Divergent evolution of a structural proteome: phenomenological models

¹ Harvard University

^* To whom correspondence should be addressed. E-mail: eugene{at}belok.harvard.edu.

Submitted on January 17, 2006
Revised on April 12, 2006
Accepted on 28 August 2006

	Abstract

We develop models of the divergent evolution of genomes; the elementary object of sequence dynamics is the protein structural domain. To identify patterns of organization that reflect mechanisms of evolution, we consider the individual genomes of many prokaryote species, studying the arrangement of protein structural domains in the space of all polypeptide structures. We view the network of structural similarities as a graph, called the organismal Protein Domain Universe Graph (oPDUG); vertices represent types of structural domains and edges represent strong structural similarity. As observed before, each oPDUG is a highly non-random graph as evidenced in the vertex degree distribution, which resembles a Pareto law (which has a powerlaw asymptotic). To explain this and other peculiar properties of the oPDUGs, we construct an evolving-graph model for the long time-scale evolutionary dynamics of oPDUGs, containing only divergent mechanisms of domain discovery. The model generates degree distributions (resembling Pareto laws) and clustering-coefficient distributions that are characteristic of the oPDUGs. In the infinite-graph limit, we analytically compute the exponent for specific biological parameters, as well as the complete phase diagram of the model, finding two distinct regimes of domain innovation dynamics. Thus, divergent evolutionary dynamics quantitatively explains the non-random organization of oPDUGs.

Key Words: Divergent Models, Protein Evolution, Protein Universe, Proteome