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2017 | OriginalPaper | Buchkapitel

Application of the Mixing Partial Order to Genes

verfasst von : William Seitz, Krunoslav Brčić-Kostić, Petar T. Mitrikeski, Patricia Seitz

Erschienen in: Partial Order Concepts in Applied Sciences

Verlag: Springer International Publishing

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Abstract

The partial order that describes “mixedness” of sets of objects is applied to distributions of codons that make up genes. Because partial order usually implies incomparability, the method provides a new characterization of the relationship among genes, namely, their incomparability with one another in a genome. A randomly selected group of 15 genes from the rainbow trout (Oncorhynchus mykiss) is treated to demonstrate the methodology used to determine incomparability among them and to compute their “mixing character.” Of the 15 genes studied, the androgen receptor alpha and beta genes are found to be the most mixed.

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Fußnoten
1
Diagrams are generally rendered in two dimensions, and while they can be “viewed” in higher dimensions they are only properly described as abstract mathematical objects.
 
2
People familiar with Geographic Information Systems will recognize that directed graphs underlie ArcInfo files while shapefiles are undirected.
 
3
Recent attention has been drawn to mixing with regard to molecular genetics (Wan and Wootton 2000) and recently to quantum entanglement (Datta and Vidal 2007) as well.
 
4
Ruch also suggested that the approach to equilibrium in physical systems proceeds according to increasing mixing character (as determined by the majorization partial order)—this is a stronger requirement than increase of entropy alone, though entirely consistent with the physics of thermodynamics. As Ruch points out “…evolution toward equilibrium is not determined by a single function such as the entropy, but rather by a “quality”—the mixing character—that is determined by the majorization partial ordering. It should be noted that second law of thermodynamics discussions using arguments that refer to entropy are unaffected by the principle of increasing mixing character.”
 
5
The codon distribution was obtained from the international DNA sequence databases: status for the year 2000. Nakamura, Y., Gojobori, T. and Ikemura, T. (2000) Nucl. Acids Res. 28, 292.
 
Literatur
Zurück zum Zitat Ferrers’ Diagram|Mathematics (n.d.) Encyclopedia Britannica online. Encyclopedia Britannica. Web. 17 Nov 2015 Ferrers’ Diagram|Mathematics (n.d.) Encyclopedia Britannica online. Encyclopedia Britannica. Web. 17 Nov 2015
Zurück zum Zitat Hardy GH, Ramanujan S (1918) Asymptotic formulae in combinatory analysis. Proc Lond Math Soc 17:75–115CrossRef Hardy GH, Ramanujan S (1918) Asymptotic formulae in combinatory analysis. Proc Lond Math Soc 17:75–115CrossRef
Zurück zum Zitat Marshall AW, Olkin I (1979) Inequalities: theory of majorization and its applications. Academic, New York Marshall AW, Olkin I (1979) Inequalities: theory of majorization and its applications. Academic, New York
Zurück zum Zitat Matsen FA (1975) The unitary group formulation of the N-particle problem. Int J Quantum Chem 8:379–388CrossRef Matsen FA (1975) The unitary group formulation of the N-particle problem. Int J Quantum Chem 8:379–388CrossRef
Zurück zum Zitat Ruch E (1975) The diagram lattice as structural principle. Theor Chim Acta (Berl) 38:167–183CrossRef Ruch E (1975) The diagram lattice as structural principle. Theor Chim Acta (Berl) 38:167–183CrossRef
Zurück zum Zitat Rutherford DE (1948) Substitutional analysis. University Press, Edinburgh Rutherford DE (1948) Substitutional analysis. University Press, Edinburgh
Zurück zum Zitat Seitz W, Kirwan AD (2014) Entropy vs. majorization, what determines complexity. Entropy 16:3793–3807CrossRef Seitz W, Kirwan AD (2014) Entropy vs. majorization, what determines complexity. Entropy 16:3793–3807CrossRef
Zurück zum Zitat Shiner JS, Davison M, Landsberg PT (1999) Simple measure for complexity. Phys Rev A 59:459–1464 Shiner JS, Davison M, Landsberg PT (1999) Simple measure for complexity. Phys Rev A 59:459–1464
Zurück zum Zitat Wan H, Wootton J (2000) A global compositional complexity measure for biological sequences: AT-rich and GC-rich genomes encode less complex proteins. Comput Chem 24:71–94CrossRef Wan H, Wootton J (2000) A global compositional complexity measure for biological sequences: AT-rich and GC-rich genomes encode less complex proteins. Comput Chem 24:71–94CrossRef
Zurück zum Zitat Wikipedia (2015) Entropy (order and disorder) Wikipedia, the free encyclopedia [Online]. Accessed 11 Feb 2015 Wikipedia (2015) Entropy (order and disorder) Wikipedia, the free encyclopedia [Online]. Accessed 11 Feb 2015
Zurück zum Zitat Young A (1900) On quantitative substitutional analysis. Proc Lond Math Soc 33:97–146CrossRef Young A (1900) On quantitative substitutional analysis. Proc Lond Math Soc 33:97–146CrossRef
Metadaten
Titel
Application of the Mixing Partial Order to Genes
verfasst von
William Seitz
Krunoslav Brčić-Kostić
Petar T. Mitrikeski
Patricia Seitz
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-45421-4_17