Abstract
The present work is divided into two parts:
The first part presents the folding of peptides using a Monte Carlo
method for the long-term dynamics of proteins.
The second part contains studies of the titration and redox behavior
of the bacterial photosynthetic reaction center and of myoglobin.
By combining both parts, I suggest a new method to calculate titration
behavior taking into account full conformational flexibility.
The Knapp group has been working on a Monte Carlo
method for the long-term dynamics of proteins for a long time.
I improved this method for the first part of this work.
After that, it was possible to fold not only a model peptide to a
helix-turn-helix motif, as already done before, but also to simulate
the folding of a ß-hairpin.
However, so far these calculations all lacked a solvent model.
Therefore, the Analytical Continuum Solvent model of Michael Schaefer
was integrated into our method.
Using this model, the formation and melting of a polyalanine helix
could be simulated in agreement with results from a molecular dynamics
simulation with an explicit solvent model.
Also, the folding of a fragment of ribonuclease A was successful, but
the folding of the ß-hairpin forming peptide BH8 failed.
This unveiled so far unknown problems of our protein model with
rigid peptide planes and special effective torsion potentials for the
backbone torsion angles.
The folding of BH8 was successful using a fully flexible protein
model.
However, using the flexible model the folding is much less efficient as
expected for the rigid model.
The calculation of protonation and redox states of titratable and
redox-active groups of proteins is done on the basis of continuum
electrostatics, similar to the solvent model used in the folding
simulation described above. In continuum electrostatics, the solvent
is represented by a medium of a high dielectric constant. By solving
the Poisson-Boltzmann equation numerically on a grid, the resulting
electrostatic potentials (and thus also the interaction energies) can
be calculated. In this way, the total electrostatic energy of a
specific protonation and redox state of a molecular system can be
determined. A protein contains usually a lot of titratable or
redox-active groups. For n of such groups, the total number of
possible states is extremely large (2n) so that the
calculation of thermodynamical averages, which are necessary to
determine titration curves and redox potentials, by exact summation is
computationally infeasible. Therefore, I apply in the present work a
Monte Carlo method where an importance sampling of the huge number of
possible states is performed according to the Metropolis criterion.
The method yields good results after relatively short sampling times.
The statistical error of these results can be probed by evaluating a
correlation function.
By applying these methods, I could gain a lot of valuable insights.
For the first time, the energy of the electron transfer from
QA.- to QB in the bacterial reaction
center was calculated correctly. The calculations also yield
important hints for the so far unsettled sequence of the following
electron transfer and protonation events involving the quinones of the
reaction center. In addition, the conformational gating hypothesis of
the electron transfer from QA.- to QB
could be supported from the viewpoint of theory, and the insight into
the related processes was deepened. I present in this work several
approaches to include conformational ensembles and conformational
flexibility in the calculation of titration behavior. By explicit
consideration of conformational relaxation, the dielectric constant of
the protein interior could be decreased remarkably in accordance with
fundamental principles. By including an ensemble of x-ray structures,
the pH induced conformational changes of myoglobin could be
reproduced. The pKa values calculated in this
study are in better agreement with experimental values than any other
result obtained by non-trivial methods before.
In the concluding outlook, I discuss the future improvements of the
Monte Carlo method for the long-term dynamics of proteins, and the
assets and drawbacks of existing methods to calculate titration
behavior considering conformational flexibility.
I show how to avoid most of the drawbacks by a new method on the basis of a
combination of the Monte Carlo dynamics with the titration
calculation.
This method realizes the unrestricted and unbiased sampling of the
conformational space and the space of titration states at the same time. |
