Group Mathematical Modelling of Cellular Processes
Complex diseases are often characterised by an accumulation of multiple perturbations in rather large and complex cellular networks. The consequences of these perturbations, such as mutations or over-expression of proteins, can hardly be analysed by pure reasoning. Here, mathematical modelling contributes to a deeper understanding of the regulatory systems and provides thus a better basis for the interpretation of high-throughput data and identification of effective drug targets.
Our group develops and analyses mathematical models of signalling pathways and gene-regulatory networks in normal and disease states. For our investigations we use tools such as simulations, bifurcation analyses and sensitivity analyses. These give insights into the dynamical properties of the systems and help to identify most sensitive processes and critical regulations. Another important aspect is the investigation of cell specific differences in signalling and gene-regulatory networks since these are critically involved in the prediction of the efficiency and possible side-effects of drugs.
So far we use qualitative and quantitative dynamic modelling depending on the available experimental data. In the next future we also plan to apply logical modelling approaches which allow the description of large interaction maps with only minor knowledge about kinetic data (collaboration with Steffen Klamt, Magdeburg).
In collaboration with the group of Claus Scheidereit (MDC, Berlin) we develop a mathematical model for the non-canonical NF-κB pathway to elucidate its dynamic properties and the interdependence of canonical and non-canonical signalling. In particular, we are interested in the regulation of the long-time behaviour of the NF-κB system and its malfunction in Hodgkin-lymphoma and cardiac hypertrophy and failure.
Wnt/ β-catenin signalling
A mathematical model of the Wnt/ β-catenin pathway is used to analyse the effect of a β-catenin mutations critically involved in hepatocellular carcinoma. In this collaborative project with Rolf Gebhardt (Leipzig) we are interested in the impact of the mutation on the dynamics of the signalling pathway and on down-stream gene expression. In addition, we investigate cell-type specific differences in Wnt-signalling by a combination of theoretical and experimental approaches in collaboration with Andreas Hecht (Freiburg).
EGFR mediated signal transduction
In this project, which was done in collaboration with GlaxoSmithKline, we address the question to what extent the effect of oncogenic mutations depend on the regulation structure of EGFR-mediated signalling. Such an understanding is critical since regulatory feedbacks seem to be used in a cell-type specific manner in that signalling network.
Simplified schemes show the regulation structure in two model versions of the EGF pathway (upper line), and steady state response of the pathway versions towards Ras mutations activating the rate to exchange GTP for GDP varying regulatory strength (lower line), taken from Wolf et al., 2007.