Narrow Results

We model the evolution of a population on a 2D cellular automata (CA) lattice. Every individual holds a binary "genetic code". The code length and the number of "1"s in the chain correspond to the maximal and actual life-time of individual, respectively. The "genetic code" code is divided onto three life-episodes: "youth", "maturity" and "old age". Only "mature" individuals can procreate. We investigate the duration of the life-episodes and their role in protecting the population from extinction in hostile environments. We observe that in the stable environment, which does not influence the life-time of individuals, the "youth" and the "maturity" periods extend extremely long during evolution, while the "old age" remains short. The situation is different for hostile plaque-like conditions. Under these circumstances, the "youth" period vanishes, while the longer "old age" period stabilizes the population growth, increases its average age and thereby increases its chance of survival. We can conclude that the idle life-episodes set up the control mechanisms, which allow for self-adaptation of the population to varying environmental conditions.

This paper investigates the dimensionality of genetic information from the perspective of optimal representation. Recently it has been shown that optimal coding of information is in terms of the noninteger dimension of e, which is accompanied by the property of scale invariance. Since Nature is optimal, we should see this dimension reflected in the organization of the genetic code. With this as background, this paper investigates the problem of the logic behind the nature of the assignment of codons to amino acids, for they take different values that range from 1 to 6. It is shown that the non-uniformity of this assignment, which goes against mathematical coding theory that demands a near uniform assignment, is consistent with noninteger dimensions. The reason why the codon assignment for different amino acids varies is because uniformity is a requirement for optimality only in a standard vector space, and is not so in the noninteger dimensional space. It is noteworthy that there are 20 different covering regions in an e-dimensional information space, which is equal to the number of amino acids. The problem of the visualization of data that originates in an e-dimensional space but examined in a 3-dimensional vector space is also discussed. It is shown that the assignment of the codons to the amino acids is fractal-like that is well modeled by the Zipf distribution which is a power law. It is remarkable that the Zipf distribution that holds for the letter frequencies of words in a natural language also applies to the rank order of triplets in the code for amino acids.

We report on the search for symmetries in the genetic code involving the medium rank simple Lie algebras and , in the context of the algebraic approach originally proposed by one of the present authors, which aims at explaining the degeneracies encountered in the genetic code as the result of a sequence of symmetry breakings that have occurred during its evolution.

We give a list of all possible schemes for performing amino acid and codon assignments in algebraic models for the genetic code, which are consistent with a few simple symmetry principles, in accordance with the spirit of the algebraic approach to the evolution of the genetic code proposed by Hornos and Hornos. Our results are complete in the sense of covering all the algebraic models that arise within this approach, whether based on Lie groups/Lie algebras, on Lie superalgebras or on finite groups.

We give a full classification of the possible schemes for obtaining the distribution of multiplets observed in the standard genetic code by symmetry breaking in the context of finite groups, based on an extended notion of partial symmetry breaking that incorporates the intuitive idea of "freezing" first proposed by Francis Crick, which is given a precise mathematical meaning.

An in silico study of mRNA secondary structure has found a bias within the coding sequences of genes that favors "in-frame" pairing of nucleotides. This pairing of codons, each with its reverse-complement, partitions the 20 amino acids into three subsets. The genetic code can therefore be represented by a three-component graph. The composition of proteins in terms of amino acid membership in the three subgroups has been measured, and sequence runs of members within the same subgroup have been analyzed using a runs statistic based on Z-scores. In a GENBANK database of over 416,000 protein sequences, the distribution of this runs-test statistic is negatively skewed. To assess whether this statistical bias was due to a chance grouping of the amino acids in the real genetic code, several alternate partitions of the genetic code were examined by permuting the assignment of amino acids to groups. A metric was constructed to define the difference, or "distance", between any two such partitions, and an exhaustive search was conducted among alternate partitions maximally distant from the natural partition of the genetic code, to select sets of partitions that were also maximally distant from one another. The statistical skewness of the runs statistic distribution for native protein sequences were significantly more negative under the natural partition than they were under all of the maximally different partition of codons, although for all partitions, including the natural one, the randomized sequences had quite similar skewness. Hence under the natural graph theory partition of the genetic code there is a preference for more protein sequences to contain fewer runs of amino acids, than they do under the other partitions, meaning that the average run must be longer under the natural partition. This suggests that a corresponding bias may exist in the coding sequences of the actual genes that code for these proteins.

Algebraic theory of coding is one of modern fields of applications of algebra. This theory uses matrix algebra intensively. This paper is devoted to an application of Kronecker's matrix forms of presentations of the genetic code for algebraic analysis of a basic scheme of degeneracy of the genetic code. Similar matrix forms are utilized in the theory of signal processing and encoding. The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C A; U G], where C, A, U, G are the letters of the genetic alphabet. This matrix in the third Kronecker power is the (8*8)-matrix, which contains all 64 genetic triplets in a strict order with a natural binary numeration of the triplets by numbers from 0 to 63. Peculiarities of the basic scheme of degeneracy of the genetic code are reflected in the symmetrical black-and-white mosaic of this genetic (8*8)-matrix. This mosaic matrix is connected algorithmically with Hadamard matrices unexpectedly, which are famous in the theory of signal processing and encoding, spectral analysis, quantum mechanics and quantum computers. Furthermore, many kinds of cyclic permutations of genetic elements lead to reconstruction of initial Hadamard matrices into new Hadamard matrices unexpectedly. This demonstrates that matrix algebra is one of promising instruments and of adequate languages in bioinformatics and algebraic biology.

The genetic code is the rule by which DNA stores the genetic information about formation of protein molecule. In this paper, a partial ordering is equipped on the genetic code and a lattice structure has been developed from it. The codon–anticodon interaction, hydrogen bond number and the chemical types of bases play an important role in the partial ordering. We have established some relations between the lattice structure of the genetic code and physico-chemical properties of amino acids. Taking into consideration the evolutionary importance of base positions in codons we have constructed a distance matrix for the amino acids. Further with a real life example we have demonstrated the relationship between frequently occurring mutations and codon distances.

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We present a new classification scheme of the genetic code. In contrast to the standard form it clearly shows five codon symmetries: codon-anticodon, codon-reverse codon, and sense-antisense symmetry, as well as symmetries with respect to purine-pyrimidine (A versus G, U versus C) and keto-aminobase (G versus U, A versus C) exchanges. We study the number of tRNA genes of 16 archaea, 81 bacteria and 7 eucaryotes to analyze whether these symmetries are reflected in the corresponding tRNA usage patterns. Two features are especially striking: reverse stop codons do not have their own tRNAs (just one exception in human), and A** anticodons are significantly suppressed. Our classification scheme of the genetic code and the identified tRNA usage patterns support recent speculations about the early evolution of the genetic code. In particular, pre-tRNAs might have had the ability to bind their codons in two directions to the corresponding codons.

A comparison is made among diverse six-dimensional Boolean representations of the genetic code. These models were incorporated in an interactive computational tool, HyperGCode, to graphically display the topological relations among codons, amino acids, and amino acid properties. After a description of the tool's capabilities, I demonstrate its usefulness with one example. I make a comparative analysis of mutations in β-lactamases and show that, both natural mutants and those produced by directed evolution are related to one another by one and two-bit changes in their codons. The Darwinian solutions to the β-lactamase design problem, in nature and in vitro, exhibit mainly conservative amino acid substitutions in functionally important positions.

Nature offers an astonishing array of complex structures and functional devices. The most sophisticated examples of functional systems with multiple interconnected nano-scale components can be found in biology. Biology uses a limited number of building blocks to create complexity and to extend the size and the functional range of basic nano-scale structures to new domains. Three main groups of molecular tools used by biology include oligonucleotides (linear chains of nucleotides), proteins (folded chains of amino acids), and polysaccharides (chains of sugar molecules). Nature uses these tools to store information, to create structures, and to build nano-scale machines.

Recent advances in understanding the structure and function of these building blocks has enabled a number of novel uses for them outside the biological domain. Of particular interest to us is the use of these building blocks to self-assemble nano-scale electronic, photonics, or nanomechanical systems. In this chapter we will look at two groups of building blocks (oligonucleotides and proteins) and review how they have been used to self-assemble engineered structures and build functional devices in the nano-scale.

We will begin by a review of the basic structure and properties (both physical and chemical) of oligonucleotides and proteins. This section is meant to be used as a self-contained reference for the readers from the engineering community that may be less familiar with the symbols and jargon of biochemistry. The most salient properties of the biomolecules are emphasized and listed here to facilitate future research in the area. We continue by a review of recent advances in designing artificial nano-scale DNA structures that can be constructed entirely via engineered self-assembly. Rapid advances in the design and construction of self-assembled DNA structures has resulted in an impressive level of understanding and control over this type of nano-scale manufacturing. Polypeptides and proteins are decidedly less understood and their use in engineered self-assembly has been relatively limited. Nevertheless, as we discuss in the concluding sections of the chapter, both genetically engineered polypeptides and proteins can be used to guide self-assembly processes in nano-scale and help in interfacing nano-scale objects with micron-scale components and templates.

The article is devoted to an important role of the concept of resonances not only in classical and quantum mechanics but also in genetics and biological communication. Matrix representations of oscillators with many degrees of freedom are used to model some phenomena of Mendelian genetics and to analyze structures of genetic-molecular alphabets. To explain phenomena of segregation in these molecular alphabets, the existence of dominant and recessive resonances in nitrogenous bases of DNA and RNA are postulated by analogy with dominant and recessive alleles in Mendelian genetics. Relations of genetic alphabets with modulo-2 addition, dyadic groups of binary numbers and matrices of dyadic shifts are shown. A connection of structures of genetic alphabets with known formalisms of noiseimmunity coding (Rademacher and Walsh functions, Hadamard matrices) are discussed taking into account noise-immunity properties of genetic encoding.

Conventional methods of genetic engineering and more recent genome editing techniques focus on identifying genetic target sequences for manipulation. This is a result of historical concept of the gene which was also the main assumption of the ENCODE project designed to identify all functional elements in the human genome sequence. However, the theoretical core concept changed dramatically. The old concept of genetic sequences which can be assembled and manipulated like molecular bricks has problems in explaining the natural genome-editing competences of viruses and RNA consortia that are able to insert or delete, combine and recombine genetic sequences more precisely than random-like into cellular host organisms according to adaptational needs or even generate sequences de novo. Increasing knowledge about natural genome editing questions the traditional narrative of mutations (error replications) as essential for generating genetic diversity and genetic content arrangements in biological systems. This may have far-reaching consequences for our understanding of artificial genome editing.

The Standard Codon Table (SCT) records the correlation observed in nature between the complete set of 64 trinucleotide codons and the 20 amino acids plus 3 nonsense (i.e. stop or termination) signals. This table was called a frozen accident by Francis Crick, yet current evidence points to optimization that minimizes harmful effects of mutations and mistranslations while maximizing the encoding of multiple messages into a single sequence. For example, a recent article with the running title “The best of all possible codes?” concluded that “evidence is clear” for the optimized nature of the SCT, and another study found that difficult-to-encode secondary signals are minimized in the SCT. Additionally, the initiating amino acid methionine has been found to minimize the nascent peptide chain's barrier to exit the ribosome. Moreover, the symmetry in the SCT between 4- fold-synonymous and <4-fold synonymous codons has been explained in terms of minimizing mistranslation. In this paper, the hypothesis that the finely tuned optimization of the SCT originates in external intelligence is compared to the hypothesis that its fine tuning is due to the adaptive selection of earlier codes. It is concluded that, in the absence of metaphysical biases against this hypothesis, external intelligence better explains the origin of the SCT. Additionally, this hypothesis prompts lines of inquiry that, 50 years ago, would have accelerated the discovery of the now-known features of the SCT and that, today, can lead to new discoveries.

Algebraic and geometric representations of the genetic code are used to show their functions in coding for amino acids. The algebra is a 64-part vector quaternion combination, and the geometry is based on the structure of the regular icosidodecahedron. An almost perfect pattern suggests that this is a biologically significant way of representing the genetic code.