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 assume the stoichiometric steady state of the metabolic network.We will discuss 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 discuss a sparse variant of PMFA that favors flux modes that contain a small number of reactions. PMFA has several benefits: (1) it can be applied to large metabolic network in efficient way as PMFA does not enumerate elementary modes, (2) the method is more robust to the steady-state violations than competing approaches, and (3) can compactly capture the variation in the data by a few factors. This chapter will describe the detailed steps how to do the above task on experimental data from fluxomic and gene expression measurements.
Keywords: Metabolic flux analysis; Principal component analysis; Sparsity.