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J. Phys. Chem. B 2000, 104, 3692-3694
Metal Binding in Proteins: The Effect of the Dielectric Medium Todor Dudev†,§ and Carmay Lim*,†,‡ Institute of Biomedical Sciences, Academia Sinica, Taipei 11529, Taiwan, Republic of China, and Department of Chemistry, National Tsing Hua UniVersity, Hsinchu 300, Taiwan, Republic of China ReceiVed: NoVember 23, 1999; In Final Form: February 1, 2000
In proteins as well as host molecules, metal ions generally bind to a shell of polar hydrophilic residues surrounded by a shell of nonpolar hydrophobic groups. The hydrophilic protein residues tend to bind directly to the metal (inner-sphere mode), instead of indirectly via a metal-bound water molecule (outer-sphere mode). However, it is not fully understood why metal ions tend to bind in an inner-sphere fashion and at centers of high hydrophobic contrast. Ab initio and continuum dielectric calculations have been employed to compute the free energy (∆Gex) of the exchange reaction between a metal-bound water molecule and ligands of biological interest in metal complexes for various dielectric media. The results show that ∆Gex is sensitive to the dielectric constant of the environment and that a low dielectric medium favors the inner-sphere binding of protein ligands, especially negatively charged amino acid residues, to the metal.
Introduction Understanding the mechanism of metal binding to proteins is of prime importance for studying certain enzyme reactions and for engineering metal-containing proteins possessing new properties. In proteins as well as host molecules, metal ions generally bind to a shell of polar hydrophilic residues surrounded by a shell of nonpolar hydrophobic groups.1 The hydrophilic protein residues tend to bind directly to the metal (inner-sphere mode), instead of indirectly via a metal-bound water molecule (outer-sphere mode).2,3 The hydrophobic outer sphere has been hypothesized to limit solvent accessibility, thus providing a low dielectric cavity that enhances the electrostatic interactions between the metal and the hydrophilic ligands.1,4,5 However, it is not fully understood why metal ions tend to bind in an innersphere fashion and at centers of high hydrophobic contrast. In this work, ab initio and continuum dielectric calculations were employed to compute the free energy (∆Gex) of the exchange reaction between metal-bound water and ligands of biological interest in metal complexes for various dielectric media. The results show that ∆Gex is sensitive to the dielectric constant of the environment and that a low dielectric medium favors the inner-sphere binding of protein ligands to the metal. Methods Ab Initio Calculations. Ab initio calculations were carried out to evaluate ∆Gex1 of the first-water exchange reaction in metal-aqua complexes in the gas phase:
[M(H2O)6]
2+
+ L f [M(H2O)5L] z
2+z
+ H2O
side chains as well as the backbone peptide group, formate which is modeling the aspartic and glutamic acid side chains, and imidazole which is modeling the histidine side chain. The geometries of the ligands and metal complexes were fully optimized at the HF/6-311+G* level using the Gaussian 98 program.7 Vibrational frequencies were computed at the same level of theory: no imaginary frequency was found in any of the clusters. The frequencies were scaled by an empirical factor of 0.89298 and used to evaluate the zero-point energy (ZPE), thermal energy (ET), and entropy (S).9 The electronic energies (∆Eelec) were corrected for electron correlation effects by MP2/ 6-311+G*//HF/6-311+G* calculations. Because our previous study10 and other works11-13 showed that including the basis set superposition error did not improve the accuracy of the results, this correction was omitted in computing the binding energies. The differences in ∆Eelec, ∆ZPE, ∆ET, and ∆S for eq 1 gave the gas-phase free energy (∆Gex1) for the water-ligand exchange reaction at room temperature, T ) 298.15 K:
∆Gex1 ) ∆Eelec + ∆ZPE + ∆ET - T∆S
Continuum Dielectric Calculations. The exchange free energy for eq 1 in a medium characterized by a dielectric constant (∆Gexx) was evaluated using the following thermodynamic cycle: ∆Gex1
A()1) 98 B()1) ∆Gsolvx(A) V
(1)
V ∆Gsolvx(B)
A()x) 9x8 B()x) ∆Gex
In eq 1, M ) Mg2+, Ca2+, or Zn2+ and Lz (z ) 0, -1) are models of protein ligands that are most frequently found to be coordinated to these metal cations.6 The ligands studied here are formamide which is modeling the asparagine and glutamine * To whom correspondence should be addressed. † Academia Sinica. ‡ National Tsing Hua University. § On leave from the Department of Chemistry, University of Sofia, Bulgaria.
(2)
(3)
∆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 methods14,15 to yield ∆Gsolvx (see below), the exchange free energy in an environment modeled by dielectric constant x, ∆Gexx, can be computed from
∆Gexx ) ∆Gex1 + ∆Gsolvx(B) - ∆Gsolvx(A)
10.1021/jp9941559 CCC: $19.00 © 2000 American Chemical Society Published on Web 03/28/2000
(4)
Dielectric Medium on Metal Binding in Proteins
J. Phys. Chem. B, Vol. 104, No. 15, 2000 3693
TABLE 1: Calculated Enthalpies and Free Energies ∆Gexa (in kcal/mol) for the Reaction [M(H2O)6]2+ + Lz f [M(H2O)5L]2+z + H2O M
Lz
∆Hex1
∆Gex1
∆Gex2
∆Gex4
∆Gex80
Mg2+ Ca2+ Zn2+ Mg2+ Ca2+ Zn2+ Mg2+ Ca2+ Zn2+
HCOOHCOOHCOOHCONH2 HCONH2 HCONH2 imidazole imidazole imidazole
-189.9 -181.4 -194.1 -11.9 -12.2 -12.5 -18.7 -16.4 -25.1
-190.3 -181.7 -195.1 -12.7 -12.7 -13.1 -18.5 -16.3 -24.7
-90.0 -85.5 -95.1 -4.1 -5.0 -5.2 -9.7 -8.6 -16.0
-40.0 -37.6 -45.3 0.4 -0.9 -1.3 -5.4 -4.8 -11.8
7.6 8.1 2.0 4.2 2.8 1.8 -1.3 -1.1 -7.8
a The numeric superscript after ∆G denotes the dielectric constant ex of the environment.
The continuum dielectric calculations employed a 71 × 71 × 71 lattice centered on the metal cation with a grid spacing of 0.25 Å. The ab initio geometries and NBO16 partial atomic charges, which were assumed to be the same in the gas phase and the solvent medium, were employed in these calculations. The low-dielectric region of the solute was defined as the region inaccessible to contact by a 1.4-Å sphere rolling over the molecular surface. This region was assigned a dielectric constant of 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 CHARMM17 (version 22) van der Waals radii to reproduce the experimental hydration free energies of Mg2+ (-455 kcal/mol), Ca2+ (-381 kcal/mol), Zn2+ (-485 kcal/mol), H2O (-6.3 kcal/mol), imidazole (-10.2 kcal/mol), HCONH2 (-9.7 kcal/mol), and HCOO- (-82 kcal/ mol). The following atomic radii (in Å) were employed in the calculations: Mg, 1.50; Ca, 1.75; Zn, 1.40; C, 2.10; O, 1.77; O(COO-), 1.65; N, 1.77; H, 1.30; H(N), 1.30. (Note that these radii have been parametrized for NBO charges and HF geometries.) The external dielectric constant was assigned 2 or 44,5 to simulate the protein environment or 80 to characterize binding sites fully exposed to water. The difference between the electrostatic potential calculated for a given dielectric media ( ) 2 or 4 or 80) and the gas phase ( ) 1) yielded the electrostatic solvation free energy ∆Gsolv of the metal complex or ligand. Results and Discussion Table 1 lists the computed free energies for eq 1 with different values of . The dielectric constant of a protein is generally assumed to range between 2 and 4,4,5 whereas for an aqueous solution is roughly 80. Table 1 shows that in the gas phase the exchange free energy is dominated by the enthalpy term and the T∆S term contributes
