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A. Sciarrino

Publications and source records attributed to A. Sciarrino.

At least 19 recordsLinked to original sources
arXiv2017

Symmetry and Minimum Principle at the Basis of the Genetic Code

The importance of the notion of symmetry in physics is well established: could it also be the case for the genetic code? In this spirit, a model for the Genetic Code based on continuous symmetries and entitled the "Crystal Basis Model" has been proposed a few years ago. The present paper is a review of the model, of some of its first applications as well as of its recent developments. Indeed, after a motivated presentation of our mathematical model, we illustrate its pertinence by applying it for the elaboration and verification of sum rules for codon usage probabilities, as well as for establishing relations and some predictions between physical-chemical properties of amino-acids. Then, defining in this context a "bio-spin" structure for the nucleotides and codons, the interaction between a couple of codon-anticodon can simply be represented by a (bio) spin-spin potential. This approach will constitute the second part of the paper where, imposing the minimum energy principle, an analysis of the evolution of the genetic code can be performed with good agreement with the generally accepted scheme. A more precise study of this interaction model provides informations on codon bias, consistent with data.

q-bio.OT↗
arXiv2017

Metrics and Harmonic Analysis on DNA

A mathematical algorithm to describe DNA or RNA sequences of $N$ nucleotides by a string of $2N$ integers numbers is presented in the framework of the so called crystal basis model of the genetic code. The description allows to define a not trivial distance between two sequences and to perform the Discrete Fourier Transform on a sequence. Using the definition of distance the sequence of $β$-globin for Homo, Gallus and Opossum are compared. The Discrete Fourier Transform for some simple examples is computed.

q-bio.OT↗
arXiv2014

Crystal Basis Model: Codon-Anticodon Interaction and Genetic Code Evolution

Imposing a minimum principle in the framework of the so called crystal basis model of the genetic code, we determine the structure of the minimum set of 22 anticodons which allows the translational-transcription for animal mitochondrial code. The results are in very good agreement with the observed anticodons. Then, we analyze the evolution of the genetic code, with 20 amino acids encoded from the beginning, from the viewpoint of codon-anticodon interaction. Following the same spirit as above, we determine the structure of the anticodons in the Ancient, Archetypal and Early Genetic codes. Most of our results agree with the generally accepted scheme.

q-bio.QM↗
arXiv2011

A Minimum Principle in Codon-Anticodon Interaction

Imposing a minimum principle in the framework of the so called crystal basis model of the genetic code, we determine the structure of the minimum set of anticodons which allows the translational-transcription for animal mitochondrial code. The results are in very good agreement with the observed anticodons.

q-bio.QM↗
arXiv2005

Standard and Non-standard Extensions of Lie algebras

We study the problem of quadruple extensions of simple Lie algebras. We find that, adding a new simple root $α_{+4}$, it is not possible to have an extended Kac-Moody algebra described by a Dynkin-Kac diagram with simple links and no loops between the dots, while it is possible if $α_{+4}$ is a Borcherds imaginary simple root. We also comment on the root lattices of these new algebras. The folding procedure is applied to the simply-laced triple extended Lie algebras, obtaining all the non-simply laced ones. Non- standard extension procedures for a class of Lie algebras are proposed. It is shown that the 2-extensions of $E_{8}$, with a dot simply linked to the Dynkin-Kac diagram of $E_{9}$, are rank 10 subalgebras of $E_{10}$. Finally the simple root systems of a set of rank 11 subalgebras of $E_{11}$, containing as sub-algebra $E_{10}$, are explicitly written.

hep-th↗
arXiv2005

Mutation model for nucleotide sequences based on crystal basis

A nucleotides sequence is identified, in the two (four) letters alphabet, by the the labels of a vector state of an irreducible representation of U_q(sl(2)) (U_q(sl(2) + sl(2))), in the limit q -> 0. A master equation for the distribution function is written, where the intensity of the one-spin flip is assumed to depend from the variation of the labels of the state. In the two letters approximation, the numerically computed equilibrium distribution for short sequences is nicely fitted by a Yule distribution, which is the observed distribution of the ranked short oligonucleotides frequency in DNA. The four letter alphabet description, applied to the codons, is able to reproduce the form of the fitted rank ordered usage frequencies distribution.

q-bio.BM↗
arXiv2004

Mutation model for oligonucleotides fitting a Yule distribution

A spin chain, describing a nucleotides sequence, is identified by the labels of a vector state of an irreducible representation of U_q->0(sl2). A master equation for the distribution function is written, where the intensity of the one-spin flip is assumed to depend on the variation of the labels. The numerically computed equilibrium distribution is nicely fitted by a Yule distribution, which is the observed distribution of the ranked short oligonucleotides frequency in DNA

q-bio.BM↗
arXiv2004

Hyperbolic Kac-Moody superalgebras

We present a classification of the hyperbolic Kac-Moody (HKM) superalgebras. The HKM superalgebras of rank larger or equal than 3 are finite in number (213) and limited in rank (6). The Dynkin-Kac diagrams and the corresponding simple root systems are determined. We also discuss a class of singular sub(super)algebras obtained by a folding procedure.

math-ph↗
arXiv2004

Quantum spin model fitting the Yule distribution of oligonucleotides in DNA

A quantum spin chain is identified by the labels of a vector state of a Kashiwara crystal basis. The intensity of the one-spin flip is assumed to depend from the variation of the labels. The rank ordered plot of the numerically computed, averaged in time, transition probabilities is nicely fitted by a Yule distribution, which is the observed distribution of the ranked short oligonucleotides frequency in DNA.

quant-ph↗
arXiv2003

Sum rules for free energy and frequency distribution of DNA dinucleotides

The large discrepancy between the values of the free energy for DNA dinucleotides (or dimers) measured by different teams has raised a yet unsettled debate. Here the free energy is fitted by a three parameter empiric formula derived in the framework of the crystal basis model of genetic code. Sum rules are derived and compared satisfactorily with the data. On the basis of theoretical and phenomenological arguments, a relation between the correlation functions of dimer distribution and the free energy is assumed. From consistency conditions, sum rules are derived. A check of these conditions with different samples of experimental data is performed, allowing us to argue on the reliability of the different sets of experimental data.

cond-mat↗
arXiv2003

Universality and Shannon entropy of codon usage

The distribution functions of the codon usage probabilities, computed over all the available GenBank data, for 40 eukaryotic biological species and 5 chloroplasts, do not follow a Zipf law, but are best fitted by the sum of a constant, an exponential and a linear function in the rank of usage. For mitochondriae the analysis is not conclusive. A quantum-mechanics-inspired model is proposed to describe the observed behaviour. These functions are characterized by parameters that strongly depend on the total GC content of the coding regions of biological species. It is predicted that the codon usage is the same in all exonic genes with the same GC content. The Shannon entropy for codons, also strongly depending on the exonic GC content, is computed.

cond-mat↗
arXiv2003

Correlation matrix for quartet codon usage

It has been argued that the sum of usage probabilities for codons, belonging to quartets, that have as third nucleotide C or A, is independent of the biological species for vertebrates. The comparison between the theoretical correlation matrix derived from these sum rules and the experimentally computed matrix for 26 species shows a satisfactory agreement. The Shannon entropy, weakly depending on the biological species, gives further support. Suppression of codons containing the dinucleotides CG or AU is put in evidence.

cond-mat↗
arXiv2002

Sum rules of codon usage probabilities

In the crystal basis model of the genetic code, it is deduced that the sum of usage probabilities of the codons with C and A in the third position for the quartets and/or sextets is independent of the biological species for vertebrates. A comparison with experimental data shows that the prediction is satisfied within about 5 %.

physics.bio-ph↗
arXiv2001

A minimum principle in mRNA editing ?

mRNA editing of sequences of many species is analyzed. The nature of the inserted nucleotides and the position of the insertion sites, once fixed the edited peptide chain, are explained by introducing a minimum principle in the framework of the crystal basis model of the genetic code introduced by the authors.

physics.bio-ph↗