Chirality in a quaternionic representation of the genetic code
| Title: | Chirality in a quaternionic representation of the genetic code |
|---|---|
| Authors: | Carlevaro, C. Manuel, Irastorza, Ramiro M., Vericat, Fernando |
| Publication Year: | 2015 |
| Collection: | Quantitative Biology |
| Subject Terms: | Quantitative Biology - Other Quantitative Biology |
| More Details: | A quaternionic representation of the genetic code, previously reported by the authors, is updated in order to incorporate chirality of nucleotide bases and amino acids. The original representation assigns to each nucleotide base a prime integer quaternion of norm 7 and involves a function that associates with each codon, represented by three of these quaternions, another integer quaternion (amino acid type quaternion) in such a way that the essentials of the standard genetic code (particulaty its degeneration) are preserved. To show the advantages of such a quaternionic representation we have, in turn, associated with each amino acid of a given protein, besides of the type quaternion, another real one according to its order along the protein (order quaternion) and have designed an algorithm to go from the primary to the tertiary structure of the protein by using type and order quaternions. In this context, we incorporate chirality in our representation by observing that the set of eight integer quaternions of norm 7 can be partitioned into a pair of subsets of cardinality four each with their elements mutually conjugates and by putting they in correspondence one to one with the two sets of enantiomers (D and L) of the four nucleotide bases adenine, cytosine, guanine and uracil, respectively. Thus, guided by two diagrams proposed for the codes evolution, we define functions that in each case assign a L- (D-) amino acid type integer quaternion to the triplets of D- (L-) bases. The assignation is such that for a given D-amino acid, the associated integer quaternion is the conjugate of that one corresponding to the enantiomer L. The chiral type quaternions obtained for the amino acids are used, together with a common set of order quaternions, to describe the folding of the two classes, L and D, of homochiral proteins. Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1505.04656 |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/1602.05847 |
| Accession Number: | edsarx.1602.05847 |
| Database: | arXiv |
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| Items | – Name: Title Label: Title Group: Ti Data: Chirality in a quaternionic representation of the genetic code – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Carlevaro%2C+C%2E+Manuel%22">Carlevaro, C. Manuel</searchLink><br /><searchLink fieldCode="AR" term="%22Irastorza%2C+Ramiro+M%2E%22">Irastorza, Ramiro M.</searchLink><br /><searchLink fieldCode="AR" term="%22Vericat%2C+Fernando%22">Vericat, Fernando</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2015 – Name: Subset Label: Collection Group: HoldingsInfo Data: Quantitative Biology – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Quantitative+Biology+-+Other+Quantitative+Biology%22">Quantitative Biology - Other Quantitative Biology</searchLink> – Name: Abstract Label: Description Group: Ab Data: A quaternionic representation of the genetic code, previously reported by the authors, is updated in order to incorporate chirality of nucleotide bases and amino acids. The original representation assigns to each nucleotide base a prime integer quaternion of norm 7 and involves a function that associates with each codon, represented by three of these quaternions, another integer quaternion (amino acid type quaternion) in such a way that the essentials of the standard genetic code (particulaty its degeneration) are preserved. To show the advantages of such a quaternionic representation we have, in turn, associated with each amino acid of a given protein, besides of the type quaternion, another real one according to its order along the protein (order quaternion) and have designed an algorithm to go from the primary to the tertiary structure of the protein by using type and order quaternions. In this context, we incorporate chirality in our representation by observing that the set of eight integer quaternions of norm 7 can be partitioned into a pair of subsets of cardinality four each with their elements mutually conjugates and by putting they in correspondence one to one with the two sets of enantiomers (D and L) of the four nucleotide bases adenine, cytosine, guanine and uracil, respectively. Thus, guided by two diagrams proposed for the codes evolution, we define functions that in each case assign a L- (D-) amino acid type integer quaternion to the triplets of D- (L-) bases. The assignation is such that for a given D-amino acid, the associated integer quaternion is the conjugate of that one corresponding to the enantiomer L. The chiral type quaternions obtained for the amino acids are used, together with a common set of order quaternions, to describe the folding of the two classes, L and D, of homochiral proteins.<br />Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1505.04656 – Name: TypeDocument Label: Document Type Group: TypDoc Data: Working Paper – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="http://arxiv.org/abs/1602.05847" linkWindow="_blank">http://arxiv.org/abs/1602.05847</link> – Name: AN Label: Accession Number Group: ID Data: edsarx.1602.05847 |
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| RecordInfo | BibRecord: BibEntity: Subjects: – SubjectFull: Quantitative Biology - Other Quantitative Biology Type: general Titles: – TitleFull: Chirality in a quaternionic representation of the genetic code Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Carlevaro, C. Manuel – PersonEntity: Name: NameFull: Irastorza, Ramiro M. – PersonEntity: Name: NameFull: Vericat, Fernando IsPartOfRelationships: – BibEntity: Dates: – D: 30 M: 12 Type: published Y: 2015 |
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