Toolbox model of evolution of prokaryotic metabolic networks and their regulation

Abstract

It has been reported that the number of transcription factors encoded in prokaryotic genomes scales approximately quadratically with their total number of genes. We propose a conceptual explanation of this finding and illustrate it using a simple model in which metabolic and regulatory networks of prokaryotes are shaped by horizontal gene transfer of coregulated metabolic pathways. Adapting to a new environmental condition monitored by a new transcription factor (e.g., learning to use another nutrient) involves both acquiring new enzymes and reusing some of the enzymes already encoded in the genome. As the repertoire of enzymes of an organism (its toolbox) grows larger, it can reuse its enzyme tools more often and thus needs to get fewer new ones to master each new task. From this observation, it logically follows that the number of functional tasks and their regulators increases faster than linearly with the total number of genes encoding enzymes. Genomes can also shrink, e.g., because of a loss of a nutrient from the environment, followed by deletion of its regulator and all enzymes that become redundant. We propose several simple models of network evolution elaborating on this toolbox argument and reproducing the empirically observed quadratic scaling. The distribution of lengths of pathway branches in our model agrees with that of the real-life metabolic network of Escherichia coli. Thus, our model provides a qualitative explanation for broad distributions of regulon sizes in prokaryotes.

Fig. 1.

“Toolbox” rules for evolving metabolic networks in our model. (A) Addition of a new metabolic pathway (red) that is long enough to connect the red nutrient to a previously existing pathway (blue) that further converts it to the central metabolic core (dark green). (B) Removal of a part of the blue pathway after loss of the blue nutrient. The upstream portion of the blue pathway that is no longer required is removed down to the point where it merges with another pathway (red). The light green circle denotes all metabolites in the universal biochemistry network from which new pathways are drawn.

Fig. 2.

Schematic diagrams illustrating several possible regulatory network architectures for control of metabolic enzymes/pathways. Four panels correspond to different versions of our model discussed in the article. (A) In the basic model there is no coordination of activity between red and blue metabolic pathways. (B–D) More realistic models include extra regulatory interactions (purple dashed lines) and transcription factors (purple TF3 in D), ensuring that only the part of the blue pathway necessary for utilization of the red nutrient is turned on by the corresponding transcription factor (red TF2).

Fig. 3.

Visual comparison of a real-life metabolic network with that generated by our model. (A) The backbone of the metabolic network in E. coli (8) located upstream of the central metabolism (green). (B) A similarly sized model network (red). Note the hierarchy of branch lengths in both images in which shorter pathways tend to be attached to progressively longer pathways. The branch length distributions in real and model networks are shown as green circles and red squares in Fig. 4B.

Fig. 4.

Scaling plots in real and model networks. (A) The number of transcription factors scales approximately quadratically with the total number of genes in real prokaryotic genomes (8, 27) (green) and our model (red) simulated on the KEGG universal network with N_univ = 1,800. The number of metabolic reactions in the model was rescaled to approximate the total number of genes in a genome (see Results for more details). Error bars correspond to data scatter in multiple simulations of the model. The solid line with slope 2 is the best power-law fit to the scaling in real prokaryotic genomes (the best fit to our model is 1.8 ± 0.2), whereas the dashed line with slope 1 is shown for comparison to emphasize deviations from linearity. (B) Cumulative distributions of pathway/branch lengths in the E. coli metabolic network (green circles) and our model of comparable size (red symbols) have similar tail exponents. The negative slope of the best power-law fit γ − 1 = 1.9 ± 0.2 (solid line) is consistent with our analytical result γ = 3 (see text for details). The toolbox model with N_met = 400 was simulated on universal networks of KEGG reactions with N_univ = 1,800 (red diamonds) and N_univ = 900 (red squares) nodes.