Principal metabolic flux mode analysis.

Motivation: In the analysis of metabolism, two distinct and complementary approaches are frequently used: Principal component analysis (PCA) and stoichiometric flux analysis. PCA is able to capture the main modes of variability in a set of experiments and does not make many prior assumptions about the data, but does not inherently take into account the flux mode structure of metabolism. Stoichiometric flux analysis methods, such as Flux Balance Analysis (FBA) and Elementary Mode Analysis, on the other hand, are able to capture the metabolic flux modes, however, they are primarily designed for the analysis of single samples at a time, and not best suited for exploratory analysis on a large sets of samples. Results: We propose a new methodology for the analysis of metabolism, called Principal Metabolic Flux Mode Analysis (PMFA), which marries the PCA and stoichiometric flux analysis approaches in an elegant regularized optimization framework. In short, the method incorporates a variance maximization objective form PCA coupled with a stoichiometric regularizer, which penalizes projections that are far from any flux modes of the network. For interpretability, we also introduce a sparse variant of PMFA that favours flux modes that contain a small number of reactions. Our experiments demonstrate the versatility and capabilities of our methodology. The proposed method can be applied to genome-scale metabolic network in efficient way as PMFA does not enumerate elementary modes. In addition, the method is more robust on out-of-steady steady-state experimental data than competing flux mode analysis approaches.