A new approach to obtaining EFMs using graph methods based on the shortest path between end nodes

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Genome-scale metabolic networks let us understand the behaviour of the metabolism in the cells of living organisms. The availability of great amounts of such data gives the scientific community the opportunity to infer in silico new metabolic knowledge. Elementary Flux Modes (EFM) are minimal contained pathways or subsets of a metabolic network that are very useful to achieving the comprehension of a very specific metabolic function (as well as dysfunctions), and to get the knowledge to develop new drugs. Metabolic networks can have large connectivity and, therefore, EFMs resolution faces a combinational explosion challenge to be solved. In this paper we propose a new approach to obtain EFMs based on graph theory, the balanced graph concept and the shortest path between end nodes. Our proposal uses the shortest path between end nodes (input and output nodes) that finds all the pathways in the metabolic network and is able to prioritise the pathway search accounting the biological mean pursued. Our technique has two phases, the exploration phase and the characterisation one, and we show how it works in a well-known case study. We also demonstrate the relevance of the concept of balanced graph to achieve to the full list of EFMs.