An analytic and systematic framework for estimating metabolic flux ratios from 13C tracer experiments

We present a novel analytic framework for estimating metabolic flux ratios in the cell from 13C isotopomer measurement data. In the presented framework, equation systems constraining the fluxes are derived automatically from the model of the metabolism of an organism. The framework is designed to be applicable with all metabolic network topologies, 13C isotopomer measurement techniques, substrates and substrate labelling patterns.By analyzing nuclear magnetic resonance (NMR) and mass spectrometry (MS) measurement data obtained from the experiments on glucose with the model micro-organisms Bacillus subtilis and Saccharomyces cerevisiae we show that our framework is able to automatically produce the flux ratios discovered so far by the domain experts with tedious manual analysis. Furthermore, we show by in silico calculability analysis that our framework can rapidly produce flux ratio equations – as well as predict when the flux ratios are unobtainable by linear means – also for substrates not related to glucose.The core of 13C metabolic flux analysis framework introduced in this article constitutes of flow and independence analysis of metabolic fragments and techniques for manipulating isotopomer measurements with vector space techniques. These methods facilitate efficient, analytic computation of the ratios between the fluxes of pathways that converge to a common junction metabolite. The framework can been seen as a generalization and formalization of existing tradition for computing metabolic flux ratios where equations constraining flux ratios are manually derived, usually without explicitly showing the formal proofs of the validity of the equations.From microorganisms to animals and plants, cells adjust their metabolic operations to fulfill the demand of energy and biosynthetic precursors. In nature this is a challenging task because substrate availability is typically limited and often changing in its composition. To ensure viability on a broad palette of chemic