Influence of chemical similarity and distance on the retention of duplicates. (a) Frequencies of retained duplicates (histogram bars) in EcoKegg are shown for the whole reaction set (ALL), and the subsets of chemically similar reactions (CSRs) and chemically different reactions (CDRs) at different distances (metabolic steps). Blue bars indicate three standard deviations (σ) from these frequencies. Deviations were obtained by random sampling. Red dots represent the average expected frequencies ± 3σ obtained using Maslov-Sneppen models. The rewiring to construct the null model is shown below the graph. (b) A similar procedure to (a) was carried out, using null functionally similar models to control the influence of the preferential biochemical coupling of reactions. Symbols as in (a). Compared with Maslov-Sneppen models, in which all nodes are equally eligible for change, in functionally similar models the preferential biochemical coupling of reactions restricts the choices. (c) Retention of duplicates in the gene regulatory network of E. coli as a function of the distance (number of regulatory interactions) between transcription factors and target genes. (d) Retention of duplicates in a protein-protein interaction network of E. coli. The full set of interactions (ALL), and the subsets of enzyme-enzyme (EC-EC) and non-enzymatic protein-protein (P-P) interactions are shown. In (c) and (d) red dots represent averages obtained using Maslov-Sneppen models.