Quantum Mechanics/Molecular Mechanics Studies in Biological Systems

This thesis contains four projects in Quantum Mechanics/Molecular Mechanics (QM/MM) applications and methodology developments for biological systems. The first part (chapter 2 - chapter 3) is mainly focused on enzymatic reaction mechanism studies; the second part (chapter 4 - chapter 5) is to develop new methods to effectively calculate solvation free energy; the third part (chapter 6) is about methodology development to visualize non-covalent interaction in fluctuating biological environment; the fourth part (chapter 7) is to further apply QM/MM method on understanding proton coupled electron transfer reaction mechanism.

Catalytic mechanism is the key to understand how enzyme facilitates chemical reactions. A comprehensive understanding of the mechanism would shed light on developing new drug candidates or find similar protein targets. In the first two sections, we explored two enzyme systems, 4-oxalocrotonate tautomerase (4-OT) and anhydro-N-acetylmuramic acid kinase (AnmK). 4-OT is an essential enzyme in the degradative metabolism pathway occurring in the Krebs cycle. The proton transfer process catalyzed by 4-OT was studied to elaborate its catalytic mechanism. With QM/MM simulation, we demonstrated that the enzyme works under half-of-the-sites occupation, i.e. only three of its six active sites are occupied by the substrates. Two sequential proton transfers occur: one proton from the C3 position of 2o4hex is initially transferred to the nitrogen atom of the general base, Pro1. Subsequently, the same proton is shuttled back to the position C5 of 2o4hex to complete the proton transfer process in 4-OT. During the catalytic reaction, conformational changes (i.e., 1-carboxyl group rotation) of 2o4hex cannot proceed in the natural hexametric structure. We further found that the docking process of 2o4hex can influence the specific reactant conformations and an alternative substrate (2-hydroxymuconate) may serve as reactant under a different reaction mechanism than 2o4hex. The other enzyme, AnmK, plays an important role in the cell wall recycling process in Escherichia coli. The catalytic process involves four entangled steps: water nucleophile attack, 1, 6-anhydro bond breaking, phosphorylation, and saccharide conformational change. This is a great challenge to present enzymatic simulation methods. We proposed a comprehensive scheme to tackle this problem, and our results indicate a proton shuttle network may exist, which position a water molecule well for the nucleophile attack.

Solvation free energy strongly relates with the molecule solubility and is an important indicator to screen potential drug candidates. To improve the computational speed and simulation accuracy on evaluating solvation free energy, we developed a new approach to combine λ dynamics with metadynamics to compute free energy surface with respect to λ, we named it λ-metadynamics. Particularly, the λ-metadynamics method extends metadynamics to a single virtual variable λ, i.e., the coupling parameter between solute and solvent, to compute absolute solvation free energy as an exemplary application. We demonstrated that λ-metadynamics simulations can recover the potential of mean force surface with respect to λ compared to the benchmark results from traditional λ-dynamics with umbrella sampling. The solvation free energy results for five small organic molecules from λ-metadynamics simulations using the same filling scheme show that the statistical errors are within ±0.5 kcal/mol. Further, a detailed exploration over λ-metadynamics found out the intrinsic problems associated with metadynamics on high second derivative free energy surfaces. We introduced new techniques, such as transformation of virtual variable, region segmentation, mirror filling procedure and independent trajectory average, integrating with the original λ-metadynamics to improve its power. The revised λ-metadynamics is applied to investigate the solvation free energy of 20 molecular sets, and its result suggests a minimum QM basis set (3-21G) with point charge model perform better than more complex ones.

Non-covalent interaction is prevalent, such as hydrogen bond, van der Waals, steric clashes, and it plays a central role in many chemical and biological systems. Although the atomic distance may indicate strength of a specific interaction, a quantitative description is very difficult. We extended a recently introduced non-covalent interaction index (NCI) into its ensemble averaged counterpart, averaged non-covalent interaction index (aNCI). NCI is suitable for quantitatively characterize non-covalent interactions for any static system, while aNCI is capable to determine and visualize non-covalent interactions for fluctuating biological systems. We further applied aNCI on various systems including solute-solvent and ligand-protein non-covalent interactions. For water and benzene molecules in aqueous solution, solvation structures and the specific hydrogen bond patterns were visualized clearly. For the Cl-+CH3Cl SN2 reaction in aqueous solution, charge reorganization influences over solvation structure along SN2 reaction were revealed. For ligand-protein systems, aNCI can recover several key fluctuating hydrogen bond patterns that have potential applications for drug design. Therefore, aNCI, as a complementary approach to the original NCI method, can extract and visualize non-covalent interactions from thermal noise in fluctuating environments.

Proton-coupled electron transfer is a reaction mechanism involves simultaneous transfer of both proton(s) and electron(s). It is pervasive in redox reactions and has significant importance in photosynthesis, respiration, and electrochemical process such as hydrogen-ion discharge. We applied the fractional number of electron approach and QM/MM scheme to study the basic principle about how electron transfer (ET) and proton transfer (PT) coupled together. This approach was employed in the oxidation of an intra-molecular hydrogen bonded phenol (PhOH...N<), with two well-defined reactions coordinates (PT: proton position; ET: energy gap). The computed absolute redox potential agrees well with the experimental data. We found that at a low applied overpotential (< 5.0 eV), proton transfer occurs prior to electron, and this gives a stepwise proton-electron transfer pathway (PT-ET). With a high overpotential (> 7.0 eV), the reaction occurs in a reverse sequence with proton motion triggered by electron transfer (ET-PT). When the overpotential is between 5.0 and 7.0 eV, the reaction proceeds by concerted proton-electron transfer (CPET) mechanism. Our work suggests that the mechanistic details of PCET process can be changed by altering electrode potentials.