Evaluation of correlation networks (CN) and Gaussian graphical models (GGM) on artificial systems. Line widths represent relative edge weights in the respective networks (scaled to the strongest edges). A: Linear chain of three metabolites with reversible intermediate reactions. While the standard Pearson correlation network (CN) is fully connected, implying an overall high correlation of all metabolites, the GGM correctly discriminates between direct and indirect interactions. B: Linear chain with irreversible intermediate reactions. Neither CN nor GGM can distinguish direct from indirect effects, as metabolite A equally determines the levels of both B and C. C: Linear chain with irreversible reactions and input/output reactions for each metabolite. Although the edge weights for both CN and GGM are generally lower, the GGM now correctly predicts the network topology. D: Branched-chain first-order networks are correctly reconstructed by the GGM. E: End-product inhibition modules. When modeled as an open system, A is decoupled from the other metabolites and reconstruction fails at this point. Dashed lines mark enzyme inhibition interactions, larger arrows to the right indicate faster forward than backward reactions. F: Cofactor-driven network resembling the first three reactions from the glycolysis pathway. A correlation network fails to predict the correct pathway relationships. G: Non-linear system with a bi-molecular reaction. The GGM predicts only a only weak interaction between B and C. This is due to counterantagonistic processes of isomerization and substrate participation in the same reaction.
Krumsiek et al. BMC Systems Biology 2011 5:21 doi:10.1186/1752-0509-5-21