Network analysis of metabolic enzyme evolution in Escherichia coli

Abstract

Background: The two most common models for the evolution of metabolism are the patchwork evolution model, where enzymes are thought to diverge from broad to narrow substrate specificity, and the retrograde evolution model, according to which enzymes evolve in response to substrate depletion. Analysis of the distribution of homologous enzyme pairs in the metabolic network can shed light on the respective importance of the two models. We here investigate the evolution of the metabolism in E. coli viewed as a single network using EcoCyc.

Results: Sequence comparison between all enzyme pairs was performed and the minimal path length (MPL) between all enzyme pairs was determined. We find a strong over-representation of homologous enzymes at MPL 1. We show that the functionally similar and functionally undetermined enzyme pairs are responsible for most of the over-representation of homologous enzyme pairs at MPL 1.

Conclusions: The retrograde evolution model predicts that homologous enzymes pairs are at short metabolic distances from each other. In general agreement with previous studies we find that homologous enzymes occur close to each other in the network more often than expected by chance, which lends some support to the retrograde evolution model. However, we show that the homologous enzyme pairs which may have evolved through retrograde evolution, namely the pairs that are functionally dissimilar, show a weaker over-representation at MPL 1 than the functionally similar enzyme pairs. Our study indicates that, while the retrograde evolution model may have played a small part, the patchwork evolution model is the predominant process of metabolic enzyme evolution.

Figure 1

Common representation of the biotin metabolism. In the most common representation of biochemical reactions the reactants represent the vertices of the network and the enzymes represent the edges. The drawing of the biotin metabolism was redrawn from EcoCyc [19].

Figure 2

Protein-centric representation of the biotin metabolism. The protein-centric or reaction graph representation which was used in our study has enzymes as vertices and reactants as edges. EC 2.3.1.47 is a neighbor of EC 2.6.1.62 because there is an edge leading from EC 2.6.1.62 to EC 2.3.1.47. In the same manner, EC 2.6.1.62 is a neighbor of 2.3.1.47. In the biotin metabolism example there are 8 enzyme neighbor pairs. Note that in our definition an edge can consist of one or more compounds and there can only be one edge in each direction between two enzymes. The edges in blue font, representing CO₂, between EC 2.3.1.47 and EC 6.3.3.3, are eliminated when the 20 most promiscuous compounds are removed from the network.

Figure 3

Compound frequency distribution histogram for the metabolic network of E. coli. The 20 most promiscuous compounds have been removed in the network analyzed here. The histogram shows how many compounds (y-axis, logged scale) that occur with a certain frequency (x-axis) in the network. Compound frequency is defined as the number of times a compound occurs as part of an edge.

Figure 4

Minimal path length (MPL) between enzymes. a) The reactions catalyzed by EC 1.1.1.1 (alcohol dehydrogenase), EC 1.5.1.12 (1-pyrroline-5-carboxylate dekydrogenase) and EC 1.2.1.3 (aldehyde dehydrogenase). b) There are severeral paths leading from EC 1.1.1.1 to EC 1.2.1.3. The shortest path goes from EC 1.1.1.1 through aldehyde to EC 1.2.1.3 and is of length 1 (MPL = 1).

Figure 5

Preservation of network topology. The left side of the figure shows the numbers of vertices and edges in the original example graph. The right side of the figure shows the numbers of vertices and edges for the randomized graph where the vertex identities (A, B, C. D, E, F, G, H) have been shuffled. The topological properties of the original graph are preserved in the randomized graph.

Figure 6

Homology vs minimal path length (MPL) for the whole metabolic network of E. coli. The plot shows the correlation between homology and MPL when all compounds are included. The solid line represents the real metabolic network of E. coli. The dotted vertical lines represent three standard deviations of the number of homologous enzyme pairs for the randomized networks. The number of homologous enzyme pairs has been normalized by the average number of homologous enzyme pairs for the randomized networks.

Figure 7

Homology vs minimal path length (MPL) without the 20 most promiscuous compounds. The plot shows the correlation between homology and MPL when the 20 most promiscuous compounds (Table 2) have been removed. The solid line represents the metabolic network of E. coli.The dotted vertical lines represent three standard deviations of the number of homologous enzyme pairs for the randomized networks. The number of homologous enzyme pairs has been normalized by the average number of homologous enzyme pairs for the randomized networks.

Figure 8

Different types of homologous enzyme pairs at minimal path length (MPL) 1. a) Enzymes that catalyze similar reactions. The enzymes are at MPL 1 because they both catalyse reactions involving the metabolite fructose-1,6-bisphosphate. b) Enzymes that catalyze reactions that are mechanistically different. These enzymes are at MPL 1 because they both catalyse reactions involving chorismate.

Figure 9

Homology vs minimal path length (MPL) without the 20 most promiscuous compounds for functionally similar enzyme pairs. The plots show the correlation between homology and MPL for functionally similar (shared primary EC number) enzyme pairs when the 20 most promiscuous compounds have been removed. The solid line represents the metabolic network of E. coli. The dotted vertical lines represent three standard deviations of the number of homologous enzyme pairs for the randomized networks. The number of homologous enzyme pairs has been normalized by the average number of homologous enzyme pairs for the randomized networks.

Figure 10

Homology vs minimal path length (MPL) without the 20 most promiscuous compounds for functionally dissimilar enzyme pairs. The plots show the correlation between homology and MPL for functionally dissimilar (different primary EC number) enzyme pairs when the 20 most promiscuous compounds have been removed. The solid line represents the metabolic network of E. coli. The dotted vertical lines represent three standard deviations of the number of homologous enzyme pairs for the randomized networks. The number of homologous enzyme pairs has been normalized by the average number of homologous enzyme pairs for the randomized networks.

Figure 11

Main algorithm. a) Determination of neighbors for each enzyme. b) Determination of minimal path length (MPL). The algorithm is a bread-first search for the shortest distance between all pairs of enzymes. MAX_MPL is the maximum MPL under investigation.