Related papers: The genetic code invariance: when Euler and Fibona…
In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial…
The sequence of amino acid monomers in the primary structure of a protein is decided by the corresponding sequence of codons (triplets of nucleic acid monomers) on the template messenger RNA (mRNA). The polymerization of a protein, by…
Evolution of genetic code is studied as the change in the choice of enzymes that are used to synthesize amino acids from the genetic information of nucleic acids. We propose the following theory: the differentiation of physiological states…
Eukaryotic DNA is packaged into chromatin: one-dimensional arrays of nucleosomes separated by stretches of linker DNA are folded into 30-nm chromatin fibers which in turn form higher-order structures. Each nucleosome, the fundamental unit…
We discuss the similarity of the degeneration structure of the genetic code with a pure number theoretic -- ``divisors code.'' The most interesting thing about our observation is not that there is a connection between number theory and the…
The genetic code is profoundly shaped by an origin in ancient RNA-mediated interactions, needing an extended development to reach the Standard Genetic Code (SGC). That development can serially use RNA specificities, a ribonucleopeptide…
Statistical models of evolution are algebraic varieties in the space of joint probability distributions on the leaf colorations of a phylogenetic tree. The phylogenetic invariants of a model are the polynomials which vanish on the variety.…
The focus of this paper is the study of generalized Fibonacci polynomials and Fibonomial coefficients. The former are polynomials {n} in variables s and t given by {0} = 0, {1} = 1, and {n} = s{n-1}+t{n-2} for n ge 2. The latter are defined…
The GC-content is very variable in different genome regions and species but although many hypothesis we still do not know the reason why. Here we show that a relationship exists with the mutation rate, in particular we noticed a new…
Proteins are large biomolecules that regulate all living organisms and consist of one or several chains. The primary structure of a protein chain is a sequence of amino acid residues whose three main atoms (alpha-carbon, nitrogen, and…
We present A-CODE, a fully atomic unified one-stage protein co-design model that simultaneously refines discrete atom types and continuous atom coordinates. Unlike predominant two-stage methods that cascade structure design with amino…
We propose a physical model to describe the mechanisms of two major scenarios of the genetic code evolution, the codon capture and ambiguous intermediate scenarios, in a consistent manner. We sketch the lowest dimensional version of our…
Codes have been used for centuries to convey secret information.To a cryptanalyst, the interception of a code is only the first step in recovering a secret message.Deoxyribonucleic acid (DNA) is a biological and molecular code.Through the…
Although several synonymous codons can encode the same aminoacid, this symmetry is generally broken in natural genetic systems. In this article, we show that the symmetry breaking can result from selective pressures due to the violation of…
Given k>1, let a_n be the sequence defined by the recurrence a_n=c_1a_{n-1}+c_2a_{n-2}+...+c_ka_{n-k} for n>=k, with initial values a_0=a_1=...=a_{k-2}=0 and a_{k-1}= 1. We show under a couple of assumptions concerning the constants c_i…
It has been shown recently that chemical bond lengths, in general, like those in the components of nucleic acids, caffeine related compounds, all essential amino acids, methane, benzene, graphene and fullerene are sums of the radii of…
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…
Rotation symmetric bosonic codes are an attractive encoding for qubits into oscillator degrees of freedom, particularly in superconducting qubit experiments. While these codes can tolerate considerable loss and dephasing, they will need to…
In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed-Solomon codes and algebraic geometry codes. This lemma states that two vector…
Seven commuting elements of the Clifford algebra $Cl_{7,7}$ define seven binary eigenvalues that distinguish the $2^7=128$ states of 32 fermions, and determine their parity, electric charge and interactions. Three commuting elements of the…