Parkinson's Law in bacterial regulation

It has been reported [1] that in prokaryotic genomes the number of transcription factors is proportional to the **square** of the total number of genes. As a consequence of this trend the fraction of regulators (the so-called "regulatory overhead") is less than 0.5% in small (< 500 genes) bacterial genomes, while in large genomes (~10,000 genes) it reaches as high as 10%. We recently proposed [2] a general explanation of this empirical scaling law and illustrated it using a simple model in which metabolic and regulatory networks co-evolve together. In our model prokaryotic organisms acquire new metabolic functions by the virtue of horizontal gene transfer of entire co-regulated metabolic pathways from a shared gene pool (the "universal metabolic network"). This transfer is followed by the removal of redundant enzymes. Pathways can also be lost following long-term changes in the environment or lifestyle of the organism. The whole process can be compared to a homeowner buying sets of tools from a hardware store and later returning duplicate or unnecessary items. We view the full repertoire of metabolic enzymes (or more generally all non-regulatory proteins) encoded in the genome of an organism as its collection of tools. Adapting to a new environmental condition (e.g. learning to use a new nutrient source) involves acquiring new enzymes as well as reusing some of the enzymes/tools that are already encoded in the genome. As the toolbox of an organism grows larger, it can reuse its existing tools more often and thus needs to acquire fewer new enzymes to master each new functional task. From this argument it follows that, in general, the number of regulators in the genome should always scale faster than linearly with its total number of proteins. The empirically observed quadratic scaling between these two numbers can be mathematically derived for a broad range of universal network topologies. Furthermore, sizes of evolutionary conserved pathways in our model have a long-tailed power-law distribution that agrees well with the empirical observations. This offers a conceptual explanation for the empirically observed broad distribution of out-degrees of transcription factors in regulatory networks.

References:

[1] E van Nimwegen, "Scaling laws in the functional content of genomes", Trends Genet 19:479-84 2003. [2] S Maslov, S Krishna, T Y Pang, K Sneppen, "Toolbox model of evolution of prokaryotic metabolic networks and their regulation", PNAS 106, 9743-9748 2009.