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

Abstract

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.

Complete Quantum Information in the DNA Genetic Code

“…This prompted the authors of Ref. [20,21] to propose a model of the genetic code and its degeneracy distribution based on a boolean number system and/or a tessera code. See also [22] about the ribosomal translation.…”

DNA as information

“…He suggests that the regularities and apparent optimality of the genetic code are inevitable consequences of the originary mechanism he proposes. Gonzalez et al [35] consider how arithmetical representations of the map from trinucleotide codons to amino acids can potentially reveal hidden correlations and symmetries that are not evident in normal tabular representations of the genetic code. Each codon C is represented by a sequence of six binary digits d k ∈ {1, 0 : k = 1, 6} and then transformed into an integer N C through a set of weights w k by arithmetic summation: N C = w k d k .…”

“…However, as the work of Varn & Crutchfield [14] shows, there is a much broader class of structures that could potentially mimic the function of 'DNA as information' in molecular biological-like systems. And the work of Gonzalez et al [35] and Fimmel et al [36] demonstrates that the one example we have of meaningful information stored in molecular structures, that is, life on this planet, relies on a system of interpretation that is intricately bound to exquisite details of both the historical process through which it has emerged and the perhaps diverse possibilities, consistent with the laws of physics and chemistry, of self-referential molecular structures and functionalities coevolving. It might be possible, in completely different environments, for systems of nanoscopic processes to bootstrap themselves into existence and evolve as a result of their association with a colocalized repository of non-DNA information, which they manage to interpret as a programme for their construction through a network of processes not involving a simple translation step.…”

DNA as information: at the crossroads between biology, mathematics, physics and chemistry

“…The issue contains also two opinion papers that review some of the contributions: the piece by Ball [38] focuses on the concept of information in biology and includes comments on the works in [25][26][27][28][29][30][31][32]. The piece by Wills [39] discusses the matter of information in biology also in an evolutionary context by taking into account the problem of the origin of life and of the genetic code; the contributions commented on are those of [26][27][28][29][30][31][32][33][34][35][36][37]. The issue closes with the three seminal articles by Yury Borisovich Rumer on the symmetry of the genetic code that have been expressly translated from Russian for this publication [14][15][16][17] and the epilogue by Cartwright [8].…”

“…The issue has a strong interdisciplinary character, bringing together scientists from different fields such as biology, mathematics, statistics, physics and engineering. The aim of the editors is that the contributions in the issue [25][26][27][28][29][30][31][32][33][34][35][36][37] should stimulate discussions and scientific exchange that will lead to new research on why and how life can exist from the point of view of the coding and decoding of genetic information. The issue contains also two opinion papers that review some of the contributions: the piece by Ball [38] focuses on the concept of information in biology and includes comments on the works in [25][26][27][28][29][30][31][32].…”