A unified model of the standard genetic code

Self-Organisation of Prediction Models

Living organisms are active open systems far from thermodynamic equilibrium. The ability to behave actively corresponds to dynamical metastability: minor but supercritical internal or external effects may trigger major substantial actions such as gross mechanical motion, dissipating internally accumulated energy reserves. Gaining a selective advantage from the beneficial use of activity requires a consistent combination of sensual perception, memorised experience, statistical or causal prediction models, and the resulting favourable decisions on actions. This information processing chain originated from mere physical interaction processes prior to life, here denoted as structural information exchange. From there, the self-organised transition to symbolic information processing marks the beginning of life, evolving through the novel purposivity of trial-and-error feedback and the accumulation of symbolic information. The emergence of symbols and prediction models can be described as a ritualisation transition, a symmetry-breaking kinetic phase transition of the second kind previously known from behavioural biology. The related new symmetry is the neutrally stable arbitrariness, conventionality, or code invariance of symbols with respect to their meaning. The meaning of such symbols is given by the structural effect they ultimately unleash, directly or indirectly, by deciding on which actions to take. The early genetic code represents the first symbols. The genetically inherited symbolic information is the first prediction model for activities sufficient for survival under the condition of environmental continuity, sometimes understood as the "final causality" property of the model.

Groups of Symmetries of the Two Classes of Synthetases in the Four-Dimensional Hypercubes of the Extended Code Type II

Aminoacyl-tRNA synthetases (aaRSs) originated from an ancestral bidirectional gene (mirror symmetry), and through the evolution of the genetic code, the twenty aaRSs exhibit a symmetrical distribution in a 6-dimensional hypercube of the Standard Genetic Code. In this work, we assume a primeval RNY code and the Extended Genetic RNA code type II, which includes codons of the types YNY, YNR, and RNR. Each of the four subsets of codons can be represented in a 4-dimensional hypercube. Altogether, these 4 subcodes constitute the 6-dimensional representation of the SGC. We identify the aaRSs symmetry groups in each of these hypercubes. We show that each of the four hypercubes contains the following sets of symmetries for the two known Classes of synthetases: RNY: dihedral group of order 4; YNY: binary group; YNR: amplified octahedral group; and RNR: binary group. We demonstrate that for each hypercube, the group of symmetries in Class 1 is the same as the group of symmetries in Class 2. The biological implications of these findings are discussed.

The Evolution of Life Is a Road Paved with the DNA Quadruplet Symmetry and the Supersymmetry Genetic Code

Symmetries have not been completely determined and explained from the discovery of the DNA structure in 1953 and the genetic code in 1961. We show, during 10 years of investigation and research, our discovery of the Supersymmetry Genetic Code table in the form of 2 × 8 codon boxes, quadruplet DNA symmetries, and the classification of trinucleotides/codons, all built with the same physiochemical double mirror symmetry and Watson-Crick pairing. We also show that single-stranded RNA had the complete code of life in the form of the Supersymmetry Genetic Code table simultaneously with instructions of codons' relationship as to how to develop the DNA molecule on the principle of Watson-Crick pairing. We show that the same symmetries between the genetic code and DNA quadruplet are highly conserved during the whole evolution even between phylogenetically distant organisms. In this way, decreasing disorder and entropy enabled the evolution of living beings up to sophisticated species with cognitive features. Our hypothesis that all twenty amino acids are necessary for the origin of life on the Earth, which entirely changes our view on evolution, confirms the evidence of organic natural amino acids from the extra-terrestrial asteroid Ryugu, which is nearly as old as our solar system.

Designing Collagen-Binding Peptide with Enhanced Properties Using Hydropathic Free Energy Predictions

Collagen is fundamental to a vast diversity of health functions and potential therapeutics. Short peptides targeting collagen are attractive for designing modular systems for site-specific delivery of bioactive agents. Characterization of peptide-protein binding involves a larger number of potential interactions that require screening methods to target physiological conditions. We build a hydropathy-based free energy estimation tool which allows quick evaluation of peptides binding to collagen. Previous studies showed that pH plays a significant role in collagen structure and stability. Our design tool enables probing peptides for their collagen-binding property across multiple pH conditions. We explored binding features of currently known collagen-binding peptides, collagen type I alpha chain 2 sense peptide (TKKTLRT) and decorin LRR-10 (LRELHLNNN). Based on these analyzes, we engineered a collagen-binding peptide with enhanced properties across a large pH range in contrast to LRR-10 pH dependence. To validate our predictions, we used a quantum-dots-based binding assay to compare the coverage of the peptides on type I collagen. The predicted peptide resulted in improved collagen binding. Hydropathy of the peptide-protein pair is a promising approach to finding compatible pairings with minimal use of computational resources, and our method allows for quick evaluation of peptides for binding to other proteins. Overall, the free-energy-based tool provides an alternative computational screening approach that impacts protein interaction search methods.

The Spike Protein of SARS-CoV-2 Is Adapting Because of Selective Pressures

The global scale of the COVID-19 pandemic has demonstrated the evolution of SARS-CoV-2 and the clues of adaptation. After two years and two months since the declaration of the pandemic, several variants have emerged and become fixed in the human population thanks to extrinsic selective pressures but also to the inherent mutational capacity of the virus. Here, we applied a neutral substitution evolution test to the spike (S) protein of Omicron’s protein and compared it to the others’ variant of concern (VOC) neutral evolution. We carried out comparisons among the interactions between the S proteins from the VOCs (Alpha, Beta, Gamma, Delta and Omicron) and the receptor ACE2. The shared amino acids among all the ACE2 binding S proteins remain constant, indicating that these amino acids are essential for the accurate binding to the receptor. The complexes of the RBD for every variant with the receptor were used to identify the amino acids involved in the protein—protein interaction (PPI). The RBD of Omicron establishes 82 contacts, compared to the 74 of the Wuhan original viral protein. Hence, the mean number of contacts per residue is higher, making the contact thermodynamically more stable. The RBDs of the VOCs are similar in sequence and structure; however, Omicron’s RBD presents the largest deviation from the structure by 1.11 Å RMSD, caused by a set of mutations near the glycosylation N343. The chemical properties and structure near the glycosylation N343 of the Omicron S protein are different from the original protein, which provoke reduced recognition by the neutralizing antibodies. Our results hint that selective pressures are induced by mass vaccination throughout the world and by the persistence of recurrent infections in immunosuppressed individuals, who did not eliminate the infection and ended up facilitating the selection of viruses whose characteristics are different from the previous VOCs, less pathogenic but with higher transmissibility.

Neutral evolution test of the spike protein of SARS-CoV-2 and its implications in the binding to ACE2

As the SARS-CoV-2 has spread and the pandemic has dragged on, the virus continued to evolve rapidly resulting in the emergence of new highly transmissible variants that can be of public health concern. The evolutionary mechanisms that drove this rapid diversity are not well understood but neutral evolution should open the first insight. The neutral theory of evolution states that most mutations in the nucleic acid sequences are random and they can be fixed or disappear by purifying selection. Herein, we performed a neutrality test to better understand the selective pressures exerted over SARS-CoV-2 spike protein from homologue proteins of Betacoronavirus, as well as to the spikes from human clinical isolates of the virus. Specifically, Tyr and Asn have higher occurrence rates on the Receptor Binding Domain (RBD) and in the overall sequence of spike proteins of Betacoronavirus, whereas His and Arg have lower occurrence rates. The in vivo evolutionary phenomenon of SARS-CoV-2 shows that Glu, Lys, Phe, and Val have the highest probability of occurrence in the emergent viral particles. Amino acids that have higher occurrence than the expected by the neutral control, are favorable and are fixed in the sequence while the ones that have lower occurrence than expected, influence the stability and/or functionality of the protein. Our results show that most unique mutations either for SARS-CoV-2 or its variants of health concern are under selective pressures, which could be related either to the evasion of the immune system, increasing the virus' fitness or altering protein - protein interactions with host proteins. We explored the consequences of those selected mutations in the structure and protein - protein interaction with the receptor. Altogether all these forces have shaped the spike protein and the continually evolving variants.

The novel Ideal Symmetry Genetic Code table - Common purine-pyrimidine symmetry net for all RNA and DNA species

Ever since Nirenberg's discovery in 1961 in which codons code individual amino acids, numerous scientists searched for symmetries within the genetic code. The standard genetic code (SGC) table is an alphabetic artificial construct based on the U-C-A-G ordering of nucleotides without natural symmetries. Up to the present, complete symmetry in the genetic code has not been found, leaving doubt as to whether the symmetrical nature as the protector of order even exists. Our novel Ideal Symmetry Genetic Code (ISyGC) table reflects a unique fundamental physicochemical purine-pyrimidine symmetry net for all more than thirty known variations of nuclear and mitochondrial genetic codes. The nuclear genetic code for RNA and DNA viruses also contains the same purine-pyrimidine symmetry net. We show that the ISyGC table leads to automatic transformation into a DNA sequence akin to the 5'3 codon and 3'5 anticodon patterns. As a result of purine-pyrimidine symmetries between codons in the ISyGC table, algorithms of the first two bases as well of the third base of codons show how tRNA cognate anticodons can recognize synonymous codons during mRNA decoding. We show that the ISyGC purine-pyrimidine net with its physicochemical properties represents an evolutionary common "frozen accident" at the onset of each genetic code creation and RNA to DNA evolution. As such, during all of evolution the unique fundamental purine-pyrimidine symmetry net of all genetic codes remains unchangeable. In this way, evolution is a road paved with symmetries.

Complete Quantum Information in the DNA Genetic Code

We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature G=Z5⋊H where H=Z2.S4≅2O is isomorphic to the binary octahedral group 2O and S4 is the symmetric group on four letters/bases. The second group has signature G=Z5⋊GL(2,3) and points out a threefold symmetry of base pairings. For those groups, the representations for the 22 conjugacy classes of G are in one-to-one correspondence with the multiplets encoding the proteinogenic amino acids. Additionally, most of the 22 characters of G attached to those representations are informationally complete. The biological meaning of these coincidences is discussed.

On the Importance of Asymmetry in the Phenotypic Expression of the Genetic Code upon the Molecular Evolution of Proteins

The standard genetic code (SGC) is a mapping between the 64 possible arrangements of the four RNA nucleotides (C, A, U, G) into triplets or codons, where 61 codons are assigned to a specific amino acid and the other three are stop codons for terminating protein synthesis. Aminoacyl-tRNA synthetases (aaRSs) are responsible for implementing the SGC by specifically amino-acylating only its cognate transfer RNA (tRNA), thereby linking an amino acid with its corresponding anticodon triplets. tRNAs molecules bind each codon with its anticodon. To understand the meaning of symmetrical/asymmetrical properties of the SGC, we designed synthetic genetic codes with known symmetries and with the same degeneracy of the SGC. We determined their impact on the substitution rates for each amino acid under a neutral model of protein evolution. We prove that the phenotypic graphs of the SGC for codons and anticodons for all the possible arrangements of nucleotides are asymmetric and the amino acids do not form orbits. In the symmetrical synthetic codes, the amino acids are grouped according to their codonicity, this is the number of triplets encoding a given amino acid. Both the SGC and symmetrical synthetic codes exhibit a probability of occurrence of the amino acids proportional to their degeneracy. Unlike the SGC, the synthetic codes display a constant probability of occurrence of the amino acid according to their codonicity. The asymmetry of the phenotypic graphs of codons and anticodons of the SGC, has important implications on the evolutionary processes of proteins.

Genetic codes optimized as a traveling salesman problem

The Standard Genetic Code (SGC) is robust to mutational errors such that frequently occurring mutations minimally alter the physio-chemistry of amino acids. The apparent correlation between the evolutionary distances among codons and the physio-chemical distances among their cognate amino acids suggests an early co-diversification between the codons and amino acids. Here we formulated the co-minimization of evolutionary distances between codons and physio-chemical distances between amino acids as a Traveling Salesman Problem (TSP) and solved it with a Hopfield neural network. In this unsupervised learning algorithm, macromolecules (e.g., tRNAs and aminoacyl-tRNA synthetases) associating codons with amino acids were considered biological analogs of Hopfield neurons associating "tour cities" with "tour positions". The Hopfield network efficiently yielded an abundance of genetic codes that were more error-minimizing than SGC and could thus be used to design artificial genetic codes. We further argue that as a self-optimization algorithm, the Hopfield neural network provides a model of origin of SGC and other adaptive molecular systems through evolutionary learning.

A neutral evolution test derived from a theoretical amino acid substitution model

A neutral evolution model that explicitly considers codons, amino acids, and the degeneracy of the genetic code is developed. The model is built from nucleotides up to amino acids, and it represents a refinement of the neutral theory of molecular evolution. The model is based on a stochastic process that leads to a stationary probability distribution of amino acids. The latter is used as a neutral test of evolution. We provide some examples for assessing the neutrality test for a small set of protein sequences. The Jukes-Cantor model is generalized to deal with amino acids and it is compared with our neutral model, along with the empirical BLOSUM62 substitution model. The neutral test provides a baseline to which the evolution of any protein can be analyzed, and it clearly helps in discerning putative amino acids with unexpected frequencies that might be under positive or negative selection. Our model and neutral test are as universal as the standard genetic code.

The optimality of the standard genetic code assessed by an eight-objective evolutionary algorithm

BACKGROUND

The standard genetic code (SGC) is a unique set of rules which assign amino acids to codons. Similar amino acids tend to have similar codons indicating that the code evolved to minimize the costs of amino acid replacements in proteins, caused by mutations or translational errors. However, if such optimization in fact occurred, many different properties of amino acids must have been taken into account during the code evolution. Therefore, this problem can be reformulated as a multi-objective optimization task, in which the selection constraints are represented by measures based on various amino acid properties.

RESULTS

To study the optimality of the SGC we applied a multi-objective evolutionary algorithm and we used the representatives of eight clusters, which grouped over 500 indices describing various physicochemical properties of amino acids. Thanks to that we avoided an arbitrary choice of amino acid features as optimization criteria. As a consequence, we were able to conduct a more general study on the properties of the SGC than the ones presented so far in other papers on this topic. We considered two models of the genetic code, one preserving the characteristic codon blocks structure of the SGC and the other without this restriction. The results revealed that the SGC could be significantly improved in terms of error minimization, hereby it is not fully optimized. Its structure differs significantly from the structure of the codes optimized to minimize the costs of amino acid replacements. On the other hand, using newly defined quality measures that placed the SGC in the global space of theoretical genetic codes, we showed that the SGC is definitely closer to the codes that minimize the costs of amino acids replacements than those maximizing them.

CONCLUSIONS

The standard genetic code represents most likely only partially optimized systems, which emerged under the influence of many different factors. Our findings can be useful to researchers involved in modifying the genetic code of the living organisms and designing artificial ones.

Symmetrical Properties of Graph Representations of Genetic Codes: From Genotype to Phenotype

It has long been claimed that the mitochondrial genetic code possesses more symmetries than the Standard Genetic Code (SGC). To test this claim, the symmetrical structure of the SGC is compared with noncanonical genetic codes. We analyzed the symmetries of the graphs of codons and their respective phenotypic graph representation spanned by the RNY (R purines, Y pyrimidines, and N any of them) code, two RNA Extended codes, the SGC, as well as three different mitochondrial genetic codes from yeast, invertebrates, and vertebrates. The symmetry groups of the SGC and their corresponding phenotypic graphs of amino acids expose the evolvability of the SGC. Indeed, the analyzed mitochondrial genetic codes are more symmetrical than the SGC.

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.

Phenotypic Graphs and Evolution Unfold the Standard Genetic Code as the Optimal

In this work, we explicitly consider the evolution of the Standard Genetic Code (SGC) by assuming two evolutionary stages, to wit, the primeval RNY code and two intermediate codes in between. We used network theory and graph theory to measure the connectivity of each phenotypic graph. The connectivity values are compared to the values of the codes under different randomization scenarios. An error-correcting optimal code is one in which the algebraic connectivity is minimized. We show that the SGC is optimal in regard to its robustness and error-tolerance when compared to all random codes under different assumptions.

On the Uniqueness of the Standard Genetic Code

In this work, we determine the biological and mathematical properties that are sufficient and necessary to uniquely determine both the primeval RNY (purine-any base-pyrimidine) code and the standard genetic code (SGC). These properties are: the evolution of the SGC from the RNY code; the degeneracy of both codes, and the non-degeneracy of the assignments of aminoacyl-tRNA synthetases (aaRSs) to amino acids; the wobbling property; the consideration that glycine was the first amino acid; the topological and symmetrical properties of both codes.