# Quantitative flux coupling analysis

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## Abstract

*Flux coupling analysis* (FCA) aims to describe the functional dependencies among reactions in a metabolic network. Currently studied coupling relations are qualitative in the sense that they identify pairs of reactions for which the activity of one reaction necessitates the activity of the other one, but without giving any numerical bounds relating the possible activity rates. The potential applications of FCA are heavily investigated, however apart from some trivial cases there is no clue of what bottleneck in the metabolic network causes each dependency. In this article, we introduce a quantitative approach to the same flux coupling problem named *quantitative flux coupling analysis* (QFCA). It generalizes the current concepts as we show that all the qualitative information provided by FCA is readily available in the quantitative flux coupling equations of QFCA, without the need for any additional analysis. Moreover, we design a simple algorithm to efficiently identify these flux coupling equations which scales up to the genome-scale metabolic networks with thousands of reactions and metabolites in an effective way. Furthermore, this framework enables us to quantify the “strength” of the flux coupling relations. We also provide different biologically meaningful interpretations, including one which gives an intuitive certificate of precisely which metabolites in the network enforce each flux coupling relation. Eventually, we conclude by suggesting the probable application of QFCA to the metabolic gap-filling problem, which we only begin to address here and is left for future research to further investigate.

## Keywords

Systems biology Metabolic network analysis Flux coupling analysis FCA QFCA Flux coupling equation## Mathematics Subject Classification

92C42 90C05 49N15## References

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