Positive Systems pp 163-171
Analysis of Degenerate Chemical Reaction Networks
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.
Unable to display preview. Download preview PDF.
- 3.Feinberg, M.: Chemical reaction network structure and the stability of complex isothermal reactors – I. The deficiency zero and deficiency one theorems. Chemical Engineering Science 42(10), 2229–2268 (1987)Google Scholar
- 4.Feinberg, M.: Chemical reaction network structure and the stability of complex isothermal reactors – II. Multiple steady states for networks of deficiency one. Chemical Engineering Science 43(1), 1–25 (1988)Google Scholar
- 5.Flockerzi, D., Conradi, C.: Subnetwork analysis for multistationarity in mass action kinetics. Journal of Physics: Conference Series 138, 36 pages (012006) (2008)Google Scholar
- 7.Gunawardena, J.: Chemical reaction network theory for in-silico biologists. Bauer Center for Genomics Research (2003)Google Scholar