Eliminating Imaginary Vibrational Frequencies in Quantum-Chemical Cluster Models of Enzymatic Active Sites

In constructing finite models of enzyme active sites for quantum-chemical calculations, atoms at the periphery of the model must be constrained to prevent unphysical rearrangements during geometry relaxation. A simple fixed-atom or "coordinate-lock" approach is commonly employed but leads to undesirable artifacts in the form of small imaginary frequencies. These preclude evaluation of finite-temperature free-energy corrections, limiting thermochemical calculations to enthalpies only. Full-dimensional vibrational frequency calculations are possible by replacing the fixed-atom constraints with harmonic confining potentials. Here, we compare that approach to an alternative strategy in which fixed-atom contributions to the Hessian are simply omitted. While the latter strategy does eliminate imaginary frequencies, it tends to underestimate both the zero-point energy and the vibrational entropy while introducing artificial rigidity. Harmonic confining potentials eliminate imaginary frequencies and provide a flexible means to construct active-site models that can be used in unconstrained geometry relaxations, affording better convergence of reaction energies and barrier heights with respect to the model size, as compared to models with fixed-atom constraints.

The Glycine N-Methyltransferase Case Study: Another Challenge for QM-Cluster Models?

The methyl transfer reaction between SAM and glycine catalyzed by glycine N-methyltransferase (GNMT) was examined using QM-cluster models generated by Residue Interaction Network ResidUe Selector (RINRUS). RINRUS is a Python-based tool that can build QM-cluster models with rules-based processing of the active site residue interaction network. This way of enzyme model-building allows quantitative analysis of residue and fragment contributions to kinetic and thermodynamic properties of the enzyme. Many residue fragments are important for the GNMT catalytic reaction, such as Gly137, Asn138, and Arg175, which interact with the glycine substrate, and Trp30, Asp85, and Tyr242, which interact with the SAM cofactor. Our study shows that active site fragments that interact with the glycine substrate and the SAM cofactor must both be included in the QM-cluster models. Even though the proposed mechanism is a simple one-step reaction, GNMT may be a rather challenging case study for QM-cluster models because convergence in energetics requires models with >350 atoms. "Maximal" QM-cluster models built with either qualitative contact count ranking or quantitative interaction energies from functional group symmetry adapted perturbation theory provide acceptable results. Hence, important residue fragments that contribute to the energetics of the methyl-transfer reaction in GNMT are correctly identified in the RIN. Observations from this work suggest new directions to better establish an effective approach for constructing atomic-level enzyme models.

Evaluating the active site-substrate interplay between x-ray crystal structure and molecular dynamics in chorismate mutase

Designing realistic quantum mechanical (QM) models of enzymes is dependent on reliably discerning and modeling residues, solvents, and cofactors important in crafting the active site microenvironment. Interatomic van der Waals contacts have previously demonstrated usefulness toward designing QM-models, but their measured values (and subsequent residue importance rankings) are expected to be influenceable by subtle changes in protein structure. Using chorismate mutase as a case study, this work examines the differences in ligand-residue interatomic contacts between an x-ray crystal structure and structures from a molecular dynamics simulation. Select structures are further analyzed using symmetry adapted perturbation theory to compute ab initio ligand-residue interaction energies. The findings of this study show that ligand-residue interatomic contacts measured for an x-ray crystal structure are not predictive of active site contacts from a sampling of molecular dynamics frames. In addition, the variability in interatomic contacts among structures is not correlated with variability in interaction energies. However, the results spotlight using interaction energies to characterize and rank residue importance in future computational enzymology workflows.

A Case Study of the Glycoside Hydrolase Enzyme Mechanism Using an Automated QM-Cluster Model Building Toolkit

Glycoside hydrolase enzymes are important for hydrolyzing the β-1,4 glycosidic bond in polysaccharides for deconstruction of carbohydrates. The two-step retaining reaction mechanism of Glycoside Hydrolase Family 7 (GH7) was explored with different sized QM-cluster models built by the Residue Interaction Network ResidUe Selector (RINRUS) software using both the wild-type protein and its E217Q mutant. The first step is the glycosylation, in which the acidic residue 217 donates a proton to the glycosidic oxygen leading to bond cleavage. In the subsequent deglycosylation step, one water molecule migrates into the active site and attacks the anomeric carbon. Residue interaction-based QM-cluster models lead to reliable structural and energetic results for proposed glycoside hydrolase mechanisms. The free energies of activation for glycosylation in the largest QM-cluster models were predicted to be 19.5 and 31.4 kcal mol⁻¹ for the wild-type protein and its E217Q mutant, which agree with experimental trends that mutation of the acidic residue Glu217 to Gln will slow down the reaction; and are higher in free energy than the deglycosylation transition states (13.8 and 25.5 kcal mol⁻¹ for the wild-type protein and its mutant, respectively). For the mutated protein, glycosylation led to a low-energy product. This thermodynamic sink may correspond to the intermediate state which was isolated in the X-ray crystal structure. Hence, the glycosylation is validated to be the rate-limiting step in both the wild-type and mutated enzyme.

QM-Cluster Model Study of the Guaiacol Hydrogen Atom Transfer and Oxygen Rebound with Cytochrome P450 Enzyme GcoA

The key step of the O-demethylation of guaiacol by GcoA of the cytochrome P450-reductase pair was studied with DFT using two 10-residue and three 15-residue QM-cluster models. For each model, two reaction pathways were examined, beginning with a different guaiacol orientation. Based on this study, His354, Phe349, Glu249, and Pro250 residues were found to be important for keeping the heme in a planar geometry throughout the reaction. Val241 and Gly245 residues were needed in the QM-cluster models to provide the hydrophobic pocket for an appropriate guaiacol pose in the reaction. The aromatic triad Phe75, Phe169, and Phe395 may be necessary to facilitate guaiacol migrating into the enzyme active site, but it does not qualitatively affect kinetics and thermodynamics of the proposed mechanism. All QM-cluster models created by RINRUS agree very well with previous experimental work. This study provides details for better understanding enzymatic O-demethylation of lignins to form catechol derivatives by GcoA.

Acylation and deacylation mechanism and kinetics of penicillin G reaction with Streptomyces R61 DD-peptidase

Two quantum mechanical (QM)-cluster models are built for studying the acylation and deacylation mechanism and kinetics of Streptomyces R61 DD-peptidase with the penicillin G at atomic level detail. DD-peptidases are bacterial enzymes involved in the cross-linking of peptidoglycan to form the cell wall, necessary for bacterial survival. The cross-linking can be inhibited by antibiotic beta-lactam derivatives through acylation, preventing the acyl-enzyme complex from undergoing further deacylation. The deacylation step was predicted to be rate-limiting. Transition state and intermediate structures are found using density functional theory in this study, and thermodynamic and kinetic properties of the proposed mechanism are evaluated. The acyl-enzyme complex is found lying in a deep thermodynamic sink, and deacylation is indeed the severely rate-limiting step, leading to suicide inhibition of the peptidoglycan cross-linking. The usage of QM-cluster models is a promising technique to understand, improve, and design antibiotics to disrupt function of the Streptomyces R61 DD-peptidase.