On the origin of the mitochondrial genetic code: Towards a unified mathematical framework for the management of genetic information

González, Diego; Giannerini, Simone; Rosa, Rodolfo

doi:10.1038/npre.2012.7136.1

Cited by 38 publications

(22 citation statements)

References 6 publications

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“…Moreover, the energy interaction argument presupposes an origin of genetic coding in the form of a triplet in which only the first two bases are read. Our recent results point to a radically new hypothesis (not necessarily in contrast with former theories) about the origin of protein coding: the degeneracy of the genetic code arises from key symmetry properties of codons in a nontriplet assignment [35]. In such schemes, the degeneracy assumes a clear physical meaning-that is, the existence of different states of a system with the same energy.…”

Section: Discussionmentioning

confidence: 94%

“…However, the genetic code has some variants, which can be a product of successive evolution. In any case, it is surprising that the mathematical model based on non-univocal representations of numbers is able to encompass almost all these variants in a unified framework [35]. This fact points to an origin of genetic coding of proteins based on strong organizational principles.…”

Section: Discussionmentioning

confidence: 99%

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

Giannerini

González

Rosa

2012

Phil. Trans. R. Soc. A.

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In this article, we show how a new mathematical model of the genetic code can be exploited for investigating the almost periodic properties of DNA and mRNA protein-coding sequences. We present the main mathematical features of the model and highlight its connections with both number theory and group theory. The group theoretic framework presents interesting analogies with the theory of crystals. Moreover, we exploit the information provided by dichotomic classes, binary variables naturally derived from the mathematical model, in order to build statistical classifiers for retrieving and predicting the normal reading frame used by the ribosome in protein synthesis. The results show that coding sequences possess a local informational structure that can be related to frame synchronization processes. The information for retrieving the normal reading frame, which implies the existence of short-range correlations and almost periodic structures related to the organization of codons, offers an interesting analogy with the properties of quasi-crystals. From a theoretical point of view, our results might contribute to clarifying the relation between biological information and shape in nucleic acids and proteins. Also, from the point of view of applications, we present new promising tools for designing efficient algorithms for frame synchronization, which plays a crucial role in faithful synthesis of proteins.

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Section: Discussionmentioning

confidence: 94%

Section: Discussionmentioning

confidence: 99%

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

Giannerini

González

Rosa

2012

Phil. Trans. R. Soc. A.

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“…This nice property alert us on the important role of inversion symmetries along coding sequences. In fact, in Gonzalez et al (2012) it has been shown that the symmetries of complementarity and inversion can be used to derive a complete version of a hypothetical primeval mitochondrial code composed of codons of four letters (tesserae). We conclude the section with a corollary and a remark:…”

Section: Structure Of a Circular Codementioning

confidence: 99%

Circular codes, symmetries and transformations

et al. 2014

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Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes.

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“…This genetic information could in part be related to traces of ancestral codes (El Soufi and Michel, 2017). Indeed, in recent years, various authors have formulated hypotheses about the origin of the modern genetic code in which it is assumed that single amino acids were first encoded by dinucleotides or tetranucleotides, and then later by trinucleotides (see, among others, Baranov et al, 2009;Gonzalez et al, 2012;Patel, 2005; Seligmann, 2014; Wilhelm and Nikolaeva, 2004;Wu et al, 2005). This coding process could have been necessary because the number of amino acids to be encoded increased during the evolution while at the same time nature needed robustness against mutations and translational errors.…”

Section: {A N D Q E G I L F T Y V }mentioning

confidence: 99%

Mixed circular codes

Fimmel

Michel

Pirot

et al. 2019

Mathematical Biosciences

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By an extensive statistical analysis in genes of bacteria, archaea, eukaryotes, plasmids and viruses, a maximal C 3-self-complementary trinucleotide circular code has been found to have the highest average occurrence in the reading frame of the ribosome during translation. Circular codes may play an important role in maintaining the correct reading frame. On the other hand, as several evolutionary theories propose primeval codes based on dinucleotides, trinucleotides and tetranucleotides, mixed circular codes are investigated. By using a graph-theoretical approach of circular codes recently developed, we study mixed circular codes, which are the union of a dinucleotide circular code, a trinucleotide circular code and a tetranucleotide circular code. Maximal mixed circular codes of (di,tri)-nucleotides, (tri,tetra)-nucleotides and (di,tri,tetra)-nucleotides are constructed, respectively. In particular, we show that any maximal dinucleotide circular code of size 6 can be embedded into a maximal mixed (di,tri)-nucleotide circular code such that its trinucleotide component is a maximal C 3-comma-free code. The growth function of self-complementary mixed circular codes of dinucleotides and trinucleotides is given. Self-complementary mixed circular codes could have been involved in primitive genetic processes.

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On the origin of the mitochondrial genetic code: Towards a unified mathematical framework for the management of genetic information

Cited by 38 publications

References 6 publications

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

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

Circular codes, symmetries and transformations

Mixed circular codes

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