Related papers: Quaternionic representation of the genetic code
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
A phenomenological model hamiltonian to describe the folding of a protein with any given sequence is proposed. The protein is thought of as a collection of pieces of helices; as a consequence its configuration space increases with the…
Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution. Quantum computation is a new computational paradigm which exploits quantum resources to speed up information processing tasks. Therefore, it is…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution, which are characterized by successfully finding robust solutions for optimization problems. Here, we propose a subroutine-based quantum genetic…
Quaternions provide a unified algebraic and geometric framework for representing three-dimensional rotations without the singularities that afflict Euler-angle parametrisations. This article develops a pedagogical and conceptual analysis of…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
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 show that our recently published Arithmetic Model of the genetic code based on Godel Encoding is robust against symmetry transformations, specially Rumer s one U > G, A > C, and constitutes a link between the degeneracy structure and the…
The genetic code is the set of rules by which information encoded in genetic material (DNA or RNA sequences) is translated into proteins (amino acid sequences) by living cells. The code defines a mapping between tri-nucleotide sequences,…
Protein folding, which dictates the protein structure from its amino acid sequence, is half a century old problem of biology. The function of the protein correlates with its structure, emphasizing the need of understanding protein folding…
The genetic code is nearly universal, and the arrangement of the codons in the standard codon table is highly non-random. The three main concepts on origin and evolution of the code are the stereochemical theory; the coevolution theory; and…
The classical Hamilton equations are reinterpreted by means of complex analysis, in a non standard way. This suggests a natural extension of the Hamilton equations to the quaternionic case, extension which coincides with the one introduced…
How proteins fold remains a central unsolved problem in biology. While the idea of a folding code embedded in the amino acid sequence was introduced more than 6 decades ago, this code remains undefined. While we now have powerful predictive…
Background The theoretical requirements for a genetic code were well defined and modeled by George Gamow and Francis Crick in the 50-es. Their models failed. However the valid Genetic Code, provided by Nirenberg and Matthaei in 1961,…
Protein folding is one of the age-old biological problems that refers to the mechanism of understanding and predicting how a protein's linear sequence of amino acids folds into its specific three dimensional structure.This structure is…
This paper presents a method of reconstruction a primary structure of a protein that folds into a given geometrical shape. This method predicts the primary structure of a protein and restores its linear sequence of amino acids in the…
From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through…
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…
The applications of quaternion in physics are discussed with an emphasis on elementary particle symmetry and interaction. Three colours of the quark and the quantum chromodynamics (QCD) can be introduced directly from the invariance of…