Symbolic Methods for Biological Networks (SYMBIONT)

Abstract

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Description

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 in turn benchmarked against models from computational biology databases. Computational models in systems biology are built from molecular interaction networks and rate parameters resulting in large systems of differential equations. These networks are foundational for systems medicine. The currently prevailing numerical approaches shall be complemented with our novel algorithmic symbolic methods, which will address fundamental problems in this area. 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. The parametric uncertainty (with wide potential variations of parameters by several orders of magnitudes) leads to severe limitations of numerical approaches even for rather small and low dimensional models. Furthermore, extant model inference and analysis methods suffer from the curse of dimensionality that sets an upper limit of about ten variables to the tractable models. For those reasons, the formal deduction of principle properties of large and very large models has a very high relevance. The main goal of SYMBIONT is to combine symbolic methods with model reduction methods for the analysis of biological networks. We propose new methods for symbolic analysis, which overcome the above mentioned obstacles and therefore can be applied to large networks. 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 computational methods are diverse and involve various branches of mathematics such as tropical geometry, real algebraic geometry, theories of singular perturbations, invariant manifolds and symmetries of differential systems. The foundations and validity of our methods will be carefully secured by mathematical investigation. Corresponding computer algebra problems are NP-hard, but experiments point at their feasibility for biological networks. We have already shown that complexity parameters such as tree-width or number of distinct metastable regimes grow only slowly with size for models available in existing biological databases. We will exploit this observation 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. The methods developed in this project will be benchmarked against existing biological models and also against more challenging models, closer to the needs of systems and precision medicine that will be generated using biological pathways databases.

 


Publications

 
 
Satya Samal, Jeyashree Krishnan, Christoph Lüders, Andreas Schuppert, Andreas Weber, and Ovidiu Radulescu
International Conference on Systems Biology of Human Disease (SBHD), Heidelberg. Poster, 2017
 
 
Matthew England, Hassan Errami, Dima Grigoriev, Ovidiu Radulescu, and Andreas Weber
In proceedings of Computer Algebra in Scientific Computing - 19th International Workshop (CASC 2017), Beijing, China, Springer, Sept. 2017
 
 
Russell Bradford, James Davenport, Matthew England, Hassan Errami, Vladimir P. Gerdt, Dima Grigoriev, Charles Hoyt, Marek Kosta, Ovidiu Radulescu, Thomas Sturm, and Andreas Weber
In proceedings of Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation (ISSAC '17), Kaiserslautern, Germany, pages 45-52, ACM, July 2017
 
 
Satya Samal, Aurélien Naldi, Dima Grigoriev, Andreas Weber, Nathalie Thèret, and Ovidiu Radulescu
In: Biosystems (July 2016)
 
 
Dima Grigoriev, Satya Samal, Sergey Vakulenko, and Andreas Weber
In: Mathematical Modelling of Natural Phenomena (2015), 10:5(100-118)
 
Hassan Errami, Markus Eiswirth, Dima Grigoriev, Werner M. Seiler, Thomas Sturm, and Andreas Weber
In: Journal of Computational Physics (2015), 291(279-302)
 
 
Olivier F. Roux and Jérémie Bourdon (Editors)
Ovidiu Radulescu, Satya Samal, Aurélien Naldi, Dima Grigoriev, and Andreas Weber
In proceedings of Computational Methods in Systems Biology - 13th International Conference (CMSB 2015), Nantes, France, pages 104-120, Springer, 2015
 
 
Satya Samal, Dima Grigoriev, Holger Fröhlich, Andreas Weber, and Ovidiu Radulescu
In: Bulletin of Mathematical Biology (Dec. 2015), 77:12(2180-2211)
 
 
Satya Samal, Ovidiu Radulescu, Dima Grigoriev, Holger Fröhlich, and Andreas Weber
In proceedings of 9th European Conference on Mathematical and Theoretical Biology, 2014
 
 
Francois Boulier, Anne J. Shiu, Thomas Sturm, and Andreas Weber
In: Dagstuhl Reports; Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik (2013), 2:11
 
Hassan Errami, Markus Eiswirth, Dima Grigoriev, W. M. Seiler, Thomas Sturm, and Andreas Weber
In proceedings of Computer Algebra in Scientific Computing - 15th International Workshop (CASC 2013), Berlin, Germany, Springer, Sept. 2013