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Biophys J. 2011 Feb 2;100(3):544-53. doi: 10.1016/j.bpj.2010.12.3707.

Elimination of thermodynamically infeasible loops in steady-state metabolic models.

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Bioinformatics and Systems Biology Program, University of California, San Diego, California, USA.

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  • Biophys J. 2011 Mar 2;100(5):1381.


The constraint-based reconstruction and analysis (COBRA) framework has been widely used to study steady-state flux solutions in genome-scale metabolic networks. One shortcoming of current COBRA methods is the possible violation of the loop law in the computed steady-state flux solutions. The loop law is analogous to Kirchhoff's second law for electric circuits, and states that at steady state there can be no net flux around a closed network cycle. Although the consequences of the loop law have been known for years, it has been computationally difficult to work with. Therefore, the resulting loop-law constraints have been overlooked. Here, we present a general mixed integer programming approach called loopless COBRA (ll-COBRA), which can be used to eliminate all steady-state flux solutions that are incompatible with the loop law. We apply this approach to improve flux predictions on three common COBRA methods: flux balance analysis, flux variability analysis, and Monte Carlo sampling of the flux space. Moreover, we demonstrate that the imposition of loop-law constraints with ll-COBRA improves the consistency of simulation results with experimental data. This method provides an additional constraint for many COBRA methods, enabling the acquisition of more realistic simulation results.

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