A network perspective on the evolution of metabolism by gene duplication

Abstract

Background: Gene duplication followed by divergence is one of the main sources of metabolic versatility. The patchwork and stepwise models of metabolic evolution help us to understand these processes, but their assumptions are relatively simplistic. We used a network-based approach to determine the influence of metabolic constraints on the retention of duplicated genes.

Results: We detected duplicated genes by looking for enzymes sharing homologous domains and uncovered an increased retention of duplicates for enzymes catalyzing consecutive reactions, as illustrated by the ligases acting in the biosynthesis of peptidoglycan. As a consequence, metabolic networks show a high retention of duplicates within functional modules, and we found a preferential biochemical coupling of reactions that partially explains this bias. A similar situation was found in enzyme-enzyme interaction networks, but not in interaction networks of non-enzymatic proteins or gene transcriptional regulatory networks, suggesting that the retention of duplicates results from the biochemical rules governing substrate-enzyme-product relationships. We confirmed a high retention of duplicates between chemically similar reactions, as illustrated by fatty-acid metabolism. The retention of duplicates between chemically dissimilar reactions is, however, also greater than expected by chance. Finally, we detected a significant retention of duplicates as groups, instead of single pairs.

Conclusion: Our results indicate that in silico modeling of the origin and evolution of metabolism is improved by the inclusion of specific functional constraints, such as the preferential biochemical coupling of reactions. We suggest that the stepwise and patchwork models are not independent of each other: in fact, the network perspective enables us to reconcile and combine these models.

Figure 1

Preferential biochemical coupling of reactions in metabolic networks. (a) Homologous transferases PurF and Gpt from E. coli catalyze consecutive chemically similar reactions. Their origin can be explained by both the stepwise and the patchwork models. (b) Homologous ligases involved in peptidoglycan biosynthesis whose origin can be explained by both the stepwise and the patchwork models. A distant homolog (FolC) acts in folate metabolism. (c) Frequencies of reaction types (EC:a.b) in the E. coli K12 metabolic network, according to KEGG (hereafter called EcoKegg). (d) Frequencies of consecutive reaction types (EC:a.b → EC:w.x) in EcoKegg were compared against the expected values using a set of null Maslov-Sneppen models (see Materials and methods). The Z-score (color-scale bar at top) indicates the number of standard deviations between the real and the average expected frequencies. Consecutive reaction types overrepresented in real networks are shown in green-to-yellow, underrepresented ones are shown in red. The diagonal (pink box) highlights consecutive chemically similar reactions, including the ligases synthesizing peptidoglycan (pink arrow). Reaction types were sorted vertically using a hierarchical clustering to detect highly related reaction types, such as EC:1.5, EC:1.7 and EC:2.1. (center of plot).

Figure 2

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.

Figure 3

Influence of network modularity on the retention of duplicates. (a) A hierarchical clustering was carried out to delimit modules in metabolic networks. Colors denote different modules in EcoKegg. (b) Metabolic pathways (branches in the trees) within and across modules were compared using a measure of evolutionary distance (ED). Modules comprising related branches are indicated by color as in (a). A value of (ED) closer to zero (the darker squares) implies a greater retention of duplicates between the two given pathways. (c) Observed (ED) values were compared against those expected by chance - after random shuffling of protein-domains. A Z-score < -3 (green) refers to significant (ED) values (P < 0.001).

Figure 4

Retention of duplicates as groups and single entities. (a) The fatty-acid degradative and biosynthetic routes illustrate the retention of duplicates as groups. The same colors in EC number boxes denote duplicates. (b) Retention of duplicates acting consecutively. Five hypothetical scenarios were analyzed (left panel). Boxes of the same color denote duplicates. The number and letter (for example, E2 and E2') indicate the place of the reaction in the series. Scenarios (I) and (V) have a common reaction followed or preceded by two possible reactions. In (I) gene duplication was detected, in (V) it was not. Scenarios (II), (III) and (IV) involve pairs of consecutive reactions in two branches of the network. In (II) both pairs are duplicates, in (III) only one pair is duplicated, and in (IV) none of the pairs are duplicates. From this diagram one can see that one pair can participate in more than one scenario, looking upstream or downstream in the network flux. The histogram on the right shows the frequency for each scenario. We present the results for the four databases analyzed herein. The networks were reconstructed eliminating the top 20 hubs. These results are the comparison of all-against-all pairs (EC:a.b → EC:w.x), including CSRs as well as CDRs. Red dots represent the expected average frequencies ± 3σ obtained using Maslov-Sneppen models.