Complementary elementary modes for fast and efficient analysis of metabolic networks

• We proposed the complementary elementary modes (cEMs) to efficiently analyze a large-scale metabolic network.
• The cEM analysis enables one to accurately predict the flux distributions of genetically modified mutants.
• The cEM analysis consists of the flux balance analysis, EM decomposition method, and maximum entropy principle.

Metabolic pathway analysis facilitates understanding or designing a complex metabolic system and enables prediction of steady-state metabolic flux distributions. A serious problem of elementary mode (EM) or extreme pathway (Expa) analysis is that the computational time increases exponentially with an increase in network sizes, which makes the computation of the EMs/Expas expensive and infeasible for large-scale networks. To overcome such problems, we proposed a fast and efficient algorithm named complementary EM (cEM) analysis. To achieve the computational time improvement, we employ the EM decomposition method that explores EMs or linear combinations of them which are responsible for the metabolic flux distributions. Flux balance analysis (FBA) is used to determine possible ranges of metabolic flux distributions as the input data necessary for the EM decomposition method. The maximum entropy principle (MEP) is employed as an objective function for estimating the coefficients of cEMs. To demonstrate the feasibility of cEM analysis, we compared it with EM/Expa analysis by using two medium-scale metabolic networks of Escherichia coli and a genome-scale metabolic network of head and neck cancer cells. The cEM analysis greatly reduces the computational time and memory cost, exposing a new window for large-scale metabolic network analysis.

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