Study of the genetic code adaptability by means of a genetic algorithm

We used simulated evolution to study the adaptability level of the canonical genetic code. An adapted genetic algorithm (GA) searches for optimal hypothetical codes. Adaptability is measured as the average variation of the hydrophobicity that the encoded amino acids undergo when errors or mutations are present in the codons of the hypothetical codes. Different types of mutations and point mutation rates that depend on codon base number are considered in this study. Previous works have used statistical approaches based on randomly generated alternative codes or have used local search techniques to determine an optimum value. In this work, we emphasize what can be concluded from the use of simulated evolution considering the results of previous works. The GA provides more information about the difficulty of the evolution of codes, without contradicting previous studies using statistical or engineering approaches. The GA also shows that, within the coevolution theory, the third base clearly improves the adaptability of the current genetic code.     

The extension reached by the minimization of the polarity distances during the evolution of the genetic code

Summary The level reached by the optimization of the polarity distances during the evolution of the genetic code was investigated. The results, although not conclusive, indicate that this optimization level is higher than the data reported in the literature. The results seem compatible with the reaching of an evolutionary minimum, with respect to the optimization of the polarity distances, by the genetic code during its formation.     

Some mathematical refinements concerning error minimization in the genetic code

The genetic code is known to have a high level of error robustness and has been shown to be very error robust compared to randomly selected codes, but to be significantly less error robust than a certain code found by a heuristic algorithm. We formulate this optimization problem as a Quadratic Assignment Problem and use this to formally verify that the code found by the heuristic algorithm is the global optimum. We also argue that it is strongly misleading to compare the genetic code only with codes sampled from the fixed block model, because the real code space is orders of magnitude larger. We thus enlarge the space from which random codes can be sampled from approximately 2.433 × 10(18) codes to approximately 5.908 × 10(45) codes. We do this by leaving the fixed block model, and using the wobble rules to formulate the characteristics acceptable for a genetic code. By relaxing more constraints, three larger spaces are also constructed. Using a modified error function, the genetic code is found to be more error robust compared to a background of randomly generated codes with increasing space size. We point out that these results do not necessarily imply that the code was optimized during evolution for error minimization, but that other mechanisms could be the reason for this error robustness.     

A hardware interpretation of the evolution of the genetic code

A quantitative rationale for the evolution of the genetic code is developed considering the principle of minimal hardware. This principle defines an optimal code as one that minimizes for a given amount of information encoded, the product of the number of physical devices used by the average complexity of each device. By identifying the number of different amino acids, number of nucleotide positions per codon and number of base types that can occupy each such position with, respectively, the amount of information, number of devices and the complexity, we show that optimal codes occur for 3, 7 and 20 amino acids with codons having a single, two and three base positions per codon, respectively. The advantage of a code of exactly 4 symbols is deduced, as well as a plausible evolutionary pathway from a code of doublets to triplets. The present day code of 20 amino acids encoded by 64 codons is shown to be the most optimal in an absolute sense. Using a tetraplet code further evolution to a code in which there would be 55 amino acids is in principle possible, but such a code would deviate slightly more than the present day code from the minimal hardware configuration. The change from a triplet code to a tetraplet code would occur at about 32 amino acids. Our conclusions are independent of, but consistent with, the observed physico-chemical properties of the amino acids and codon structures. These correlations could have evolved within the constrains imposed by the minimal hardware principle.     

A change in the genetic code inMycoplasma capricolum

Summary Mycoplasma capricolum was previously found to use UGA instead of UGG as its codon for tryptophan and to contain 75%A+ T in its DNA. The codon change could have been due to mutational pressure to replace C+G by A+T, resulting in the replacement of UGA stop codons by UAA, change of the anticodon in tryptophan tRNA from CCA to UCA, and replacement of UGG tryptophan codons by UGA. None of these changes should have been deleterious.     

Arithmetic inside the universal genetic code

The first information system emerged on the earth as primordial version of the genetic code and genetic texts. The natural appearance of arithmetic power in such a linguistic milieu is theoretically possible and practical for producing information systems of extremely high efficiency. In this case, the arithmetic symbols should be incorporated into an alphabet, i.e. the genetic code. A number is the fundamental arithmetic symbol produced by the system of numeration. If the system of numeration were detected inside the genetic code, it would be natural to expect that its purpose is arithmetic calculation e.g., for the sake of control, safety, and precise alteration of the genetic texts. The nucleons of amino acids and the bases of nucleic acids seem most suitable for embodiments of digits. These assumptions were used for the analyzing the genetic code.

The compressed, life-size, and split representation of the Escherichia coli and Euplotes octocarinatus code versions were considered simultaneously. An exact equilibration of the nucleon sums of the amino acid standard blocks and/or side chains was found repeatedly within specified sets of the genetic code. Moreover, the digital notations of the balanced sums acquired, in decimal representation, the unique form 111, 222, …, 999. This form is a consequence of the criterion of divisibility by 037. The criterion could simplify some computing mechanism of a cell if any and facilitate its computational procedure. The cooperative symmetry of the genetic code demonstrates that possibly a zero was invented and used by this mechanism. Such organization of the genetic code could be explained by activities of some hypothetical molecular organelles working as natural biocomputers of digital genetic texts.

It is well known that if mutation replaces an amino acid, the change of hydrophobicity is generally weak, while that of size is strong. The antisymmetrical correlation between the amino acid size and the degeneracy number is known as well. It is shown that these and some other familiar properties may be a physicochemical effect of arithmetic inside the genetic code.

The “frozen accident” model, giving unlimited freedom to the mapping function, could optimally support the appearance of both arithmetic symbols and physicochemical protection inside the genetic code.     

Pattern and chance in the use of the genetic code

Summary The use of triplet code words inE. coli,X174, MS2, and rabbit globin was examined. A significant deficiency of purines in the third position of fourfold degenerate codons was noted, although its significance is not understood. There has been no consistent selection against uracil in pyrimidine restricted codons. For many amino acids the choice between code words appears random, while for arginine, isoleucine, and probably glycine, distinct biases exist which can be explained in terms of tRNA availability.     

An algebraic hypothesis about the primeval genetic code architecture

A plausible architecture of an ancient genetic code is derived from an extended base triplet vector space over the Galois field of the extended base alphabet {D, A, C, G, U}, where symbol D represents one or more hypothetical bases with unspecific pairings. We hypothesized that the high degeneration of a primeval genetic code with five bases and the gradual origin and improvement of a primeval DNA repair system could make possible the transition from ancient to modern genetic codes. Our results suggest that the Watson-Crick base pairing G ≡ C and A = U and the non-specific base pairing of the hypothetical ancestral base D used to define the sum and product operations are enough features to determine the coding constraints of the primeval and the modern genetic code, as well as, the transition from the former to the latter. Geometrical and algebraic properties of this vector space reveal that the present codon assignment of the standard genetic code could be induced from a primeval codon assignment. Besides, the Fourier spectrum of the extended DNA genome sequences derived from the multiple sequence alignment suggests that the called period-3 property of the present coding DNA sequences could also exist in the ancient coding DNA sequences. The phylogenetic analyses achieved with metrics defined in the N-dimensional vector space (B³)^N of DNA sequences and with the new evolutionary model presented here also suggest that an ancient DNA coding sequence with five or more bases does not contradict the expected evolutionary history.     

Structure of the genetic code suggested by the hydropathy correlation between anticodons and amino acid residues

The correlation between hydropathies of anticodons and amino acids, detected by other authors utilizing scales of amino acid molecules in solution, was improved with the utilization of scales of amino acid residues in proteins. Three partitions were discerned in the correlation plot with the principal dinucleotides of anticodons (pDiN, excluding the wobble position). (a) The set of outliers of the correlation: Gly-CC, Pro-GG, Ser-GA and Ser-CU. The amino acids are consistently small, hydro-apathetic, stabilizers of protein N-ends, preferred in aperiodic protein conformations and belong to synthetases class II. The pDiN sequences are representative of the homogeneous sector (triplets NRR and NYY), distinguished from the mixed sector (triplets NRY and NYR), that depict a 70% correspondence to the synthetases class II and I, respectively. The triplet pairs proposed to be responsible for the coherence in the set of outliers are of the palindromic kind, where the lateral bases are the same, CCC: GGG and AGA: UCU. This suggests that UCU previously belonged to Ser, adding to other indications that the attribution of Arg to YCU was due to an expansion of the Arg-tRNA synthetase specificity. The other attributions produced two correlation sets. (b) One corresponds to the remaining pDiN of the homogeneous sector, containing both synthetase classes; its regression line overlapped the one formed by the remaining attributions to class II. (c) The other contains the pDiN of the mixed sector and produced steeper slopes, especially with the class I attributions. It is suggested that the correlation was established when the amino acid composition of the protein synthetases became progressively enriched and that the set of outliers were the earliest to have been fixed.     

Hemoglobin and the genetic code

Summary One-half of the twenty amino acids of the genetic code are just one mutational step away from the chain-terminator codons UAA, UAG, and UGA. It is postulated that somatic mutation to terminator is a hazard to which the organism has had to respond by adjusting certain proteins in the direction of fewer mutable residues. This view is supported by calculations based on the primary structure of five of the human hemoglobin chains. Each chain is scored for mutability to terminator in accord with the numbers and kinds of amino acids present. Among the adult chains, the most essential one, the alpha, has lowest mutability. The beta and delta follow, and in order of the presumed harm to the organism of a shortage of chain copies. Ante-natal chains tend to have higher mutabilities, supporting the view that cumulative mutational change in DNA can do little harm if the gene ceases to transcribe early in life. Two other predictions based on the supposition of effective selection against mutability to terminator are also met: chain length of polypeptides is negatively correlated with their scores for mutability to terminator, and examination of the recently determined sequence of beta messenger RNA shows preferential use of codons that are not readily mutable to terminator.Supported in part by the National Institutes of Health, Grant HL-16005     

On the origin and evolution of the genetic code

Two ideas have essentially been used to explain the origin of the genetic code: Crick's frozen accident and Woese's amino acid-codon specific chemical interaction. Whatever the origin and codon-amino acid correlation, it is difficult to imagine the sudden appearance of the genetic code in its present form of 64 codons coding for 20 amino acids without appealing to some evolutionary process. On the contrary, it is more reasonable to assume that it evolved from a much simpler initial state in which a few triplets were coding for each of a small number of amino acids. Analysis of genetic code through information theory and the metabolism of pyrimidine biosynthesis provide evidence that suggests that the genetic code could have begun in an RNA world with the two letters A and U grouped in eight triplets coding for seven amino acids and one stop signal. This code could have progressively evolved by making gradual use of letters G and C to end with 64 triplets coding for 20 amino acids and three stop signals. According to proposed evidence, DNA could have appeared after the four-letter structure was already achieved. In the newborn DNA world, T substituted U to get higher physicochemical and genetic stability.     

Noise immunity of the genetic code

Error detection and correction properties are fundamental for informative codes. Hamming's distance allows us to study this noise resistance. We present codes characterized by the resistance optimization to nonsense mutational effects. The calculation of the cumulated Hamming's distance allowing to determine the number of optimal codes and their structure can be detailed. The principle of these laws of optimization of resistance consists of choosing constituent codons connected by mutational neighbouring in such a way that random application of mutations on such a code minimize the occurrence of nonsense n-uplets or terminators. New coding symmetries are then described and screened using Galois's polynomials properties and Baudot's code. Such a study can be applied to any length of the codons. Here we present the principles of this optimization for the most simple doublet codes. Another constraint is discussed: the distribution of optimal subcodes for synonymity and the frequencies of utilization of the different codons.We compare these results to those of the present genetic code, and we observe that all coded amino acids (except the particular case of SER) are using optimal sub-codes of synonymity.This work suggests that the appearance of the genetic code was provoked by mutations while optimizing on several levels its resistance to their effects. Thus genetic coding would have been the best automata that could be produced in prebiotic conditions.     

The fourfold way of the genetic code

We describe a compact representation of the genetic code that factorizes the table in quartets. It represents a “least grammar” for the genetic language. It is justified by the Klein-4 group structure of RNA bases and codon doublets. The matrix of the outer product between the column-vector of bases and the corresponding row-vector V^T = (C G U A), considered as signal vectors, has a block structure consisting of the four cosets of the K × K group of base transformations acting on doublet AA. This matrix, translated into weak/strong (W/S) and purine/pyrimidine (R/Y) nucleotide classes, leads to a code table with mixed and unmixed families in separate regions. A basic difference between them is the non-commuting (R/Y) doublets: AC/CA, GU/UG. We describe the degeneracy in the canonical code and the systematic changes in deviant codes in terms of the divisors of 24, employing modulo multiplication groups. We illustrate binary sub-codes characterizing mutations in the quartets. We introduce a decision-tree to predict the mode of tRNA recognition corresponding to each codon, and compare our result with related findings by Jestin and Soulé [Jestin, J.-L., Soulé, C., 2007. Symmetries by base substitutions in the genetic code predict 2′ or 3′ aminoacylation of tRNAs. J. Theor. Biol. 247, 391–394], and the rearrangements of the table by Delarue [Delarue, M., 2007. An asymmetric underlying rule in the assignment of codons: possible clue to a quick early evolution of the genetic code via successive binary choices. RNA 13, 161–169] and Rodin and Rodin [Rodin, S.N., Rodin, A.S., 2008. On the origin of the genetic code: signatures of its primordial complementarity in tRNAs and aminoacyl-tRNA synthetases. Heredity 100, 341–355], respectively.     

Exploring the energy landscape of the genetic code

New insights into the arrangement of the genetic code table, based on the analysis of the physico-chemical properties of its molecular constituents, are reported in this paper. It will be demonstrated that the code has a twofold symmetry that is not apparent from the conventional code table, but becomes apparent when the codon-anticodon energies are listed for each triplet. The evolutionary development of the current code based on single base replacement mutations (transitions) from an 'iso-energetic' degenerated subset of 16 of the 64 codons is discussed. The energy landscape of all 64 codons is presented. A detailed analysis of the energy changes due to mutations in the 3rd, 1st or 2nd position of a codon reveals that the modern genetic code is highly robust. Changes come in small discrete steps that can be quantified in relation to the thermal noise of the system. The relation of the individual codon to its neighbours in the rearranged codon table can be completely understood based on thermodynamic considerations.     

A harmonic structure of the genetic code

In this paper is presented a new, very harmonic structure of the genetic code (GC) within a system of "4 x 5" (and/or of "5 x 4") of amino acids (AAs) in two variants. In first variant, the five rows within the system start with one polar charged amino acid (AA) each, making first column, consisting from five polar charged AAs (D, R, K, H, E). Five polar non-charged AAs (N, P, Y, W, Q) follow, then five non-polar AAs as last column (A, L, F, V, I) and, finally, five polar or non-polar AAs, in a combination, as first to last column (A as non-polar; S, T as polar, and G, P as ambivalent AAs). A second variant is subsequent to this one-"4 x 5" system with five nitrogen AAs (K, R, P, H, W), five oxygen (D, E, Y, S, T), five solely carbon (A, L, F, V, I) and five "combined" AAs (G with hydrogen as side chain; C and M with carbon and sulfur; N and Q with carbon, oxygen and nitrogen). A strict balance of atom and nucleon number as well as molecule mass follows the classification in both system variants.     

On the classes of aminoacyl-tRNA synthetases and the error minimization in the genetic code

As a consequence of the existence of two classes of aminoacyl-tRNA synthetases (aaRSs), we defined two types of mutations: g (mutations that do not change the class of the involved amino acids) and u (those which change the class). We have found that the mean chemical distance resulting from g mutations is smaller than that corresponding to u mutations, indicating that g mutations are responsible for most of the known minimization of the genetic code. This supports models for the origin and evolution of the code, in which new amino acids were added after duplications or modification of existing aaRSs.     

Speculations on the origin of the genetic code

The most primitive code is assumed to be a GC code: GG coding for glycine, CC coding for proline, GC coding for alanine, CG coding for arginine. The genetic code is assumed to have originated with the coupling of glycine to its anticodon CC mediated by a copper-montmorillonite. The polymerization of polyproline followed when it was coupled to its anticodon GG. In this case the aminoacyl-tRNA synthetase was a copper-montmorillonite. The first membrane is considered to be a sheet formed from polyglycine. As the code grew more complicated, the alternative hydrophobic-hydrophilic polypeptide (alanine-arginine) was coded for by the alternating CG copolymer. This alternating polypeptide (ala-arg) began to function as both a primitive membrane and as an aminoacyl-tRNA synthetase. The evolution of protein structure is tightly coupled to the evolution of the membrane. The a helix was evolved as lipids became part of the structure of biological membranes. The membrane finally became the fluid mosaic structure that is now universal.Based on a presentation made at a workshop-Aminoacyl-tRNA Synthetases and the Evolution of the Genetic Code-held at Berkeley, CA, July 17–20, 1994