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In this thesis, we apply the information-theoretic approach in the context of quantum dynamics and wave packet motion: Information-theoretic measures are calculated from position and momentum densities, which are obtained from time-dependent quantum wave functions. The aim of this thesis is to benchmark, analyze and interpret these quantities and relate their features to the wave packet dynamics. Firstly, this is done for the harmonic oscillator (HO) with and without static disorder. In the unperturbed HO, the analytical study of coherent and squeezed states reveals time-dependent entropy expressions related to the localization of the wave function. In the disordered HO, entropies from classical and quantum dynamics are compared for short and long times. In the quantum case, imprints of wave packet revivals are found in the entropy. Then, the energy dependence of the entropy for very long times is discussed. Secondly, this is donefor correlated electron-nuclear motion. Here, entropies derived from the total, electronic and nuclear density, respectively, are calculated in position and momentum space for weak and strong adiabatic electronic coupling. The correlation between electron and nucleus is investigated using different correlation measures, where some of these functions are sensitive to the nodal structure of the wave function. An analytic ansatz to interpret the information-theoretical quantities is applied as well.
Theoretical Investigations on the Interactions of Small Compounds with their Molecular Environments
(2015)
In the first part of this work, a combination of theoretical methods for the rational design of covalent inhibitor is presented. Starting from the crystal structure of the covalent complex of a lead compound, quantum mechanical and QM/MM calculations were used to derive the exact geometry of the preceeding non-covalent enzyme inhibitor complex. The geometry of the latter mainly determines the reactivity of the inhibitor against its target enzyme concerning the formation of the covalent bond towards an active site residue. Therefore, this geometry was used as starting point for the optimization of the substitution pattern of the inhibitor such as to increase its binding affinity without loosing its ability to covalently bind to the target protein. The optimization of the chemical structure was supported by using docking procedures, which are best suited to estimate binding affinities that arise from the introduced changes. A screening of the novel substitution patterns resulted in a first generation of model compounds which were further tested for their reactivity against the target. Dynamic simulations on the novel compounds revealed that the orientation that compounds adopt within the active site are such that a covalent interaction with the enzyme is no longer possible. Hence, the chemical structure was further modified, including not only changes in the substituents but also within the core of the molecule. Docking experiments have been conducted to assure sufficiently high binding affinities and to obtain the most favored binding poses. Those have then again been used for dynamic simulations which resulted in structures, for which the bond formation process appeared feasible. A final series of QM/MM calculations considering various protonation states was computed to estimate the reaction energies for the covalent attachment of the inhibitor to the enzyme. The theoretical results indicate a reasonable high inhibition potency of the novel compounds.
The second part concentrates on the environmental influences on the electron density of an inhibitor molecule. Therefore, a vinylsulfone-based model compound was selected for which an experimental crystal structure for the pure compound as well as a theoretically determined enzyme-inhibitor complex have been available. To provide reference data for the larger systems, the conformational space of the isolated molecule was screened for favorable geometries which were later compared to those within the crystal and protein surrounding. The geometry of the crystal structure could readily be taken from the experimental data whereas calculations on the protein complex revealed four potential non-covalent complexes exhibiting different arrangements of the molecule within the active site of the protein as well as two possible protonation states of the catalytic dyad. Hence, all four protein complexes have been compared to the crystal structure of the molecule as well as against the more favorable geometries of the isolated molecule being determined within vacuum or aqueous surrounding. Whereas the molecule itself was found to adopt comparable geometries within all investigated environments, the interactions pattern between the crystal surrounding and the protein differed largely from each other. The favorable formation of dimers within the crystal has a strong stabilizing effect and explains the extraordinarily good quality of the crystal. Within the protein however, repulsive forces have been found between the protein and the inhibitor. The origin of the repulsion could be traced back to effect of on of the substituents to the vinyl scaffold. The difference in the chemical structure in comparison to a well known inhibitor might also explain the experimentally found loss of activity for the model compound in comparison to K11777.