Arithmetic inside the universal genetic code

The first information system emerged on the earth as primordial version of the genetic code and genetic texts. The natural appearance of arithmetic power in such a linguistic milieu is theoretically possible and practical for producing information systems of extremely high efficiency. In this case, the arithmetic symbols should be incorporated into an alphabet, i.e. the genetic code. A number is the fundamental arithmetic symbol produced by the system of numeration. If the system of numeration were detected inside the genetic code, it would be natural to expect that its purpose is arithmetic calculation e.g., for the sake of control, safety, and precise alteration of the genetic texts. The nucleons of amino acids and the bases of nucleic acids seem most suitable for embodiments of digits. These assumptions were used for the analyzing the genetic code.

The compressed, life-size, and split representation of the Escherichia coli and Euplotes octocarinatus code versions were considered simultaneously. An exact equilibration of the nucleon sums of the amino acid standard blocks and/or side chains was found repeatedly within specified sets of the genetic code. Moreover, the digital notations of the balanced sums acquired, in decimal representation, the unique form 111, 222, …, 999. This form is a consequence of the criterion of divisibility by 037. The criterion could simplify some computing mechanism of a cell if any and facilitate its computational procedure. The cooperative symmetry of the genetic code demonstrates that possibly a zero was invented and used by this mechanism. Such organization of the genetic code could be explained by activities of some hypothetical molecular organelles working as natural biocomputers of digital genetic texts.

It is well known that if mutation replaces an amino acid, the change of hydrophobicity is generally weak, while that of size is strong. The antisymmetrical correlation between the amino acid size and the degeneracy number is known as well. It is shown that these and some other familiar properties may be a physicochemical effect of arithmetic inside the genetic code.

The “frozen accident” model, giving unlimited freedom to the mapping function, could optimally support the appearance of both arithmetic symbols and physicochemical protection inside the genetic code.     

Block structure and stability of the genetic code

It is known that different codons may be unified into larger groups related to the hierarchical structure, approximate hidden symmetries, and evolutionary origin of the universal genetic code. Using a simplified evolutionary motivated two-letter version of genetic code, the general principles of the most stable coding are discussed. By the complete enumeration in such a reduced code it is strictly proved that the maximum stability with respect to point mutations and shifts in the reading frame needs the fixation of the middle letters within codons in groups with different physico-chemical properties, thus, explaining a key feature of the universal genetic code. The translational stability of the genetic code is studied by the mapping of code onto de Bruijn graph providing both the compact visual representation of mutual relationships between different codons as well as between codons and protein coding DNA sequence and a powerful tool for the investigation of stability of protein coding. Then, the results are extended to four-letter codes. As is shown, the universal genetic code obeys mainly the principles of optimal coding. These results demonstrate the hierarchical character of optimization of universal genetic code with strictly optimal coding being evolved at the earliest stages of molecular evolution. Finally, the universal genetic code is compared with the other natural variants of genetic codes.     

Construction of genetic code from evolutionary stability

The construction of the genetic code is investigated based on a stability principle. The concept and formulation of mutational deterioration (MD) of the genetic code is proposed. It is proved that the degeneracies of codon multiplets obey the rule to best resist MD. The MD for each ideal multiplet of codons is expressed by four parameters and it takes on a minimum value for real distributions of codons in the multiplet. Then the global mutational deterioration (GMD) of code table is calculated and the minimal code is deduced. The domain-like distribution of hydrophobic and hydrophilic amino acids on the genetic code is explained from the minimization of GMD. It is demonstrated that the standard code is approximately GMD-minimal. By introducing some constraints that are related to the initial condition of the system, we have deduced the standard genetic code from the minimization of GMD. The minimization shows the general trend of evolutionary process to some stable state while the constraints reflect a 'frozen accident.' Many deviant codon assignments are also explained through MD minimization assuming the changeable degrees of degeneracies for some multiplets. So, a possible answer to the question of "Why are synonymous codons and amino acids distributed in the code table just as they are?" is given.     

Early fixation of an optimal genetic code

The evolutionary forces that produced the canonical genetic code before the last universal ancestor remain obscure. One hypothesis is that the arrangement of amino acid/codon assignments results from selection to minimize the effects of errors (e.g., mistranslation and mutation) on resulting proteins. If amino acid similarity is measured as polarity, the canonical code does indeed outperform most theoretical alternatives. However, this finding does not hold for other amino acid properties, ignores plausible restrictions on possible code structure, and does not address the naturally occurring nonstandard genetic codes. Finally, other analyses have shown that significantly better code structures are possible. Here, we show that if theoretically possible code structures are limited to reflect plausible biological constraints, and amino acid similarity is quantified using empirical data of substitution frequencies, the canonical code is at or very close to a global optimum for error minimization across plausible parameter space. This result is robust to variation in the methods and assumptions of the analysis. Although significantly better codes do exist under some assumptions, they are extremely rare and thus consistent with reports of an adaptive code: previous analyses which suggest otherwise derive from a misleading metric. However, all extant, naturally occurring, secondarily derived, nonstandard genetic codes do appear less adaptive. The arrangement of amino acid assignments to the codons of the standard genetic code appears to be a direct product of natural selection for a system that minimizes the phenotypic impact of genetic error. Potential criticisms of previous analyses appear to be without substance. That known variants of the standard genetic code appear less adaptive suggests that different evolutionary factors predominated before and after fixation of the canonical code. While the evidence for an adaptive code is clear, the process by which the code achieved this optimization requires further attention.     

Optimization and the genetic code

The present paper will focus on the relation between the structure of the table of the genetic code and the evolution of primitive organisms: it will be shown that the organization of the code table according to an optimization principle based on the notion of resistance to errors can provide a criterium for selection. The ordered aspect of the genetic code table makes this result a plausible starting point for studies of the origin and evolution of the genetic code: these could include, besides a more refined optimization principle at the logical level, some effects more directly related to the physico-chemical context, and the construction of realistic models incorporating both aspects.     

Evolutionary changes in the genetic code

The genetic code has been influenced by directional mutation pressure affecting the base composition of DNA, sometimes in the direction of increased GC content and at other times, in the direction of AT. Such pressure led to changes in species-specific usages of codons and tRNA anticodons, and also in amino acid assignments of codons in mitochondria and in several intact organisms. These code changes are probably recent evolutionary events. The genetic code is not 'frozen', but instead it is still evolving.     

The genetic code and the origin of life

The problem of the origin of life understandably counts as one of the most exciting questions in the natural sciences, but in spite of almost endless speculation on this subject, it is still far from its final solution. The complexity of the functional correlation between recent nucleic acids and proteins can e.g. give rise to the assumption that the genetic code (and life) could not originate on the Earth. It was Portelli (1975) who published the hypothesis that the genetic code could not originate during the history of the Earth. In his opinion the recent genetic code represents the informational message transmitted by living systems of the previous cycle of the Universe. Here however, we defend the existence of a certain strategy in the syntheses of the genetic code during the history of the Earth. The strategy of correlation between amino acid and nucleotide polymers made an increasing velocity of the chemical evolution possible, that is, it increased the velocity of formation of the genetic code. Thus, life with the recent genetic code could originate on the Earth within the present cycle of the Universe.Present address: Institute for Pharmacy and Biochemistry, 533 51 Pardubice, Czechoslovakia.     

The standard genetic code enhances adaptive evolution of proteins

The standard genetic code, by which most organisms translate genetic material into protein metabolism, is non-randomly organized. The Error Minimization hypothesis interprets this non-randomness as an adaptation, proposing that natural selection produced a pattern of codon assignments that buffers genomes against the impact of mutations. Indeed, on the average any given point mutation has a lesser effect on the chemical properties of the utilized amino acid than expected by chance. Might it also, however, be the case that the non-random nature of the code effects the rate of adaptive evolution? To investigate this, here we develop population genetic simulations to test the rate of adaptive gene evolution under different genetic codes. We identify two independent properties of a genetic code that profoundly influence the speed of adaptive evolution. Noting that the standard genetic code exhibits both, we offer a new insight into the effects of the "error minimizing" code: such a code enhances the efficacy of adaptive sequence evolution.     

Parallel evolution of the genetic code in arthropod mitochondrial genomes

The genetic code provides the translation table necessary to transform the information contained in DNA into the language of proteins. In this table, a correspondence between each codon and each amino acid is established: tRNA is the main adaptor that links the two. Although the genetic code is nearly universal, several variants of this code have been described in a wide range of nuclear and organellar systems, especially in metazoan mitochondria. These variants are generally found by searching for conserved positions that consistently code for a specific alternative amino acid in a new species. We have devised an accurate computational method to automate these comparisons, and have tested it with 626 metazoan mitochondrial genomes. Our results indicate that several arthropods have a new genetic code and translate the codon AGG as lysine instead of serine (as in the invertebrate mitochondrial genetic code) or arginine (as in the standard genetic code). We have investigated the evolution of the genetic code in the arthropods and found several events of parallel evolution in which the AGG codon was reassigned between serine and lysine. Our analyses also revealed correlated evolution between the arthropod genetic codes and the tRNA-Lys/-Ser, which show specific point mutations at the anticodons. These rather simple mutations, together with a low usage of the AGG codon, might explain the recurrence of the AGG reassignments.     

Phases of degeneracy of the genetic code

The universally valid genetic code is the final result of a multi-stage course of development. Degeneracy, as an important property of the genetic code, was possibly not yet present in the earliest code, first appearing at a later stage of development (Code III). Possibly this step in development is coupled with the presence of a total of four amino acid groups (L, I, E, F). Each group contains a specific number of amino acid (AL, AI, AE, AF). Amino acid groups: - (L) hydrophobic - (I) weakly hydrophobic or polar but uncharged - (E) hydrophilic, acidic - (F) hydrophilic, basic - (D) hydrophobic, aromatic (only in Code IV and Code M. This group is not considered in the calculations below.) In a subsequent stage of development the number of amino acids increases further. At the same time the code becomes more degenerate. The universal genetic code is characterized by three constants of being degenerate. Its immediate predecessor has linear degeneration with two constants. The mitochondrial code represents a transitional form between these two codes.     

The triplet genetic code had a doublet predecessor

Information theoretic analysis of genetic languages indicates that the naturally occurring 20 amino acids and the triplet genetic code arose by duplication of 10 amino acids of class-II and a doublet genetic code having codons NNY and anticodons GNN. Evidence for this scenario is presented based on the properties of aminoacyl-tRNA synthetases, amino acids and nucleotide bases.     

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.     

Some theoretical aspects of reprogramming the standard genetic code

Reprogramming of the standard genetic code to include non-canonical amino acids (ncAAs) opens new prospects for medicine, industry, and biotechnology. There are several methods of code engineering, which allow us for storing new genetic information in DNA sequences and producing proteins with new properties. Here, we provided a theoretical background for the optimal genetic code expansion, which may find application in the experimental design of the genetic code. We assumed that the expanded genetic code includes both canonical and non-canonical information stored in 64 classical codons. What is more, the new coding system is robust to point mutations and minimizes the possibility of reversion from the new to old information. In order to find such codes, we applied graph theory to analyze the properties of optimal codon sets. We presented the formal procedure in finding the optimal codes with various number of vacant codons that could be assigned to new amino acids. Finally, we discussed the optimal number of the newly incorporated ncAAs and also the optimal size of codon groups that can be assigned to ncAAs.     

Natural history and experimental evolution of the genetic code

The standard genetic code is a set of rules that relates the 20 canonical amino acids in proteins to groups of three bases in the mRNA. It evolved from a more primitive form and the attempts to reconstruct its natural history are based on its present-day features. Genetic code engineering as a new research field was developed independently in a few laboratories during the last 15 years. The main intention is to re-program protein synthesis by expanding the coding capacities of the genetic code via re-assignment of specific codons to un-natural amino acids. This article focuses on the question as to which extent hypothetical scenarios that led to codon re-assignments during the evolution of the genetic code are relevant for its further evolution in the laboratory. Current attempts to engineer the genetic code are reviewed with reference to theoretical works on its natural history. Integration of the theoretical considerations into experimental concepts will bring us closer to designer cells with target-engineered genetic codes that should open not only tremendous possibilities for the biotechnology of the twenty-first century but will also provide a basis for the design of novel life forms.     

Local stability and evolution of the genetic code

The standard genetic code is known to be robust to translation errors and point mutations. We studied how small modifications of the standard code affect its robustness. The robustness was assessed in terms of a proper stability function, the negative variations of which correspond to a more robust code. The fraction of more robust codes obtained under small modifications appeared to be unexpectedly high, about 0.1-0.4 depending on the choice of stability function and code modifications, yet significantly lower than the corresponding fraction in the random codes (about a half). In this sense the standard code ought to be considered distinctly non-random in accordance with previous observations. The distribution of the negative variations of stability function revealed very abrupt drop beyond one standard deviation, much sharper than for Gaussian distribution or for the random codes with the same number of codons in the sets coding for amino acids or stop-codons. This behavior holds for both the standard code as a whole and its binary NRN-NYN, NWN-NSN, and NMN-NKN blocks. Previously, it has been proved that such binary block structure is necessary for the robustness of a code and is inherent to the standard genetic code. The modifications of the standard code corresponding to more robust coding may be related to the different variants of the code. These effects may also contribute to the rates of replacements of amino acids. The observed features demonstrate the joint impact of random factors and natural selection during evolution of the genetic code.     

Structuring of the genetic code took place at acidic pH

I have observed that in multiple regression the number of codons specifying amino acids in the genetic code is positively correlated with the isoelectric point of amino acids and their molecular weight. Therefore basic amino acids are, on average, codified in the genetic code by a larger number of codons, which seems to imply that the genetic code originated in an acidic 'intracellular' environment. Moreover, I compare the proteins from Picrophilus torridus and Thermoplasma volcanium, which have different intracellular pH and I define the ranks of acidophily for the amino acids. A simple index of acidophily (AI), which can be easily obtained from acidophily ranks, can be associated to any protein and, therefore, can also be associated to the genetic code if the number of synonymous codons attributed to the amino acids in the code is assumed to be the frequency with which the amino acids appeared in ancestral proteins. Finally, the sampling of the variable AI among organisms having an intracellular pH less than or equal to 6.6 and those having a non-acidic intracellular pH leads to the conclusion that the value of the genetic code's AI is not typical of proteins of the latter organisms. As the genetic code's AI value is also statistically not different from that of proteins of the organisms having an acidic intracellular pH, this supports the hypothesis that the structuring of the genetic code took place in acidic pH conditions.     

A search for symmetries in the genetic code

A search for symmetrics based on the classification theorem of Cartan for the compact simple Lie algebras is performed to verify to what extent the genetic code is a manifestation of some underlying symmetry. An exact continuous symmetry group can not be found to reproduce the present, universal code. However a unique approximate symmetry group is compatible with codon assignment for the fundamental amino acids and the termination codon. In order to obtain the actual genetic code, the symmetry must be slightly broken.     

The arbitrariness of the genetic code

The genetic code has been regarded as arbitrary in the sense that the codon-amino acid assignments could be different than they actually are. This general idea has been spelled out differently by previous, often rather implicit accounts of arbitrariness. They have drawn on the frozen accident theory, on evolutionary contingency, on alternative causal pathways, and on the absence of direct stereochemical interactions between codons and amino acids. It has also been suggested that the arbitrariness of the genetic code justifies attributing semantic information to macromolecules, notably to DNA. I argue that these accounts of arbitrariness are unsatisfactory. I propose that the code is arbitrary in the sense of Jacques Monod's concept of chemical arbitrariness: the genetic code is arbitrary in that any codon requires certain chemical and structural properties to specify a particular amino acid, but these properties are not required in virtue of a principle of chemistry. This notion of arbitrariness is compatible with several recent hypotheses about code evolution. I maintain that the code's chemical arbitrariness is neither sufficient nor necessary for attributing semantic information to nucleic acids.