On the Effect of Varying Constraints in the Quantum Mechanics Only Modeling of Enzymatic Reactions: The Case of Acetylene Hydratase

Abstract

Quantum mechanics only (QM-only) studies of enzymatic reactions employ a coordinate-locking scheme, in which certain key atoms at the periphery of the chosen cluster model are fixed to their crystal structure positions. We report a case study on acetylene hydratase to assess the uncertainties introduced by this scheme. Random displacements of 0.1, 0.15, and 0.2 Å were applied at the ten terminal atoms fixed in the chosen 116-atom cluster model to generate sets of ten distorted structures for each given displacement. The relevant stationary points were reoptimized under these modified constraints to determine the variations of the computed energies and geometries induced by the displacements of the fixed atoms. Displacements of 0.1 Å cause a relatively minor perturbation that can be accommodated during geometry optimization, resulting in rather small changes in key bond distances and relative energies (typically of the order of 0.01 Å and 1 kcal/mol), whereas displacements of 0.2 Å lead to larger fluctuations (typically twice as high) and may sometimes even cause convergence to different local minima during geometry optimization. A literature survey indicates that protein crystal structures with a resolution higher than 2.0 Å are normally associated with a coordinate error of less than 0.1 Å for the backbone atoms. Judging from the present results for acetylene hydratase, such uncertainties seem tolerable in the design of QM-only models with more than 100 atoms, which are flexible enough to adapt during geometry optimization and thus keep the associate uncertainties in the computed energies and bond distances at tolerable levels (around 1 kcal/mol and 0.01 Å, respectively). On the other hand, crystal structures with significantly lower resolution should be used with great caution when setting up QM-only models because the resulting uncertainties in the computational results may become larger than acceptable. The present conclusions are mostly based on systematic DFT­(B3LYP) calculations with a medium-size basis set. Test calculations on selected structures confirm that similar results are obtained for larger basis sets, different functionals (ωB97X, BMK, M06), and upon including solvation and zero-point corrections, even though the fluctuations in the computed relative energies become somewhat larger in some cases