Pentamers with Non-redundant Frames: Bias for Natural Circular Code Codons

Genes on the circular code alphabet

The X motifs, motifs from the circular code X, are enriched in the (protein coding) genes of bacteria, archaea, eukaryotes, plasmids and viruses, moreover, in the minimal gene set belonging to the three domains of life, as well as in tRNA and rRNA sequences. They allow to retrieve, maintain and synchronize the reading frame in genes, and contribute to the regulation of gene expression. These results lead here to a theoretical study of genes based on the circular code alphabet. A new occurrence relation of the circular code X under the hypothesis of an equiprobable (balanced) strand pairing is given. Surprisingly, a statistical analysis of a large set of bacterial genes retrieves this relation on the circular code alphabet, but not on the DNA alphabet. Furthermore, the circular code X has the strongest balanced circular code pairing among 216 maximal C³ self-complementary trinucleotide circular codes, a new property of this circular code X. As an application of this theory, different tRNAs studied on the circular code alphabet reveal an unexpected stem structure. Thus, the circular code X would have constructed a coding stem in tRNAs as an outline of the future gene structure and the future DNA double helix.

Equivalence classes of circular codes induced by permutation groups

In the 1950s, Crick proposed the concept of so-called comma-free codes as an answer to the frame-shift problem that biologists have encountered when studying the process of translating a sequence of nucleotide bases into a protein. A little later it turned out that this proposal unfortunately does not correspond to biological reality. However, in the mid-90s, a weaker version of comma-free codes, so-called circular codes, was discovered in nature in J Theor Biol 182:45–58, 1996. Circular codes allow to retrieve the reading frame during the translational process in the ribosome and surprisingly the circular code discovered in nature is even circular in all three possible reading-frames (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^3$$\end{document}C3-property). Moreover, it is maximal in the sense that it contains 20 codons and is self-complementary which means that it consists of pairs of codons and corresponding anticodons. In further investigations, it was found that there are exactly 216 codes that have the same strong properties as the originally found code from J Theor Biol 182:45–58. Using an algebraic approach, it was shown in J Math Biol, 2004 that the class of 216 maximal self-complementary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^3$$\end{document}C3-codes can be partitioned into 27 equally sized equivalence classes by the action of a transformation group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L \subseteq S_4$$\end{document}L⊆S4 which is isomorphic to the dihedral group. Here, we extend the above findings to circular codes over a finite alphabet of even cardinality \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|\Sigma |=2n$$\end{document}|Σ|=2n for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \in {\mathbb {N}}$$\end{document}n∈N. We describe the corresponding group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_n$$\end{document}Ln using matrices and we investigate what classes of circular codes are split into equally sized equivalence classes under the natural equivalence relation induced by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_n$$\end{document}Ln. Surprisingly, this is not always the case. All results and constructions are illustrated by examples.

Combinatorial Fusion Rules to Describe Codon Assignment in the Standard Genetic Code

We propose combinatorial fusion rules that describe the codon assignment in the standard genetic code simply and uniformly for all canonical amino acids. These rules become obvious if the origin of the standard genetic code is considered as a result of a fusion of four protocodes: Two dominant AU and GC protocodes and two recessive AU and GC protocodes. The biochemical meaning of the fusion rules consists of retaining the complementarity between cognate codons of the small hydrophobic amino acids and large charged or polar amino acids within the protocodes. The proto tRNAs were assembled in form of two kissing hairpins with 9-base and 10-base loops in the case of dominant protocodes and two 9-base loops in the case of recessive protocodes. The fusion rules reveal the connection between the stop codons, the non-canonical amino acids, pyrrolysine and selenocysteine, and deviations in the translation of mitochondria. Using fusion rules, we predicted the existence of additional amino acids that are essential for the development of the standard genetic code. The validity of the proposed partition of the genetic code into dominant and recessive protocodes is considered referring to state-of-the-art hypotheses. The formation of two aminoacyl-tRNA synthetase classes is compatible with four-protocode partition.

Negative CG dinucleotide bias: An explanation based on feedback loops between Arginine codon assignments and theoretical minimal RNA rings

Theoretical minimal RNA rings are candidate primordial genes evolved for non-redundant coding of the genetic code's 22 coding signals (one codon per biogenic amino acid, a start and a stop codon) over the shortest possible length: 29520 22-nucleotide-long RNA rings solve this min-max constraint. Numerous RNA ring properties are reminiscent of natural genes. Here we present analyses showing that all RNA rings lack dinucleotide CG (a mutable, chemically instable dinucleotide coding for Arginine), bearing a resemblance to known CG-depleted genomes. CG in "incomplete" RNA rings (not coding for all coding signals, with only 3-12 nucleotides) gradually decreases towards CG absence in complete, 22-nucleotide-long RNA rings. Presumably, feedback loops during RNA ring growth during evolution (when amino acid assignment fixed the genetic code) assigned Arg to codons lacking CG (AGR) to avoid CG. Hence, as a chemical property of base pairs, CG mutability restructured the genetic code, thereby establishing itself as genetically encoded biological information.

Codon assignment evolvability in theoretical minimal RNA rings

Genetic code codon-amino acid assignments evolve for 15 (AAA, AGA, AGG, ATA, CGG, CTA, CTG. CTC, CTT, TAA, TAG, TCA, TCG, TGA and TTA (GNN codons notably absent)) among 64 codons (23.4%) across the 31 genetic codes (NCBI list completed with recently suggested green algal mitochondrial genetic codes). Their usage in 25 theoretical minimal RNA rings is examined. RNA rings are designed in silico to code once over the shortest length for all 22 coding signals (start and stop codons and each amino acid according to the standard genetic code). Though designed along coding constraints, RNA rings resemble ancestral tRNA loops, assigning to each RNA ring a putative anticodon, a cognate amino acid and an evolutionary genetic code integration rank for that cognate amino acid. Analyses here show 1. biases against/for evolvable codons in the two first vs last thirds of RNA ring coding sequences, 2. RNA rings with evolvable codons have recent cognates, and 3. evolvable codon and cytosine numbers in RNA ring compositions are positively correlated. Applying alternative genetic codes to RNA rings designed for nonredundant coding according to the standard genetic code reveals unsuspected properties of the standard genetic code and of RNA rings, notably on codon assignment evolvability and the special role of cytosine in relation to codon assignment evolvability and of the genetic code's coding structure.

First arrived, first served: competition between codons for codon-amino acid stereochemical interactions determined early genetic code assignments

Stereochemical nucleotide-amino acid interactions, in the form of noncovalent nucleotide-amino acid interactions, potentially produced the genetic code's codon-amino acid assignments. Empirical estimates of single nucleotide-amino acid affinities on surfaces and in solution are used to test whether trinucleotide-amino acid affinities determined genetic code assignments pending the principle "first arrived, first served": presumed early amino acids have greater codon-amino acid affinities than ulterior ones. Here, these single nucleotide affinities are used to approximate all 64 × 20 trinucleotide-amino acid affinities. Analyses show that (1) on surfaces, genetic code codon-amino acid assignments tend to match high affinities for the amino acids that integrated earliest the genetic code (according to Wong's metabolic coevolution hypothesis between nucleotides and amino acids) and (2) in solution, the same principle holds for the anticodon-amino acid assignments. Affinity analyses match best genetic code assignments when assuming that trinucleotides competed for amino acids, rather than amino acids for trinucleotides. Codon-amino acid affinities stick better to genetic code assignments than anticodon-amino acid affinities. Presumably, two independent coding systems, on surfaces and in solution, converged, and formed the current translation system. Proto-translation on surfaces by direct codon-amino acid interactions without tRNA-like adaptors coadapted with a system emerging in solution by proto-tRNA anticodon-amino acid interactions. These systems assigned identical or similar cognates to codons on surfaces and to anticodons in solution. Results indicate that a prebiotic metabolism predated genetic code self-organization.

Footprints of a Singular 22-Nucleotide RNA Ring at the Origin of Life

(1) Background: Previous experimental observations and theoretical hypotheses have been providing insight into a hypothetical world where an RNA hairpin or ring may have debuted as the primary informational and functional molecule. We propose a model revisiting the architecture of RNA-peptide interactions at the origin of life through the evolutionary dynamics of RNA populations. (2) Methods: By performing a step-by-step computation of the smallest possible hairpin/ring RNA sequences compatible with building up a variety of peptides of the primitive network, we inferred the sequence of a singular docosameric RNA molecule, we call the ALPHA sequence. Then, we searched for any relics of the peptides made from ALPHA in sequences deposited in the different public databases. (3) Results: Sequence matching between ALPHA and sequences from organisms among the earliest forms of life on Earth were found at high statistical relevance. We hypothesize that the frequency of appearance of relics from ALPHA sequence in present genomes has a functional necessity. (4) Conclusions: Given the fitness of ALPHA as a supportive sequence of the framework of all existing theories, and the evolution of Archaea and giant viruses, it is anticipated that the unique properties of this singular archetypal ALPHA sequence should prove useful as a model matrix for future applications, ranging from synthetic biology to DNA computing.

Why Is AUG the Start Codon?: Theoretical Minimal RNA Rings: Maximizing Coded Information Biases 1st Codon for the Universal Initiation Codon AUG

The rational design of theoretical minimal RNA rings predetermines AUG as the universal start codon. This design maximizes coded amino acid diversity over minimal sequence length, defining in silico theoretical minimal RNA rings, candidate ancestral genes. RNA rings code for 21 amino acids and a stop codon after three consecutive translation rounds, and form a degradation-delaying stem-loop hairpin. Twenty-five RNA rings match these constraints, ten start with the universal initiation codon AUG. No first codon bias exists among remaining RNA rings. RNA ring design predetermines AUG as initiation codon. This is the only explanation yet for AUG as start codon. RNA ring design determines additional RNA ring gene- and tRNA-like properties described previously, because it presumably mimics constraints on life's primordial RNAs.

RNA Rings Strengthen Hairpin Accretion Hypotheses for tRNA Evolution: A Reply to Commentaries by Z.F. Burton and M. Di Giulio

Theoretical minimal RNA ring design ensures coding over the shortest length once for each coding signal (start and stop codons, and each amino acid) and their hairpin configuration. These constraints define 25 RNA rings which surprisingly resemble ancestral tRNA loops, suggesting commonalities between RNA ring design and proto-tRNAs. RNA rings share several other properties with tRNAs, suggesting that primordial RNAs were multifunctional peptide coding sequences and structural RNAs. Two hypotheses, respectively, by M. Di Giulio and Z.F. Burton, derived from cloverleaf structural symmetries suggest that two and three, respectively, stem-loop hairpins agglutinated into tRNAs. Their authors commented that their respective structure-based hypotheses reflect better tRNA structure than RNA rings. Unlike these hypotheses, RNA ring design uses no tRNA-derived information, rendering model predictive power comparisons senseless. Some analyses of RNA ring primary and secondary structures stress RNA ring splicing in their predicted anticodon's midst, indicating ancestrality of split tRNAs, as the two-piece model predicts. Advancement of knowledge, rather than of specific hypotheses, gains foremost by examining independent hypotheses for commonalities, and only secondarily for discordances. RNA rings mimick ancestral biomolecules including tRNAs, and their evolution, and constitute an interesting synthetic system for early prebiotic evolution tests/simulations.

Accretion history of large ribosomal subunits deduced from theoretical minimal RNA rings is congruent with histories derived from phylogenetic and structural methods

Accretions of tRNAs presumably formed the large complex ribosomal RNA structures. Similarities of tRNA secondary structures with rRNA secondary structures increase with the integration order of their cognate amino acid in the genetic code, indicating tRNA evolution towards rRNA-like structures. Here analyses rank secondary structure subelements of three large ribosomal RNAs (Prokaryota: Archaea: Thermus thermophilus; Bacteria: Escherichia coli; Eukaryota: Saccharomyces cerevisiae) in relation to their similarities with secondary structures formed by presumed proto-tRNAs, represented by 25 theoretical minimal RNA rings. These ranks are compared to those derived from two independent methods (ranks provide a relative evolutionary age to the rRNA substructure), (a) cladistic phylogenetic analyses and (b) 3D-crystallography where core subelements are presumed ancient and peripheral ones recent. Comparisons of rRNA secondary structure subelements with RNA ring secondary structures show congruence between ranks deduced by this method and both (a) and (b) (more with (a) than (b)), especially for RNA rings with predicted ancient cognate amino acid. Reconstruction of accretion histories of large rRNAs will gain from adequately integrating information from independent methods. Theoretical minimal RNA rings, sequences deterministically designed in silico according to specific coding constraints, might produce adequate scales for prebiotic and early life molecular evolution.

The primordial tRNA acceptor stem code from theoretical minimal RNA ring clusters

BACKGROUND

Theoretical minimal RNA rings code by design over the shortest length once for each of the 20 amino acids, a start and a stop codon, and form stem-loop hairpins. This defines at most 25 RNA rings of 22 nucleotides. As a group, RNA rings mimick numerous prebiotic and early life biomolecular properties: tRNAs, deamination gradients and replication origins, emergence of codon preferences for the natural circular code, and contents of early protein coding genes. These properties result from the RNA ring's in silico design, based mainly on coding nonredundancy among overlapping translation frames, as the genetic code's codon-amino acid assignments determine. RNA rings resemble ancestral tRNAs, defining RNA ring anticodons and corresponding cognate amino acids. Surprisingly, all examined RNA ring properties coevolve with genetic code integration ranks of RNA ring cognates, as if RNA rings mimick prebiotic and early life evolution.

METHODS

Distances between RNA rings were calculated using different evolutionary models. Associations between these distances and genetic code evolutionary hypotheses detect evolutionary models best describing RNA ring diversification.

RESULTS

Here pseudo-phylogenetic analyses of RNA rings produce clusters corresponding to the primordial code in tRNA acceptor stems, more so when substitution matrices from neutrally evolving pseudogenes are used rather than from functional protein coding genes reflecting selection for conserving amino acid properties.

CONCLUSIONS

Results indicate RNA rings with recent cognates evolved from those with early cognates. Hence RNA rings, as designed by the genetic code's structure, simulate tRNA stem evolution and prebiotic history along neutral chemistry-driven mutation regimes.