Abstract
In present work, the electrostatic
interactions governing the electron transfer (ET) processes in several
proteins with redox-active cofactors were investigated theoretically. For
these purposes, several methods were combined and applied to elucidate
the function of a number of protein systems. Our attention was focused
on calculating the energetics of the protonation and oxidation processes
in redox-active proteins. The coupling between electron and proton transfer
reactions, which is of the electrostatic nature was studied by using a
continuum electrostatic method. The pH dependence of the redox potentials
in proteins (the so-called redox-Bohr effect) was investigated using the
available methods. The heme-proteins that have axially coordinated histidines
to the heme iron, as for instance the mitochondrial cytochrome bc1
(Cbc1) protein complex involved in the
respiratory electron transport chain and the artificial cytochrome b (Cb)
were studied. The protonation and redox behavior of several other cofactors
and redox-active residues in DNA photolyase were also investigated. The
results of the theoretical work presented here, are divided into three
mutually related parts.
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.
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