Selected Aspects of Enzymatic Catalytic Activity Studied by Theoretical Methods and Implementation of the Analytic Second Derivatives of Hartree-Fock and Hybrid Density Functional Energies

Abstract

This thesis deals with application of modern theoretical methods for studying enzymatic reactivity as well as with the efficient implementation of second analytical energy derivatives on the self-consistent field (SCF) theory level. The enzymatic mechanisms were investigated in the framework of electronic structure theory with special accent put on kinetics, proton-coupled electron transfer and theoretical support of EPR and Mössbauer experiments. <br /> In particular, cytochrome <em>c</em> nitrite reductase (C<em>c</em>NiR) enzyme mechanism was under consideration. The possible role of second-sphere active site amino acids as proton donors was investigated by taking different possible protonation states and geometrical conformations into account. It was found that the most probable proton donor is His₂₇₇, whose spatial orientation and fine-tuned acidity lead to energetically feasible, low-barrier protonation reactions. However, substrate protonation may also be accomplished by Arg₁₁₄. The activation barriers for the various proton and electron transfer steps were estimated in the framework of Marcus theory. <br /> The cd₁ nitrite reductase (NIR) enzyme was also investigated. NIR is a key enzyme in the denitrification process that reduces nitrite to nitric oxide (NO). There are three residues at the “distal” side of the active site heme (Tyr₁₀, His₃₂₇ and His₃₆₉) and in this work the focus was set on the identification and characterization of possible H-bonds they can form with the NO, thereby affecting the stability of the complex. It was shown that the NO in the nitrosyl d₁-heme complex of cd₁ NIR forms H-bonds with Tyr₁₀ and His₃₆₉ whereas the second conserved histidine, His₃₂₇, appears to be less involved in NO H-bonding. Moreover, it was shown that the H-bonding network within the active site is dynamic and that a change in the protonation state of one of the residues does affect the strength and position of the H-bonds formed by the others. <br /> The electronic structure of the [4Fe-3S] cluster in Hydrogenase I (Hase I) was considered. The cluster performs two redox transitions within a very small potential range, forming a super-oxidized state above +200 mV vs SHE. The field-dependent ⁵⁷Fe-Mössbauer and EPR data for Hase I is presented, which in conjunction with spectroscopically calibrated DFT calculations, reveal the distribution of Fe valences and spin-coupling schemes for the iron-sulfur clusters. <br /> The theory part of the thesis includes conventional implementation of SCF second derivatives into ORCA set of programs combined with efficient approximations. The second derivatives of electronic energy are the base for the calculation of force constants, harmonic vibration frequencies, infra red (IR) and Raman intensities. To speed up the evaluation of the hessian, in particular the two-electron integrals and their derivatives, the resolution of the identity (RI) and the Chain of Spheres (COS) approximations can be applied. As part of the present work, the RI and COS approximations are introduced at various stages of the molecular Hessian evaluation procedure, e.g., the reference energy calculation, various steps of the coupled-perturbed SCF procedure, and the final integral derivative evaluation. The performance of the approximations and possible errors introduced are discussed in details. The applicability of the Hessian program was also greatly extended by the additional functionality such as effective core potentials (ECP), Van der Waals corrected second derivatives and QM/MM hessian.