Elimination of Thermodynamically Infeasible Loops in Steady-State Metabolic Models

• Published in: Biophysical journal 2011-02, Vol.100 (3), p.544-553
• Main Authors: Schellenberger, Jan, Lewis, Nathan E., Palsson, Bernhard Ø.
• Format: Article
• Language: English
• Subjects: Biological Systems and Multicellular Dynamics; Computation; Computer simulation; Consistency; electronic circuits; Escherichia coli - genetics; Flux; Genomes; Kinetics; Law; Mathematical models; Metabolic Networks and Pathways; Metabolism; Models, Biological; Monte Carlo Method; Monte Carlo methods; Monte Carlo simulation; Networks; prediction; Simulation; Studies; Thermodynamics
• ISSN: 0006-3495; 1542-0086
• DOI: 10.1016/j.bpj.2010.12.3707

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.