title: Size distribution of function-based human gene sets and the split-merge model.
abstract: The sizes of paralogues-gene families produced by ancestral duplication-are known to follow a power-law distribution. We examine the size distribution of gene sets or gene families where genes are grouped by a similar function or share a common property. The size distribution of Human Gene Nomenclature Committee (HGNC) gene sets deviate from the power-law, and can be fitted much better by a beta rank function. We propose a simple mechanism to break a power-law size distribution by a combination of splitting and merging operations. The largest gene sets are split into two to account for the subfunctional categories, and a small proportion of other gene sets are merged into larger sets as new common themes might be realized. These operations are not uncommon for a curator of gene sets. A simulation shows that iteration of these operations changes the size distribution of Ensembl paralogues and could lead to a distribution fitted by a rank beta function. We further illustrate application of beta rank function by the example of distribution of transcription factors and drug target genes among HGNC gene families.
authors.affiliation: The Robert S. Boas Center for Genomics and Human Genetics , The Feinstein Institute for Medical Research , Northwell Health, Manhasset, NY, USA.
authors.forename: Wentian
authors.identifier: 0000-0003-1155-110X
authors.initials: W
authors.lastname: Li
authors.affiliation: Departamento de Matemáticas, Facultad de Ciencias , Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria , México 04510 DF, México.
authors.forename: Oscar
authors.initials: O
authors.lastname: Fontanelli
authors.affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México 04510 DF, México; Bioinformatics Group and Interdisciplinary Center for Bioinformatics, University of Leipzig, Haertelstrasse 16-18, 04107 Leipzig, Germany.
authors.forename: Pedro
authors.initials: P
authors.lastname: Miramontes
keywords: beta rank function; gene family sizes; gene set sizes; power-law