Soft constraints-based multiobjective framework for flux balance analysis.

The current state of the art for linear optimization in Flux Balance Analysis has been limited to single objective functions. Since mammalian systems perform various functions, a multiobjective approach is needed when seeking optimal flux distributions in these systems. In most of the available multiobjective optimization methods, there is a lack of understanding of when to use a particular objective, and how to combine and/or prioritize mutually competing objectives to achieve a truly optimal solution. To address these limitations we developed a soft constraints based linear physical programming-based flux balance analysis (LPPFBA) framework to obtain a multiobjective optimal solutions. The developed framework was first applied to compute a set of multiobjective optimal solutions for various pairs of objectives relevant to hepatocyte function (urea secretion, albumin, NADPH, and glutathione syntheses) in bioartificial liver systems. Next, simultaneous analysis of the optimal solutions for three objectives was carried out. Further, this framework was utilized to obtain true optimal conditions to improve the hepatic functions in a simulated bioartificial liver system. The combined quantitative and visualization framework of LPPFBA is applicable to any large-scale metabolic network system, including those derived by genomic analyses.