In the Morris water maze, a laboratory rat can avoid constant swimming in a circular shaped pool
by finding a small platform hidden under the water surface.
Visual clues placed outside the pool allow the rat to triangulate its position
and learn the location of the platform.
By tracking the rat's position over time different aspects of
spatial memory (e.g. working memory) and
non-spatial discrimination learning can be studied.

Study of learning and memory usually use only simple statistics such as
the time the rat needs until it finds the platforms (escape latencies)
or the time the rats spends in different areas of the pool.
Here we develop a dynamic model of the rats swimming behaviour
based on a random walk. Identification of the model revealed that rats use different feedback strategies depending on the availability of navigational cues. By implementing different search strategies
and/or learning protocols
describing mental representations of the rat's environment,
we can analyse those for their respective contribution to the
the rat's overall performance.
Trade offs between randomness and strategies/protocols during the
learning process can be revealed.

Systems biology is a vivid multidisciplinary field that investigates biology from a wholistic perspective, using both, wet-lab Experiments and mathematical models. Especially dynamic models rely critically on the values of their kinetic parameters, which usually cannot be measured directly. Thus their reliable and accurate estimation from experimental data is crucial.

In the past, there has been a gap between mathematically reliable and accurate parameter estimation methods, and those that find practical application. Mathematical correct estimation methods are often linear or restricted to a few special cases. Biological models however, are highly nonlinear and complex, which is why in practice heuristic methods are used, for which there is no guarantee of an accurate estimation.

My research proposes several methodologies significantly reducing the above mentioned gap. Exploiting the form of the nonlinearities that are most common in biology allows us to guarantee accuracy by mathematical proof.

One methodology uses semi-definite programming to reduce the parameter search space. The methodology is applicable to measurements of only a view time points that allow to calculate a derivative, whereby no apriori conditions (such as identifiability) are necessary. Such limited information is generally not enough to estimate the parameter values, however, the proposed methodology can prove entire parameter regions inconsistent with data and model.

Another methodology utilizes state space extensions and nonlinear observers (dynamic state estimators). In theory an accurate parameter estimation is guaranteed for most models of gene regulation, signal transduction, metabolic pathways. In practice, difficulties concern the number of variables that have to be measured, sparse sampling and measurement noise. Partly, these difficulties can be overcome by modularisation and data preprocessing. Further, the methodology is robust against modelling errors and even allows to reveal non-modelled interactions.

The fundamental process underlying all brain function is the ability of the neurons to adapt to external inputs in the context of the neuronal state. The adaptive processes span multiple spatial and temporal scales ranging from millisecond dynamics of the ion channels, seconds to minutes time scale of the signalling pathways, and tens of minutes to hours time scale of the gene regulation and its feedback onto the signalling pathways and electro-physiology.

With the focus on the immediate AT1 receptor signalling dynamics and the consequences on the firing behaviour, we used mathematical modelling and analysis to decipher how the signals are integrated in this complex multi-scale system.

*Work based at the Daniel Baugh Institute of functional genomics and computational biology at the Thomas Jefferson University in Philadelphia, **within the master thesis project of Engineering Cybernetics at the University Stuttgart.*

[1] | Rajanikanth
Vadigepalli, **Dirk Fey**, and James S. Schwaber.
Modeling neuronal adaptation in the brain: Integrating receptor signaling and electrophysiology.
In FOSBE, 2007.
(pdf 532kb) |

[2] | **Dirk Fey**, Rajanikanth Vadigepalli, Thomas Sauter, and James Schwaber.
Integration and anlalysis of ang ii induced neuronal plasticity by means of multi-scale modeling.
Master's thesis, Thomas Jefferson University (TJU) & University Stuttgart, Daniel Baugh Institute for functional genomics and computaional biology, TJU Philadelphia, October 2006.
(pdf 2335kb) |

In signal transduction, the formation of multi-protein complexes results in an unsuitable large models including a huge number of different species. For example, a transmembrane receptor is often subject of phosphorylation and multiple signalling protein assembly on several binding domains. Thereby the resulting number of species that are to include in the model (model dimension) increases exponentially with the number binding-sites and -proteins.

The model reduction method is based on a-priory knowledge on domain interactions, and reduces the model dimension dramatically (linear increase) in the case of independent domains. Extending this earlier approach, the application on a receptor dimerization revealed the systems inherent structure of its information flow.

*Work based at the Institute for System Dynamics (ISys) at the University Stuttgart.*