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

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences - Tập 370 Số 1969 - Trang 2987-3006 - 2012
Simone Giannerini1, Diego Luis Gonzalez2,1, Rodolfo Rosa2,1
1Dipartimento di Scienze Statistiche, Università di Bologna, via delle Belle Arti 41, 40126 Bologna, Italy
2CNR-IMM Sezione di Bologna, Via Gobetti 101, 40129 Bologna, Italy

Tóm tắt

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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Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

Tập 370 Số 1969

2987-3006

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