Related papers: Lie Superalgebras and the Multiplet Structure of t…
Background: There is a 3-fold redundancy in the Genetic Code; most amino acids are encoded by more than one codon. These synonymous codons are not used equally; there is a Codon Usage Bias (CUB). This article will provide novel information…
In this work it is shown that 20 canonical amino acids (AAs) within genetic code appear to be a whole system with strict distinction in Genetic Code Table (GCT) into some different quantums: 20, 23, 61 amino acid molecules. These molecules…
The matrix form of the presentation of the genetic code is described as the cognitive form to analyze structures of the genetic code. A similar matrix form is utilized in the theory of signal processing. The Kronecker family of the genetic…
This letter reports complete sets of two-fold symmetries between partitions of the universal genetic code. By substituting bases at each position of the codons according to a fixed rule, it happens that properties of the degeneracy pattern…
We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is…
Present day data allow significant reconsideration of ideas on mechanisms underlying the degeneracy in the genetic code. Here a hypothesis is presented which links the degeneracy to possible conformational alterations in the codon-anticodon…
The codons, sixtyfour in number, are distributed over the coding parts of DNA sequences. The distribution function is the plot of frequency-versus-rank of the codons. These distributions are characterised by parameters that are almost…
The origin and organizing principles of the genetic code remain fundamental puzzles in life science. The vanishingly low probability of the natural codon-to-amino acid mapping arising by chance has spurred the hypothesis that its structure…
The genetic code is connection between 64 codons, which are building blocks of the genes, and 20 amino acids, which are building blocks of the proteins. In addition to coding amino acids, a few codons code stop signal, which is at the end…
A plausible architecture of an ancient genetic code is derived from an extended base triplet vector space over the Galois field of the extended base alphabet {D, G, A, U, C}, where the letter D represents one or more hypothetical bases with…
In this paper, we give a purely cohomological interpretation of the extension problem for (super) Lie algebras; that is the problem of extending a Lie algebra by another Lie algebra. We then give a similar interpretation of infinitesimal…
Many modified genetic codes are found in specific genomes in which one or more codons have been reassigned to a different amino acid from that in the canonical code. We present a model that unifies four possible mechanisms for reassignment,…
This work aims at showing the relevance and the applications possibilities of the Fibonacci sequence, and also its q-deformed or quantum extension, in the study of the genetic code(s). First, after the presentation of a new formula, an…
We investigate the degeneracy of the central configuration formed by a regular $n$-gon of equal masses together with an additional mass at the center. While degeneracy of such configurations has traditionally been studied through direct…
Recently we have started a program to describe the action of Lie algebras associated with Dynkin-type diagrams on generic Verma modules in terms of polynomial vector fields. In this paper we explain that the results for the classical ABCD…
Several technological applications require the translation of a protein into a nucleic acid that codes for it (``backtranslation''). The degeneracy of the genetic code makes this translation ambiguous; moreover, not every translation is…
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…
In the framework of the crystal basis model of the genetic code, where each codon is assigned to an irreducible representation of $U_{q \to 0}(sl(2) \oplus sl(2))$, single base mutation matrices are introduced. The strength of the mutation…
We develop an algebraic approach to the branching of representations of the general linear Lie superalgebra $\mathfrak{gl}_{p|q}({\mathbb C})$, by constructing certain super commutative algebras whose structure encodes the branching rules.…
We have presented the basic knowledge on the structure of molecules coding the genetic information, mechanisms of transfer of this information from DNA to proteins and phenomena connected with replication of DNA. In particular, we have…