LAMOS: A linear algorithm to identify the origin of multiple optimal flux distributions in metabolic networks

In flux balance analysis, where flux distribution within a cell metabolic network is estimated by optimizing an objective function, there commonly exist multiple optimal flux distributions. Although finding all optimal solutions is possible, their interpretation is a challenge. A new four-phase algorithm (LAMOS) is therefore proposed in this work to efficiently enumerate all of these solutions based on iterative substitution of a current non-basic variable with a basic variable. These basic and non-basic variables are called key reaction pairs that their successive activity or inactivity causes alternate optimal solutions. LAMOS was implemented on E. coli metabolic models and the results proved it as a simple and fast method capable of finding the key reactions as well as reactions participating in the futile cycles. Key reactions were 1-3% of all reactions for the large-scale models and these reactions were identified using only 1% of optimal solutions.