Email updates

Keep up to date with the latest news and content from BMC Systems Biology and BioMed Central.

Open Access Highly Accessed Research article

A proof for loop-law constraints in stoichiometric metabolic networks

Elad Noor1*, Nathan E Lewis23* and Ron Milo1

Author Affiliations

1 Department of Plant Sciences, 234 Herzl st., Weizmann Institute of Science, Rehovot 76100, Israel

2 Department of Bioengineering, 9500 Gilman Drive, University of California San Diego, La Jolla, CA 92093-0412, USA

3 Wyss Institute for Biologically Inspired Engineering and Department of Genetics, 77 Avenue Louis Pasteur, Harvard Medical School, Boston, MA 02115, USA

For all author emails, please log on.

BMC Systems Biology 2012, 6:140  doi:10.1186/1752-0509-6-140

Published: 12 November 2012



Constraint-based modeling is increasingly employed for metabolic network analysis. Its underlying assumption is that natural metabolic phenotypes can be predicted by adding physicochemical constraints to remove unrealistic metabolic flux solutions. The loopless-COBRA approach provides an additional constraint that eliminates thermodynamically infeasible internal cycles (or loops) from the space of solutions. This allows the prediction of flux solutions that are more consistent with experimental data. However, it is not clear if this approach over-constrains the models by removing non-loop solutions as well.


Here we apply Gordan’s theorem from linear algebra to prove for the first time that the constraints added in loopless-COBRA do not over-constrain the problem beyond the elimination of the loops themselves.


The loopless-COBRA constraints can be reliably applied. Furthermore, this proof may be adapted to evaluate the theoretical soundness for other methods in constraint-based modeling.

Thermodynamics; Gordan’s theorem; Metabolism