Tetracoding increases with body temperature in Lepidosauria

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.

Natural pyrrolysine-biased translation of stop codons in mitochondrial peptides entirely coded by expanded codons

During the noncanonical deletion transcription, k nucleotides are systematically skipped/deleted after each transcribed trinucleotide producing deletion-RNAs (delRNAs). Peptides matching delRNAs either result from (a) canonical translation of delRNAs; or (b) noncanonical translation of regular transcripts along expanded codons. Only along frame "0" (start site) (a) and (b) produce identical peptides. Here, mitochondrial mass spectrometry data analyses assume expanded codon/del-transcription with 3 + k (k from 0 to 12) nucleotides. Detected peptides map preferentially on previously identified delRNAs. More peptides were detected for k (1-12) when del-transcriptional and expanded codon translations start sites coincide (i.e. the 0^th frame) than for frames +1 or +2. Hence, both (a) and (b) produced peptides identified here. Biases for frame 0 decrease for k > 2, reflecting codon/anticodon expansion limits. Further analyses find preferential pyrrolysine insertion at stop codons, suggesting Pyl-specific mitochondrial suppressor tRNAs loaded by Pyl-specific tRNA synthetases with unknown origins. Pyl biases at stops are stronger for regular than expanded codons suggesting that Pyl-tRNAs are less competitive with near-cognate tRNAs in expanded codon contexts. Statistical biases for these findings exclude that detected peptides are experimental and/or bioinformatic artefacts implying both del-transcription and expanded codons translation occur in human mitochondria.

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.

Deamination gradients within codons after 1<->2 position swap predict amino acid hydrophobicity and parallel β-sheet conformational preference

Deaminations C->T and A->G are frequent mutations producing nucleotide content gradients across genomes proportional to singlestrandedness during replication/transcription. Hence, within single codons, deamination risks increase from first to third codon positions, while second codon positions are functionally most crucial. Here genetic codes are analyzed assuming that after anticodons protected codons from deaminations, first and second codon positions swapped (N2N1N3->N1N2N3), with lowest deamination risks for N2 in presumed primitive N2N1N3 codons. N2N1N3, not standard N1N2N3, codon structure minimizes deaminations inversely proportionally to cognate amino acid hydrophobicity and parallel betasheet conformational preference. For N1N2N3, deamination minimization increases with genetic code integration order of cognate amino acids: during the presumed N2N1N3->N1N2N3 codon structure transition, protein synthesis combined direct codon-amino acid interactions for late amino acids and tRNA-based translation for early amino acids. Hence N2N1N3 codons would correspond to tRNA-free translation by spontaneous codon-amino acid affinities, and tRNA-mediated translation presumably caused N2N1N3->N1N2N3 swaps. Results show that rational, not arbitrary rules link codon and amino acid structures. Some analyses detect mitochondrial RNAs and peptides in public data corresponding to systematic position swaps, suggesting occasional swapping polymerase activity.

Fail-safe genetic codes designed to intrinsically contain engineered organisms

One challenge in engineering organisms is taking responsibility for their behavior over many generations. Spontaneous mutations arising before or during use can impact heterologous genetic functions, disrupt system integration, or change organism phenotype. Here, we propose restructuring the genetic code itself such that point mutations in protein-coding sequences are selected against. Synthetic genetic systems so-encoded should fail more safely in response to most spontaneous mutations. We designed fail-safe codes and simulated their expected effects on the evolution of so-encoded proteins. We predict fail-safe codes supporting expression of 20 or 15 amino acids could slow protein evolution to ∼30% or 0% the rate of standard-encoded proteins, respectively. We also designed quadruplet-codon codes that should ensure all single point mutations in protein-coding sequences are selected against while maintaining expression of 20 or more amino acids. We demonstrate experimentally that a reduced set of 21 tRNAs is capable of expressing a protein encoded by only 20 sense codons, whereas a standard 64-codon encoding is not expressed. Our work suggests that biological systems using rationally depleted but otherwise natural translation systems should evolve more slowly and that such hypoevolvable organisms may be less likely to invade new niches or outcompete native populations.

Chimeric Translation for Mitochondrial Peptides: Regular and Expanded Codons

Frameshifting protein translation occasionally results from insertion of amino acids at isolated mono- or dinucleotide-expanded codons by tRNAs with expanded anticodons. Previous analyses of two different types of human mitochondrial MS proteomic data (Fisher and Waters technologies) detect peptides entirely corresponding to expanded codon translation. Here, these proteomic data are reanalyzed searching for peptides consisting of at least eight consecutive amino acids translated according to regular tricodons, and at least eight adjacent consecutive amino acids translated according to expanded codons. Both datasets include chimerically translated peptides (mono- and dinucleotide expansions, 42 and 37, respectively). The regular tricodon-encoded part of some chimeric peptides corresponds to standard human mitochondrial proteins (mono- and dinucleotide expansions, six (AT6, CytB, ND1, 2xND2, ND5) and one (ND1), respectively). Chimeric translation probably increases the diversity of mitogenome-encoded proteins, putatively producing functional proteins. These might result from translation by tRNAs with expanded anticodons, or from regular tricodon translation of RNAs where transcription/posttranscriptional edition systematically deleted mono- or dinucleotides after each trinucleotide. The pairwise matched combination of adjacent peptide parts translated from regular and expanded codons strengthens the hypothesis that translation of stretches of consecutive expanded codons occurs. Results indicate statistical translation producing distributions of alternative proteins. Genetic engineering should account for potential unexpected, unwanted secondary products.

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.

Mining for missed sORF-encoded peptides

INTRODUCTION

Small open reading frames (sORFs) with potential protein-coding capacity have been disclosed in various transcripts, including long noncoding RNAs (LncRNAs), mRNAs (5'-upstream, coding domain, and 3'-downstream), circular RNAs, pri-miRNAs, and ribosomal RNAs (rRNAs). Recent characterization of several sORF-encoded peptides (SEPs or micropeptides) revealed their important roles in many fundamental biological processes in a broad range of species from yeast to human. The success in the mining of micropeptides attributes to the advanced bioinformatics and high-throughput sequencing techniques. Areas covered: sORFs and SEPs were overlooked for their tiny size and the difficulty of identification by bioinformatics analyses. With more and more sORFs and SEPs have been identified, this field has attracted more attention. This review covers recent advances in the strategies for the detection and identification of sORFs and SEPs. Expert commentary: The advantages and drawbacks of the strategies for detection and identification of sORFs and SEPs are discussed, as well as the techniques that are used to decipher the roles of micropeptides in organisms are described.

Protein Sequences Recapitulate Genetic Code Evolution

Several hypotheses predict ranks of amino acid assignments to genetic code's codons. Analyses here show that average positions of amino acid species in proteins correspond to assignment ranks, in particular as predicted by Juke's neutral mutation hypothesis for codon assignments. In all tested protein groups, including co- and post-translationally folding proteins, 'recent' amino acids are on average closer to gene 5' extremities than 'ancient' ones. Analyses of pairwise residue contact energies matrices suggest that early amino acids stereochemically selected late ones that stablilize residue interactions within protein cores, presumably producing 5'-late-to-3'-early amino acid protein sequence gradients. The gradient might reduce protein misfolding, also after mutations, extending principles of neutral mutations to protein folding. Presumably, in self-perpetuating and self-correcting systems like the genetic code, initial conditions produce similarities between evolution of the process (the genetic code) and 'ontogeny' of resulting structures (here proteins), producing apparent teleonomy between process and product.

Bijective codon transformations show genetic code symmetries centered on cytosine's coding properties

Homology of some RNAs with template DNA requires systematic exchanges between nucleotides. Such exchanges produce 'swinger' RNA along 23 bijective transformations (nine symmetric, X ↔ Y; and 14 asymmetric, X → Y → Z → X, for example A ↔ C and A → C → G → A, respectively). Here, analyses compare amino acids coded by swinger-transformed codons to those coded by untransformed codons, defining coding invariance after transformations. Swinger transformations cluster according to coding invariance in four groups characterized by transformations into cytosine (C = C, T → C, A → C, and G → C). C's central mutational coding role shows that swinger transformations constrained genetic code genesis. Coding invariance post-transformations correlate positively/negatively with mitochondrial swinger transcription/lepidosaurian body temperature. Presumably, low/high temperatures stabilize/revert rare swinger polymerization modes, producing long swinger sequences/point mutations, respectively. Coding invariance after swinger transformations might compensate effects of swinger polymerizations in species with low body temperatures. Hypothetically, swinger transcription increased coding potential of RNA self-replicating protolife systems under heating/cooling cycles.

Genetic Code Optimization for Cotranslational Protein Folding: Codon Directional Asymmetry Correlates with Antiparallel Betasheets, tRNA Synthetase Classes

A new codon property, codon directional asymmetry in nucleotide content (CDA), reveals a biologically meaningful genetic code dimension: palindromic codons (first and last nucleotides identical, codon structure XZX) are symmetric (CDA = 0), codons with structures ZXX/XXZ are 5'/3' asymmetric (CDA = - 1/1; CDA = - 0.5/0.5 if Z and X are both purines or both pyrimidines, assigning negative/positive (-/+) signs is an arbitrary convention). Negative/positive CDAs associate with (a) Fujimoto's tetrahedral codon stereo-table; (b) tRNA synthetase class I/II (aminoacylate the 2'/3' hydroxyl group of the tRNA's last ribose, respectively); and (c) high/low antiparallel (not parallel) betasheet conformation parameters. Preliminary results suggest CDA-whole organism associations (body temperature, developmental stability, lifespan). Presumably, CDA impacts spatial kinetics of codon-anticodon interactions, affecting cotranslational protein folding. Some synonymous codons have opposite CDA sign (alanine, leucine, serine, and valine), putatively explaining how synonymous mutations sometimes affect protein function. Correlations between CDA and tRNA synthetase classes are weaker than between CDA and antiparallel betasheet conformation parameters. This effect is stronger for mitochondrial genetic codes, and potentially drives mitochondrial codon-amino acid reassignments. CDA reveals information ruling nucleotide-protein relations embedded in reversed (not reverse-complement) sequences (5'-ZXX-3'/5'-XXZ-3').

Reviewing evidence for systematic transcriptional deletions, nucleotide exchanges, and expanded codons, and peptide clusters in human mitochondria

Polymerization sometimes transforms sequences by (a) systematic deletions of mono-, dinucleotides after trinucleotides, or (b) 23 systematic nucleotide exchanges (9 symmetric, X<>Y, e.g. G<>T, 14 asymmetric, X > Y > Z > X, e.g. A > G > T > A), producing del- and swinger RNAs. Some peptides correspond to del- and swinger RNA translations, also according to tetracodons, codons expanded by a silent nucleotide. Here new analyzes assume different proteolytic patterns, partially alleviating false negative peptide detection biases, expanding noncanonical mitoproteome profiles. Mito-genomic, -transcriptomic and -proteomic evidence for noncanonical transcriptions and translations are reviewed and clusters of del- and swinger peptides (also along tetracodons) are described. Noncanonical peptide clusters indicate regulated expression of cryptically encoded mitochondrial protein coding genes. These candidate noncanonical proteins don't resemble known proteins.

Natural mitochondrial proteolysis confirms transcription systematically exchanging/deleting nucleotides, peptides coded by expanded codons

Protein sequences have higher linguistic complexities than human languages. This indicates undeciphered multilayered, overprinted information/genetic codes. Some superimposed genetic information is revealed by detections of transcripts systematically (a) exchanging nucleotides (nine symmetric, e.g. A<->C, fourteen asymmetric, e.g. A->C->G->A, swinger RNAs) translated according to tri-, tetra- and pentacodons, and (b) deleting mono-, dinucleotides after each trinucleotide (delRNAs). Here analyses of two independent proteomic datasets considering natural proteolysis confirm independently translation of these non-canonical RNAs, also along tetra- and pentacodons, increasing coverage of putative, cryptically encoded proteins. Analyses assuming endoproteinase GluC and elastase digestions (cleavages after residues D, E, and A, L, I, V, respectively) detect additional peptides colocalizing with detected non-canonical RNAs. Analyses detect fewer peptides matching GluC-, elastase- than trypsin-digestions: artificial trypsin-digestion outweighs natural proteolysis. Results suggest occurrences of complete proteins entirely matching non-canonical, superimposed encoding(s). Protein-coding after bijective transformations could explain genetic code symmetries, such as along Rumer's transformation.

Unbiased Mitoproteome Analyses Confirm Non-canonical RNA, Expanded Codon Translations

Proteomic MS/MS mass spectrometry detections are usually biased towards peptides cleaved by experimentally added digestion enzyme(s). Hence peptides resulting from spontaneous degradation and natural proteolysis usually remain undetected. Previous analyses of tryptic human proteome data (cleavage after K, R) detected non-canonical tryptic peptides translated according to tetra- and pentacodons (codons expanded by silent mono- and dinucleotides), and from transcripts systematically (a) deleting mono-, dinucleotides after trinucleotides (delRNAs), (b) exchanging nucleotides according to 23 bijective transformations. Nine symmetric and fourteen asymmetric nucleotide exchanges (X ↔ Y, e.g. A ↔ C; and X → Y → Z → X, e.g. A → C → G → A) produce swinger RNAs. Here unbiased reanalyses of these proteomic data detect preferentially non-canonical tryptic peptides despite assuming random cleavage. Unbiased analyses couldn't reconstruct experimental tryptic digestion if most detected non-canonical peptides were false positives. Detected non-tryptic non-canonical peptides map preferentially on corresponding, previously described non-canonical transcripts, as for tryptic non-canonical peptides. Hence unbiased analyses independently confirm previous trypsin-biased analyses that showed translations of del- and swinger RNA and expanded codons. Accounting for natural proteolysis completes trypsin-biased mitopeptidome analyses, independently confirms non-canonical transcriptions and translations.

Natural chymotrypsin-like-cleaved human mitochondrial peptides confirm tetra-, pentacodon, non-canonical RNA translations

Mass spectra of human mitochondrial peptides match non-canonical transcripts systematically (a) deleting mono/dinucleotides after trinucleotides (delRNA), (b) exchanging nucleotides (swinger RNA), translated according to tri, (c) tetra- and pentacodons (codons expanded by a 4th (and 5th) silent nucleotide(s)). Swinger transcriptions are 23 bijective transformations, nine symmetric (X<->Y, e.g. A<->C) and fourteen asymmetric exchanges (X->Y->Z->X, e.g. A->C->G->A). Here, proteomic analyses assuming cleavage after W,Y, F (chymotrypsin-like, for trypsinized samples) detect fewer chymotrypsinized than trypsinized peptides. Detected non-canonical peptides map preferentially on detected non-canonical RNAs for chymotrypsinized peptides, as previously found for trypsinized peptides. This suggests residual natural chymotrypsin-like digestion detectable within experimentally trypsinized peptide data. Some trypsinized peptides are detected twice, by analyses assuming trypsin, and those assuming chymotrypsin cleavages. They have higher spectra counts than peptides detected only once, meaning that abundant peptides are more frequently detected, but detection certainties resemble those for peptides detected only once. Analyses assuming 'incorrect' digestions are inadequate negative controls for digestion enzymes naturally active in biological samples. Chymotrypsin-analyses confirm non-canonical transcriptions/translations independently of results obtained assuming trypsinization, increase non-canonical peptidome coverage, indicating mitogenome-encoding of yet undetected proteins.

Chimeric mitochondrial peptides from contiguous regular and swinger RNA

Previous mass spectrometry analyses described human mitochondrial peptides entirely translated from swinger RNAs, RNAs where polymerization systematically exchanged nucleotides. Exchanges follow one among 23 bijective transformation rules, nine symmetric exchanges (X ↔ Y, e.g. A ↔ C) and fourteen asymmetric exchanges (X → Y → Z → X, e.g. A → C → G → A), multiplying by 24 DNA's protein coding potential. Abrupt switches from regular to swinger polymerization produce chimeric RNAs. Here, human mitochondrial proteomic analyses assuming abrupt switches between regular and swinger transcriptions, detect chimeric peptides, encoded by part regular, part swinger RNA. Contiguous regular- and swinger-encoded residues within single peptides are stronger evidence for translation of swinger RNA than previously detected, entirely swinger-encoded peptides: regular parts are positive controls matched with contiguous swinger parts, increasing confidence in results. Chimeric peptides are 200 × rarer than swinger peptides (3/100,000 versus 6/1000). Among 186 peptides with > 8 residues for each regular and swinger parts, regular parts of eleven chimeric peptides correspond to six among the thirteen recognized, mitochondrial protein-coding genes. Chimeric peptides matching partly regular proteins are rarer and less expressed than chimeric peptides matching non-coding sequences, suggesting targeted degradation of misfolded proteins. Present results strengthen hypotheses that the short mitogenome encodes far more proteins than hitherto assumed. Entirely swinger-encoded proteins could exist.

•

Chimeric peptides are translated from contiguous regular and swinger RNA

•

They are 200x rarer than mitochondrial swinger peptides

•

Chimeric peptides integrated in regular mitochondrial proteins are downregulated

•

Contiguous regular parts are matched positive controls for swinger parts

•

The last point validates results beyond other statistical tests for robustness

Swinger RNA self-hybridization and mitochondrial non-canonical swinger transcription, transcription systematically exchanging nucleotides

Stem-loop hairpins punctuate mitochondrial post-transcriptional processing. Regulation of mitochondrial swinger transcription, transcription producing RNAs matching the mitogenome only assuming systematic exchanges between nucleotides (23 bijective transformations along 9 symmetric exchanges X<>Y, e.g. A<>G, and 14 asymmetric exchanges X>Y>Z>X, e.g. A>G>C>A) remains unknown. Does swinger RNA self-hybridization regulate swinger, as regular, transcription? Groups of 8 swinger transformations share canonical self-hybridization properties within each group, group 0 includes identity (regular) transcription. The human mitogenome has more stem-loop hairpins than randomized sequences for all groups. Group 2 transformations reveal complementarity of the light strand replication origin (OL) loop and a neighboring tRNA gene, detecting the longtime presumed OL/tRNA homology. Non-canonical G=U pairings in hairpins increases with swinger RNA detection. These results confirm biological relevancy of swinger-transformed DNA/RNA, independently of, and in combination with, previously detected swinger DNA/RNA and swinger peptides. Swinger-transformed mitogenomes include unsuspected multilayered information.

Systematically frameshifting by deletion of every 4th or 4th and 5th nucleotides during mitochondrial transcription: RNA self-hybridization regulates delRNA expression

In mitochondria, secondary structures punctuate post-transcriptional RNA processing. Recently described transcripts match the human mitogenome after systematic deletions of every 4th, respectively every 4th and 5th nucleotides, called delRNAs. Here I explore predicted stem-loop hairpin formation by delRNAs, and their associations with delRNA transcription and detected peptides matching their translation. Despite missing 25, respectively 40% of the nucleotides in the original sequence, del-transformed sequences form significantly more secondary structures than corresponding randomly shuffled sequences, indicating biological function, independently of, and in combination with, previously detected delRNA and thereof translated peptides. Self-hybridization decreases delRNA abundances, indicating downregulation. Systematic deletions of the human mitogenome reveal new, unsuspected coding and structural informations.

n-Nucleotide circular codes in graph theory

The circular code theory proposes that genes are constituted of two trinucleotide codes: the classical genetic code with 61 trinucleotides for coding the 20 amino acids (except the three stop codons {TAA,TAG,TGA}) and a circular code based on 20 trinucleotides for retrieving, maintaining and synchronizing the reading frame. It relies on two main results: the identification of a maximal C(3) self-complementary trinucleotide circular code X in genes of bacteria, eukaryotes, plasmids and viruses (Michel 2015 J. Theor. Biol. 380, 156-177. (doi:10.1016/j.jtbi.2015.04.009); Arquès & Michel 1996 J. Theor. Biol. 182, 45-58. (doi:10.1006/jtbi.1996.0142)) and the finding of X circular code motifs in tRNAs and rRNAs, in particular in the ribosome decoding centre (Michel 2012 Comput. Biol. Chem. 37, 24-37. (doi:10.1016/j.compbiolchem.2011.10.002); El Soufi & Michel 2014 Comput. Biol. Chem. 52, 9-17. (doi:10.1016/j.compbiolchem.2014.08.001)). The univerally conserved nucleotides A1492 and A1493 and the conserved nucleotide G530 are included in X circular code motifs. Recently, dinucleotide circular codes were also investigated (Michel & Pirillo 2013 ISRN Biomath. 2013, 538631. (doi:10.1155/2013/538631); Fimmel et al. 2015 J. Theor. Biol. 386, 159-165. (doi:10.1016/j.jtbi.2015.08.034)). As the genetic motifs of different lengths are ubiquitous in genes and genomes, we introduce a new approach based on graph theory to study in full generality n-nucleotide circular codes X, i.e. of length 2 (dinucleotide), 3 (trinucleotide), 4 (tetranucleotide), etc. Indeed, we prove that an n-nucleotide code X is circular if and only if the corresponding graph [Formula: see text] is acyclic. Moreover, the maximal length of a path in [Formula: see text] corresponds to the window of nucleotides in a sequence for detecting the correct reading frame. Finally, the graph theory of tournaments is applied to the study of dinucleotide circular codes. It has full equivalence between the combinatorics theory (Michel & Pirillo 2013 ISRN Biomath. 2013, 538631. (doi:10.1155/2013/538631)) and the group theory (Fimmel et al. 2015 J. Theor. Biol. 386, 159-165. (doi:10.1016/j.jtbi.2015.08.034)) of dinucleotide circular codes while its mathematical approach is simpler.

Translation of mitochondrial swinger RNAs according to tri-, tetra- and pentacodons

Transcriptomes and proteomes include RNA and protein fragments not matching regular transcription/translation. Some 'non-canonical' mitochondrial transcripts match mitogenomes after assuming one among 23 systematic exchanges between nucleotides, producing swinger RNAs (nine symmetric, X↔Y, example C↔T; 14 asymmetric, X→Y→Z→X, example A→T→G→A) in GenBank's EST database. Here, reanalyzes of (a) public human mitochondrial transcriptome data (Illumina: RNA-seq) allowed to detect mitochondrial swinger RNAs for all 23 exchanges and (b) independent public human mitochondrial trypsinized proteomic mass spectrometry data allowed to detect peptides predicted from translation of parts of swinger-transformed mitogenomes covered by detected swinger reads. RNA-seq and previous EST swinger transcript data converge. Swinger RNA translation frequently inserts various amino acids at stop codons. Swinger RNA-peptide associations exist also for peptides matching systematically frameshifting translation, peptides entirely coded by tetra- and pentacodons (regular codons expanded by silent mononucleotides at 4th, and silent dinucleotides at 4th and 5th position(s), respectively). Swinger peptides differ from regular mitochondrial proteins: not membrane embedded, reflect warmer, anaerobic, low resource conditions, reminding a free-living ancestor. Tetra- and pentacoded peptides associate with low, high GC contents, respectively, suggesting expanded codon translations associate with thermic stresses. Results confirm experimentally predicted swinger, tetra- and pentacoded mitochondrial peptides, increasing mitogenomic coding density.

Codon expansion and systematic transcriptional deletions produce tetra-, pentacoded mitochondrial peptides

Genes include occasionally isolated codons with a fourth (and fifth) silent nucleotide(s). Assuming tetracodons, translated hypothetical peptides align with regular GenBank proteins; predicted tetracodons coevolve with predicted tRNAs with expanded anticodons in each mammal, Drosophila and Lepidosauria mitogenomes, GC contents and with lepidosaurian body temperatures, suggesting that expanded codons are an adaptation of translation to high temperature. Hypothetically, continuous stretches of tetra- and pentacodons code for peptides. Both systematic nucleotide deletions during transcription, and translation by tRNAs with expanded anticodons could produce these peptides. Reanalyses of human nanoLc mass spectrometry peptidome data detect numerous tetra- and pentapeptides translated from the human mitogenome. These map preferentially on (BLAST-detected) human RNAs matching the human mitogenome, assuming systematic mono- and dinucleotide deletions after each third nucleotide (delRNAs). Translation by expanded anticodons is incompatible with silent nucleotides in the midst rather than at codon 3' extremity. More than 1/3 of detected tetra- and pentapeptides assume silent positions at codon extremity, suggesting that both mechanisms, regular translation of delRNAs and translation of regular RNAs by expanded anticodons, produce this peptide subgroup. Results show that systematically deleting polymerization occurs, and confirm serial translation of expanded codons. Non-canonical transcriptions and translations considerably expand the coding potential of DNA and RNA sequences.

Swinger RNAs with sharp switches between regular transcription and transcription systematically exchanging ribonucleotides: Case studies

During RNA transcription, DNA nucleotides A,C,G, T are usually matched by ribonucleotides A, C, G and U. However occasionally, this rule does not apply: transcript-DNA homologies are detectable only assuming systematic exchanges between ribonucleotides. Nine symmetric (X ↔ Y, e.g. A ↔ C) and fourteen asymmetric (X ↔ Y ↔ Z, e.g. A ↔ C ↔ G) exchanges exist, called swinger transcriptions. Putatively, polymerases occasionally stabilize in unspecified swinger conformations, possibly similar to transient conformations causing punctual misinsertions. This predicts chimeric transcripts, part regular, part swinger-transformed, reflecting polymerases switching to swinger polymerization conformation(s). Four chimeric Genbank transcripts (three from human mitochondrion and one murine cytosolic) are described here: (a) the 5' and 3' extremities reflect regular polymerization, the intervening sequence exchanges systematically between ribonucleotides (swinger rule G ↔ U, transcript (1), with sharp switches between regular and swinger sequences; (b) the 5' half is 'normal', the 3' half systematically exchanges ribonucleotides (swinger rule C ↔ G, transcript (2), with an intercalated sequence lacking homology; (c) the 3' extremity fits A ↔ G exchanges (10% of transcript length), the 5' half follows regular transcription; the intervening region seems a mix of regular and A ↔ G transcriptions (transcript 3); (d) murine cytosolic transcript 4 switches to A ↔ U + C ↔ G, and is fused with A ↔ U + C ↔ G swinger transformed precursor rRNA. In (c), each concomitant transcript 5' and 3' extremities match opposite genome strands. Transcripts 3 and 4 combine transcript fusions with partial swinger transcriptions. Occasional (usually sharp) switches between regular and swinger transcriptions reveal greater coding potential than detected until now, suggest stable polymerase swinger conformations.

Sharp switches between regular and swinger mitochondrial replication: 16S rDNA systematically exchanging nucleotides A<->T+C<->G in the mitogenome of Kamimuria wangi

Swinger DNAs are sequences whose homology with known sequences is detected only by assuming systematic exchanges between nucleotides. Nine symmetric (X<->Y, i.e. A<->C) and fourteen asymmetric (X->Y->Z, i.e. A->C->G) exchanges exist. All swinger DNA previously detected in GenBank follow the A<->T+C<->G exchange, while mitochondrial swinger RNAs distribute among different swinger types. Here different alignment criteria detect 87 additional swinger mitochondrial DNAs (86 from insects), including the first swinger gene embedded within a complete genome, corresponding to the mitochondrial 16S rDNA of the stonefly Kamimuria wangi. Other Kamimuria mt genome regions are "regular", stressing unanswered questions on (a) swinger polymerization regulation; (b) swinger 16S rDNA functions; and (c) specificity to rDNA, in particular 16S rDNA. Sharp switches between regular and swinger replication, together with previous observations on swinger transcription, suggest that swinger replication might be due to a switch in polymerization mode of regular polymerases and the possibility of swinger-encoded information, predicted in primordial genes such as rDNA.

The human mitochondrial genome may code for more than 13 proteins

The human mitochondrial (mt) DNA is commonly described as a small, maternally inherited molecule that encodes 13 protein components of the oxidative phosphorylation system and 24 structural RNAs required for their translation. However, recent studies indicate that the human mtDNA has a larger functional repertoire than previously believed. This paper briefly summarizes these studies, which suggest to reconsider our way to describe the human mitochondrial DNA as it may code for more than 13 proteins.

Mitochondrial swinger replication: DNA replication systematically exchanging nucleotides and short 16S ribosomal DNA swinger inserts

Assuming systematic exchanges between nucleotides (swinger RNAs) resolves genomic 'parenthood' of some orphan mitochondrial transcripts. Twenty-three different systematic nucleotide exchanges (bijective transformations) exist. Similarities between transcription and replication suggest occurrence of swinger DNA. GenBank searches for swinger DNA matching the 23 swinger versions of human and mouse mitogenomes detect only vertebrate mitochondrial swinger DNA for swinger type AT+CG (from five different studies, 149 sequences) matching three human and mouse mitochondrial genes: 12S and 16S ribosomal RNAs, and cytochrome oxidase subunit I. Exchange A<->T+C<->G conserves self-hybridization properties, putatively explaining swinger biases for rDNA, against protein coding genes. Twenty percent of the regular human mitochondrial 16S rDNA consists of short swinger repeats (from 13 exchanges). Swinger repeats could originate from recombinations between regular and swinger DNA: duplicated mitochondrial genes of the parthenogenetic gecko Heteronotia binoei include fewer short A<->T+C<->G swinger repeats than non-duplicated mitochondrial genomes of that species. Presumably, rare recombinations between female and male mitochondrial genes (and in parthenogenetic situations between duplicated genes), favors reverse-mutations of swinger repeat insertions, probably because most inserts affect negatively ribosomal function. Results show that swinger DNA exists, and indicate that swinger polymerization contributes to the genesis of genetic material and polymorphism.

Species radiation by DNA replication that systematically exchanges nucleotides?

RNA and DNA syntheses share many properties. Therefore, the existence of 'swinger' RNAs, presumed 'orphan' transcripts matching genomic sequences only if transcription systematically exchanged nucleotides, suggests replication producing swinger DNA. Transcripts occur in many short-lived copies, the few cellular DNA molecules are long-lived. Hence pressures for functional swinger DNAs are greater than for swinger RNAs. Protein coding properties of swinger sequences differ from original sequences, suggesting rarity of corresponding swinger DNA. For genes producing structural RNAs, such as tRNAs and rRNAs, three exchanges (A<->T, C<->G and A<->T+C<->G) conserve self-hybridization properties. All nuclear eukaryote swinger DNA sequences detected in GenBank are for rRNA genes assuming A<->T+C<->G exchanges. In brachyuran crabs, 25 species had A<->T+C<->G swinger 18S rDNA, all matching the reverse-exchanged version of regular 18S rDNA of a related species. In this taxon, swinger replication of 18S rDNA apparently associated with, or even resulted in species radiation. A<->T+C<->G transformation doesn't invert sequence direction, differing from inverted repeats. Swinger repeats (detectable only assuming swinger transformations, A<->T+C<->G swinger repeats most frequent) within regular human rRNAs, independently confirm swinger polymerizations for most swinger types. Swinger replication might be an unsuspected molecular mechanism for ultrafast speciation.