Einstein Center for Mathematics Berlin
Mathematical modeling in biological and medical applications is almost always faced with the problem of incomplete and often noisy data. Rather than adding unsupported assumptions to obtain a unique model, a different approach generates a pool of models in agreement with all available observations. Analysis and classification of such models allow linking the constraints imposed by the data to essential model characteristics and showcase different implementations of key mechanisms. The results are exploitable for experimental design, may uncover specificity due to cell lines, tissues or environmental conditions and can be utilized for designing control strategies under model uncertainty.
Approaches to tackle this problem have been developed for different modeling formalisms.
For discrete models such as boolean networks it is possible to generate model pools based on uncertainty both in the network topology and the logical parameters. Further analysis focuses on filtering the pool for models in agreement with available data, e.g., time series data, utilizing formal verification methods.
For ordinary differential equation models, clustering and Bayesian approaches allow one to evaluate the impact of data uncertainty.
Within the project, we aim at combining the advantages of logical and continuous modeling to arrive at a comprehensive system analysis under data uncertainty. Model classification will integrate qualitative aspects such as characteristics of the network topology with more quantitative information extracted from clustering of joint parameter distributions derived from Bayesian approaches. The theory development is accompanied by and tested in application to oncogenic signaling networks.
Prof. Dr. Heike Siebert, Freie Universität Berlin
Prof. Dr. Susanna Röblitz, Freie Universität Berlin