Chapter

Positive Systems

Volume 389 of the series Lecture Notes in Control and Information Sciences pp 163-171

Analysis of Degenerate Chemical Reaction Networks

  • Markus UhrAffiliated withDept. Biosystems Science & Engineering, ETH Zurich
  • , Hans-Michael KaltenbachAffiliated withDept. Biosystems Science & Engineering, ETH Zurich
  • , Carsten ConradiAffiliated withMax-Planck-Institute Magdeburg
  • , Jörg StellingAffiliated withDept. Biosystems Science & Engineering, ETH Zurich

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Abstract

Positivity of states and parameters in dynamic models for chemical reaction networks are exploited by Chemical Reaction Network Theory (CRNT) to predict the potential for multistationarity of ‘regular’ networks without knowledge of parameter values. Especially for biochemical systems, however, CRNT’s large application potential cannot be realized because most realistic networks are degenerate in the sense of CRNT. Here, we show how degenerate networks can be regularized such that the theorems and algorithms of CRNT apply. We employ the method in a case study for a bacterial reaction network of moderate size.