My main research interests lie in the development and application
of theoretical methods that aid in the understanding of biomolecular function.
I believe that such methods can make a great contribution
to our understanding of bioenergetic systems.
On the application side,
I'm particularly interested in the complex machinery of the
energy transducing protein complexes that supply living organisms
with energy.

The complexity of these systems makes it very difficult or impossible
to study mechanistically important aspects of their function with experimental methods.
Consequently, the mechanistic details of these bioenergetic complexes are
not yet well understood.
Theoretical methods and in particular structure based calculations can help
to gain a better understanding of these systems by supplementing and sometimes
guiding experiment.
These methods make it possible to study even such large and complex systems like
the mitochondrial cytochrome *bc*\(_{1}\) complex or the photosynthetic
reaction centers of plants and bacteria at atomic detail.

Effective use of these methods to harness the full potential of modern supercomputers
is an additional objective that is made more complex by the diversity and
heterogeneous architecture of these systems.
Here, diversity means that recent supercomputers use different CPU architectures
and a growing variety of computing accelerators like
general purpose graphics processing units of
NVIDIA
and
AMD
or the
Intel coprocessors based on their
MIC architecture.
Heterogeneneous architecture means that these supercomputers can combine
different CPU and accelerator types.
The task of using all available computing units in a single software
often requires the combination of different programming models as
further complication.
Currently, I'm learning to master these difficulties.

I believe that theoretical methods can make a great contribution to our understanding of bioenergetic systems. Molecular simulations based on physical models and structural information from experiment have become increasingly successful in providing insight into molecular function at a detail level that is often not directly accessible to experimental methods.

Therefore, I have a strong interest in the development and application of such methods for studying the function of bioenergetic systems. The ultimate aim of such work would be to understand not only the mechanism of these fascinating molecular machines but also the design principles behind them. As a vision for the future, one could hope that such true understanding of these complex systems can ultimately be used to overcome mere imitation of biological systems by creating something new, ideally something that is tailored to human needs. In the course of my PhD project, I could already make some small steps in this direction.

During the work for my PhD thesis in the group of
Prof. G. Matthias Ullmann,
I could gain experience with a variety of different theoretical methods
and help to improve them.
The group focuses on structure based calculations using
continuum electrostatics/ molecular mechanics models
augmented with a quantum mechanical treatment of regions of special interest.

My current work
also comprises the porting and adaption of many of the previous
developments to more complex and computationally more expensive
fully atomistic molecular mechanics models.
Instead discrete states sampled by Metropolis Mont Carlo,
the Molecular Dynamics adaption will employ \(\lambda\)-dynamics
to allow smooth interconversion between the different chemical
forms of a site.
Smooth interconversion is needed in the densely packed environment
modeled by molecular dynamics with explicit solvent, because
otherwise abrupt changes of the charge distribution or even overlaps
of appearing or disapperaring atoms with the solvent would lead to
frequent crashes of the simulation due to the appearance of excessively
large forces leading to particles accelerated extremely and shooting
through the simulation system.
Another challenge lies in modeling not only two chemical forms of a
titratable site but any number \(n\), which is not as easy as with
discrete states.
Additional methods
like the fast multipole method (FMM)
and λ-dynamics are beeing adapted and improved
to aid in this objective.

The following paragraphs of this page summarize my previous publications.

Despite the conceptual simplicity of representing a molecule and its surroundings by different dielectric continua, continuum electrostatics can give a very accurate quantitative description of biomolecular energetics. The complexity of the continuum electrostatics model system is greatly reduced relative to an all-atom treatment of molecular flexibility. For most systems of biological interest, the model system is still too complex for an analytical calculation of thermodynamic or kinetic properties. Simulation methods can be used in these cases to calculate properties of interest. Monte Carlo (MC) simulation methods are often especially efficient. The efficiency of the MC methods in combination with the continuum electrostatics model makes it possible to study even such large systems as the bioenergetic complexes.

I wrote the program GCEM which uses a continuum electrostatics / molecular mechanics model to compute energy matrices which are used by our MC simulation suite GMCT . I extended GMCT with different MC methods and free energy calculation techniques based on them. GMCT and the continuum electrostatics / molecular mechanics model of GCEM are described in →this paper. Application of the free energy perturbation (FEP) method to our models with their discrete microstates posed unexpected and interesting problems, which could be solved by our recent generalized FEP theory which is described in →this paper.

The mechanism of bioenergetic systems can involve a multitude of events as for example
ligand binding, proton transfer, electron transfer and conformational changes.
The thermodynamic coupling of such events provides the basis of the energy transducing
function of these systems.
The identity of the coupled events and of the corresponding mechanistically important
parts of the system is often far from obvious.
An especially interesting feature of
GMCT
in this respect is the possibility to calculate free energy measures of cooperativity
between events in a molecular system.
These cooperativity measures quantify the cooperativity in a thermodynamically meaningful way
and give an indication of possible mechanistic relations between parts of the the system.
A first application of the cooperativity measures to study
the coupling of protonation, reduction and conformational change
in *Pseudomonas aeruginosa* azurin is presented in
→this paper.

Transmembrane transport is at the heart of bioenergetics as
described by
Peter Mitchell's chemiosmotic theory
.
Sometimes, the transported substrate can adapt multiple protonation
(or other binding) forms.
The resulting coupling of the electrochemical potentials of
all species involved can lead to a complex dependence of the
transport thermodynamics on the system parameters
(pH value, permeant concentration, proton-motive force ...).
An example for such a case is the thermodynamics of permeation through
the ammonium/ammonia transporter Amt-1 from *Archaeoglobus fulgidus*.
In this system and its homologues, it is debated which protonation form
of the substrate is actually transported by which microscopic mechanism.
A second application of our free energy calculation methods
sheds some light on these questions, as described in
→this paper.
The formalism developed in this paper for the description
of binding equilibria of ligands with multiple binding forms
is of general utility.
Similar problems arise, for example, in the calculation of
binding free energies for drug molecules with multiple
protonation forms or tautomers.

Ultimately, the investigation of mechanistic questions requires simulation methods that
provide time information.
A master equation approach formulated in terms of transitions between discrete microstates
forms the theoretical basis of such simulation methods.
For systems with a limited number of microstates, one can employ analytical methods
to solve the resulting system of differential equations.
During my Diploma thesis, I was involved in a study that applied such methods to the
electron transfer through the tetraheme subunit of the bacterial reaction center
of *Blastochloris viridis* (presented in
→this paper).
We could demonstrate that a microstate description of the system in combination with
a continuum electrostatics model yields very good agreement of the calculated kinetics
with experimental data.

Kinetic MC methods allow the simulation of large systems modeled in terms of discrete microstates like our continuum electrostatics models and account for the inherent stochasticity of processes on a molecular scale. A problem that hampers the application of these methods to bioenergetic systems is that they become very inefficient if there are events that occur on very disparate time scales, like electron and proton transfer events. Coupled electron and proton transfer events are often of vital importance for the energy transducing function of bioenergetic systems. Thus, it would be very desirable to find a kinetic MC method which is able to simulate such systems efficiently without resorting to approximations that would impair the credibility of the simulation results.

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