This article introduces a novel binary representation of the canonical genetic code based on both the structural similarities of the nucleotides, as well as the physicochemical properties of the encoded amino acids. Each of the four mRNA bases is assigned a unique 2-bit identifier, so that the 64 triplet codons are each indexed by a 6-bit label. The ordering of the bits reflects the hierarchical organization manifested by the DNA replication/repair and tRNA translation systems. In this system, transition and transversion mutations are naturally expressed as binary operations, and the severities of the different point mutations can be analyzed. Using a principal component analysis, it is shown that the physicochemical properties of amino acids related to protein folding also correlate with certain bit positions of their respective labels. Thus, the likelihood for a point mutation to be conservative, and less likely to cause a change in protein functionality, can be estimated.
A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin and evolution of the code as well as with the chronological order of appearence of the amino acids along the evolution as inferred from work that mixtures known experimental results with theoretical speculations. Suggested by the diagram we propose a Hamilton quaternions based mathematical representation of the code as it stands now-a-days. The…
Molecular evidence regarding the genetic code has been examined and the findings on the nature of the early events responsible for the amino acid distribution in the code are reported.
Requiring stability of genetic code against translation errors, modelised by suitable mathematical operators in the crystal basis model of the genetic code, the main features of the organisation in multiplets of the mitochondrial and of the standard genetic code are explained.
Using the crystal basis model of the genetic code, a set of relations between the physical-chemical properties of the amino acids are derived and compared with the experimental data. A prevision for the not yet measured thermodynamical parameters of three amino acids is done.
The ratios of the codon usage in the quartets and sextets for the vertebrate series exhibit a correlated behaviour which fits naturally in the framework of the crystal basis model of the genetic code. Moreover the observed universal behaviour of these suitably normalized ratios can be easily explained.
Why is the genetic code the way it is? The most successful theory states that the codon assignments minimise the effects of errors arising in primordial living systems. Here a transversion is reported that leaves invariant degeneracy in the genetic code. A model was established to address the question: How should sets of synonymous codons be chosen to minimise the deleterious effects of non synonymous substitutions? It is shown that the arithmetic theory of quadratic forms provides the framework for degeneracy in the genetic code.
Modelising the translation errors by suitable mathematical operators in the crystal basis model of the genetic code and requiring that codons prone to be misread encode the same amino-acid, the main features of the organisation in multiplets of the genetic code are described.
The present paper is devoted to foundations of p-adic modelling in genomics. Considering nucleotides, codons, DNA and RNA sequences, amino acids, and proteins as information systems, we have formulated the corresponding p-adic formalisms for their investigations. Each of these systems has its characteristic prime number used for construction of the related information space. Relevance of this approach is illustrated by some examples. In particular, it is shown that degeneration of the genetic code is a p-adic phenomenon. We have also put forward a hypothesis on evolution of the genetic code as…
Important aspects of the process of information storage and retrieval in DNA and RNA, and its evolution, are the role of the anticodons and associated $t$RNA's, and correlations between anticodons and amino acids; the degeneracy of the genetic code, and the periodicity of many amino acid physico-chemical properties. Such factors are analysed in the context of a $sl(6/1)$ supersymmetric model of the genetic code.
The systematics of indices of physico-chemical properties of codons and amino acids across the genetic code are examined. Using a simple numerical labelling scheme for nucleic acid bases, data can be fitted as low-order polynomials of the 6 coordinates in the 64-dimensional codon weight space. The work confirms and extends recent studies by Siemion of amino acid conformational parameters. The connections between the present work, and recent studies of the genetic code structure using dynamical symmetry algebras, are pointed out.
Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are nucleotides, codons and genes. We show that a 5-adic model is appropriate for DNA sequence. This 5-adic model, combined with 2-adic distance, is also suitable for genetic code and for a more advanced employment in genomics. We find that genetic code degeneracy is related to the p-adic distance between codons.
How robust is the natural genetic code with respect to mistranslation errors? It has long been known that the genetic code is very efficient in limiting the effect of point mutation. A misread codon will commonly code either for the same amino acid or for a similar one in terms of its biochemical properties, so the structure and function of the coded protein remain relatively unaltered. Previous studies have attempted to address this question more quantitatively, namely by statistically estimating the fraction of randomly generated codes that do better than the genetic code regarding its overa…
Degeneracy of the genetic code is a biological way to minimize effects of the undesirable mutation changes. Degeneration has a natural description on the 5-adic space of 64 codons $\mathcal{C}_5 (64) = \{n_0 + n_1 5 + n_2 5^2 : n_i = 1, 2, 3, 4 \} ,$ where $n_i$ are digits related to nucleotides as follows: C = 1, A = 2, T = U = 3, G = 4. The smallest 5-adic distance between codons joins them into 16 quadruplets, which under 2-adic distance decay into 32 doublets. p-Adically close codons are assigned to one of 20 amino acids, which are building blocks of proteins, or code termination of protei…
The set of known dialects of the genetic code (GC) is analyzed from the viewpoint of the genetic octave Yin-Yang-algebra. This algebra was described in the previous author's publications. The algebra was discovered on the basis of structural features of the GC in the matrix form of its presentation ("matrix genetics"). The octave Yin-Yang-algebra is considered as the pre-code or as the model of the GC. From the viewpoint of this algebraic model, for example, the sets of 20 amino acids and of 64 triplets consist of sub-sets of "male", "female" and "androgynous" molecules, etc. This algebra perm…
Using the shape space of codons and tRNAs we give a physical description of the genetic code evolution on the basis of the codon capture and ambiguous intermediate scenarios in a consistent manner. In the lowest dimensional version of our description, a physical quantity, codon level is introduced. In terms of the codon levels two scenarios are typically classified into two different routes of the evolutional process. In the case of the ambiguous intermediate scenario we perform an evolutional simulation implemented cost selection of amino acids and confirm a rapid transition of the code chang…
We address the question, related with the origin of the genetic code, of why are there three bases per codon in the translation to protein process. As a followup to our previous work, we approach this problem by considering the translocation properties of primitive molecular machines, which capture basic features of ribosomal/messenger RNA interactions, while operating under prebiotic conditions. Our model consists of a short one-dimensional chain of charged particles(rRNA antecedent) interacting with a polymer (mRNA antecedent) via electrostatic forces. The chain is subject to external forcin…
New developments are presented in the framework of the model introduced by the authors in refs. [1,2] and in which nucleotides as well as codons are classified in crystal bases of the quantum group U_q(sl(2)+sl(2)) in the limit q -> 0. An operator which gives the correspondence between the amino-acids and the codons is now obtained for any known genetic code. The free energy released by base pairing of dinucleotides as well as the relative hydrophilicity and hydrophobicity of the dinucleosides are also computed. For the vertebrate series, a universal behaviour in the ratios of codon usage freq…
The genetic code underlying protein synthesis is a canonical example of a degenerate biological system. Degeneracies in physical and biological systems can be lifted by external perturbations thus allowing degenerate systems to exhibit a wide range of behaviors. Here we show that the degeneracy of the genetic code is lifted by environmental perturbations to regulate protein levels in living cells. By measuring protein synthesis rates from a synthetic reporter library in Escherichia coli, we find that environmental perturbations, such as reduction of cognate amino acid supply, lift the degenera…
Several technological applications require the translation of a protein into a nucleic acid that codes for it (``backtranslation''). The degeneracy of the genetic code makes this translation ambiguous; moreover, not every translation is equally viable. The common answer to this problem is the imitation of the codon usage of the target species. Here we discuss several other features of coding sequences (``coding statistics'') that are relevant for the ``genomic style'' of different species. A genetic algorithm is then used to obtain backtranslations that mimic these styles, by minimizing the di…
The genetic code maps the sixty-four nucleotide triplets (codons) to twenty amino-acids. Some argue that the specific form of the code with its twenty amino-acids might be a 'frozen accident' because of the overwhelming effects of any further change. Others see it as a consequence of primordial biochemical pathways and their evolution. Here we examine a scenario in which evolution drives the emergence of a genetic code by selecting for an amino-acid map that minimizes the impact of errors. We treat the stochastic mapping of codons to amino-acids as a noisy information channel with a natural fi…
The previously formulated model for the evolution of the genetic code was shown to clarify why base triplets of some precursor amino acids differ by a single base from product amino acid codons, while others show less homology. First, the model indicated that the direction of code evolution changed on expansion from the N-fixers code (stage 2). Growth of the code from 16 codons in the NAN column (N, any standard nucleotide) proceeded by assignment of codons in the GNN, ANN, CNN and UNN rows. Expansion phase (stage 4 to 7) precursor/product pairs that spanned this shift included aspartate/threo…
The quantum enveloping algebra U_q(sl(2) \oplus sl(2)) in the limit q \to 0 is proposed as a symmetry algebra for the genetic code. In this approach the triplets of nucleotids or codons in the DNA chain are classified in crystal bases, tensor product of U_{q \to 0}(sl(2) \oplus sl(2)) representations. Such a construction might be compared to the baryon classification from quark building blocks in elementary particles physics, one of the main differences standing in the property of a crystal base to provide a natural order in the state constituents, this order being crucial in the codon. Then a…
Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We evolve connectivity in a single Boolean network, and demonstrate how the sole requirement of sequential matching of attractors may open for an evolution that exhibits punctuated equilibrium.
The genetic code maps the sixty-four nucleotide triplets (codons) to twenty amino-acids. While the biochemical details of this code were unraveled long ago, its origin is still obscure. We review information-theoretic approaches to the problem of the code's origin and discuss the results of a recent work that treats the code in terms of an evolving, error-prone information channel. Our model - which utilizes the rate-distortion theory of noisy communication channels - suggests that the genetic code originated as a result of the interplay of the three conflicting evolutionary forces: the needs …
