-31++G(2d,2p) experiment -487.1 (2.5) -450.3 (-5.2) -80.0 (-2.0) -75.8 (-0.2) -10.1 (0.1) -10.0 (-0.2) -7.2 (0.5)

-487.1 (2.5) -450.3 (-5.2) -80.3 (-1.7) -10.1 (-0.1)

-484.6b -455.5b -82c -76d -10.0e -10.2f -6.7f

a Values in parantheses indicate the deviation (in kcal/mol) from the experimental value. b From Burgess, 1978.47 c Experimental hydration free energy of CH3COO- from Lim et al., 1991.32 d Experimental hydration free energy of HS- from Chambers et al., 1996.48 e Experimental solvation free energy of HCONH(CH3) from Wolfenden et al, 1978.49 f From Wolfenden et al, 1981.50

Results Zn2+ as a Substitute for Mg2+ in Magnesium-Binding Sites. This was assessed by the following model reactions:

[Mg‚Qn‚Lm‚(H2O)6-m-n]2-n + [Zn(H2O)6]2+ f [Zn‚Qn‚Lm‚(H2O)6-m-n]2-n + [Mg(H2O)6]2+ (3) [Mg‚Qn‚(H2O)6-n]2-n + [Zn(H2O)6]2+ f {[Zn‚Qn‚(H2O)4-n]‚(H2O)2}2-n + [Mg(H2O)6]2+ (4) where Q ) HCOO-; L ) HCONH2; n ) 1, 2 and m ) 0, 1. The CN of Zn2+ and Mg2+ in aqueous solution is found experimentally to be six.36 Therefore, hydrated Zn2+ and Mg2+ were modeled as hexa-aqua complexes possessing octahedral symmetry. Reaction 3 mimics the exchange of Mg2+ for Zn2+ in a rigid binding site where the protein matrix does not permit any amino acid rearrangements upon metal substitution. Consequently the incoming Zn2+ retains the octahedral coordination geometry of the outgoing Mg2+. Reaction 4 models the metal exchange in a more flexible binding site where Zn2+ is able to readjust the number of protein ligands according to its stereochemical preference. In reaction 4, Zn2+ adopts a tetrahedral geometry since this is the preferred coordination geometry in proteins.37 The Mg2+fZn2+ exchange free energies evaluated for the gas phase and different dielectric media are summarized in Table 2. The results show that when Mg2+ is bound to one or two acidic residues, it may be displaced by Zn2+ (the ∆Gex for the first two and last two reactions in Table 2 is negative over the entire range of , from 1 to 80). However, for buried sites with a single carboxylate bound to the metal, the free energy gain upon Mg2+fZn2+ exchange is greater for flexible sites that allow Zn2+ to adopt a tetrahedral instead of an octahedral geometry (the ∆Gex2/4 value is between -2 to -3 kcal/mol if Zn2+ retains the coordination geometry of Mg2+, but it is around -10 kcal/mol if Zn2+ decreases its CN to four). When Mg2+ is bound to two carboxylate side chains as well as a carbonyl group, the results are not so clear-cut as the exchange free energies are near the accuracy limits of the present calculations (1 to 2 kcal/mol). Mg2+ as a Substitute for Zn2+ in Zinc-Binding Sites. This was assessed by the following model reactions:

{[Zn‚Ln‚P4-n]‚H2Om}k + [Mg(H2O)6]2+ ) {[Mg‚Ln‚P4-n]‚H2Om}k + [Zn(H2O)6]2+ (5)

Metal Selectivity in Metalloproteins

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TABLE 2: Enthalpies (∆Hex1) and Free Energies (∆Gexx) of Mg2+fZn2+ Exchange in Magnesium-Binding Sites for Media of Different Dielectric Constant xa ∆Hex1

∆Gex1

∆Gex2

∆Gex4

∆Gex80

Rigid Binding Sites [Mg‚HCOO‚W5]+ + [Zn‚W6]2+ f [Zn‚HCOO‚W5]+ + [Mg‚W6]2+ [Mg‚(HCOO)2‚W4]0 + [Zn‚W6]2+ f [Zn‚(HCOO)2‚W4]0 + [Mg‚W6]2+ [Mg‚(HCOO)2‚Fm‚W3]0 + [Zn‚W6]2+ f [Zn‚(HCOO)2‚Fm‚W3]0 + [Mg‚W6]2+

-3.3c -5.4d -4.3d

-2.3c -5.8d -3.7d

-2.3 -5.7 -2.2

-2.5 -5.5 -0.8

-2.7 -5.0 1.5

Flexible Binding Sites [Mg‚HCOO‚W5]+ + [Zn‚W6]2+ f {[Zn‚HCOO‚W3]‚W2}+ + [Mg‚W6]2+ [Mg‚(HCOO)2‚W4]0 + [Zn‚W6]2+ f {[Zn‚(HCOO)2‚W2]‚W2}0 + [Mg‚W6]2+

-8.6c -11.0d

-11.9c -10.1d

-10.4 -8.2

-9.8 -6.3

-9.0 -2.1

reactionb

a All energies in kcal/mol; x ) 1 corresponds to gas-phase values, x ) 2 or 4 represents buried or partially buried metal-binding sites, whereas x ) 80 represents fully solvent-exposed sites (see Methods). b W ) H2O and Fm ) HCONH2. c Using the 6-31++G(2d,2p) basis. d Using the 6-31+G* basis.

{[Zn‚L‚(H2O)3]‚H2O‚Q}l + [Mg(H2O)6]2+ ) [Mg‚(H2O)4‚L‚Q]l + [Zn(H2O)6]2+ (6) where L ) imidazole; P ) CH3S-or H2O; Q ) HCOO-, HCONH2; n ) 1-3; m ) 0, 2; k ) 0, 2; and l ) 1, 2. In reaction 5 the tetrahedral Zn2+-binding site is considered to be inflexible so that the incoming Mg2+ is forced to adopt a tetrahedral geometry. In contrast, reaction 6 models the metal exchange in a flexible binding site, which allows two ligands in the outer coordination sphere of Zn2+ to bind directly to Mg2+ in octahedral coordination geometry. The first three reactions in Table 3, which mimic the exchange of Zn2+ for Mg2+ without changing the metal CN, are characterized by large, positive ∆Gex ranging from 13 to 39 kcal/mol. Therefore, the calculations predict that for the rigid zinc-binding sites in Table 3, Mg2+ cannot displace Zn2+ regardless of the solvent-accessibility of the site. The fourth reaction in Table 3 is similar to the first one except that two water molecules from the second coordination shell of Zn2+ have been added to the first coordination shell of Mg2+. As expected, the expansion of the CN of Mg2+ from four to six decreases the magnitude of the gas-phase ∆Gex1 relative to the respective value for a rigid binding site. Furthermore, since the octahedral magnesium complex is better solvated than the tetrahedral zinc complex, the magnitude of the ∆Gex values in condensed media decreases further. However, the free energies remain positive implying that the Zn2+f Mg2+ exchange may not take place, especially in buried or partially buried sites. In many protein Zn2+-binding sites, backbone carbonyls or carboxylates constitute part of the second coordination layer of Zn2+ and are often hydrogen bonded to histidine(s) (rather than water) from the metal’s first coordination shell20-22 (see Methods). These sites are modeled in the last two reactions in Table 3. The fully optimized structure of the zinc complex, {[Zn‚imidazole‚(H2O)3]‚H2O‚HCOO}+, shown in Figure 1a is interesting. Initially the formate was placed so that it can hydrogen bond to the H(N) atom of the imidazole; i.e.,

However, after several steps of geometry optimization the H(N) proton migrated to the formate oxygen so that the final fully optimized structure was a formic acid hydrogen-bonded to a zinc-bound imidazolate anion (Figure 1a). The formic acidimidazolate-zinc structure is in accord with the findings by Yazal and Pang, who showed that the zinc-bound imidazole could be deprotonated by a carboxylate placed in the metal’s second

coordination shell.38 Because of the weaker basic properties of formamide compared to formate, such a proton transfer was not observed in the {[Zn‚imidazole‚(H2O)3]H2O‚HCONH2}2+ complex. The metal exchange free energies for complexes containing HCONH2 (reaction 5 in Table 3) were found to be positive over the entire  range. This implies that the Zn2+fMg2+ exchange is not likely to occur in the protein even if Mg2+ can expand its CN to six by incorporating a nearby water molecule and backbone carbonyl group into its first coordination shell. The last reaction in Table 3 is particularly interesting as it is characterized by large, negatiVe ∆Gex values ranging from -10 to -15 kcal/mol. Note that, in computing the ∆Gsolvx for the zinc complex in Figure 1a, the radius for the imidazolate nitrogen that is hydrogen bonded to formic acid was assumed to be equal to that for a imidazole nitrogen; i.e., RN ) 1.77 Å. However, decreasing the latter by 0.1 Å to 1.67 Å changes ∆Gex80 by only 0.3 kcal/mol, hence the nitrogen radius employed in computing ∆Gsolvx for the zinc complex is unlikely to change the sign of the ∆Gex values in Table 3. It appears that innersphere binding of a negatively charged ligand to Mg2+ is so favorable that it can reverse the reaction trend observed for the other binding sites in Table 3. The Mg2+-bound formate forms a hydrogen bond with a neighboring water molecule, which presumably further stabilizes the complex in Figure 1b. The Relative Stability of Zn2+ and Mg2+ Mono-Ligand Complexes. Tables 2 and 3 show that the thermodynamics of metal exchange is governed by the gas-phase exchange free energy (∆Gex1 . ∆∆Gsolvx) and solvation effects generally do not reverse the trend observed in the gas phase. Hence, to gain further insight into the factors governing the gas phase ∆Gex1 values, we computed the formation free energies of Zn2+ and Mg2+ with various ligands in the gas phase. The data collected in Table 4 show that the formation free energies of zinc complexes are always lower than those of the magnesium counterparts (by 24 to 77 kcal/mol). This implies that the ligands in Table 4 prefer Zn2+ to Mg2+. As shown in previous works,15,39 the zinc complexes are more stable than the magnesium ones because each of the ligands transfers more charge to Zn2+ than to Mg2+. Table 4 also shows that the nonaqua ligands discriminate between the two metals more than water, which has the least charge difference between Zn2+ and Mg2+. In particular, methanethiolate is the most discriminatory ligand with the second largest magnitude of the charge transfer difference between Zn2+ and Mg2+. In view of the above findings it is not surprising that Zn2+ can successfully compete with Mg2+ in rigid buried sites where the number of ligands coordinated to the metal does not change during the exchange reaction (Tables 2 and 3). It can also prevail over Mg2+ in flexible Zn2+-binding sites with neutral, as opposed to negatiVely charged, ligands in the second coordina-

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TABLE 3: Enthalpies (∆Hex1) and Free Energies (∆Gexx) of Zn2+fMg2+ Exchange in Zinc-Binding Sites for Media of Different Dielectric Constant xa ∆Hex1

∆Gex1

∆Gex2

∆Gex4

∆Gex80

Rigid Binding Sites {[Zn‚Im‚W3]‚W2}2+ + [Mg‚W6]2+ f {[Mg‚Im‚W3]‚W2}2+ + [Zn‚W6]2+ [Zn‚(Im)3‚W]2+ + [Mg‚W6]2+ f [Mg‚(Im)3‚W]2+ + [Zn‚W6]2+ [Zn‚(Im)2‚(CH3S)2]0 + [Mg‚W6]2+ f [Mg‚(Im)2‚(CH3S)2]0 + [Zn‚W6]2+

15.8c 29.0d 42.0d

15.6c 25.7d 39.9d

14.8 25.1 39.1

14.3 24.5 38.3

12.9 23.1 36.5

Flexible Binding Sites {[Zn‚Im‚W3]‚W2}2+ + [Mg‚W6]2+ f [Mg‚Im‚W5]2+ + [Zn‚W6]2+ {[Zn‚Im‚W3]W‚Fm}2+ + [Mg‚W6]2+ f [Mg‚Im‚Fm‚W4]2+ + [Zn‚W6]2+ {[Zn‚Im‚W3]‚W‚HCOO}+ + [Mg‚W6]2+ f [Mg‚Im‚HCOO‚W4]+ + [Zn‚W6]2+

14.6c 5.2d -19.2d

13.9c 6.4d -19.3d

8.0 5.0 -14.9

4.9 4.5 -12.4

0.5 3.7 -9.9

reactionb

a

See footnote a for Table 2. b Im ) imidazole, W ) H2O, and Fm ) HCONH2. c Using the 6-31++G(2d,2p) basis. d Using the 6-31+G* basis.

Figure 1. Ball and stick diagram of fully optimized (A) Zn2+ tetrahedrally coordinated to one imidazolate and three water molecules in the first shell with one water and one formic acid in the second shell; (B) Mg2+ octahedrally coordinated to one imidazole, one formate, and four water molecules in the first shell.

TABLE 4: Formation Free Energies (in kcal/mol) of Some Magnesium and Zinc Complexes in the Gas Phase Computed at the B3LYP/6-31++G(2d,2p) Level ligand

∆Gform (Zn-Mg)a

∆Gform (Zn)b

∆Gform (Mg)c

q(Zn)q(Mg)d

H2O HCONH2 H2PO4HCOOimidazole OHHPO42imidazolateCH3S-

-23.5 -31.0 -42.4 -45.5 -48.3 -53.6 -54.6 -68.9 -76.9

-96.5 -147.8 -400.1 -403.6 -176.0 -431.7 -637.6 -394.9 -431.1

-73.0 -116.8 -357.7 -358.1 -127.7 -378.1 -583.0 -326.0 -354.2

-0.07 -0.17 -0.17 -0.23 -0.19 -0.27 -0.21 -0.31 -0.30

a ∆G b form(Zn-Mg) ) ∆Gform(Zn) - ∆Gform(Mg). Formation free energy for Zn2+ + Ln f [Zn‚L]2+n. c Formation free energy for Mg2+ + Ln f [Mg‚L]2+n. d Difference between NBO charges on zinc and magnesium.

tion sphere. The trend is reversed, however, for zinc complexes containing negatiVely charged ligand(s) in the second coordination shell, which eventually become part of the first coordination layer of Mg2+ (Table 3, last reaction). This is probably because the free energy gain upon Mg2+ binding to a negatiVely charged ligand is significantly higher (by more than 200 kcal/mol) than that for Mg2+ binding to a neutral ligand (Table 4). Flexibility of Mg2+- and Zn2+-Binding Sites. The normalized Bnorm factors (see Methods) for several representative Mg2+and Zn2+-binding sites found in the PDB are listed in Table 5. Most of these sites are modeled in the present calculations (Tables 2 and 3). Although very low or very high B values may reflect problems with the X-ray data collection and/or structure

refinement, the B-factors are used here to indicate the statistical trends of the relative rigidity/flexibility of the metal sites. Table 5 shows that most of the binding sites seem to be rigid, as evidenced by average residue Bnorm less than 1.0 (see Discussion). However, two binding sites, viz., the Mg2+-binding site in scallop myosin and the Zn2+-binding site in colicin E7, were found to be relatively flexible. Note that unlike the Zn2+-binding site in colicin E7, the other four three-histidine, Zn2+-binding sites in Table 5 are relatively rigid. Discussion Assessment of Errors. In computing the metal-exchange free energies in Tables 2 and 3, systematic errors in the computed gas-phase and solvation free energies of the reactants are likely to partially cancel those of the respective products. Errors in the computed gas-phase ∆Hex were minimized by calibrating the basis sets employed.14,15 The gas-phase energy dominates the computed ∆Gex1 (Tables 2 and 3), hence errors in computing the entropy are unlikely to change the key findings of this work. By using a set of atomic radii that were adjusted to reproduce the experimental hydration free energies of the metal cations and ligands (Table 1), the various approximations made in computing ∆Gsolv80 were taken into account implicitly.15 Furthermore, by including the first, and sometimes second, coordination shell around the metal explicitly, the errors in the computed ∆Gsolvx were reduced since the dielectric boundary was extended from the central metal atom. Taking all the aforementioned factors into consideration, the error in ∆Gexx is estimated to be generally ∼2 kcal/mol. Note, however, that the conclusions reached in this work were based primarily on the

Metal Selectivity in Metalloproteins

J. Phys. Chem. B, Vol. 105, No. 19, 2001 4451

TABLE 5: Normalized B-Factors (Å2) for Some Mg2+- and Zn2+-Binding Sites PDB entrya 1BGL (2.5) 1DBR (2.4) 1PYS (2.9) 1VSD (1.7) 1CHN (1.8) 1RDD (2.8) 1EBH (1.9) 1WDC (2.0) 1XYA (1.8)

description of protein

ligandsb (Bnorm)

Mg2+-Binding Sites β-galactosidase (site I) E416 (0.8)c, E461 (0.8)c phosphorybosylE146 (0.8)d, D147 (0.8)d transferase phenylalanyl-tRNA E262 (0.4), E461 (0.4) synthetase ASV integrase D64 (0.6), D121 (0.7) CheY D13 (0.7), D57 (0.6), N59bb (1.5) ribonuclease HI D10 (0.8), G11bb (0.9), E48 (0.6) enolase D246 (0.7), E295 (0.6), D320 (0.5) scallop myosin D28 (1.0), D30 (1.3), D32 (1.3) F34bb (1.2), D39 (0.9) xylose isomerase E180 (1.0), E216 (0.9), (site I) D244 (0.9), D286 (0.9) xylose isomerase E216 (0.9), H219 (0.7), (site II) D254 (1.0), D256 (0.8)

Zn2+-Binding Sites 1GUQ (1.8) galactose-1-phosphate C52 (0.6), C55 (0.6), uridyltransferase H115 (0.9), H164 (0.7) 1A7T (1.85) metallo-β-lactamase H82 (0.4), H84 (0.5), H145 (0.6) 1IAG (2.0) adamalysin II H142 (0.5), H146 (0.9), H152 (1.0) 1SLM (1.9) stromelysin-1 H201 (0.5), H205 (0.5), H211 (0.7) 2CBA (2.15) carbonic anhydrase II H94 (0.4), H96 (0.3), H119 (0.3) 1UNK (2.3) colicin E7 H544 (1.2), H569 (1.2), H573 (1.4) 1LAM (1.6) LEU aminopeptidase D255 (0.6), D332 (0.6), E334 (0.6) (site I) LEU aminopeptidase K250 (0.6), D255 (0.6), (site II) D273 (0.6), E334 (0.6) a The value in parentheses is the resolution in Angstroms. b Unless the residue has a superscript “bb”, denoting a backbone carbonyl oxygen, the side chain oxygen or nitrogen or sulfur atom of the residue coordinates to the metal. The number in brackets is the normalized atomic B-factor (see Methods); values greater than unity are highlighted in bold. c B-factors in site I were averaged over the eight protein chains in the structure. d B-factors were averaged over the four protein chains in the crystal asymmetric unit.

trends in the free energy changes of the various model reactions. Furthermore, the findings of this work appear to be consistent with experimental observations, as discussed below. Comparison with Experiment. The flexibility calculations in Table 5, showing nonflexible metal-binding sites in enolase, xylose isomerase, and leucine aminopeptidase are supported by experiment. For two of the proteins, enolase and xylose isomerase whose natural cofactor is Mg2+,40 the crystal structures with Mg2+ replaced by Zn2+ have also been solved. The X-ray structures of the Zn-bound enolase (PDB entry 4ENL) and xylose isomerase (1XLL) show that Zn2+ occupies the same binding site and coordinates to the same set of ligands as Mg2+. However, xylose isomerase loses its activity upon Zn2+ substitution.22 The X-ray structures of both Zn2+-bound (PDB entry 1LAM) and Mg2+-bound (1BPM) leucine aminopeptidase have been solved. They show that the metal site is not flexible and preserves its structure upon exchanging the natural cofactor Zn2+ for Mg2+, consistent with the results in Table 5. The results in Table 2 imply that in general Zn2+ can dislodge Mg2+ octahedrally bound to one or two acidic residues from magnesium-binding sites. This finding is in agreement with several experimental observations. Lukat et al. have shown that Zn2+ (with a dissociation constant KD ) 97 µM) binds to the bacterial chemotaxis protein CheY more tightly than its natural cofactor, Mg2+ (KD ) 500 µM).7 In the CheY X-ray structure (PDB entry 1CHN), Mg2+ is bound to two aspartate side chains, one backbone carbonyl group, and three water molecules (Table 5) in a relatively buried site. Such a Mg2+ site was modeled in this study (Table 2, reaction 3), and the substitution of Mg2+

by Zn2+ in a buried pocket was found to be thermodynamically favorable. Ciancaglini et al. have shown that Zn2+ inhibits alkaline phosphatase catalytic activity by displacing its natural cofactor, Mg2+.4 In the crystal structure of E. Coli alkaline phosphatase (1ALK), Mg2+ is octahedrally coordinated to the side chains of an aspartic acid, a glutamic acid and a threonine as well as three water molecules. In the same vein, Sun and Budde have reported that Zn2+ inhibits Csk kinase catalytic activity by binding to the second Mg2+-binding site of protein tyrosine kinase Csk with a 13 200-fold higher affinity than Mg2+.8 Unfortunately the three-dimensional structure of Csk has not been solved, but comparison with another tyrosine kinase (insulin receptor kinase) shows that an aspartic acid is directly bound to Mg2+.8 The results in Table 3 imply that in general Mg2+ cannot displace Zn2+ bound tetrahedrally to one or more histidines from zinc-binding sites, unless a nearby negatively charged side chain can be added to the first shell in an octahedral geometry. This finding is also in line with the following experimental observations. By measuring the affinity of a series of divalent cations to the Zn2+-binding site in L-ribulose-5-phosphate 4-epimerase, Lee et al. found that Zn2+, the physiological activator, binds to the protein (KD ) 0.17 µM) more tightly than Mg2+ (KD ) 1350 µM).9 The X-ray structure of the Zn2+-bound epimerase shows that Zn2+ is bound to three histidines.9 Such a Zn2+ site was modeled in this study (Table 3, reaction 2), and substitution of Zn2+ by Mg2+ was indeed found to be thermodynamically unfavorable over the entire  range. The same type of binding site with three histidines has been proposed for the hamster dihydroorotase domain, which binds Zn2+ under physiological conditions.41 Using atomic absorption spectroscopy, Mg2+ binding to the apo-form of the protein was not detected,41 consistent with the results in Table 3. Biological Implications. Our theoretical results together with available experimental data imply that magnesium-binding sites are not very specific for Mg2+. Other divalent metals, especially Zn2+, may replace Mg2+. On the contrary, rigid zinc-binding sites generally prefer Zn2+ to Mg2+. These findings raise some interesting questions. For example, how do proteins, whose natural cofactor is Mg2+, select this cation from the surrounding fluids? Furthermore, how do these proteins prevent other cations, particularly Zn2+, from replacing Mg2+? Magnesium is the most abundant divalent cation in eukaryotic cells with concentrations of free Mg2+ ranging from 0.1 to 1 mM.42 There is increasing evidence that the concentration of free Mg2+ in the cells is subject to tight regulation.43 Zinc is the second-most abundant transition metal in living organisms after iron. However, the concentration of free Zn2+ in the cell is kept very low with estimates in the femtomolar range.44 Some recent studies have emphasized the role of metallothionein (a cysteine-rich protein that traps up to seven Zn2+ in its two domains) in maintaining the intracellular concentration of free Zn2+. Metallothionein has been assigned several roles. One of its proposed roles is to maintain cellular homeostasis by metal ion detoxification.45 Metallothionein has been proposed to scavenge Zn2+ from extracellular sources when intracellular supplies of Zn2+ are low.44 It has also been postulated to play a role in the redistribution of Zn2+ within the cell via zinc-thiol/disulfide interchange.46 In view of the facts outlined above it seems likely that during evolution some proteins have chosen Mg2+ as a natural cofactor based mainly on its natural abundance in living cells. Magnesiumbinding sites appear to be weakly protected against other divalent

4452 J. Phys. Chem. B, Vol. 105, No. 19, 2001 metals like Zn2+, which can replace Mg2+ and, in some cases, inhibit enzymatic activity. Therefore, it seems that it is not the protein that has evolved to select Mg2+ from other cations. Instead, it is the cell machinery that regulates the process of metal binding by regulating appropriate concentrations of Mg2+ and other cations (Zn2+ in particular) in various biological compartments. Relative to Mg2+, Zn2+ has a higher affinity for a given protein ligand (Table 4) and strongly prefers a tetrahedral geometry.15 Consequently, rigid Zn2+-binding sites, especially those lined by cysteine residues, appear to be more selective than Mg2+-binding sites. Thus, a protein can generally select Zn2+ against the background of a much higher Mg2+ concentration. Acknowledgment. We thank Drs. Tse Wen Chang and Hanna Yuan for stimulating discussions. We are grateful to D. Bashford, M. Sommer and M. Karplus for the program to solve the Poisson equation. T.D. is supported by a fellowship from the Institute of Biomedical Sciences. This work is supported by the Institute of Biomedical Sciences at Academia Sinica, the National Center for High Performance Computing, and the National Science Council, Republic of China (NSC-88-2113M-001). References and Notes (1) Falke, J. J.; Snyder, E. E.; Thatcher, K. C.; Voertler, C. S. Biochemistry 1991, 30, 8690. (2) Needham, J. V.; Chen, T. Y.; Falke, J. J. Biochemistry 1993, 32, 3363. (3) Payne, J. C.; Horst, M. A. t.; Godwin, H. A. J. Am. Chem. Soc. 1999, 121, 6850. (4) Ciancaglini, P.; Pizauro, J. M.; Curti, C.; Tedesco, A. C.; Leone, F. A. Int. J. Biochem. 1990, 22, 747. (5) Bock, C. W.; Katz, A. K.; Markham, G. D.; Glusker, J. P. J. Am. Chem. Soc. 1999, 121, 7360. (6) Krizek, B. A.; Merkle, D. L.; Berg, J. M. Inorg. Chem. 1993, 32, 937. (7) Lukat, G. S.; Stock, A. M.; Stock, J. B. Biochemistry 1990, 29, 5436. (8) Sun, G.; Budde, R. J. A. Biochemistry 1999, 38, 5659. (9) Lee, L. V.; Poyner, R. R.; Vu, M. V.; Cleland, W. W. Biochemistry 2000, 39, 4821. (10) Cowan, J. A.; Biological Chemistry of Magnesium; VCH: New York, 1995. (11) Brown, I. D. Acta Crystallogr. 1988, B44, 545. (12) Yamashita, M. M.; Wesson, L.; Eisenman, G.; Eisenberg, D. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 5648. (13) Dudev, T.; Lim, C. J. Phys. Chem. B 2000, 104, 3692. (14) Dudev, T.; Cowan, J. A.; Lim, C. J. Am. Chem. Soc. 1999, 121, 7665. (15) Dudev, T.; Lim, C. J. Am. Chem. Soc. 2000, 122, 11146. (16) Dudev, T.; Lim, C. J. Phys. Chem. A 1999, 103, 8093. (17) Berg, J. M.; Godwin, H. A. Annu. ReV. Biophys. Biomol. Struct. 1997, 26, 357.

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