Scaling Law in Sizes of Protein Sequence Families: from Super-families to Orphan Genes

It has been observed that the size of protein sequence families is unevenly distributed, with few super families with a large number of members and many "orphan" proteins that do not belong to any family. Here it is shown that the distribution of sizes of protein families in different databases and classifications (Protomap, Prodom, Cog) follows a power-law behavior with similar scaling exponents, which is characteristic of self-organizing systems. Since large databases are used in this study, a more detailed analysis of the data than in previous studies was possible. Hence, it is shown that the size distribution is governed by two exponents, different for the super families and the orphan proteins. A simple model of protein evolution is proposed, in which proteins are dynamically generated and clustered into families. The model yields a scaling behavior very similar to the distribution observed in the actual sequence databases, including the two distinct regimes for the large and small families, and thus suggests that the existence of "super families" of proteins and "orphan" proteins are two manifestations of the same evolutionary process.