Scaling laws in the functional content of genomes: Fundamental constants of evolution?

A few years ago it was noticed that the distributions of gene-family sizes in fully-sequenced genomes follow power-law distributions [8, 6]. Since then different authors have shown that there is in fact a large array of genomic features that show power law distributions. Almost all of these concern the distributions of genomic features within a single genome. For instance, it is shown in [13] that the number of genomic occurrences of DNA words, protein folds, superfamilies, and families all follow power-law distributions. Power-law distributions are also found in the structure of the ‘protein universe’ [12]; the number of protein families per fold is power-law distributed, and so is the number of different assigned biological functions per fold [13]. Power-laws also appear in the structure of cellular interaction and regulatory networks. For example, the number of genes that a given gene interacts with is power-law distributed. This holds both when one defines ’interaction’ between genes on the level of the proteins that they encode [17, 9, 14] or if one defines it at the level of co-regulation of the expression of the genes [16]. The experimental data on transcription regulatory networks is rather incomplete but they also suggest that the number of genes regulated per transcription factor might have power-law tails [7, 15]. Finally, power-laws also appear in cellular metabolic networks; the number of substrates that any given substrate interacts with is power-law distributed [10, 19].