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Qualitative Properties of Biochemical Reaction Networks

From Fachgebiet Regelungssysteme TU Berlin

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In this project, we have investigated whether a proposed biochemical reaction network with unknown or incompletely known parameters can generate an observed qualitative behavior. Clearly, if this is not the case, the suggested structure has been falsified and can be excluded from further consideration. The focus has been on mass action networks described by ODE models and their ability to admit the existence of multiple steady states (multistationarity) as a prerequisite for bi-stability. For mass action networks with certain structural properties, conditions for multistationarity are derived. These conditions take the form of linear inequality systems that are independent of parameter values [[1], [2],[3], [4] ]. Some realistic reaction networks, however, do not possess the required structural properties. To address this problem, a unique decomposition has been proposed such that necessary and sufficient multistationarity conditions for the resulting subnetworks are guaranteed to take the form of linear inequalities. Given multistationarity in a subnetwork, an algorithm for the computation of rate constants in the overall network is proposed that guarantees steady states close to those of the subnetwork [[5], [6]]. These results are currently applied to networks describing the post translational modification of proteins (PTM networks). Such PTM networks are, for example, biochemical realizations of check points controlling the cell cycle (e.g., Sic1 in budding yeast). Another line of research investigates the Jacobian of mass-action network models and establishes conditions for points where the networks possess saddle-node type steady states. This has been successfully applied to a doublephosphorylation mechanism. Finally, together with the Biophysics Group at OvGU, D. Flockerzi has investigated bi-stability effects in gene regulation of Rhodobacter Sphaeroides [[7]], which explain the switch between aerobic and anaerobic mode.

People involved



  1. Carsten Conradi. Multistationarity in (bio)chemical reaction networks: model discrimination, robustness and beyond. Technical University Berlin, 2008.
  2. Carsten Conradi, Dietrich Flockerzi, Jörg Raisch. Multistationarity in the activation of an MAPK : parametrizing the relevant region in parameter space. Mathematical Biosciences, 211 (1):105–131, October 2008.
  3. Julio Saez-Rodriguez, Andrea Hammerle-Fickinger, Onkar Dalal, Steffen Klamt, Ernst Dieter Gilles, Carsten Conradi. Multistability of signal transduction motifs. IET Systems Biology, 2 (2):80–93, July 2008.
  4. Carsten Conradi, Dietrich Flockerzi. Multistationarity in Mass Action Networks with Applications to ERK Activation. Journal of Mathematical Biology, July 2011.
  5. Dietrich Flockerzi, Carsten Conradi. Subnetwork Analysis for Multistationarity in Mass Action Kinectics. Journal of Physics: Conference Series, 138 page 012006, April 2008.
  6. Markus Uhr, Hans-Michael Kaltenbach, Carsten Conradi, Jörg Stelling. Analysis of Degenerate Chemical Reaction Networks. In Rafael Bru and Sergio Romero-Vivo, editor, Positive Systems, volume 389 of Lecture Notes in Control and Information Sciences, pages 163-182. Springer Berlin/Heidelberg, 2009.
  7. Rakesh Pandey, Dietrich Flockerzi, Markus J. B. Hauser, Ronny Straube. Modeling the Light- and Redox-Dependent Interaction of PpsR/AppA in Rhodobacter sphaeroides. Biophysical Journal, 100 (10):2347-2355, May 2011.

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