Figure 1

Methods overview. A bipartite graph representation of a metabolic network connects enzymes (squares) to metabolites (circles). (A) The number of metabolites shared by two enzymes can be used to rank the functional association of the pair. This raw count can be corrected to account for enzyme degree, using a hypergeometric distribution under a null hypothesis. (B) Hub metabolites, such as M1, can be down- weighted when assessing shared neighbours. One approach is to remove these high-degree metabolites from the network. An alternative threshold-free approach is to incorporate the metabolite degree distribution, as carried out here with a Poisson distribution. (C) One failing of shared neighbour scores is that they are inherently local, providing information only about enzymes that share at least one metabolite. Global methods provide information about all enzyme pairs, no matter how far separated. An improved approach to shortest path between two enzymes is to count paths of all length, with decreasing weight given to longer paths. This method is termed a graph diffusion kernel, with a single parameter used to determine the discount rate for longer paths. (D) Edges in metabolic networks correspond to metabolic fluxes, which have directions and are constrained by maximum capacities and reaction stoichiometry. Functionally related enzymes may have correlated fluxes. The flux correlations can be calculated by repeated sampling, which is computationally intensive but provides a more realistic model for the metabolic network than simpler topological models.