(398e) Elucidating the Meaning of Alternative Optimal Solutions in Flux Balance Analysis

The genotype-phenotype relationship of an organism is fundamental to biology. Predicting different phenotypes based on the sequenced genome is one of the main goals for genome-scale metabolic model development. These models provide a holistic view of the organismâ??s metabolism. One common approach for analyzing metabolic models is flux balance analysis (FBA) which uses linear program to optimize an objective function, which in most applications is biomass growth. A stoichiometric matrix consisting of metabolites as rows and reactions as column is created based on the reactions included in the model. The elements of the matrix consist of the stoichiometric coefficient of a metabolite if it is involved in the reaction. The rows (metabolites) represent the linear equations that define the model, and the columns (reactions) represent the variables. For FBA, a carbon source and oxygen is provided to the model, and a flux distribution that provides the optimal amount of biomass growth is given by the linear program solver. As is common in metabolic network models, there are more reactions than metabolites giving an underdetermined system of linear equations. Since the system is underdetermined, a unique optimal solution is not guaranteed. The presence of alternative optimal solutions may lead to mischaracterization and/or undetected phenotypes.

Last year, we presented a systems identification enhanced phenotype phase plane (SID-PhPP) analysis to help characterize different phenotypes predicted by a model, how different pathways interact with each other for a given phenotype, and how such interactions differ from different phenotypes. We utilized SID-PhPP on an Escherichia coli (E. coli) core model which is a central carbon metabolic network. Traditional PhPP identified four phenotypes for the core model. By applying SID-PhPP, we discovered that one of the phenotypes is actually two distinct phenotypes undetectable by the traditional PhPP analysis. It is undetectable because the shadow prices for oxygen and carbon are the same in both phenotypes; however, SID-PhPP elucidated the presence of different active reaction sets in each phase confirming that the phases are unique phenotypes.

In this work, we further investigated the two â??sub-phasesâ?, P3â?? and P3â??â??, using a uniform random sampling algorithm, optGpSampler developed by Megchelenbrink et al., which also revealed the presence of alternative solutions. To better understand the alternative optimal solutions existing in P3â??, we applied our SID-PhPP to analyze all alternative solutions corresponding to the same carbon and oxygen uptake rates. Our analyses showed that the alternative solutions correspond to different linear combinations of two extreme reaction pathways that produce the same amount of NADPH. In addition, we developed a systems approach for calculating shadow price of each metabolite through utilizing the loadings obtained by SID-PhPP. The obtained shadow prices agree with the shadow prices obtained from the traditional PhPP method. But SID-PhPP based shadow price provides further insight into how the metabolite is utilized by the network.