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

Toolbox model of evolution of prokaryotic metabolic networks and their regulation