Birth and death of protein domains: a simple model of evolution explains power law behavior.

摘要: Power distributions appear in numerous biological, physical and other contexts, which to be fundamentally different. In biology, power laws have been claimed describe the of connections enzymes metabolites metabolic networks, number interactions partners a given protein, members paralogous families, quantities. network analysis, imply evolution with preferential attachment, i.e. greater likelihood nodes being added pre-existing hubs. Exploration different types evolutionary models an attempt determine them lead law has potential revealing non-trivial aspects genome evolution. A simple model domain composition proteomes was developed, following elementary processes: i) birth (duplication divergence), ii) death (inactivation and/or deletion), iii) innovation (emergence from non-coding or non-globular sequences acquisition via horizontal gene transfer). This formalism can described as b irth, d eath i nnovation m odel (BDIM). The formulas for equilibrium frequencies families size total at are derived general BDIM. All asymptotics possible type found their appearance depending on parameters is investigated. It proved that appears if, only balanced, duplication deletion rates asymptotically equal up second order. further any asymptotic degree not -1 if hypothesis independence duplication/deletion family rejected. Specific cases BDIMs, namely simple, linear, polynomial rational models, considered details determined each case. We apply BDIM analysis prokaryotic eukaryotic show excellent fit between these empirical data particular form model, second-order balanced linear Calculation suggests surprisingly high rates, comparable (duplication) elimination particularly genomes. straightforward evolution, does explicitly include selection, sufficient explain observed sizes, asymptotic. However, compatible data, there precise balance birth, this likely maintained by selection. developed approach oriented mathematical description proteomes, but reformulation could applied evolving networks attachment.