In first part, factors determining the orientations of imidazole axially coordinated to heme were investigated by analyzing 693 hemes in 432 crystal structures of heme-proteins from the Protein Data Bank (PDB). The results from the PDB data mining were interpreted by evaluating the corresponding relevant interactions with molecular force field computations.

An important contribution made with this doctoral work was the procedure to generate the atomic coordinates of the model structure of an artificial protein from scratch, by using a sophisticated modeling technique with stepwise energy relaxation. This quite new approach was applied on the de novo synthetic protein recently synthesized by Rau & Haehnel (1998), which mimics the central part of the four-helix bundle of the native cytochrome b. The stability of the computer generated structure was tested by monitoring the conformational changes and fluctuations during a long-term molecular dynamics simulation and by comparing the results with values obtained from the crystal structure of a native Cb. The results of the MD simulations suggest that the modeled structure is stable and strain free.

In third part, the protonation and oxidation probabilities of titratable groups were computed simultaneously by the continuum electrostatic method, solving the linearized Poisson-Boltzmann equation (LPBE) numerically on a grid with a subsequent Monte Carlo titration of all titratable groups in the protein. Quantum-chemical computations were carried out for each bis-imidazole-heme system yielding atomic partial charges that represent faithfully the electrostatic potentials of these redox-active groups in their neighborhood. The theoretical frame work applied here allows to calculate protonation and oxidation patterns of proteins as a function of pH and redox potential of the solution. The existent method was extended to perform the redox titration of a protein, by varying the solution potential and keeping the pH value constant. In this way, I obtained valuable insights about the function of redox centers in proteins.

The continuum electrostatic approach was applied on the artificial and native Cb to examine the titration behavior of ionizable residues, to evaluate the redox potential of the hemes and to study phenomena related to the Bohr effect. The factors that determine the redox potential of the two hemes in the artificial Cb were analyzed in terms of the influence of different structural parts, enabling us to understand how the protein environment tunes the redox potentials of cofactors. In order to investigate the energetics of the photoactivation process, and to determine the redox potential of different redox pairs (tryptophans, tyrosines, FAD) involved in electron and proton transfer reactions in the DNA photolyase from E. coli, the same approach was applied there. An empirical expression (based on the Marcus theory) was used to estimate the rates of ET reactions.

Good agreement between calculated and experimentally observed titration behavior and the reaction rates, suggests that the applied theoretical method captures most of the electrostatic behavior in these systems, even though it ignores conformational fluctuations and the differences in the average structures that may exist between crystal and solution. It also indicates that electrostatic interactions are the most relevant for these protein systems, while non-electrostatic interactions that are theoretically less easy accessible, play a minor role.