Interplay of Shadow Price, Phenotype and Alternative Optimal Solutions in Flux Balance Analysis

Abstract

Genome-scale metabolic network models (GEMs) have been applied successfully in many applications, and one important application is to predict different growth phenotypes in various genetic and environmental conditions. Phenotype phase plane (PhPP) analysis is a powerful tool that uses flux balance analysis (FBA) with the GEM to provide a global perspective on the genotype-phenotype relationship, which relies on shadow prices of different metabolites to characterize different metabolic phenotypes. In PhPP analysis, the determination and characterization of different phenotypes rely on the concept of shadow price. Despite many successful applications of PhPP analysis, sometimes results obtained based on shadow price alone can be confusing. As shown in this work, for an E. coli core model, two different phenotypes actually share the same set of the shadow prices and will be missed by the PhPP analysis. To find the reason for the existence of such “hidden” phenotypes, we applied a system identification (SID) based framework to analyze the “hidden” phenotypes, and identified that the existence of the alternative optimal solutions to FBA is the root cause of such hidden phenotypes. Using the SID-based framework, we further elucidate the biological meaning of the alternative FBA optima for the E. coli core model.