Evolution of the Genetic Triplet Code via Two Types of Doublet Codons

On the Origin of Frameshift-Robustness of the Standard Genetic Code

The standard genetic code (SGC) has been extensively analyzed for the biological ramifications of its nonrandom structure. For instance, mismatch errors due to point mutation or mistranslation have an overall smaller effect on the amino acid polar requirement under the SGC than under random genetic codes (RGCs). A similar observation was recently made for frameshift errors, prompting the assertion that the SGC has been shaped by natural selection for frameshift-robustness-conservation of certain amino acid properties upon a frameshift mutation or translational frameshift. However, frameshift-robustness confers no benefit because frameshifts usually create premature stop codons that cause nonsense-mediated mRNA decay or production of nonfunctional truncated proteins. We here propose that the frameshift-robustness of the SGC is a byproduct of its mismatch-robustness. Of 564 amino acid properties considered, the SGC exhibits mismatch-robustness in 93-133 properties and frameshift-robustness in 55 properties, respectively, and that the latter is largely a subset of the former. For each of the 564 real and 564 randomly constructed fake properties of amino acids, there is a positive correlation between mismatch-robustness and frameshift-robustness across one million RGCs; this correlation arises because most amino acid changes resulting from a frameshift are also achievable by a mismatch error. Importantly, the SGC does not show significantly higher frameshift-robustness in any of the 55 properties than RGCs of comparable mismatch-robustness. These findings support that the frameshift-robustness of the SGC need not originate through direct selection and can instead be a site effect of its mismatch-robustness.

On the context-sensitive grammar of the genetic code

We address the possibilities of the semiotic description of the genetic information as a dual and self-replicative system of correspondence between its biochemical substance and semiotic form of organization. Combining the principles of contextual dependence and arbitrariness of sign leads to the conclusion that the genetic code's primary elements (nucleotides) can be considered not as biochemical constants but as semiotic or, more precisely, grammatical variables. We suggest describing the genetic code as a language, consisting of 1) units of the alphabet; 2) a vocabulary that includes meaningful items and the rules of correspondence between units of different levels; 3) context-sensitive grammar - a system of rules for the formation of units based on abstract grammatical categories.

Infinite combinatorics in mathematical biology

Is it possible to apply infinite combinatorics and (infinite) set theory in theoretical biology? We do not know the answer yet but in this article we try to present some techniques from infinite combinatorics and set theory that have been used over the last decades in order to prove existence results and independence theorems in algebra and that might have the flexibility and generality to be also used in theoretical biology. In particular, we will introduce the theory of forcing and an algebraic construction technique based on trees and forests using infinite binary sequences. We will also present an overview of the theory of circular codes. Such codes had been found in the genetic information and are assumed to play an important role in error detecting and error correcting mechanisms during the process of translation. Finally, examples and constructions of infinite mixed circular codes using binary sequences hopefully show some similarity between these theories - a starting point for future applications.

From Matter to Form: the Evolution of the Genetic Code as Semio-Poiesis

The code is meaningless unless translated. (Monod 1971, 143)

We address issues of a description of the origin and evolution of the genetic code from the semiotics standpoint. Developing the concept of codepoiesis introduced by M. Barbieri, a new idea of semio-poiesis is proposed. Semio-poiesis, a recursive auto-referential processing of a semiotic system, becomes a form of organization of the bio-world when and while notions of meaning and aiming are introduced into it. The description of the genetic code as a semiotic system (grammar and vocabulary) allows us to apply the method of internal reconstruction to it: on the basis of heterogeneity and irregularity of the current state, to explicate possible previous states and various ways of forming coding and textualization mechanisms. The revealed patterns and irregularities are consistent with hypotheses about the origin and evolution of the genetic code.

Circular Tessera Codes in the Evolution of the Genetic Code

The origin of the modern genetic code and the mechanisms that have contributed to its present form raise many questions. The main goal of this work is to test two hypotheses concerning the development of the genetic code for their compatibility and complementarity and see if they could benefit from each other. On the one hand, Gonzalez, Giannerini and Rosa developed a theory, based on four-based codons, which they called tesserae. This theory can explain the degeneracy of the modern vertebrate mitochondrial code. On the other hand, in the 1990s, so-called circular codes were discovered in nature, which seem to ensure the maintenance of a correct reading-frame during the translation process. It turns out that the two concepts not only do not contradict each other, but on the contrary complement and enrichen each other.

Linear codes and the mitochondrial genetic code

The origin of the genetic code can certainly be regarded as one of the most challenging problems in the theory of molecular evolution. Thus the known variants of the genetic code and a possible common ancestry of them haven been studied extensively in the literature. Gonzalez et al. (2012) developed the theory of a primeval mitochondrial genetic code composed of four base codons. These were called tesserae and it was shown that the tesserae code has some remarkable error detection capabilities. In our paper we will show that using classical coding theory we can construct the tessera code as a linear coding of the standard genetic code and at the same time it can be deduced from the code of all dinucleotides by Plotkin's construction. It shows that the tessera model of the mitochondrial code does not just have a biological explanation but also has a clear mathematical structure. This underlines the role that the tessera model might have played in evolution.

Mixed circular codes

By an extensive statistical analysis in genes of bacteria, archaea, eukaryotes, plasmids and viruses, a maximal C³-self-complementary trinucleotide circular code has been found to have the highest average occurrence in the reading frame of the ribosome during translation. Circular codes may play an important role in maintaining the correct reading frame. On the other hand, as several evolutionary theories propose primeval codes based on dinucleotides, trinucleotides and tetranucleotides, mixed circular codes were investigated. By using a graph-theoretical approach of circular codes recently developed, we study mixed circular codes, which are the union of a dinucleotide circular code, a trinucleotide circular code and a tetranucleotide circular code. Maximal mixed circular codes of (di,tri)-nucleotides, (tri,tetra)-nucleotides and (di,tri,tetra)-nucleotides are constructed, respectively. In particular, we show that any maximal dinucleotide circular code of size 6 can be embedded into a maximal mixed (di,tri)-nucleotide circular code such that its trinucleotide component is a maximal C³-comma-free code. The growth function of self-complementary mixed circular codes of dinucleotides and trinucleotides is given. Self-complementary mixed circular codes could have been involved in primitive genetic processes.

Detecting Periodicities in Eukaryotic Genomes by Ramanujan Fourier Transform

Ramanujan Fourier transform (RFT) nowadays is becoming a popular signal processing method. RFT is used to detect periodicities in exons and introns of eukaryotic genomes in this article. Genomic sequences of nine species were analyzed. The highest peak in the spectrum amplitude corresponding to each exon or intron is regarded as the significant signal. Accordingly, the periodicity corresponding to the significant signal can be also regarded as a valuable periodicity. Exons and introns have different periodic phenomena. The computational results reveal that the 2-, 3-, 4-, and 6-base periodicities of exons and introns are four kinds of important periodicities based on RFT. It is the first time that the 2-base periodicity of introns is discovered through signal processing method. The frequencies of the 2-base periodicity and the 3-base periodicity occurrence are polar opposite between the exons and the introns. With regard to the cyclicality of the Ramanujan sums, which is the base function of the transformation, RFT is suggested for studying the periodic features of dinucleotides, trinucleotides, and q nucleotides.

Dinucleotide circular codes and bijective transformations

The presence of circular codes in mRNA coding sequences is postulated to be involved in informational mechanisms aimed at detecting and maintaining the normal reading frame during protein synthesis. Most of the recent research is focused on trinucleotide circular codes. However, also dinucleotide circular codes are important since dinucleotides are ubiquitous in genomes and associated to important biological functions. In this work we adopt the group theoretic approach used for trinucleotide codes in Fimmel et al. (2015) to study dinucleotide circular codes and highlight their symmetry properties. Moreover, we characterize such codes in terms of n-circularity and provide a graph representation that allows to visualize them geometrically. The results establish a theoretical framework for the study of the biological implications of dinucleotide circular codes in genomic sequences.

Probable relationship between partitions of the set of codons and the origin of the genetic code

Here we study the distribution of randomly generated partitions of the set of amino acid-coding codons. Some results are an application from a previous work, about the Stirling numbers of the second kind and triplet codes, both to the cases of triplet codes having four stop codons, as in mammalian mitochondrial genetic code, and hypothetical doublet codes. Extending previous results, in this work it is found that the most probable number of blocks of synonymous codons, in a genetic code, is similar to the number of amino acids when there are four stop codons, as well as it could be for a primigenious doublet code. Also it is studied the integer partitions associated to patterns of synonymous codons and it is shown, for the canonical code, that the standard deviation inside an integer partition is one of the most probable. We think that, in some early epoch, the genetic code might have had a maximum of the disorder or entropy, independent of the assignment between codons and amino acids, reaching a state similar to "code freeze" proposed by Francis Crick. In later stages, maybe deterministic rules have reassigned codons to amino acids, forming the natural codes, such as the canonical code, but keeping the numerical features describing the set partitions and the integer partitions, like a "fossil numbers"; both kinds of partitions about the set of amino acid-coding codons.

Evolution of complete proteomes: guanine-cytosine pressure, phylogeny and environmental influences blend the proteomic architecture

Background

Guanine-cytosine (GC) composition is an important feature of genomes. Likewise, amino acid composition is a distinct, but less valued, feature of proteomes. A major concern is that it is not clear what valuable information can be acquired from amino acid composition data. To address this concern, in-depth analyses of the amino acid composition of the complete proteomes from 63 archaea, 270 bacteria, and 128 eukaryotes were performed.

Results

Principal component analysis of the amino acid matrices showed that the main contributors to proteomic architecture were genomic GC variation, phylogeny, and environmental influences. GC pressure drove positive selection on Ala, Arg, Gly, Pro, Trp, and Val, and adverse selection on Asn, Lys, Ile, Phe, and Tyr. The physico-chemical framework of the complete proteomes withstood GC pressure by frequency complementation of GC-dependent amino acid pairs with similar physico-chemical properties. Gln, His, Ser, and Val were responsible for phylogeny and their constituted components could differentiate archaea, bacteria, and eukaryotes. Environmental niche was also a significant factor in determining proteomic architecture, especially for archaea for which the main amino acids were Cys, Leu, and Thr. In archaea, hyperthermophiles, acidophiles, mesophiles, psychrophiles, and halophiles gathered successively along the environment-based principal component. Concordance between proteomic architecture and the genetic code was also related closely to genomic GC content, phylogeny, and lifestyles.

Conclusions

Large-scale analyses of the complete proteomes of a wide range of organisms suggested that amino acid composition retained the trace of GC variation, phylogeny, and environmental influences during evolution. The findings from this study will help in the development of a global understanding of proteome evolution, and even biological evolution.

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.

On the organizational dynamics of the genetic code

The organization of the canonical genetic code needs to be thoroughly illuminated. Here we reorder the four nucleotides—adenine, thymine, guanine and cytosine—according to their emergence in evolution, and apply the organizational rules to devising an algebraic representation for the canonical genetic code. Under a framework of the devised code, we quantify codon and amino acid usages from a large collection of 917 prokaryotic genome sequences, and associate the usages with its intrinsic structure and classification schemes as well as amino acid physicochemical properties. Our results show that the algebraic representation of the code is structurally equivalent to a content-centric organization of the code and that codon and amino acid usages under different classification schemes were correlated closely with GC content, implying a set of rules governing composition dynamics across a wide variety of prokaryotic genome sequences. These results also indicate that codons and amino acids are not randomly allocated in the code, where the six-fold degenerate codons and their amino acids have important balancing roles for error minimization. Therefore, the content-centric code is of great usefulness in deciphering its hitherto unknown regularities as well as the dynamics of nucleotide, codon, and amino acid compositions.

Stability of the genetic code and optimal parameters of amino acids

The standard genetic code is known to be much more efficient in minimizing adverse effects of misreading errors and one-point mutations in comparison with a random code having the same structure, i.e. the same number of codons coding for each particular amino acid. We study the inverse problem, how the code structure affects the optimal physico-chemical parameters of amino acids ensuring the highest stability of the genetic code. It is shown that the choice of two or more amino acids with given properties determines unambiguously all the others. In this sense the code structure determines strictly the optimal parameters of amino acids or the corresponding scales may be derived directly from the genetic code. In the code with the structure of the standard genetic code the resulting values for hydrophobicity obtained in the scheme "leave one out" and in the scheme with fixed maximum and minimum parameters correlate significantly with the natural scale. The comparison of the optimal and natural parameters allows assessing relative impact of physico-chemical and error-minimization factors during evolution of the genetic code. As the resulting optimal scale depends on the choice of amino acids with given parameters, the technique can also be applied to testing various scenarios of the code evolution with increasing number of codified amino acids. Our results indicate the co-evolution of the genetic code and physico-chemical properties of recruited amino acids.

Exceptional error minimization in putative primordial genetic codes

Background

The standard genetic code is redundant and has a highly non-random structure. Codons for the same amino acids typically differ only by the nucleotide in the third position, whereas similar amino acids are encoded, mostly, by codon series that differ by a single base substitution in the third or the first position. As a result, the code is highly albeit not optimally robust to errors of translation, a property that has been interpreted either as a product of selection directed at the minimization of errors or as a non-adaptive by-product of evolution of the code driven by other forces.

Results

We investigated the error-minimization properties of putative primordial codes that consisted of 16 supercodons, with the third base being completely redundant, using a previously derived cost function and the error minimization percentage as the measure of a code's robustness to mistranslation. It is shown that, when the 16-supercodon table is populated with 10 putative primordial amino acids, inferred from the results of abiotic synthesis experiments and other evidence independent of the code's evolution, and with minimal assumptions used to assign the remaining supercodons, the resulting 2-letter codes are nearly optimal in terms of the error minimization level.

Conclusion

The results of the computational experiments with putative primordial genetic codes that contained only two meaningful letters in all codons and encoded 10 to 16 amino acids indicate that such codes are likely to have been nearly optimal with respect to the minimization of translation errors. This near-optimality could be the outcome of extensive early selection during the co-evolution of the code with the primordial, error-prone translation system, or a result of a unique, accidental event. Under this hypothesis, the subsequent expansion of the code resulted in a decrease of the error minimization level that became sustainable owing to the evolution of a high-fidelity translation system.

Reviewers

This article was reviewed by Paul Higgs (nominated by Arcady Mushegian), Rob Knight, and Sandor Pongor. For the complete reports, go to the Reviewers' Reports section.

Codon size reduction as the origin of the triplet genetic code

The genetic code appears to be optimized in its robustness to missense errors and frameshift errors. In addition, the genetic code is near-optimal in terms of its ability to carry information in addition to the sequences of encoded proteins. As evolution has no foresight, optimality of the modern genetic code suggests that it evolved from less optimal code variants. The length of codons in the genetic code is also optimal, as three is the minimal nucleotide combination that can encode the twenty standard amino acids. The apparent impossibility of transitions between codon sizes in a discontinuous manner during evolution has resulted in an unbending view that the genetic code was always triplet. Yet, recent experimental evidence on quadruplet decoding, as well as the discovery of organisms with ambiguous and dual decoding, suggest that the possibility of the evolution of triplet decoding from living systems with non-triplet decoding merits reconsideration and further exploration. To explore this possibility we designed a mathematical model of the evolution of primitive digital coding systems which can decode nucleotide sequences into protein sequences. These coding systems can evolve their nucleotide sequences via genetic events of Darwinian evolution, such as point-mutations. The replication rates of such coding systems depend on the accuracy of the generated protein sequences. Computer simulations based on our model show that decoding systems with codons of length greater than three spontaneously evolve into predominantly triplet decoding systems. Our findings suggest a plausible scenario for the evolution of the triplet genetic code in a continuous manner. This scenario suggests an explanation of how protein synthesis could be accomplished by means of long RNA-RNA interactions prior to the emergence of the complex decoding machinery, such as the ribosome, that is required for stabilization and discrimination of otherwise weak triplet codon-anticodon interactions.

Origin and evolution of the genetic code: the universal enigma

The genetic code is nearly universal, and the arrangement of the codons in the standard codon table is highly nonrandom. The three main concepts on the origin and evolution of the code are the stereochemical theory, according to which codon assignments are dictated by physicochemical affinity between amino acids and the cognate codons (anticodons); the coevolution theory, which posits that the code structure coevolved with amino acid biosynthesis pathways; and the error minimization theory under which selection to minimize the adverse effect of point mutations and translation errors was the principal factor of the code's evolution. These theories are not mutually exclusive and are also compatible with the frozen accident hypothesis, that is, the notion that the standard code might have no special properties but was fixed simply because all extant life forms share a common ancestor, with subsequent changes to the code, mostly, precluded by the deleterious effect of codon reassignment. Mathematical analysis of the structure and possible evolutionary trajectories of the code shows that it is highly robust to translational misreading but there are numerous more robust codes, so the standard code potentially could evolve from a random code via a short sequence of codon series reassignments. Thus, much of the evolution that led to the standard code could be a combination of frozen accident with selection for error minimization although contributions from coevolution of the code with metabolic pathways and weak affinities between amino acids and nucleotide triplets cannot be ruled out. However, such scenarios for the code evolution are based on formal schemes whose relevance to the actual primordial evolution is uncertain. A real understanding of the code origin and evolution is likely to be attainable only in conjunction with a credible scenario for the evolution of the coding principle itself and the translation system.

Folding at the rhythm of the rare codon beat

The persistent difficulties in the production of protein at high levels in heterologous systems, as well as the inability to understand pathologies associated with protein aggregation, highlight our limited knowledge on the mechanisms of protein folding in vivo. Attempts to improve yield and quality of recombinant proteins are diverse, frequently involving optimization of the cell growth temperature, the use of synonymous codons and/or the co-expression of tRNAs, chaperones and folding catalysts among others. Although protein secondary structure can be determined largely by the amino acid sequence, protein folding within the cell is affected by a range of factors beyond amino acid sequence. The folding pathway of a nascent polypeptide can be affected by transient interactions with other proteins and ligands, the ribosome, translocation through a pore membrane, redox conditions, among others. The translation rate as well as the translation machinery itself can dramatically affect protein folding, and thus the structure and function of the protein product. This review addresses current efforts to better understand how the use of synonymous codons in the mRNA and the availability of tRNAs can modulate translation kinetics, affecting the folding, the structure and the biological activity of proteins.

A model for the origin of protein synthesis as coreplicational scanning of nascent RNA

The origin of protein synthesis is one of the major riddles of molecular biology. It was proposed a decade ago that the ribosomal RNA evolved from an earlier RNA-replisome (a ribozyme fulfilling RNA replication) while transfer RNA (tRNA) evolved from a genomic replication origin. Applying these hypotheses, I suggest that protein synthesis arose for the purpose of segregating copy and template RNA during replication through the conventional formation of a complementary strand. Nascent RNA was scanned in 5' to 3' direction following the progress of replication. The base pairing of several tRNA-like molecules with nascent RNA released the replication intermediates trapped in duplex. Synthesis of random peptides evolved to fuel the turnover of tRNAs. Then the combination of replication-coupled peptide formation and the independent development of amino acid-specific tRNA aminoacylation resulted in template-based protein synthesis. Therefore, the positioning of tRNAs adjacent to each other developed for the purpose of replication rather than peptide synthesis. This hypothesis does not include either selection for useful peptides or specific recognition of amino acids at the initial evolution of translation. It does, however, explain a number of features of modern translation apparatus, such as the relative flexibility of genetic code, the number of proteins shared by the transcription and translation machines, the universal participation of an RNA subunit in co-translational protein secretion, 'unscheduled translation', and factor-independent translocation. Assistance of original ribosomes in keeping apart the nascent transcript from its template is still widely explored by modern bacteria and perhaps by other domains of life.

Anticodons, frameshifts, and hidden periodicities in tRNA sequences

Fourier analysis of the short-range periodicities for the complete set of sequences coding for tRNA genes in genome of Bacillus subtilis proves that periodicities with periods p = 2, 3, 4, and 6 sites are the inherent properties of tRNAs. The related periodicities should be understood in a broad statistical sense and their identifying needs the elaborate statistical methods. To improve the statistics, the analysis of significant periodicities was performed for the binary R-Y, S-W, and K-M sequences. Generally, such short-range periodicities are produced via biased positioning of particular nucleotides rather than via the tandem multiplication and subsequent modifications of repeats, though the latter mechanism may also be realized. Quasi-coherently piercing long segments of tRNA, the short-range periodicities create the effective long-range structural coupling between the acceptor stem and the anticodon loop and may participate in the mechanisms of molecular recognition. The periodicities with p = 2 and 4 provide the natural ground for the translation with spontaneous or programmed frameshifting and are present in tRNAs decoding the most frameshift-prone codons. The observation of short-range periodicities suggests that the mechanisms of amino-acylation of tRNAs and codon-anticodon pairing are not independent. Their study may also provide the important information related to the origin and evolution of the genetic code.

Genetic code from tRNA point of view

The possible codon-anticodon pairings follow the standard genetic code, yet in a different mode. The corresponding rules for decoding sequence of the codons in mRNA with tRNA may be called "tRNA code". In this paper we analyse the mutational and translational stability of such tRNA code. Our approach is based on the model of "ambiguous intermediate" and on the study of underlying block structure and Eulerean graph technique. It is shown that the wobble rules and the reduced number of tRNA anticodons strongly affect the mutational and translational stability of the code. The selection of tRNA anticodons, besides the optimization of translation, also ensures the more reliable start and, to a lesser extent, the stop of translation. The attribution of tRNA anticodons to the groups [WWW, WWS, SWW, SWS] and [SSS, SSW, WSS, WSW] as well as [MMM, MMK, KMM, KMK] and [KKK, KKM, MKK, MKM] clearly correlates with class I and class II aminoacyl-tRNA synthetases and obeys the principle of the optimal coding in both cases. Both W-S and M-K groupings also refer to the encoding of amino acids with the large and small side-chain volumes, which may provide such an attribution. The higher variability of tRNA code agrees with the suggestions that the variations in an assignment of tRNA anticodons may serve as the driving force generating the different variants of the genetic code.