On lifting poorly-scaled flux balance analysis problems

Background Biological processes such as metabolism, signaling, and macromolecular synthesis can be modeled as large networks of biochemical reactions. Large and comprehensive networks, like Metabolic-Expression networks that explicitly accounts for the demands of macromolecular synthesis at single nucleotide resolution, are inherently multiscale because reaction rates can vary over many orders of magnitude. Naively using standard optimization systems to conduct flux balance analysis can produce inaccurate or infeasible results. Results We describe lifting techniques that enable off-the-shelf optimization software to compute accurate solutions to the poorly scaled optimization problems arising from flux balance analysis of multiscale biochemical reaction networks. We demonstrate the benefits of lifting using the first integrated reconstruction of metabolism and macromolecular synthesis for E. coli. Conclusion Lifting techniques enable accurate flux balance analysis of multiscale networks using off-the-shelf optimization software. Although we describe these techniques in the context of flux balance analysis, our methods can be used to handle a variety of optimization problems arising from analysis of multiscale network reconstructions. Technical report SOL 2013-2 Department of Management Science and Engineering, Stanford University, Stanford, California, July 30, 2013