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A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology
BACKGROUND: Previously, we suggested prototypal models that describe some clinical states based on group postulates. Here, we demonstrate a group/category theory-like model for molecular/genetic biology as an alternative application of our previous model. Specifically, we focus on deoxyribonucleic a...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
BioMed Central
2014
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4057574/ https://www.ncbi.nlm.nih.gov/pubmed/24885369 http://dx.doi.org/10.1186/1742-4682-11-18 |
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author | Sawamura, Jitsuki Morishita, Shigeru Ishigooka, Jun |
author_facet | Sawamura, Jitsuki Morishita, Shigeru Ishigooka, Jun |
author_sort | Sawamura, Jitsuki |
collection | PubMed |
description | BACKGROUND: Previously, we suggested prototypal models that describe some clinical states based on group postulates. Here, we demonstrate a group/category theory-like model for molecular/genetic biology as an alternative application of our previous model. Specifically, we focus on deoxyribonucleic acid (DNA) base sequences. RESULTS: We construct a wallpaper pattern based on a five-letter cruciform motif with letters C, A, T, G, and E. Whereas the first four letters represent the standard DNA bases, the fifth is introduced for ease in formulating group operations that reproduce insertions and deletions of DNA base sequences. A basic group Z(5) = {r, u, d, l, n} of operations is defined for the wallpaper pattern, with which a sequence of points can be generated corresponding to changes of a base in a DNA sequence by following the orbit of a point of the pattern under operations in group Z(5). Other manipulations of DNA sequence can be treated using a vector-like notation ‘D(j)’ corresponding to a DNA sequence but based on the five-letter base set; also, ‘D(j)’s are expressed graphically. Insertions and deletions of a series of letters ‘E’ are admitted to assist in describing DNA recombination. Likewise, a vector-like notation R(j) can be constructed for sequences of ribonucleic acid (RNA). The wallpaper group B = {Z(5)(×∞), ●} (an ∞-fold Cartesian product of Z(5)) acts on D(j) (or R(j)) yielding changes to D(j) (or R(j)) denoted by ‘D(j)◦B((j→k)) = D(k)’ (or ‘R(j)◦B((j→k)) = R(k)’). Based on the operations of this group, two types of groups—a modulo 5 linear group and a rotational group over the Gaussian plane, acting on the five bases—are linked as parts of the wallpaper group for broader applications. As a result, changes, insertions/deletions and DNA (RNA) recombination (partial/total conversion) are described. As an exploratory study, a notation for the canonical “central dogma” via a category theory-like way is presented for future developments. CONCLUSIONS: Despite the large incompleteness of our methodology, there is fertile ground to consider a symmetry model for genetic coding based on our specific wallpaper group. A more integrated formulation containing “central dogma” for future molecular/genetic biology remains to be explored. |
format | Online Article Text |
id | pubmed-4057574 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2014 |
publisher | BioMed Central |
record_format | MEDLINE/PubMed |
spelling | pubmed-40575742014-06-23 A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology Sawamura, Jitsuki Morishita, Shigeru Ishigooka, Jun Theor Biol Med Model Research BACKGROUND: Previously, we suggested prototypal models that describe some clinical states based on group postulates. Here, we demonstrate a group/category theory-like model for molecular/genetic biology as an alternative application of our previous model. Specifically, we focus on deoxyribonucleic acid (DNA) base sequences. RESULTS: We construct a wallpaper pattern based on a five-letter cruciform motif with letters C, A, T, G, and E. Whereas the first four letters represent the standard DNA bases, the fifth is introduced for ease in formulating group operations that reproduce insertions and deletions of DNA base sequences. A basic group Z(5) = {r, u, d, l, n} of operations is defined for the wallpaper pattern, with which a sequence of points can be generated corresponding to changes of a base in a DNA sequence by following the orbit of a point of the pattern under operations in group Z(5). Other manipulations of DNA sequence can be treated using a vector-like notation ‘D(j)’ corresponding to a DNA sequence but based on the five-letter base set; also, ‘D(j)’s are expressed graphically. Insertions and deletions of a series of letters ‘E’ are admitted to assist in describing DNA recombination. Likewise, a vector-like notation R(j) can be constructed for sequences of ribonucleic acid (RNA). The wallpaper group B = {Z(5)(×∞), ●} (an ∞-fold Cartesian product of Z(5)) acts on D(j) (or R(j)) yielding changes to D(j) (or R(j)) denoted by ‘D(j)◦B((j→k)) = D(k)’ (or ‘R(j)◦B((j→k)) = R(k)’). Based on the operations of this group, two types of groups—a modulo 5 linear group and a rotational group over the Gaussian plane, acting on the five bases—are linked as parts of the wallpaper group for broader applications. As a result, changes, insertions/deletions and DNA (RNA) recombination (partial/total conversion) are described. As an exploratory study, a notation for the canonical “central dogma” via a category theory-like way is presented for future developments. CONCLUSIONS: Despite the large incompleteness of our methodology, there is fertile ground to consider a symmetry model for genetic coding based on our specific wallpaper group. A more integrated formulation containing “central dogma” for future molecular/genetic biology remains to be explored. BioMed Central 2014-05-07 /pmc/articles/PMC4057574/ /pubmed/24885369 http://dx.doi.org/10.1186/1742-4682-11-18 Text en Copyright © 2014 Sawamura et al.; licensee BioMed Central Ltd. http://creativecommons.org/licenses/by/2.0 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. |
spellingShingle | Research Sawamura, Jitsuki Morishita, Shigeru Ishigooka, Jun A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology |
title | A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology |
title_full | A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology |
title_fullStr | A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology |
title_full_unstemmed | A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology |
title_short | A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology |
title_sort | symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base e: towards category theory-like systematization of molecular/genetic biology |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4057574/ https://www.ncbi.nlm.nih.gov/pubmed/24885369 http://dx.doi.org/10.1186/1742-4682-11-18 |
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