Degeneracy in the genetic code and its symmetries by base substitutions

Degeneracy in the genetic code is known to minimise the deleterious effects of the most frequent base substitutions: transitions at the third base of codons are generally synonymous substitutions. Transversions that alter degeneracy were reported by Rumer. Here the other transversions are shown to leave invariant degeneracy when applied to the first base of codons. As a summary, degeneracy is considered with respect to all three types of base substitutions, the transitions and the two types of transversions. The symmetries of degeneracy by base substitutions are independent of the representation of the genetic code and discussed with respect to the quasi-universality of the genetic code.     

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.     

A conformational rationale for the wobble behaviour of the first base of the anticodon triplet in tRNA

We present a conformational rationale for wobble behaviour of the first base in the anticodon triplet of tRNA and hence for the well-known degeneracy of the genetic code. The U-turn hydrogen bond plays an important role in the structure of the anticodon arm and particularly for the anticodon triplet to be in a geometry suitable for the process of recognition in the adaptor-mediated synthesis of proteins. This hydrogen bond in turn precludes a hydrogen bond between the first two sugars of the anticodon triplet, allowing the first base to wobble, while it facilitates one between the second and third sugars of the triplet, positioning these bases for the standard base-pairing with the codon. This neatly explains why there is a degeneracy in the code and why a RNA happens to be the adaptor for protein synthesis. Relevent conformational calculations are presented in support of the theory.     

Evidence of the accumulation of allele-specific non-synonymous substitutions in the young region of recombination suppression within the mating-type chromosomes of Neurospora tetrasperma

Currently, little is known about the origin and early evolution of sex chromosomes. This is largely due to the fact that ancient non-recombining sex chromosomes are highly degenerated, and thus provide little information about the early genomic events in their evolution. The Neurospora tetrasperma mating-type (mat) chromosomes contain a young (<6 Mya) and large region (>6.6 Mb) of suppressed recombination, thereby providing a model system to study early stages of sex chromosome evolution. Here, we examined alleles of 207 genes located on the N. tetrasperma mat a and mat A chromosomes to test for signs of genomic alterations at the protein level in the young region of recombination suppression. We report that the N. tetrasperma mat a and mat A chromosomes have each independently accumulated allele-specific non-synonymous codon substitutions in a time-dependent, and gene-specific manner in the recombinationally suppressed region. In addition, examination of the ratio (ω) of non-synonymous substitutions (dN) to synonymous substitutions (dS) using maximum likelihood analyses, indicates that such changes are associated with relaxed purifying selection, a finding consistent with genomic degeneration. We also reveal that sex specific biases in mutation rates or selection pressures are not necessary for genomic alterations in sex chromosomes, and that recombination suppression in itself is sufficient to explain these results. The present findings extend our current understanding of genomic events associated within the young region of recombination suppression in these fungal sex-regulating chromosomes.     

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.     

Phase-dependent nucleotide substitution in protein-coding sequences

It is well known that due to the degeneracy of genetic code, most of the silent substitutions appear in the third codon position, so the mutation frequency of the third codon position is much higher than that of the first two positions. However, it remains unknown whether the directionality of point mutation in three codon positions is similar or not. In this paper, through analyzing 15 sets of orthologous genes, it is revealed that most of the substitution types are significantly different between any two codon positions, especially between the 2nd and the 3rd phases. Furthermore, the average frequencies of each type of substitution calculated from the fifteen sets of orthologous genes are similar to those identified in single nucleotide polymorphisms (SNPs) of human and mouse genome. The present analyses suggest that the nucleotide substitution in protein-coding sequences is not only context-dependent (so called neighboring-nucleotide effects), but also phase-dependent, which is of significance to improving the prevalent nucleotide-evolution models.     

Configuration of wobble base pairs having pyrimidines as anticodon wobble bases: significance for codon degeneracy

Degeneracy of the genetic code was attributed by Crick to imprecise hydrogen-bonded base-pairing at the wobble position during codon–anticodon pairing. The Crick wobble rules define but do not explain the RNA base pair combinations allowed at this position. We select six pyrimidine bases functioning as anticodon wobble bases (AWBs) to study their H-bonded pairing properties with the four major RNA bases using density functional theory at the B3LYP/6-31G(d,p) level. This is done to assess the extent to which the configuration of a solitary RNA wobble base pair may in itself determine specificity and degeneracy of the genetic code by allowing or disallowing the given base pair during codon–anticodon pairing. Calculated values of select configuration markers for the base pairs screen well between allowed and disallowed base pairs for most cases examined here, where the base pair width emerges as an important factor. A few allowed wobble pairs invoke the involvement of RNA nucleoside conformation, as well as involvement of the exocyclic substituent in H-bonding. This study, however, cannot explain the disallowed status of the Ura?Gua wobble pair on the basis of configuration alone. Explanation of the allowed status of the V?Ura pair requires further study on the mediatory role of water molecules. Apart from these two cases, these computational results are sufficient, on the basis of base pair configuration alone, to account for the specificity and degeneracy of the genetic code for all known cases of codon–anticodon pairing which involve the pyrimidine AWBs studied here.     

A thermodynamic theory of codon bias in viral genes

The relationship between degeneracy in the genetic code and the occurrence of a strong codon bias is examined, with particular reference to a group of viral genomes. The present paper shows how codon bias may have been imposed by thermodynamic considerations at the time the primitive DNA first formed in the primordial soup. Using a four-state Ising-like model with stacking interactions between successive base pairs, we show how primeval periodic DNA polymers could have arisen the remnants of which are still observed in codon biases today.     

The new classification scheme of the genetic code, its early evolution, and tRNA usage

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.     

Genetic code degeneracy is established by the decoding center of the ribosome

The degeneracy of the genetic code confers a wide array of properties to coding sequences. Yet, its origin is still unclear. A structural analysis has shown that the stability of the Watson–Crick base pair at the second position of the anticodon–codon interaction is a critical parameter controlling the extent of non-specific pairings accepted at the third position by the ribosome, a flexibility at the root of degeneracy. Based on recent cryo-EM analyses, the present work shows that residue A1493 of the decoding center provides a significant contribution to the stability of this base pair, revealing that the ribosome is directly involved in the establishment of degeneracy. Building on existing evolutionary models, we show the evidence that the early appearance of A1493 and A1492 established the basis of degeneracy when an elementary kinetic scheme of translation was prevailing. Logical considerations on the expansion of this kinetic scheme indicate that the acquisition of the peptidyl transferase center was the next major evolutionary step, while the induced-fit mechanism, that enables a sharp selection of the tRNAs, necessarily arose later when G530 was acquired by the decoding center.     

Molecular evolution of the ent-kaurenoic acid oxidase gene in Oryzeae

We surveyed the substitution patterns in the ent-kaurenoic acid oxidase (KAO) gene in 11 species of Oryzeae with an outgroup in the Ehrhartoidaea. The synonymous and non-synonymous substitution rates showed a high positive correlation with each other, but were negatively correlated with codon usage bias and GC content at third codon positions. The substitution rate was heterogenous among lineages. Likelihood-ratio tests showed that the non-synonymous/synonymous rate ratio changed significantly among lineages. Site-specific models provided no evidence for positive selection of particular amino acid sites in any codon of the KAO gene. This finding suggested that the significant rate heterogeneity among some lineages may have been caused by variability in the relaxation of the selective constraint among lineages or by neutral processes.     

Codon sextets with leading role of serine create “ideal” symmetry classification scheme of the genetic code

The standard classification scheme of the genetic code is organized for alphabetic ordering of nucleotides. Here we introduce the new, “ideal” classification scheme in compact form, for the first time generated by codon sextets encoding Ser, Arg and Leu amino acids. The new scheme creates the known purine/pyrimidine, codon–anticodon, and amino/keto type symmetries and a novel A + U rich/C + G rich symmetry. This scheme is built from “leading” and “nonleading” groups of 32 codons each. In the ensuing 4 × 16 scheme, based on trinucleotide quadruplets, Ser has a central role as initial generator. Six codons encoding Ser and six encoding Arg extend continuously along a linear array in the “leading” group, and together with four of six Leu codons uniquely define construction of the “leading” group. The remaining two Leu codons enable construction of the “nonleading” group. The “ideal” genetic code suggests the evolution of genetic code with serine as an initiator.     

The amino acid composition of proteins: a method of analysis.

Four quasiloglinear models are proposed for describing relationships between the amino acid composition of proteins and the structure of the genetic code. The models allow estimation of base frequencies in all three codon positions and can be used to investigate “interactions” between any two codon positions. The estimation procedure proposed by Ohta and Kimura (Genetics64 (1970), 387–395) is discussed and using two of the proposed quasiloglinear models an analysis of the amino acid composition of human cytochrome c is presented. The analysis suggests that of the six codons which code for leucine (CUU, CUC, CUA and CUG) do not occur in human cytochrome c.     

Comparative Molecular Evolution of Primary (<Emphasis Type="BoldItalic">Buchnera</Emphasis>) and Secondary Symbionts of Aphids Based on Two Protein-Coding Genes

A+T content, phylogenetic relationships, codon usage, evolutionary rates, and ratio of synonymous versus non-synonymous substitutions have been studied in partial sequences of the atpD and aroQ/pheA genes of primary (Buchnera) and secondary symbionts of aphids and a set of selected non-symbiotic bacteria, belonging to the five subdivisions of the Proteobacteria. Compared to the homologous genes of the last group, both genes belonging to Buchnera behave in a similar way, showing a higher A+T content, forming a monophyletic group, a loss in codon bias, especially in third base position, an evolutionary acceleration and an increase in the number of non-synonymous substitutions, confirming previous results reported elsewhere for other genes. When available, these properties have been partly observed with the secondary symbionts, but with values that are intermediate between Buchnera and free living Proteobacteria. They show high A+T content, but not as high as Buchnera, a non-solved phylogenetic position between Buchnera, and the other γ-Proteobacteria, a loss in codon bias, again not as high as in Buchnera and a significant evolutionary acceleration in the case of the three atpD genes, but not when considering aroQ/pheA genes. These results give support to the hypothesis that they are symbionts at different stages of the symbiotic accommodation to the host.     

Theory of degenerate coding and informational parameters of protein coding genes

The theory of degenerate coding is presented in a way enabling further application to molecular biology. There are two kinds of redundancy of a degenerate code. The first is due to the excess in codon length and the second to the code degeneracy. If the code is asymmetrically degenerate, the second kind of redundancy can be profitable for control of error rate. This control can be performed just by selective synonymous codon usage. Utilisation of the genetic code is partially influenced by this theoretical possibility. In particular the degree of error protectivity is well correlated with deviation from equiprobability in synonymous codon usage. The biological significance of this fact is discussed.     

Challenges of the genetic code for exploring sequence space in directed protein evolution

Directed protein evolution is the most versatile method for studying protein structure-function relationships, and for tailoring a protein's properties to the needs of industrial applications. In this review, we performed a statistical analysis on the genetic code to study the extent and consequence of the organization of the genetic code on amino acid substitution patterns generated in directed evolution experiments. In detail, we analyzed amino acid substitution patterns caused by (a) a single nucleotide (nt) exchange at each position of all 64 codons, and (b) two subsequent nt exchanges (first and second nt, first and third nt, second and third nt). Additionally, transitions and transversions mutations were compared at the level of amino acid substitution patterns. The latter analysis showed that single nucleotide substitution in a codon generates only 39.5% of the natural diversity on the protein level with 5.2-7 amino acid substitutions per codon. Transversions generate more complex amino acid substitution patterns (increased number and chemically more diverse amino acid substitutions) than transitions. Simultaneous nt exchanges at both first and second nt of a codon generates very diverse amino acid substitution patterns, achieving 83.2% of the natural diversity. The statistical analysis described in this review sets the objectives for novel random mutagenesis methods that address the consequences of the organization of the genetic code. Random mutagenesis methods that favor transversions or introduce consecutive nt exchanges can contribute in this regard.