Modeling and comparing the organization of circular genomes

Abstract

Motivation: Most prokaryotic genomes are circular with a single chromosome (called circular genomes), which consist of bacteria and archaea. Orthologous genes (abbreviated as orthologs) are genes directly evolved from an ancestor gene, and can be traced through different species in evolution. Shared orthologs between bacterial genomes have been used to measure their genome evolution. Here, organization of circular genomes is analyzed via distributions of shared orthologs between genomes. However, these distributions are often asymmetric and bimodal; to date, there is no joint distribution to model such data. This motivated us to develop a family of bivariate distributions with generalized von Mises marginals (BGVM) and its statistical inference.Results: A new measure based on circular grade correlation and the fraction of shared orthologs is proposed for association between circular genomes, and a visualization tool developed to depict genome structure similarity. The proposed procedures are applied to eight pairs of prokaryotes separated from domain down to species, and 13 mycoplasma bacteria that are mammalian pathogens belonging to the same genus. We close with remarks on further applications to many features of genomic organization, e.g. shared transcription factor binding sites, between any pair of circular genomes. Thus, the proposed procedures may be applied to identifying conserved chromosome backbones, among others, for genome construction in synthetic biology.Availability: All codes of the BGVM procedures and 1000+ prokaryotic genomes are available at http://www.stat.sinica.edu.tw/∼gshieh/bgvm.htm.Contact: gshieh@stat.sinica.edu.twSupplementary information: Supplementary data are available at Bioinformatics online.

Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture

“…However, toroidal data can also be observed in other fields, for example, in meteorology (wind directions at two different times of day) and medicine (peak systolic blood pressure during two separate time periods). For the interested reader, some applications of toroidal models can be found in [25][26][27][28][29].…”

“…Given the fact that no closed-form expressions exist, it is necessary to use numerical methods to obtain the MLEs. Operationally, the maximization of ( 26) and (27) with respect to ζ is obtained by the DEoptim package in the R software [38] based on the differential evolution (DE) algorithm [39]. Extensive studies have validated its significant performance as a global optimization algorithm for continuous numerical minimization problems [40].…”

Protein Structure Parameterization via Mobius Distributions on the Torus

“…But the toroidal data can also be observed in other areas; for example, in meteorology (the wind directions at two different times of the day) and medicine (the peak systolic blood pressure during two separate time periods). Some applications of toroidal models can be found in Kato et al (2008), Shieh and Johnson (2005), Shieh et al (2011), Liu et al (2006 and Downs and Mardia (2002).…”

On circular correlation for data on the torus

“…An important and recent overall review of statistical methods for analyzing circular data was presented by Lee (2010) and Pewsey et al (2013). Relevant studies include Abe and Pewsey (2011), Shieh et al (2011), Kim and Sengupta (2013), Kato and Eguchi (2016), Liu et al (2016) and SenGupta and Kim (2016).…”