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Projekt Druckansicht

Symbolische Methoden für biologische Netzwerke

Fachliche Zuordnung Mathematik
Bioinformatik und Theoretische Biologie
Datenmanagement, datenintensive Systeme, Informatik-Methoden in der Wirtschaftsinformatik
Statistische Physik, Nichtlineare Dynamik, Komplexe Systeme, Weiche und fluide Materie, Biologische Physik
Theoretische Informatik
Förderung Förderung von 2018 bis 2022
Projektkennung Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 391322026
 
Erstellungsjahr 2022

Zusammenfassung der Projektergebnisse

SYMBIONT is an interdisciplinary project ranging from mathematics via computer science to systems biology and systems medicine. The project has a clear focus on fundamental research on mathematical methods, and prototypes in software, which is benchmarked against models from computational biology databases. In systems biology, computational models are built from molecular interaction networks and rate parameters resulting in large systems of differential equations. These networks are foundational for systems medicine. One important problem is that statistical estimation of model parameters is computationally expensive and many parameters are not identifiable from experimental data. In addition, there is typically a considerable uncertainty about the exact form of the mathematical model itself, responsible to the introduction of parameters with wide potential variations of by several orders of magnitudes. This in turn causes severe limitations of numerical approaches even for rather small and low dimensional models. Furthermore, existant model inference and analysis methods suffer from the curse of dimensionality that sets an upper limit of about ten variables to the tractable models. Hence the formal deduction of principal qualitative properties of large and very large models is highly relevant. Symbolic methods. In order to cope more effectively with the parameter uncertainty problem we impose an entirely new paradigm replacing thinking about single instances with thinking about orders of magnitude. Our symbolic computational methods are diverse and involve various branches of mathematics such as automated reasoning, tropical geometry, real algebraic geometry, theories of singular perturbations, invariant manifolds and symmetries of differential systems. The validity of our methods is established on within rigorous mathematical frameworks. Although, we are frequently dealing with NP-hard problems, which would be categorized as “infeasible” in theoretical computer science, we achieve feasibility in the special case of biological networks. For instance, we observe that natural complexity parameters such as tree-width or number of distinct metastable regimes grow only slowly with size for models in biological databases. This allows to combine symbolic methods with model reduction methods for the analysis of biological networks in order to solve challenging problems in network analysis including determination of parameter regions for the existence and stability of attractors, model reduction, and characterization of qualitative dynamics of nonlinear networks. Major results of the project. We have obtained a geometric understanding the steady states of reaction kinetics, even in the presence of parametric reaction rates. We furthermore have developed an algorithmic framework for reducing reaction kinetics to multiple time scales, with a solid foundation in Analysis.

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