Systems biology is a new area of biology that studies how the various components of a biological system (genes, RNA, proteins) interact in order to perform complex biological functions. Given that biological information is typically incomplete, the idea of constraint-based modeling is to describe a biological system by a set of constraints, which characterize its possible behaviors, but in general do not allow to make a precise prediction. The classical starting point of constraint-based modeling is flux balance analysis of metabolic networks at steady state. Mathematically speaking, this involves computing a basis of the underlying polyhedral cone. Existing methods focus on pointed cones, and the metabolic networks have to be reconfigured in order to obtain this property. Within the project, we are currently developing a new method, which works on non-pointed cones, and which allows us to characterize the possible behaviors of a metabolic network in a much more compact way. While existing mathematical models in systems biology often concern metabolic networks, these cover only a small part of the activities of a cell. Equally important are signal transduction and gene regulatory networks, which have been studied much less. New mathematical approaches, based on a higher level of abstraction, seem necessary to handle these biological processes. Since quantitative biochemical information is often not available, qualitative modeling techniques like the discrete logical networks of R. Thomas become increasingly important. Within the project, we are studying different mathematical and computational problems related to the reconstruction and analysis of such networks, with special emphasis on incorporating time delays into the logical analysis of regulatory networks.

Publications

Siebert, Heike: Analysis of discrete bioregulatory networks using symbolic steady states. Bull. Math. Biol., 73 (4): 873-898, 2011.

Larhlimi, Abdelhalim and Bockmayr, Alexander:  A new constraint-based description of the steady-state flux cone of metabolic networks. Discrete Applied Mathematics, 157, 2257-2266, 2009.

Siebert, Heike: Dynamical and structural modularity of discrete regulatory networks. Computational Models for Cell Processes, CompMod 2009, Eindhoven, Netherlands, volume 6 of EPTCS, pages 109-124, 2009.

Larhlimi, Abdelhalim: New Concepts and Tools in Constraint-based Analysis of Metabolic Networks, 2008.

Larhlimi, Abdelhalim and Bockmayr, Alexander: On Inner and Outer Descriptions of the Steady-State Flux Cone of a Metabolic Network. Computational Methods in Systems Biology, CMSB 2008, Rostock. Springer, LNBI 5307, 308-327, 2008.

Siebert, Heike and Bockmayr, Alexander: Temporal Constraints in the Logical Analysis of Regulatory Networks. Theoretical Computer Science, 391/3, 258-275, 2008.

Siebert, Heike: Local Structure and Behavior of Boolean Bioregulatory Networks. Algebraic Biology, AB 2008, Castle of Hagenberg, Austria, volume 5147 of LNCS, pages 185-199, Springer, 2008.

Siebert, Heike:  Deriving behavior of Boolean bioregulatory networks from subnetwork dynamics. Math. Comput. Sci., 2(3):421-442, 2009.

Larhlimi, Abdelhalim and Bockmayr, Alexander: Constraint-based Analysis of Gene Deletion in a Metabolic Network. Workshop on Constraint based Methods for Bioinformatics, WCB'07, Porto, 48-55, 2007.

Larhlimi, Abdelhalim and Bockmayr, Alexander: Minimal Direction Cuts in Metabolic Networks.Computational Life Sciences III, CompLife'07, Utrecht, October 2007. AIP Conference Proceedings, Vol. 940, 73-86, 2007.

Siebert, Heike and Bockmayr, Alexander: Context Sensitivity in Logical Modelling with Time Delays. Computational Methods in Systems Biology, CMSB 2007, Edinburgh. Springer, LNBI 4695, 64-79, 2007.

Siebert, Heike and Bockmayr, Alexander: Relating Attractors and Singular Steady States in the Logical Analysis of Bioregulatory Networks. Algebraic Biology, AB 2007, Hagenberg Austria. Springer, LNCS 4545, 36-50, 2007.

Siebert, Heike and Bockmayr, Alexander: Incorporating Time Delays into the Logical Analysis of Gene Regulatory Networks. Computational Methods in Systems Biology, CMSB 2006, Trento, Italy. Springer, LNBI 4210, 169-183, 2006.

Larhlimi, Abdelhalim and Bockmayr, Alexander: A New Approach to Flux Coupling Analysis of Metabolic Networks.Computational Life Sciences II, CompLife'06, Cambridge, UK. Springer LNBI 4216, 205-215, 2006.

Larhlimi, Abdelhalim and Bockmayr, Alexander: Minimal Metabolic Behaviors and the Reversible Metabolic Space. Matheon Preprint Nr. 299, December 2005.