scholarly journals Complete Quantum Information in the DNA Genetic Code

2020 ◽  
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo Amaral ◽  
Fang Fang ◽  
Klee Irwin
Keyword(s):  
Amino Acids ◽  
Quantum Information ◽  
Symmetric Group ◽  
Genetic Code ◽  
Finite Groups ◽  
Conjugacy Classes ◽  
Threefold Symmetry ◽  
Biological Meaning ◽  
Octahedral Group ◽  
Complete Quantum

We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature $G=\mathbb{Z}_5 \rtimes H$ where $H=\mathbb{Z}_2 . S_4\cong 2O$ is isomorphic to the binary octahedral group $2O$ and $S_4$ is the symmetric group on four letters/bases. The second group has signature $G=\mathbb{Z}_5 \rtimes GL(2,3)$ and points out a threefold symmetry of base pairings. For those groups, the representations for the $22$ conjugacy classes of $G$ are in one-to-one correspondence with the multiplets encoding the proteinogenic amino acids. Additionally, most of the $22$ characters of $G$ attached to those representations are informationally complete. The biological meaning of these coincidences is discussed.

scholarly journals Complete Quantum Information in the DNA Genetic Code

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1993
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo M. Amaral ◽  
Fang Fang ◽  
Klee Irwin
Keyword(s):  
Amino Acids ◽  
Quantum Information ◽  
Symmetric Group ◽  
Genetic Code ◽  
Finite Groups ◽  
Conjugacy Classes ◽  
Threefold Symmetry ◽  
Biological Meaning ◽  
Octahedral Group ◽  
Complete Quantum

We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature G=Z5⋊H where H=Z2.S4≅2O is isomorphic to the binary octahedral group 2O and S4 is the symmetric group on four letters/bases. The second group has signature G=Z5⋊GL(2,3) and points out a threefold symmetry of base pairings. For those groups, the representations for the 22 conjugacy classes of G are in one-to-one correspondence with the multiplets encoding the proteinogenic amino acids. Additionally, most of the 22 characters of G attached to those representations are informationally complete. The biological meaning of these coincidences is discussed.

scholarly journals Complete Quantum Information in the DNA Genetic Code

2020 ◽  
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo Amaral ◽  
Fang Fang ◽  
Klee Irwin
Keyword(s):  
Amino Acids ◽  
Quantum Information ◽  
Symmetric Group ◽  
Genetic Code ◽  
Finite Groups ◽  
Conjugacy Classes ◽  
Threefold Symmetry ◽  
Biological Meaning ◽  
Octahedral Group ◽  
Complete Quantum

We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature $G=\mathbb{Z}_5 \rtimes H$ where $H=\mathbb{Z}_2 . S_4\cong 2O$ is isomorphic to the binary octahedral group $2O$ and $S_4$ is the symmetric group on four letters/bases. The second group has signature $G=\mathbb{Z}_5 \rtimes GL(2,3)$ and points out a threefold symmetry of base pairings. For those groups, the representations for the $22$ conjugacy classes of $G$ are in one-to-one correspondence with the multiplets encoding the proteinogenic amino acids. Additionally, most of the $22$ characters of $G$ attached to those representations are informationally complete. The biological meaning of these coincidences is discussed.

scholarly journals Finite Groups for the Kummer Surface: the Genetic Code and a Quantum Gravity Analogy

2021 ◽  
Author(s):  
Michel Planat --- ◽  
David Chester ◽  
Raymond Aschheim ◽  
Marcelo Amaral ◽  
Fang Fang ◽  
...  
Keyword(s):  
Finite Group ◽  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Genetic Code ◽  
Finite Groups ◽  
Vital Role ◽  
Recent Model ◽  
Biological Functions ◽  
Kummer Surface ◽  
Octahedral Group

The Kummer surface was constructed in 1864. It corresponds to the desingularisation of the quotient of a 4-torus by 16 complex double points. Kummer surface is kwown to play a role in some models of quantum gravity. Following our recent model of the DNA genetic code based on the irreducible characters of the finite group G5:=(240,105)≅Z5⋊2O (with 2O the binary octahedral group), we now find that groups G6:=(288,69)≅Z6⋊2O and G7:=(336,118)≅Z7⋊2O can be used as models of the symmetries in hexamer and heptamer proteins playing a vital role for some biological functions. Groups G6 and G7 are found to involve the Kummer surface in the structure of their character table. An analogy between quantum gravity and DNA/RNA packings is suggested.

scholarly journals Finite Groups for the Kummer Surface: The Genetic Code and a Quantum Gravity Analogy

2021 ◽  
Vol 3 (1) ◽  
pp. 68-79
Author(s):  
Michel Planat ◽  
David Chester ◽  
Raymond Aschheim ◽  
Marcelo M. Amaral ◽  
Fang Fang ◽  
...  
Keyword(s):  
Finite Group ◽  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Genetic Code ◽  
Finite Groups ◽  
Vital Role ◽  
Recent Model ◽  
Biological Functions ◽  
Kummer Surface ◽  
Octahedral Group

The Kummer surface was constructed in 1864. It corresponds to the desingularization of the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in some models of quantum gravity. Following our recent model of the DNA genetic code based on the irreducible characters of the finite group G5:=(240,105)≅Z5⋊2O (with 2O the binary octahedral group), we now find that groups G6:=(288,69)≅Z6⋊2O and G7:=(336,118)≅Z7⋊2O can be used as models of the symmetries in hexamer and heptamer proteins playing a vital role for some biological functions. Groups G6 and G7 are found to involve the Kummer surface in the structure of their character table. An analogy between quantum gravity and DNA/RNA packings is suggested.

THE CONJUGACY CLASSES OF A SUBGROUP $S_{n}^{m} : C_{m}$ OF Smn, prime m

2008 ◽  
Vol 18 (04) ◽  
pp. 705-717
Author(s):  
KENNETH ZIMBA ◽  
MERIAM RABOSHAKGA
Keyword(s):  
Symmetric Group ◽  
Wreath Product ◽  
Direct Product ◽  
Cyclic Group ◽  
Finite Groups ◽  
Conjugacy Classes ◽  
Character Table ◽  
Split Extension ◽  
Alternative Method ◽  
Positive Integers

The conjugacy classes of any group are important since they reflect some aspects of the structure of the group. The construction of the conjugacy classes of finite groups has been a subject of research for several authors. Let n,m be positive integers and [Formula: see text] be the direct product of m copies of the symmetric group Sn of degree n. Then [Formula: see text] is a subgroup of the symmetric group Smn of degree m × n. Let g∈Smn, of type [mn] where each m-cycle contains one symbol from each set of symbols in that order on which the copies of Sn act. Then g permutes the elements of the copies of Sn in [Formula: see text] and generates a cyclic group Cm = 〈g〉 of order m. The wreath product of Sn with Cm is a split extension or semi-direct product of [Formula: see text] by Cm, denoted by [Formula: see text]. It is clear that [Formula: see text] is a subgroup of the symmetric group Smn. In this paper we give a method similar to coset analysis for constructing the conjugacy classes of [Formula: see text], where m is prime. Apart from the fact that this is an alternative method for constructing the conjugacy classes of the group [Formula: see text], this method is useful in the construction of Fischer–Clifford matrices of the group [Formula: see text]. These Fischer–Clifford matrices are useful in the construction of the character table of [Formula: see text].

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.

A NOTE ON THE NUMBER OF ZEROS IN THE COLUMNS OF THE CHARACTER TABLE OF A GROUP

2012 ◽  
Vol 12 (02) ◽  
pp. 1250150 ◽  
Author(s):  
JINSHAN ZHANG ◽  
ZHENCAI SHEN ◽  
SHULIN WU
Keyword(s):  
Finite Groups ◽  
Irreducible Character ◽  
Conjugacy Classes ◽  
Character Table ◽  
Number Of Zeros

The finite groups in which every irreducible character vanishes on at most three conjugacy classes were characterized [J. Group Theory13 (2010) 799–819]. Dually, we investigate the finite groups whose columns contain a small number of zeros in the character table.

Sign in / Sign up

Export Citation Format

Share Document