Open Access
ARTICLE
Discrete Circular Distributions with Applications to Shared Orthologs of Paired Circular Genomes
Tomoaki Imoto1, *, Grace S. Shieh2, *, Kunio Shimizu3
1 School of Management and Information, University of Shizuoka, Shizuoka, Japan.
2 Institute of Statistical Science, Academia Sinica, Taipei, Taiwan.
3 School of Statistical Thinking, The Institute of Statistical Mathematics, Tokyo, Japan.
* Corresponding Authors: Tomoaki Imoto. Email: ;
Grace S. Shieh. Email: .
(This article belongs to this Special Issue: Data Science and Modeling in Biology, Health, and Medicine)
Computer Modeling in Engineering & Sciences 2020, 123(3), 1131-1149. https://doi.org/10.32604/cmes.2020.08466
Received 29 August 2019; Accepted 07 November 2019; Issue published 28 May 2020
Abstract
For structural comparisons of paired prokaryotic genomes, an important topic in
synthetic and evolutionary biology, the locations of shared orthologous genes (henceforth
orthologs) are observed as binned data. This and other data, e.g., wind directions recorded
at monitoring sites and intensive care unit arrival times on the 24-hour clock, are counted
in binned circular arcs, thus modeling them by discrete circular distributions (DCDs) is
required. We propose a novel method to construct a DCD from a base continuous circular
distribution (CCD). The probability mass function is defined to take the normalized values
of the probability density function at some pre-fixed equidistant points on the circle. Five
families of constructed DCDs which have normalizing constants in closed form are
presented. Simulation studies show that DCDs outperform the corresponding CCDs in
modeling grouped (discrete) circular data, and minimum chi-square estimation outperforms
maximum likelihood estimation for parameters. We apply the constructed DCDs, invariant
wrapped Poisson and wrapped discrete skew Laplace to compare the structures of paired
bacterial genomes. Specifically, discrete four-parameter wrapped Cauchy (nonnegative
trigonometric sums) distribution models multi-modal shared orthologs in
Clostridium (
Sulfolobus)
better than the others considered, in terms of AIC and Freedman’s goodness-of-fit test. The result
that different DCDs fit the shared orthologs is consistent with the fact they belong to two kingdoms.
Nevertheless, these prokaryotes have a common favored site around 70° on the unit circle; this
finding is important for building synthetic prokaryotic genomes in synthetic biology. These DCDs
can also be applied to other binned circular data.
Keywords
Cite This Article
Imoto, T., Shieh, G. S., Shimizu, K. (2020). Discrete Circular Distributions with Applications to Shared Orthologs of Paired Circular Genomes.
CMES-Computer Modeling in Engineering & Sciences, 123(3), 1131–1149.