The complementarity of the chemical parameters of amino acids and anticodons in the genetic code

Chemical language of the genetic code is suggested in which elementary information code units are presented by functional groups of amino acids and nucleotides. Using this language, the existence of correspondence and conformity of chemical parameters of amino acids and of central nucleotides of their anticodons was demonstrated. These findings confirm the idea that the genetic code is determined by chemical properties of amino acids and nucleotides and that this determination is the result of direct specific interactions between amino acids and nucleotide triplets at the stage of the origin of the code. The data obtained reveal primary role of anticodon triplets in the origin of the code. Key role of the central nucleotide in triplets for amino acid coding is confirmed.     

On the origin and evolution of the genetic code

Two ideas have essentially been used to explain the origin of the genetic code: Crick's frozen accident and Woese's amino acid-codon specific chemical interaction. Whatever the origin and codon-amino acid correlation, it is difficult to imagine the sudden appearance of the genetic code in its present form of 64 codons coding for 20 amino acids without appealing to some evolutionary process. On the contrary, it is more reasonable to assume that it evolved from a much simpler initial state in which a few triplets were coding for each of a small number of amino acids. Analysis of genetic code through information theory and the metabolism of pyrimidine biosynthesis provide evidence that suggests that the genetic code could have begun in an RNA world with the two letters A and U grouped in eight triplets coding for seven amino acids and one stop signal. This code could have progressively evolved by making gradual use of letters G and C to end with 64 triplets coding for 20 amino acids and three stop signals. According to proposed evidence, DNA could have appeared after the four-letter structure was already achieved. In the newborn DNA world, T substituted U to get higher physicochemical and genetic stability.     

Laws governing degeneration of the genetic code

The laws governing degeneration of the genetic code are discussed below. Of fundamental importance in this context is the classification of the amino acids into groups on the basis of the physicochemical behaviour of their residues. From this, it is possible to formulate arithmetic relationships between the number of amino acids in the same group and the number of coding triplets.It is found that the degeneration of the genetic code obeys certain laws, the reasons for this being related to the number and the qualitative properties of the amino acids and triplets. The fact that the three bases of a coding triplet have different priorities must also be a critical factor.     

遗传密码格式的组合编码数分析

用N个密码子对m个编码对象进行编码的编码格式是m元N维空间中的一个顶点。64个密码子对20种氨基酸和终止密码子进行编码格式的组合编码数是一个十分巨大的数字。对多元高维编码空间的拓扑特性进行了分析和研究 ,并由此推导出m -N空间的特性三角的排列方式以及给出特性三角公式的数学证明。指出 ,目前的遗传密码的编码格式是21元64维编码空间的一个顶点。应用组合数学分析的方法 ,计算了遗传密码格式的最大组合编码数CM =4.19×1084 ,基因组遗传密码的组合编码数CG =1.13×1080 以及线粒体遗传密码的组合编码数CT =1.38×1079 等。分析结果表明 ,遗传密码的指定是一个小概率事件 ,可能来源于λ简并后的偶数三联密码配对的组合编码的对称破缺     

Unambiguous correspondence and complementarity of the chemical properties of amino acids and anticodons of the genetic code

The chemical language of genetic code is proposed. As a result of chemical language application for the analysis of the modern genetic code, the existence of an unambiguous correspondence between the chemical properties of amino acids and their coding triplets (codons and anticodons) is shown. This confirms the hypothesis of the code chemical determination. The complementarity between the chemical properties of amino acids and their anticodons (but not the codons) has been found also to exist. This observation supports the hypothesis of the genetic code determination by the direct recognition and also underlines the primary role of anticodon in the origin of genetic code in comparison with codons.     

Group graph of the genetic code

The genetic code doublets can be divided into two octets of completely degenerate and ambiguous coding dinucleotides. These two octets have the algebraic property of lying on continuously connected planes on the group graph (a tesseract) of the Cartesian product of two Klein 4-groups of nucleotide exchange operators. The K X K group can also be broken into four cosets, one of which has completely degenerate coding elements, and another that has completely ambiguous coding elements. The two octets of coding doublets have the further algebraic property that the product of their internal exchange operators naturally divide into two exactly equivalent sets. These properties of the genetic code are relevant to unraveling error-detecting and error-correcting (proof-reading) aspects of the genetic code and may be helpful in understanding the context-sensitive grammar of genetic language.     

Optimized Null Model for Protein Structure Networks

Much attention has recently been given to the statistical significance of topological features observed in biological networks. Here, we consider residue interaction graphs (RIGs) as network representations of protein structures with residues as nodes and inter-residue interactions as edges. Degree-preserving randomized models have been widely used for this purpose in biomolecular networks. However, such a single summary statistic of a network may not be detailed enough to capture the complex topological characteristics of protein structures and their network counterparts. Here, we investigate a variety of topological properties of RIGs to find a well fitting network null model for them. The RIGs are derived from a structurally diverse protein data set at various distance cut-offs and for different groups of interacting atoms. We compare the network structure of RIGs to several random graph models. We show that 3-dimensional geometric random graphs, that model spatial relationships between objects, provide the best fit to RIGs. We investigate the relationship between the strength of the fit and various protein structural features. We show that the fit depends on protein size, structural class, and thermostability, but not on quaternary structure. We apply our model to the identification of significantly over-represented structural building blocks, i.e., network motifs, in protein structure networks. As expected, choosing geometric graphs as a null model results in the most specific identification of motifs. Our geometric random graph model may facilitate further graph-based studies of protein conformation space and have important implications for protein structure comparison and prediction. The choice of a well-fitting null model is crucial for finding structural motifs that play an important role in protein folding, stability and function. To our knowledge, this is the first study that addresses the challenge of finding an optimized null model for RIGs, by comparing various RIG definitions against a series of network models.     

RNA–Amino Acid Binding: A Stereochemical Era for the Genetic Code

By combining crystallographic and NMR structural data for RNA-bound amino acids within riboswitches, aptamers, and RNPs, chemical principles governing specific RNA interaction with amino acids can be deduced. Such principles, which we summarize in a “polar profile”, are useful in explaining newly selected specific RNA binding sites for free amino acids bearing varied side chains charged, neutral polar, aliphatic, and aromatic. Such amino acid sites can be queried for parallels to the genetic code. Using recent sequences for 337 independent binding sites directed to 8 amino acids and containing 18,551 nucleotides in all, we show a highly robust connection between amino acids and cognate coding triplets within their RNA binding sites. The apparent probability (P) that cognate triplets around these sites are unrelated to binding sites is ≅5.3 × 10⁻⁴⁵ for codons overall, and P ≅ 2.1 × 10⁻⁴⁶ for cognate anticodons. Therefore, some triplets are unequivocally localized near their present amino acids. Accordingly, there was likely a stereochemical era during evolution of the genetic code, relying on chemical interactions between amino acids and the tertiary structures of RNA binding sites. Use of cognate coding triplets in RNA binding sites is nevertheless sparse, with only 21% of possible triplets appearing. Reasoning from such broad recurrent trends in our results, a majority (approximately 75%) of modern amino acids entered the code in this stereochemical era; nevertheless, a minority (approximately 21%) of modern codons and anticodons were assigned via RNA binding sites. A Direct RNA Template scheme embodying a credible early history for coded peptide synthesis is readily constructed based on these observations.     

Entropies of coding and noncoding sequences of DNA and proteins.

The entropies of protein coding genes from Escherichia coli were calculated according to Boltzmann's formula. Entropies of the coding regions were compared to the entropies of noncoding or miscoding ones. With nucleotides as code units, the entropies of the coding regions, when compared to the entropies of complete sequences (leader and coding region as well as trailer), were seen to be lower but with a marginal statistical significance. With triplets of nucleotides as code units, the entropies of correct reading frames were significantly lower than the entropies of frameshifts +1 and -1. With amino acids as code units, the results were opposite: Biologically functional proteins had significantly higher entropies than proteins translated from the frameshifted sequences. We attempt to explain this paradox with the hypothesis that the genetic code may have the ability of lowering information content (increasing entropy) of proteins while translating them from DNA. This ability might be beneficial to bacteria because it would make the functional proteins more probable (having a higher entropy) than nonfunctional proteins translated from frameshifted sequences.     

Error Minimization and Coding Triplet/Binding Site Associations Are Independent Features of the Canonical Genetic Code

The canonical genetic code has been reported both to be error minimizing and to show stereochemical associations between coding triplets and binding sites. In order to test whether these two properties are unexpectedly overlapping, we generated 200,000 randomized genetic codes using each of five randomization schemes, with and without randomization of stop codons. Comparison of the code error (difference in polar requirement for single-nucleotide codon interchanges) with the coding triplet concentrations in RNA binding sites for eight amino acids shows that these properties are independent and uncorrelated. Thus, one is not the result of the other, and error minimization and triplet associations probably arose independently during the history of the genetic code. We explicitly show that prior fixation of a stereochemical core is consistent with an effective later minimization of error. [Reviewing Editor : Dr. Stephen Freeland]     

Little Evidence the Standard Genetic Code Is Optimized for Resource Conservation

Selection for resource conservation can shape the coding sequences of organisms living in nutrient-limited environments. Recently, it was proposed that selection for resource conservation, specifically for nitrogen and carbon content, has also shaped the structure of the standard genetic code, such that the missense mutations the code allows tend to cause small increases in the number of nitrogen and carbon atoms in amino acids. Moreover, it was proposed that this optimization is not confounded by known optimizations of the standard genetic code, such as for polar requirement or hydropathy. We challenge these claims. We show the proposed optimization for nitrogen conservation is highly sensitive to choice of null model and the proposed optimization for carbon conservation is confounded by the known conservative nature of the standard genetic code with respect to the molecular volume of amino acids. There is therefore little evidence the standard genetic code is optimized for resource conservation. We discuss our findings in the context of null models of the standard genetic code.     

Mutually symmetric and complementary triplets: differences in their use distinguish systematically between coding and non-coding genomic sequences

The general property of asymmetry in word use in meaningful texts written in a variety of languages, motivates a quantification of the differences in the use of mutually symmetric triplets in genomic sequences. When this is done in the three reading frames, high values found for one of them are used as indication that the sequence is coding for a protein. Moreover, a similar quantification of the differences in the use of complementary triplets is introduced, again with predictive power of the coding character of a sequence. This method reflects the non-equivalence between sense and anti-sense strand of a coding segment. In both approaches, "linguistic asymmetry" in coding sequences is related to the form of the genetic code and to the bias in codon usage and amino acid use skews.     

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.     

A concept of amino acid archaeorelation: Origin of life and the genetic code

Using certain assumptions, an attempt has been made to obtain a quantitative evaluation of the similarity of the bulk amino acid compositions of various organisms and of the quantitative ratios of amino acids in the products of the presumable prebiological ructions and in the natural proteins. The results of comparison between the molar ratios of amino acids in synthesized products and in natural proteins and the quantitative distribution of triplets among amino acids in the existing genetic code are given. Proceeding from the correlations found and the data reported in literature, a concept has been suggested amounting, in essence, to the assertion that the structure of the genetic code (the quantitative distribution of the triplets) is in a certain way determined by the pre-existing, primary ratio (archaeorelation) of 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.     

Reduced representation model of protein structure prediction: statistical potential and genetic algorithms.

A reduced representation model, which has been described in previous reports, was used to predict the folded structures of proteins from their primary sequences and random starting conformations. The molecular structure of each protein has been reduced to its backbone atoms (with ideal fixed bond lengths and valence angles) and each side chain approximated by a single virtual united-atom. The coordinate variables were the backbone dihedral angles phi and psi. A statistical potential function, which included local and nonlocal interactions and was computed from known protein structures, was used in the structure minimization. A novel approach, employing the concepts of genetic algorithms, has been developed to simultaneously optimize a population of conformations. With the information of primary sequence and the radius of gyration of the crystal structure only, and starting from randomly generated initial conformations, I have been able to fold melittin, a protein of 26 residues, with high computational convergence. The computed structures have a root mean square error of 1.66 A (distance matrix error = 0.99 A) on average to the crystal structure. Similar results for avian pancreatic polypeptide inhibitor, a protein of 36 residues, are obtained. Application of the method to apamin, an 18-residue polypeptide with two disulfide bonds, shows that it folds apamin to native-like conformations with the correct disulfide bonds formed.