scholarly journals The Genetic Code, Algebraic Codes and Double Numbers

2019 ◽  
Author(s):  
Sergey V. Petoukhov
Keyword(s):  
Genetic Code ◽  
Wide Class ◽  
Communication Technologies ◽  
Hyperbolic Numbers ◽  
Double Numbers ◽  
Algebraic Codes ◽  
Structural Relations ◽  
Living Organisms ◽  
Algebraic Code

The article shows materials to the question on algebraic features of the genetic code. Presented results testify in favor that the genetic code is an algebraic code related with a wide class of algebraic codes, which are a basis of noise-immune coding of information in communication technologies. Algebraic features of the genetic code are associated with hypercomplex double (or hyperbolic) numbers. The article also presents data on structural relations of some genetically inherited macrobiological phenomena with double numbers and with their algebraic extentions. The received results confirm that multidimensional numerical systems is effective for modeling and revealing the interconnections of structures of biological bodies at various levels of their organization. This allows one to think that living organisms are algebraically encoded entities.

scholarly journals The Genetic Code, Algebraic Codes and Double Numbers

2020 ◽  
Author(s):  
Sergey V. Petoukhov
Keyword(s):  
Genetic Code ◽  
Communication Technologies ◽  
Structural Features ◽  
Rna Molecules ◽  
Doubly Stochastic ◽  
Dna And Rna ◽  
Double Numbers ◽  
Algebraic Codes ◽  
Living Organisms ◽  
Algebraic Code

The article shows materials to the question about algebraic features of the genetic code and about the dictatorial influence of the DNA and RNA molecules on the whole organism. Presented results testify in favor that the genetic code is an algebraic code related with a wide class of algebraic codes, which are a basis of noise-immune coding of information in communication technologies. Structural features of the genetic systems are associated with hypercomplex double (or hyperbolic) numbers and with bisymmetric doubly stochastic matrices. The received results confirm that represented matrix approaches are effective for modeling genetic phenomena and revealing the interconnections of structures of biological bodies at various levels of their organization. This allows one to think that living organisms are algebraically encoded entities where structures of genetic molecules have the dictatorial influence on inherited structures of the whole organism. New described algebraic approaches and results are discussed.

Multidimensional Numbers and the Genomatrices of Hydrogen Bonds

2010 ◽  
pp. 193-206
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Hydrogen Bonds ◽  
Genetic Code ◽  
Structural Features ◽  
Hyperbolic Type ◽  
Complex Numbers ◽  
Hypercomplex Numbers ◽  
Molecular Systems ◽  
Natural Systems ◽  
Double Numbers ◽  
Mathematical Properties

This chapter returns to the kind of numeric genetic matrices, which were considered in Chapter 4-6. This kind of genomatrices is not connected with the degeneracy of the genetic code directly, but it is related to some other structural features of the genetic code systems. The connection of the Kronecker families of such genomatrices with special categories of hypercomplex numbers and with their algebras is demonstrated. Hypercomplex numbers of these two categories are named “matrions of a hyperbolic type” and “matrions of a circular type.” These hypercomplex numbers are a generalization of complex numbers and double numbers. Mathematical properties of these additional categories of algebras are presented. A possible meaning and possible applications of these hypercomplex numbers are discussed. The investigation of these hyperbolic numbers in their connection with the parameters of molecular systems of the genetic code can be considered as a continuation of the Pythagorean approach to understanding natural systems.

scholarly journals A Stress-Induced Bias in the Reading of the Genetic Code in Escherichia coli

mBio ◽  
2016 ◽  
Vol 7 (6) ◽  
Author(s):  
Adi Oron-Gottesman ◽  
Martina Sauert ◽  
Isabella Moll ◽  
Hanna Engelberg-Kulka
Keyword(s):  
Escherichia Coli ◽  
Amino Acid ◽  
Ribosomal Protein ◽  
Genetic Code ◽  
Open Reading Frames ◽  
Translation Machinery ◽  
E Coli ◽  
Universal Characteristic ◽  
Living Organisms ◽  
Reading Frames

ABSTRACT Escherichia coli mazEF is an extensively studied stress-induced toxin-antitoxin (TA) system. The toxin MazF is an endoribonuclease that cleaves RNAs at ACA sites. Thereby, under stress, the induced MazF generates a stress-induced translation machinery (STM), composed of MazF-processed mRNAs and selective ribosomes that specifically translate the processed mRNAs. Here, we further characterized the STM system, finding that MazF cleaves only ACA sites located in the open reading frames of processed mRNAs, while out-of-frame ACAs are resistant. This in-frame ACA cleavage of MazF seems to depend on MazF binding to an extracellular-death-factor (EDF)-like element in ribosomal protein bS1 (bacterial S1), apparently causing MazF to be part of STM ribosomes. Furthermore, due to the in-frame MazF cleavage of ACAs under stress, a bias occurs in the reading of the genetic code causing the amino acid threonine to be encoded only by its synonym codon ACC, ACU, or ACG, instead of by ACA. IMPORTANCE The genetic code is a universal characteristic of all living organisms. It defines the set of rules by which nucleotide triplets specify which amino acid will be incorporated into a protein. Our results represent the first existing report on a stress-induced bias in the reading of the genetic code. We found that in E. coli , under stress, the amino acid threonine is encoded only by its synonym codon ACC, ACU, or ACG, instead of by ACA. This is because under stress, MazF generates a stress-induced translation machinery (STM) in which MazF cleaves in-frame ACA sites of the processed mRNAs.

scholarly journals Exploring the potential impact of an expanded genetic code on protein function

2015 ◽  
Vol 112 (22) ◽  
pp. 6961-6966 ◽  
Author(s):  
Han Xiao ◽  
Fariborz Nasertorabi ◽  
Sei-hyun Choi ◽  
Gye Won Han ◽  
Sean A. Reed ◽  
...  
Keyword(s):  
Amino Acids ◽  
Genetic Code ◽  
Conformational Changes ◽  
Protein Function ◽  
Catalytic Efficiency ◽  
Structural Basis ◽  
Active Site Residues ◽  
Functional Changes ◽  
Living Organisms ◽  
Expanded Genetic Code

With few exceptions, all living organisms encode the same 20 canonical amino acids; however, it remains an open question whether organisms with additional amino acids beyond the common 20 might have an evolutionary advantage. Here, we begin to test that notion by making a large library of mutant enzymes in which 10 structurally distinct noncanonical amino acids were substituted at single sites randomly throughout TEM-1 β-lactamase. A screen for growth on the β-lactam antibiotic cephalexin afforded a unique p-acrylamido-phenylalanine (AcrF) mutation at Val-216 that leads to an increase in catalytic efficiency by increasing kcat, but not significantly affecting KM. To understand the structural basis for this enhanced activity, we solved the X-ray crystal structures of the ligand-free mutant enzyme and of the deacylation-defective wild-type and mutant cephalexin acyl-enzyme intermediates. These structures show that the Val-216–AcrF mutation leads to conformational changes in key active site residues—both in the free enzyme and upon formation of the acyl-enzyme intermediate—that lower the free energy of activation of the substrate transacylation reaction. The functional changes induced by this mutation could not be reproduced by substitution of any of the 20 canonical amino acids for Val-216, indicating that an expanded genetic code may offer novel solutions to proteins as they evolve new activities.

scholarly journals Genetic code and number theory

2016 ◽  
Vol 14 (3) ◽  
pp. 225-241 ◽  
Author(s):  
Branko Dragovich
Keyword(s):  
Number Theory ◽  
Genetic Code ◽  
21St Century ◽  
Genetic Information ◽  
Life Science ◽  
Theoretical Approaches ◽  
Living Organisms ◽  
The Universe

Living organisms are the most complex, interesting and significant objects regarding all substructures of the universe. Life science is regarded as a science of the 21st century and one can expect great new discoveries in the near futures. This article contains an introductory brief review of genetic information, its coding and translation of genes to proteins through the genetic code. Some theoretical approaches to the modelling of the genetic code are presented. In particular, connection of the genetic code with number theory is considered and the role of p-adic numbers is underlined.

scholarly journals The Triplet Genetic Code: Key to Living Organisms

Heredity ◽  
2002 ◽  
Vol 89 (3) ◽  
pp. 236-237
Author(s):  
S J Freeland
Keyword(s):  
Genetic Code ◽  
Living Organisms

scholarly journals A Topological View of Reed–Solomon Codes

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 578
Author(s):  
Alberto Besana ◽  
Cristina Martínez
Keyword(s):  
Linear Group ◽  
Error Correcting Codes ◽  
Rational Curve ◽  
Rs Codes ◽  
Reed Solomon Codes ◽  
Normal Rational Curve ◽  
Algebraic Codes ◽  
Algebraic Code ◽  
Rational Normal Curve ◽  
Geometric Codes

We studied a particular class of well known error-correcting codes known as Reed–Solomon codes. We constructed RS codes as algebraic-geometric codes from the normal rational curve. This approach allowed us to study some algebraic representations of RS codes through the study of the general linear group GL(n,q). We characterized the coefficients that appear in the decompostion of an irreducible representation of the special linear group in terms of Gromov–Witten invariants of the Hilbert scheme of points in the plane. In addition, we classified all the algebraic codes defined over the normal rational curve, thereby providing an algorithm to compute a set of generators of the ideal associated with any algebraic code constructed on the rational normal curve (NRC) over an extension Fqn of Fq.

Reproduction

2018 ◽  
Author(s):  
Matthew S. Moses ◽  
Gregory S. Chirikjian
Keyword(s):  
Molecular Biology ◽  
Genetic Code ◽  
Mathematical Theory ◽  
Building Blocks ◽  
Model System ◽  
Biological Cells ◽  
John Von Neumann ◽  
Von Neumann ◽  
Universal Construction ◽  
Living Organisms

Computing pioneer and polymath John von Neumann introduced the concept of a Universal Constructor as part of his effort to develop a mathematical theory describing living organisms. A Universal Constructor is a kinematic machine able to manipulate and assemble primitive building blocks. Von Neumann showed how this hypothetical constructor, being itself composed of the same primitive blocks, could self-reproduce and evolve. Remarkably, although this model system pre-dates the discovery of the genetic code, it applies to cell molecular biology as well as man-made machines. This chapter describes some key laboratory demonstrations related to universal construction and machine self-reproduction, and discusses parallels between reproduction processes in machines and biological cells.

scholarly journals On Some Interactions of Organisms

1903 ◽  
Vol 1 (3) ◽  
pp. 3-18
Author(s):  
Stephen A. Forbes
Keyword(s):  
Main Stem ◽  
Common Stock ◽  
Animal Body ◽  
Functional Relations ◽  
History Of ◽  
Anatomical Characters ◽  
Structural Relations ◽  
Living Organisms

While the structural relations of living organisms, as expressed in a classification, can best he figured by a tree—the various groups, pest and present, being related to each other either as twigs to twigs, as twigs to branches,or as branches to the main stem—yet this illustration does not at all express their functional relations. While the anatomical characters of the various groups may show that they are all branches of a common stock, from which they have arisen by repeated divisions and continued divergences, the history of their lives will show that they are now much more intimately and variously bound together by mutual interactions then are twigs of the same branch—that with respect to their vital activities they occupy rather the relation of organs of the same animal body.

Sign in / Sign up

Export Citation Format

Share Document