In our research we focus on modeling and analyzing biological regulatory networks in cooperation with scientists from the life sciences, meeting the mathematical challenges posed by such applications. Of particular importance for us is to provide modeling and analysis methods respecting the constraints imposed by the available data. Data quality and uncertainties must be carefully taken into account to construct valid models. A major aim of model analysis in turn is to pinpoint ambiguities and generate hypotheses exploitable for experimental design. Combining different theoretical approaches for data analysis and modeling allows to bundle their distinct strengths and to process the available information in a systematic and holistic fashion. Developing such integrated methods is one of the central aims in our group.
As a starting point, we use logic-based models to represent the systems of interest to us. They are based on qualitative observations which are often more abundantly available than the quantitative data needed for constructing well-supported differential equation models. Analysis of such models can draw on a variety of mathematical methods, e.g., iteration and graph theory as well as methods from formal verification. This allows for comprehensive analysis of complex systems, often uncovering crucial structural and dynamical characteristics. It furthermore makes it possible to test large numbers of models for consistency with the available data, addressing the parameter identification problem and allowing to evaluate analysis results with respect to data uncertainty.
The computational strength of the logical formalism can also be exploited in tandem with more resolved modeling. Combining discrete, continuous and stochastic approaches yields methods tailored to optimally exploit the available data, to evaluate uncertainty and to uncover essential mechanisms of the system. Such integrated approaches are also promising for data analysis, where statistical methods can be combined with a network-based view to uncover the key players of system functionality.
We develop methods tailored to application in close cooperation with colleagues from the life sciences. In our current work, this includes oncogenic signaling networks, mammalian reproductive systems as well as bacterial infection mechanisms.
The following fields of research are of particular interest for our applications: