Robersy Sanchez
Department of Biology. Eberly College of Science.
Pennsylvania State University, University Park, PA 16802

ORCID: orcid.org/0000-0002-5246-1453

## Overview

This is a R package to compute the autimorphisms between pairwise aligned DNA sequences represented as elements from a Genomic Abelian group as described in the paper Genomic Abelian Finite Groups. In a general scenario, whole chromosomes or genomic regions from a population (from any species or close related species) can be algebraically represented as a direct sum of cyclic groups or more specifically Abelian p-groups. Basically, we propose the representation of multiple sequence alignments (MSA) of length N as a finite Abelian group created by the direct sum of homocyclic Abelian group of prime-power order:

G = (ℤp1α1)n1 ⊕ (ℤp1α2)n2 ⊕ … ⊕ (ℤpkαk)nk

Where, the pi’s are prime numbers, αi ∈ ℕ and ℤpiαi is the group of integer modulo piαi.

For the purpose of automorphism between two aligned DNA sequences, piαi ∈ {5, 26, 53}.

## Status

This application is under development. Watch this repo or check for updates.

## Tutotials

There are several tutorials on how to use the package at GenomAutomorphism website :

## Dependences

This package depends, so far, from: Biostrings, GenomicRanges, numbers, and S4Vectors.

## Installation of R dependencies:

    if (!requireNamespace("BiocManager")) install.packages("BiocManager")
BiocManager::install()

BiocManager::install(c("Biostrings", "GenomicRanges", "S4Vectors",
"BiocParallel", "GenomeInfoDb", "BiocGenerics"))
install.packages(c("numbers", "devtools", "doParallel", "data.table",
"foreach","parallel", "dplyr"),
dependencies=TRUE)

## You can install GenomAutomorphism package from GitHub

   devtools::install_git("https://github.com/genomaths/GenomAutomorphism.git")

# References

1. Sanchez R, Morgado E, Grau R. Gene algebra from a genetic code algebraic structure. J Math Biol. 2005 Oct;51(4):431-57. doi: 10.1007/s00285-005-0332-8. Epub 2005 Jul 13. PMID: 16012800. ( PDF).

2. Sanchez R, Grau R, Morgado E. A novel Lie algebra of the genetic code over the Galois field of four DNA bases. Math Biosci. 2006;202: 156–174. doi:10.1016/j.mbs.2006.03.017

3. Sanchez R, Grau R. An algebraic hypothesis about the primeval genetic code architecture. Math Biosci. 2009/07/18. 2009;221: 60–76. doi:S0025-5564(09)00114-X [pii] 10.1016/j.mbs.2009.07.001

4. Robersy Sanchez, Jesús Barreto (2021) Genomic Abelian Finite Groups. doi: 10.1101/2021.06.01.446543.

5. M. V José, E.R. Morgado, R. Sánchez, T. Govezensky, The 24 possible algebraic representations of the standard genetic code in six or in three dimensions, Adv. Stud. Biol. 4 (2012) 119–152.PDF.

6. R. Sanchez. Symmetric Group of the Genetic–Code Cubes. Effect of the Genetic–Code Architecture on the Evolutionary Process MATCH Commun. Math. Comput. Chem. 79 (2018) 527-560. PDF.