Toolbox model of evolution of prokaryotic metabolic networks and their regulation

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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.
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