Genomatrices and the Genetic Octet Yin-Yang-Algebras

2010 ◽  
pp. 132-167
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Amino Acids ◽  
Genetic Code ◽  
Genetic Operators ◽  
Algebraic Models ◽  
Dimensional Algebra ◽  
Black And White ◽  
Mathematical Properties ◽  
Mitochondrial Genetic Code ◽  
Algebraic Properties ◽  
Biological Organisms

Algebraic properties of the genetic code are analyzed. The investigations of the genetic code on the basis of matrix approaches (“matrix genetics”) are described. The degeneracy of the vertebrate mitochondrial genetic code is reflected in the black-and-white mosaic of the (8*8)-matrix of 64 triplets, 20 amino acids, and stop-signals. The special algorithm, which is based on features of genetic molecules, exists to transform the mosaic genomatrix into the matrices, which are members of the special 8-dimensional algebra. Main mathematical properties of this genetic algebra and its relations with other algebras are analyzed together with some important consequences from the adequate algebraic models of the genetic code. Elements of new “genovector calculation” and ideas of “genetic mechanics” are discussed. The revealed fact of the relation between the genetic code and these genetic algebras, which define new multi-dimensional numeric systems, is discussed in connection with the famous idea by Pythagoras: “All things are numbers.” Simultaneously, these genetic algebras can be utilized as the algebras of genetic operators in biological organisms. The described results are related to the problem of algebraization of bioinformatics. They draw attention to the question: what is life from the viewpoint of algebra?

Symmetries of the Degeneracy of the Vertebrate Mitochondrial Genetic Code in the Matrix Form

2010 ◽  
pp. 31-49
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Mathematical Modeling ◽  
Genetic Code ◽  
Matrix Form ◽  
Black And White ◽  
Mitochondrial Genetic Code ◽  
The Matrix

Symmetries of the degeneracy of the vertebrate mitochondrial genetic code in the mosaic matrix form of its presentation are described in this chapter. The initial black-and-white genomatrix of this code is reformed into a new mosaic matrix when internal positions in all triplets are permuted simultaneously. It is revealed unexpectedly that for all six variants of positional permutations in triplets (1-2-3, 2-3-1, 3-1-2, 1-3-2, 2-1-3, 3-2-1) the appropriate genetic matrices possess symmetrical mosaics of the code degeneracy. Moreover the six appropriate mosaic matrices in their binary presentation have the general non-trivial property of their “tetra-reproduction,” which can be utilized in particular for mathematical modeling of the phenomenon of the tetra-division of gametal cells in meiosis. Mutual interchanges of the genetic letters A, C, G, U in the genomatrices lead to new mosaic genomatrices, which possess similar symmetrical and tetra-reproduction properties as well.

scholarly journals Symmetrical Properties of Graph Representations of Genetic Codes: From Genotype to Phenotype

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 388 ◽  
Author(s):  
Marco José ◽  
Gabriel Zamudio
Keyword(s):  
Amino Acids ◽  
Genetic Code ◽  
Graph Representation ◽  
Symmetry Groups ◽  
Standard Genetic Code ◽  
Graph Representations ◽  
Symmetrical Structure ◽  
Genetic Codes ◽  
Mitochondrial Genetic Code

It has long been claimed that the mitochondrial genetic code possesses more symmetries than the Standard Genetic Code (SGC). To test this claim, the symmetrical structure of the SGC is compared with noncanonical genetic codes. We analyzed the symmetries of the graphs of codons and their respective phenotypic graph representation spanned by the RNY (R purines, Y pyrimidines, and N any of them) code, two RNA Extended codes, the SGC, as well as three different mitochondrial genetic codes from yeast, invertebrates, and vertebrates. The symmetry groups of the SGC and their corresponding phenotypic graphs of amino acids expose the evolvability of the SGC. Indeed, the analyzed mitochondrial genetic codes are more symmetrical than the SGC.

The Genetic Code, Hadamard Matrices, Noise Immunity, and Quantum Computers

2010 ◽  
pp. 115-131
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Genetic Code ◽  
Cyclic Codes ◽  
Hadamard Matrices ◽  
Matrix Form ◽  
Quantum Computers ◽  
Black And White ◽  
Discrete Signals ◽  
Mitochondrial Genetic Code ◽  
The Matrix ◽  
Genetic Alphabet

This chapter continues an analysis of the degeneracy of the vertebrate mitochondrial genetic code in the matrix form of its presentation, which possesses the symmetrical black-and-white mosaic. Taking into account a symmetry breakdown in molecular compositions of the four letters of the genetic alphabet, the connection of this matrix form of the genetic code with a Hadamard (8x8)-matrix is discovered. Hadamard matrices are one of the most famous and the most important kinds of matrices in the theory of discrete signals processing and in spectral analysis. The special U-algorithm of transformation of the symbolic genetic matrix [C A; U G](3) into the appropriate Hadamard matrix is demonstrated. This algorithm is based on the molecular parameters of the letters A, C, G, U/T of the genetic alphabet. In addition, the analogical relations is shown between Hadamard matrices and other symmetrical forms of genetic matrices, which are produced from the symmetrical genomatrix [C A; U G](3) by permutations of positions inside triplets. Many new questions arise due to the described fact of the connection of the genetic matrices with Hadamard matrices. Some of them are discussed here, including questions about an importance of amino-group NH2 in molecular-genetic systems, and about possible relations with the theory of quantum computers, where Hadamard gates are utilized. A new possible answer is proposed to the fundamental question concerning reasons for the existence of four letters in the genetic alphabet. Some thoughts about cyclic codes and a principle of molecular economy in genetic informatics are presented as well.

scholarly journals Transferability of N-terminal mutations of pyrrolysyl-tRNA synthetase in one species to that in another species on unnatural amino acid incorporation efficiency

Amino Acids ◽  
2020 ◽  
Author(s):  
Thomas L. Williams ◽  
Debra J. Iskandar ◽  
Alexander R. Nödling ◽  
Yurong Tan ◽  
Louis Y. P. Luk ◽  
...  
Keyword(s):  
Amino Acids ◽  
Amino Acid ◽  
Genetic Code ◽  
Unnatural Amino Acids ◽  
Trna Synthetase ◽  
Unnatural Amino Acid ◽  
Amino Acid Incorporation ◽  
Acid Incorporation ◽  
Genetic Code Expansion ◽  
Incorporation Efficiency

AbstractGenetic code expansion is a powerful technique for site-specific incorporation of an unnatural amino acid into a protein of interest. This technique relies on an orthogonal aminoacyl-tRNA synthetase/tRNA pair and has enabled incorporation of over 100 different unnatural amino acids into ribosomally synthesized proteins in cells. Pyrrolysyl-tRNA synthetase (PylRS) and its cognate tRNA from Methanosarcina species are arguably the most widely used orthogonal pair. Here, we investigated whether beneficial effect in unnatural amino acid incorporation caused by N-terminal mutations in PylRS of one species is transferable to PylRS of another species. It was shown that conserved mutations on the N-terminal domain of MmPylRS improved the unnatural amino acid incorporation efficiency up to five folds. As MbPylRS shares high sequence identity to MmPylRS, and the two homologs are often used interchangeably, we examined incorporation of five unnatural amino acids by four MbPylRS variants at two temperatures. Our results indicate that the beneficial N-terminal mutations in MmPylRS did not improve unnatural amino acid incorporation efficiency by MbPylRS. Knowledge from this work contributes to our understanding of PylRS homologs which are needed to improve the technique of genetic code expansion in the future.

Sign in / Sign up

Export Citation Format

Share Document