On correlated reaction sets and coupled reaction sets in metabolic networks

Two reactions are in the same "correlated reaction set" (or "Co-Set") if their fluxes are linearly correlated. On the other hand, two reactions are "coupled" if nonzero flux through one reaction implies nonzero flux through the other reaction. Flux correlation analysis has been previously used in the analysis of enzyme dysregulation and enzymopathy, while flux coupling analysis has been used to predict co-expression of genes and to model network evolution. The goal of this paper is to emphasize, through a few examples, that these two concepts are inherently different. In other words, except for the case of full coupling, which implies perfect correlation between two fluxes (R(2) = 1), there are no constraints on Pearson correlation coefficients (CC) in case of any other type of (un)coupling relations. In other words, Pearson CC can take any value between 0 and 1 in other cases. Furthermore, by analyzing genome-scale metabolic networks, we confirm that there are some examples in real networks of bacteria, yeast and human, which approve that flux coupling and flux correlation cannot be used interchangeably.