This project is a continuation of the VW project Evolution of networks: robustness, complexity and adaptability. It combines three aspects:

1. The investigation of biochemical networks, in particular metabolic ones, on the basis of known functional reactions and interactions.
2. The corresponding mathematical methods involving, in particular, hypergraphs, combinatorial vector fields and network dynamics.
3. The underlying conceptual issues, in particular around robustness.

To study the interplay between function, network evolution and structure we concentrate mainly on two promising paradigmatic model systems: metabolic networks, which are of particular interest because they are more general than graphs, and Boolean networks, which serve as abstract models of regulatory networks conveying a non-trivial dynamics on their nodes.

The project contains the following proposed work packages:

1. Intermediate-level models of chemical networks We investigate in which sense chemical reaction networks can be abstracted by combinatorial information such as graphs, hypergraphs, combinatorial vector fields or the like. We develop novel methods for the investigation of hypergraphs and their topological and geometric aspects.
2. Evolution of Metabolic Networks During the last years we developed a self-consistent model of chemical evolution and the interface between chemical networks of small molecules and the catalytic machinery of biopolymers. We use this simulation environment to conduct a series of systematic simulation studies. We investigate to what extent empirical findings in real world metabolic networks can be explained by the mechanisms in our model.
3. Evolution and dynamics of regulatory networks We study Boolean networks as a model for the regulation of metabolic networks. In particular we focus on the co-evolution of a metabolism with a Boolean regulatory network, we study the neutral graph of a given phenotype, and we investigate stability properties.
4. Interrelations of Complex Networks Metabolic networks do not exist in isolation. They are coupled in such a way that (some) nodes in a gene regulatory network (the enzymes) correspond to hyperedges (the catalysed reactions) in a metabolic network. We plan to extend results on relations between graphs using a relation-theoretic approach to the interrelationships of regulatory and metabolic networks.
5. Analyzing the structure of metabolic and Boolean networks We develop random graph and hypergraph models that are adapted to metabolic and regulatory networks and study their characteristic properties, such as their interaction complexity or motif counts.
6. System identification Understanding the interplay and function of a system’s components requires the study of the system’s response to controlled experimental perturbations. On the one hand, a biological system may not be resistant to all such perturbations, and the identity of the system may change under such perturbations. Furthermore, there are constraints dictated by the scientific and financial means at hand. In view of these limitations, one has to address the problem of specifying the kind of conclusions that can be drawn. We aim at generally specifying the class of networks that is compatible with observations. We expect our results to be applicable to biological data, in particular to metabolic and Boolean networks.
7. Robustness of functional networks A conceptual and mathematical basis for experimental perturbations is necessary not only for the design of experiments for system identification but also for the foundation of a theory of network robustness. We use an approach to robustness of a functional network against a knockouts that is based on conditional independence (CI) statements, building on the robustness theory proposed by Nihat Ay and David Krakauer. More information

People of
Bioinformatics group,
University of Leipzig:

Konstantin Klemm

Peter Stadler

People of MPI MIS:

Nihat Ay

Jürgen Jost

Eckehard Olbrich

Philipp-Jens Ostermeier

Johannes Rauh

Collaborations:

Jessica Flack

David Krakauer

Areejit Samal

Further Information:

Supported by the Volkswagen Stiftung

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