Dinucleotide circular codes and bijective transformations

Fimmel, Elena; Giannerini, Simone; González, Diego; Strüngmann, Lutz

doi:10.1016/j.jtbi.2015.08.034

Cited by 24 publications

(20 citation statements)

References 29 publications

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“…For example, all triplets, which have the order of positions 1-2-3 in Figure 3, are replaced by their reversed analogues with the order of positions 3-2-1 (the triplet CGA is replaced by the triplet AGC, etc.). In studies of genetic coding, special attention is paid to cyclic codes connected with cyclic shifts [17][18][19][20][21][22]. Let us analyze transformations of genetic matrices of 64 triplets in Figures 3 and 4 in cases of simultaneous cyclic permutations of 3 positions in each of the triplets.…”

Section: Black and White Cells Of Genetic Matrices [C A; T G] (2) Amentioning

confidence: 99%

Symmetries in Genetic Systems and the Concept of Geno-Logical Coding

Petoukhov

Petukhova

2016

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Abstract:The genetic code of amino acid sequences in proteins does not allow understanding and modeling of inherited processes such as inborn coordinated motions of living bodies, innate principles of sensory information processing, quasi-holographic properties, etc. To be able to model these phenomena, the concept of geno-logical coding, which is connected with logical functions and Boolean algebra, is put forward. The article describes basic pieces of evidence in favor of the existence of the geno-logical code, which exists in parallel with the known genetic code of amino acid sequences but which serves for transferring inherited processes along chains of generations. These pieces of evidence have been received due to the analysis of symmetries in structures of molecular-genetic systems. The analysis has revealed a close connection of the genetic system with dyadic groups of binary numbers and with other mathematical objects, which are related with dyadic groups: Walsh functions (which are algebraic characters of dyadic groups), bit-reversal permutations, logical holography, etc. These results provide a new approach for mathematical modeling of genetic structures, which uses known mathematical formalisms from technological fields of noise-immunity coding of information, binary analysis, logical holography, and digital devices of artificial intellect. Some opportunities for a development of algebraic-logical biology are opened.

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Section: Black and White Cells Of Genetic Matrices [C A; T G] (2) Amentioning

confidence: 99%

Symmetries in Genetic Systems and the Concept of Geno-Logical Coding

Petoukhov

Petukhova

2016

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“…Mathematical modeling of this geno-logical coding system is connected with dyadic groups of binary numbers, the logical operation of modulo-2 addition, Walsh functions, Hadamard matrices and the Kronecker product of matrices. These mathematical notions are well known in the theory of digital signal processing, but are relatively new in bioinformatics, where they help in developing algebraic biology [24][25][26][27][28][29][30], a wide modern branch of theoretical and mathematical biology. Possibilities of applying the above mentioned mathematical notions to study genetic structures were revealed in the so called "matrix genetics" [31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

The Matrix Method of Representation, Analysis and Classification of Long Genetic Sequences

Stepanyan

Petoukhov

2017

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Abstract:The article is devoted to a matrix method of comparative analysis of long nucleotide sequences by means of presenting each sequence in the form of three digital binary sequences. This method uses a set of symmetries of biochemical attributes of nucleotides. It also uses the possibility of presentation of every whole set of N-mers as one of the members of a Kronecker family of genetic matrices. With this method, a long nucleotide sequence can be visually represented as an individual fractal-like mosaic or another regular mosaic of binary type. In contrast to natural nucleotide sequences, artificial random sequences give non-regular patterns. Examples of binary mosaics of long nucleotide sequences are shown, including cases of human chromosomes and penicillins. The obtained results are then discussed.

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“…The genetic code includes symmetries, such as Rumer's symmetry [17], [18], [19], [20], where transformations of nucleotides into other nucleotides along specific rules reveal symmetries between codon-amino acid families.…”

Section: Introductionmentioning

confidence: 99%

“…(e) Chimeric DNA/RNA [35] and peptides [36] exist. These nucleotide and peptide sequences consist of at least two contiguous parts, where one part is ‘regular’ (= untransformed), the other is swinger-transformed according to one of the 23 potential bijective transformations of nucleotide sequences [19], [20].…”

Section: Introductionmentioning

confidence: 99%

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Unbiased Mitoproteome Analyses Confirm Non-canonical RNA, Expanded Codon Translations

Seligmann

2016

Computational and Structural Biotechnology Journal

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Proteomic MS/MS mass spectrometry detections are usually biased towards peptides cleaved by experimentally added digestion enzyme(s). Hence peptides resulting from spontaneous degradation and natural proteolysis usually remain undetected. Previous analyses of tryptic human proteome data (cleavage after K, R) detected non-canonical tryptic peptides translated according to tetra- and pentacodons (codons expanded by silent mono- and dinucleotides), and from transcripts systematically (a) deleting mono-, dinucleotides after trinucleotides (delRNAs), (b) exchanging nucleotides according to 23 bijective transformations. Nine symmetric and fourteen asymmetric nucleotide exchanges (X ↔ Y, e.g. A ↔ C; and X → Y → Z → X, e.g. A → C → G → A) produce swinger RNAs. Here unbiased reanalyses of these proteomic data detect preferentially non-canonical tryptic peptides despite assuming random cleavage. Unbiased analyses couldn't reconstruct experimental tryptic digestion if most detected non-canonical peptides were false positives. Detected non-tryptic non-canonical peptides map preferentially on corresponding, previously described non-canonical transcripts, as for tryptic non-canonical peptides. Hence unbiased analyses independently confirm previous trypsin-biased analyses that showed translations of del- and swinger RNA and expanded codons. Accounting for natural proteolysis completes trypsin-biased mitopeptidome analyses, independently confirms non-canonical transcriptions and translations.

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Dinucleotide circular codes and bijective transformations

Cited by 24 publications

References 29 publications

Symmetries in Genetic Systems and the Concept of Geno-Logical Coding

Symmetries in Genetic Systems and the Concept of Geno-Logical Coding

The Matrix Method of Representation, Analysis and Classification of Long Genetic Sequences

Unbiased Mitoproteome Analyses Confirm Non-canonical RNA, Expanded Codon Translations

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