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Background  Non-negative linear combinations of elementary flux modes (EMs) describe all feasible reaction flux distributions for a given metabolic network under the quasi steady state assumption. However, only a small subset of EMs contribute to the physiological state of a given cell.    Results  In this paper, a method is proposed that identifies the subset of EMs that best explain the physiological state captured in reaction flux data, referred to as principal EMs (PEMs), given a pre-specified universe of EM candidates. The method avoids the evaluation of all possible combinations of EMs by using a branch and bound approach which is computationally very efficient. The performance of the method is assessed using simulated and experimental data of  Pichia pastoris  and experimental fluxome data of  Saccharomyces cerevisiae . The proposed method is benchmarked against principal component analysis (PCA), commonly used to study the structure of metabolic flux data sets.    Conclusions  The overall results show that the proposed method is computationally very effective in identifying the subset of PEMs within a large set of EM candidates (cases with ~100 and ~1000 EMs were studied). In contrast to the principal components in PCA, the identified PEMs have a biological meaning enabling identification of the key active pathways in a cell as well as the conditions under which the pathways are activated. This method clearly outperforms PCA in the interpretability of flux data providing additional insights into the underlying regulatory mechanisms.    Electronic supplementary material  The online version of this article (doi:10.1186/s12859-016-1063-0) contains supplementary material, which is available to authorized users.

A principal components method constrained by elementary flux modes: analysis of flux data sets