Minimizing enzyme mass to decompose flux distribution for identifying biologically relevant elementary flux modes

The flux distribution in metabolic network can be decomposed as non-negative linear combinations of elementary flux modes (EFMs). Identifying biologically relevant EFM combination by decomposing flux distribution in metabolic network is a useful method to study metabolisms in systems biology. However, the occurrence of biologically irrelevant EFMs hinders the application of such methods. In this paper, we introduce a novel method for identifying EFM combination by minimizing enzyme mass. Our proposed method, called EMMD (Enzyme Mass Minimization Decomposition), takes into consideration both thermodynamic and enzymatic constraints in stoichiometry metabolic models. By implementing EMMD, we can decompose the flux distributions in metabolic network to detect biologically relevant EFM combinations. We demonstrate the effectiveness of our method by applying it to the core Escherichia coli metabolic network and show that the optimal EFM combinations identified by EMMD are unique. Moreover, the optimal EFM combination identified by EMMD not only aligns more closely with experimental values in terms of estimated growth rate, but it also demonstrates more favorable thermodynamics. Finally, we investigated the growth of the core Escherichia coli metabolic network in Luria-Bertani medium containing different carbon sources, revealing the impact of various carbon sources on the growth rate of flux distribution. EMMD thus could be a promising complement to the existing flux decomposition tools.