Methanethiol Binding Strengths and Deprotonation Energies in Zn(II)-Imidazole Complexes from M05-2X and MP2 Theories: Coordination Number and Geometry Influences Relevant to Zinc Enzymes

Abstract

Zn(II) is used in nature as a biocatalyst in hundreds of enzymes, and the structure and dynamics of its catalytic activity are subjects of considerable interest. Many of the Zn(II)-based enzymes are classified as hydrolytic enzymes, in which the Lewis acidic Zn(II) center facilitates proton transfer(s) to a Lewis base, from proton donors such as water or thiol. This report presents the results of a quantum computational study quantifying the dynamic relationship between the zinc coordination number (CN), its coordination geometry, and the thermodynamic driving force behind these proton transfers originating from a charge-neutral methylthiol ligand. Specifically, density functional theory (DFT) and second-order perturbation theory (MP2) calculations have been performed on a series of [(imidazole)nZn-S(H)CH3](2+) and [(imidazole)nZn-SCH3](+) complexes with the CN varied from 1 to 6, n = 0-5. As the number of imidazole ligands coordinated to zinc increases, the S-H proton dissociation energy also increases, (i.e., -S(H)CH3 becomes less acidic), and the Zn-S bond energy decreases. Furthermore, at a constant CN, the S-H proton dissociation energy decreases as the S-Zn-(ImH)n angles increase about their equilibrium position. The zinc-coordinated thiol can become more or less acidic depending upon the position of the coordinated imidazole ligands. The bonding and thermodynamic relationships discussed may apply to larger systems that utilize the [(His)3Zn(II)-L] complex as the catalytic site, including carbonic anhydrase, carboxypeptidase, β-lactamase, the tumor necrosis factor-α-converting enzyme, and the matrix metalloproteinases.

Figure 1

First coordination spheres of the catalytic zinc centers of three MMPs. Coordinates taken from published X-ray crystal structures; color scheme is CPK. TBP: trigonal bipyramidal, MMP-3, chelated by synthetic hydroxamic acid based inhibitor (PDB code: 1BIW.) SQP: square pyramidal, MMP-1, chelated by synthetic hydroxamic acid based inhibitor (PDB code: 1HFC.) Tet.: tetrahedral, cysteine thiolate from the pro domain of proMMP-3 (PDB code: 1SLM.)

Figure 2

Geometry optimized structures for the [(ImH)_nZn–S(H)CH₃]²⁺ complexes on the left and their deprotonated [(ImH)_nZn–SCH₃]⁺ counterparts on the right, n = 1 through 5 from top to bottom. Selected parameters (in Angstroms) listed at the M05-2X/cc-pVTZ level of theory.

Figure 3

Constrained geometry optimized structures for [(ImH)₂Zn–S(H)CH₃]²⁺ and [(ImH)₃Zn–S(H)CH₃]²⁺ on the left and the deprotonated [(ImH)₂Zn–SCH₃]⁺ and [(ImH)₃Zn–SCH₃]⁺ complexes on the right, at S–Zn–(ImH)_n angles of 95° (1^st and 3^rd set) and 125° (2^nd and 4^th set). Selected bonding parameters (in Angstroms) at the M05-2X/cc-pVDZ level of theory.

Figure 4

Proton dissociation energy (kJ/mol) plotted versus the S–Zn–(ImH)_n angle for [(ImH)₃Zn–S(H)CH₃]²⁺, top square data, and [(ImH)₂Zn–S(H)CH₃]²⁺, bottom triangle data. Proton dissociation energies calculated at the M05-2X/cc-pVDZ level of theory. This figure represents the energy difference between the geometry-optimized deprotonated and geometry-optimized protonated complexes, with the only constraint being ∠SZn(ImH)_2,3.

Figure 5

Relative energy versus S–Zn–N₃ angle for [(ImH)₃Zn–S(H)CH₃]²⁺, (red solid diamonds) and [(ImH)₃Zn–SCH₃]⁺, (blue square dashes) systems. Energies are with respect to the fully optimized geometries at the M05-2X/cc-pVDZ level of theory. Also shown is the difference in relative energies (magenta triangles = blue squares – red diamonds), RE([(ImH)₃Zn–SCH₃]⁺) – RE([(ImH)₃Zn–S(H)CH₃]²⁺). Points are connected by straight lines for ease of viewing. For clarity, 80° and 85° points missing from thiolate plot.

Figure 6

Plots of Zn–S, (triangles) and S–H, (squares) bond lengths as a function of the S–Zn–(ImH)_n angles, ∠SZnN_2,3 for [(ImH)₂Zn–S(H)CH₃]²⁺, open points, and [(ImH)₃Zn–S(H)CH₃]²⁺, solid points.

Figure 7

Plots of Partial Charges (atomic units) on S (squares) and H (circles) as a function of the S–Zn–(ImH)_2,3 angles, ∠SZnN_2,3, for [(ImH)₂Zn–S(H)CH₃]²⁺, open red data points, and [(ImH)₃Zn–S(H)CH₃]²⁺, solid blue data points.

Scheme 1

Depiction of the first coordination sphere of the catalytic zinc center of A) inactive proMMP, B) activated MMP, and C) inhibited MMP.