DNA, dichotomic classes and frame synchronization: a quasi-crystal framework

Giannerini, Simone; González, Diego; Rosa, Rodolfo

doi:10.1098/rsta.2011.0387

Cited by 18 publications

(7 citation statements)

References 32 publications

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“…The analysis of coding sequences of DNA by means of dichotomic classes highlighted the presence of universal strong short-range correlations that can be related to error detection [31,32]. Moreover, the theory of circular codes [52,54,56,58], a class of error detecting codes that have been proposed as strategies for frame detection and maintenance, can also be related to this mathematical framework [64].…”

Section: Resultsmentioning

confidence: 99%

On the origin of degeneracy in the genetic code

2019

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The degeneracy of amino acid coding is one of the most crucial and enigmatic aspects of the genetic code. Different theories about the origin of the genetic code have been developed. However, to date, there is no comprehensive hypothesis on the mechanism that might have generated the degeneracy as we observe it. Here, we provide a new theory that explains the origin of the degeneracy based only on symmetry principles. The approach allows one to describe exactly the degeneracy of the early code (progenitor of the genetic code of LUCA, the last universal common ancestor) which is hypothesized to have the same degeneracy as the present vertebrate mitochondrial genetic code. The theory is based upon the tessera code, that fits as the progenitor of the early code. Moreover, we describe in detail the possible evolutionary transitions implied by our theory. The approach is supported by a unified mathematical framework that accounts for the degeneracy properties of both nuclear and mitochondrial genetic codes. Our work provides a new perspective to the understanding of the origin of the genetic code and the roles of symmetry principles in the organization of genetic information.

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Section: Resultsmentioning

confidence: 99%

On the origin of degeneracy in the genetic code

2019

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“…These are important to study the problem of retrieving and maintaining of the correct reading frame [45][46][47][48]. The non-power approach allows one to study sequences of DNA and mRNA, including their codon bias, under a new perspective [13][14][15]49] and can lead to new bioinformatics tools and new applications in medicine.…”

Section: Resultsmentioning

confidence: 99%

“…In [14], we have shown that coding sequences are characterized by universal short-range correlations that show up only by looking at dichotomic classes. Moreover, in [15], we have shown that dichotomic classes can be used to design algorithms for frame retrieval.…”

Section: Nnr Xmentioning

confidence: 99%

The non-power model of the genetic code: a paradigm for interpreting genomic information

González

Giannerini

Rosa

2016

Phil. Trans. R. Soc. A.

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In this article, we present a mathematical framework based on redundant (non-power) representations of integer numbers as a paradigm for the interpretation of genomic information. The core of the approach relies on modelling the degeneracy of the genetic code. The model allows one to explain many features and symmetries of the genetic code and to uncover hidden symmetries. Also, it provides us with new tools for the analysis of genomic sequences. We review briefly three main areas: (i) the Euplotid nuclear code, (ii) the vertebrate mitochondrial code, and (iii) the main coding/decoding strategies used in the three domains of life. In every case, we show how the non-power model is a natural unified framework for describing degeneracy and deriving sound biological hypotheses on protein coding. The approach is rooted on number theory and group theory; nevertheless, we have kept the technical level to a minimum by focusing on key concepts and on the biological implications.

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“…These findings are of particular interest as the information for retrieving the normal reading frame of DNA implies the presence of short-range correlations and almost periodic structures, offering an analogy with the properties of quasicrystals (Giannerini et al, 2012).…”

Section: The Beauty Of Symmetry and The Golden Mean In Biologymentioning

confidence: 99%

Biological Quasicrystals and the Golden Mean: Relevance to Quantum Computation

Gardiner

2015

Neuroquantology

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Since the discovery of metallic quasicrystals, which lack translational symmetry, much work has been done on their characterisation. In particular mathematical aperiodic tilings have been invoked in an effort to explain their existence. It appears that in three-dimensional quasicrystals non-local quantum effects may not be required. However, here I present some instances -ribosome organisation in embryonic plants, neurotransmitter receptor complexes in animal nervous systems, the cross-section of microtubule bundles and nucleic acids -where biological two-dimensional quasicrystals may occur. Two-dimensional quasicrystals do require non-local quantum effects. This has possible ramifications for both plant development and consciousness. The golden mean is integral to the structure of aperiodic tilings and is found widely in nature, including in plant development, brain EEG waves, and in the consciousness of beauty. I suggest that somehow the encoding of the golden mean in sub-cellular quasicrystals leads to its expression in these macro systems.

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DNA, dichotomic classes and frame synchronization: a quasi-crystal framework

Cited by 18 publications

References 32 publications

On the origin of degeneracy in the genetic code

On the origin of degeneracy in the genetic code

The non-power model of the genetic code: a paradigm for interpreting genomic information

Biological Quasicrystals and the Golden Mean: Relevance to Quantum Computation

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