BioND — Dynamics of Biological Networks

Structural kinetic analysis of cell signaling and metabolism

At a rapidly increasing pace, the ongoing revolution in molecular biology is unveiling the genetic inventory of cells, the structure of proteins into which genes are translated, and the interactions between proteins, which regulate the fundamental processes of life. Thereby, the complex regulatory networks of interactions are mapped out, opening up the opportunity to gain a detailed understanding of their functioning and failure. However, function is generally linked closely to the dynamics, which is still difficult to observe in experiments. Extracting the dynamics of known or purported molecular networks is therefore an important challenge for theory.

Unlike in physics, where theory has in many areas outpaced experiments, the progress of biology is presently driven by an extremely rapid advance of experimental techniques. For the theoretician this means that the main focus cannot be on rigorous mathematical proofs, but rather on high-throughput modeling tools, allowing for the rapid integration of new biological insights.

For the rapid extraction of dynamical properties from the structure of a biological network under consideration, we have proposed the approach of generalized modeling (Gross et al. 2006) and a specific extension to biochemical models which is sometimes called structural-kinetic modeling (Steuer et al. 2009). Generalized modeling can reveal the parameter ranges in which stationary states are stable, uncover the dynamics that sets in once stability of stationary states has been lost, and identify interesting parameter regions where complex dynamics can be observed. For these tasks structural kinetic modeling is more efficient than conventional modeling, meaning both a reduction of manual work, which speeds up of the respective studies, and a decrease of computational load, which allows for the exploration of large parameter spaces by random sampling with millions or billions of sample parameter sets.

In the past we have applied generalized modeling to study system from a broad spectrum of fields including ecology, epidemiology, socio-economics, osteology, psychology, history, metabolism, signaling, and gene regulation. These studies have demonstrated that the proposed modeling approach can answer important actual questions in a wide range of applications. Recent examples of this work include investigation of the mitochondrial TCA-cycle (Steuer et al. 2007), an analysis of the dynamics of the mitogen-activated-protein signaling-cascade (Zumsande and Gross 2010) and ongoing work on the regulation of bone remodeling (Zumsande et al. 2010).

Generalized and structural kinetic modeling are particularly promising tools for the analysis of metabolic and cell signaling networks, as the need for such tools is well recognized in these areas. In particular generalized modeling is presently the only dynamical modeling approach that has a reasonable hope of being scalable to large-scale metabolic models.

Key Publications

Structural kinetic modeling of metabolic networks
Ralf Steuer, Thilo Gross, Joachim Selbig, and Bernd Blasius
Proceedings of the National Academy of Sciences 103(32), 11868-11873 , 2006.
(abstract) (supporting material) (link to publisher) (arXiv) (download preprint)

Additional Publications

General analysis of mathematical models for bone remodeling
Martin Zumsande, Dirk Stiefs, Stefan Siegmund, and Thilo Gross
Bone 48(4), 910-917, 2011.
(abstract) (link to publisher) (arXiv) (download preprint)

Bifurcations and chaos in the MAPK signaling cascade
Martin Zumsande and Thilo Gross
Journal of Theoretical Biology 265(3), 481-491, 2010.
(abstract) (link to publisher) (download preprint)

Computation and visualization of bifurcation surfaces
Dirk Stiefs, Thilo Gross, Ralf Steuer, and Ulrike Feudel
International Journal Bifurcation and Chaos 18(8), 2191-2206, 2008.
(abstract) (link to publisher) (download preprint)

From structure to dynamics of metabolic pathways: application to the plant mitochondrial TCA cycle
Ralf Steuer, Adriano Nunes Nesi, Alistair R. Fernie, Thilo Gross, Bernd Blasius, and Joachim Selbig
Bioinformatics 23(11), 1378-1385, 2007.
(abstract) (link to publisher) (download preprint)

Generalized models as an universal approach to the analysis of nonlinear dynamical systems
Thilo Gross and Ulrike Feudel
Physical Review E 73, 016205-14, 2006.
(abstract) (link to publisher) (arXiv) (download preprint)