A generalized information function applied to the genetic code

The problem of the partitioning of the degeneracy of the codons in the genetic code is considered in the framework of a generalized information function IG = c sigma kpk(ln pk + G(Ek] where k represents the number of codons in a specific degeneracy class and G(Ek) is an arbitrary real valued function. For G(Ek) = 0 the Shannon information function is recovered. For a particular choice of G(Ek) that takes the dominance of even degeneracies into account, it is found by direct numerical calculations that the correct degeneracy partitioning appears as optimal values of the Ig function. This results is also supported by optimization calculations in which the generalized information function is regarded as a continuous function in the degeneracy variables.     

线粒体遗传密码及基因组遗传密码的对称分析

病毒、细菌和真核生物的氨基酸编码都使用相同的遗传密码,表明它们可能有共同的来源。但人和牛的线粒体的遗传密码和基因组的遗传密码相比,出现以下不同;（1）ATA编码甲硫氮酸M而不是异亮氨酸I。（2）TGA不再是终止密码子X而编码色氨酸W。（3）AGA和AGG不再是精氨酸R的密码子而变为终止密码子X。应用高维空间拓扑分析的方法,对线粒体遗传密码和基因组遗传密码的6维编码空间进行对称性分析,得到如下结果：（1）线粒体遗传密码的起始密码子是2个而不是1个。（2）线粒体遗传密码的终止密码子是4个而不是3个。（3）线粒体遗传密码空间只有2、4、6三种偶数简并度而没1、3两种奇数简并度,表明其对称度较高。（4）线粒体遗传密码空间除丝氨酸S分成两个平行的子空间之外,终止密码子X亦分成两个平行的子空间,表明其连通度较低。（5）线粒体遗传密码一基因组遗传密码相比,共有3个简并平面出现变异,即：1001λλ（M和I）,011λ1λ（W和X）,以及1011λλ（S和X或S和R）。（6）基因组遗传密码的1、3两种奇数简并度可能来源于线粒体遗传密码的1001λλ平面和011λ1λ平面的对称性破缺。对线粒体遗传密码变异的生物学意义及遗传密码的起源进行了分析和讨论。     

Degeneracy in the genetic code and its symmetries by base substitutions

Degeneracy in the genetic code is known to minimise the deleterious effects of the most frequent base substitutions: transitions at the third base of codons are generally synonymous substitutions. Transversions that alter degeneracy were reported by Rumer. Here the other transversions are shown to leave invariant degeneracy when applied to the first base of codons. As a summary, degeneracy is considered with respect to all three types of base substitutions, the transitions and the two types of transversions. The symmetries of degeneracy by base substitutions are independent of the representation of the genetic code and discussed with respect to the quasi-universality of the genetic code.     

Reliability in the genetic code.

Base sequences of φ × 174 and MS2 viruses genomes and of some mRNAs (Coat protein fd virus, Rabbit B. Globin, Rat Growth Hormone and Human Chorionic, Somatomammotropin) show a preferential use of some amino-acid codons. Based on this observation the reliability of three non-degenerate codes are analyzed. All of them display higher reliability than the standing genetic code and specially one formed by a set of non-directly related codons.The absence of these type of codes in Nature is discussed in terms of a balance between reliability and mutability of the genetic information, able to preserve species and maintain evolution     

A rationale for the symmetries by base substitutions of degeneracy in the genetic code

The first symmetry by base substitutions of degeneracy in the genetic code was described by Rumer (1966) and the other symmetries were identified later by Jestin (2006) and Jestin and Soulé (2007). Here, a rationale accounting for these symmetries is reported. The number of non-synonymous substitutions over the replicated coding sequence is written as a function of the substitution matrix, whose elements are the number of substitutions from any codon to any other codon. The p-adic distance used as a similarity measure and applied to this matrix is shown to be biologically relevant. The rationale indicates that symmetries by base substitutions of degeneracy in the genetic code are symmetries of the measures of the number of non-synonymous substitutions for sets of synonymous codons.     

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.     

Simplification of the genetic code: restricted diversity of genetically encoded amino acids

At earlier stages in the evolution of the universal genetic code, fewer than 20 amino acids were considered to be used. Although this notion is supported by a wide range of data, the actual existence and function of the genetic codes with a limited set of canonical amino acids have not been addressed experimentally, in contrast to the successful development of the expanded codes. Here, we constructed artificial genetic codes involving a reduced alphabet. In one of the codes, a tRNA^Ala variant with the Trp anticodon reassigns alanine to an unassigned UGG codon in the Escherichia coli S30 cell-free translation system lacking tryptophan. We confirmed that the efficiency and accuracy of protein synthesis by this Trp-lacking code were comparable to those by the universal genetic code, by an amino acid composition analysis, green fluorescent protein fluorescence measurements and the crystal structure determination. We also showed that another code, in which UGU/UGC codons are assigned to Ser, synthesizes an active enzyme. This method will provide not only new insights into primordial genetic codes, but also an essential protein engineering tool for the assessment of the early stages of protein evolution and for the improvement of pharmaceuticals.     

同义密码子使用模式对蛋白产物表达及构象形成的影响*

鉴于遗传密码子的简并性能够将基因遗传信息的容量提升,同义密码子使用偏嗜性得以在生物体的基因组中广泛存在。虽然同义密码子之间碱基的变化并不能导致氨基酸种类的改变,在研究mRNA半衰期、编码多肽翻译效率及肽链空间构象正确折叠的准确性和翻译等这一系列过程中发现,同义密码子使用的偏嗜性在某种程度上通过精微调控翻译机制体现其遗传学功能。同义密码子指导tRNA在翻译过程中识别核糖体的速率变化是由氨基酸的特定顺序决定,并且在新生多肽链合成时,蛋白质共翻译转运机制同时调节其空间构象的正确折叠从而保证蛋白的正常生物学功能。某些同义密码子使用偏嗜性与特定蛋白结构的形成具有显著相关性,密码子使用偏嗜性一旦改变将可能导致新生多肽空间构象出现错误折叠。结合近些年来国内外在此领域的研究成果,阐述同义密码子使用偏嗜性如何发挥精微调控翻译的生物学功能与作用。     

An information theory of the genetic code

An information theory of the genetic code is given, which deals with the process by which template codes (nucleotides or codons) choose substrate codes (nucleotides or anti-codons) in accordance with the base-pairing rules in the chain elongation phase of polynucleotide or polypeptide synthesis. A definite period of recognition time (τ) required for a template code to discriminate a substrate code is proposed, and an experimental method for determining the time is suggested. A substrate word is defined to be the sequence of substrate codes which have appeared at a recognition site in turn before a substrate code complementary to a template code first appears, and the mean length of substrate words (F) is derived from the mole fractions of template codes and substrate codes. The chain elongation rate is greatest when the mole fractions of template codes is proportional to the square of those of substrate codes to minimize the mean recognition time per word (Fτ). The uncertainty of a template (G) and the uncertainty of a medium (M) respectively are derived from the minimum of the function F. The amount of genetic information contained in a template is measured by the function G. The unit of the amount of genetic information is termed “cit”. The function M, the ratio of the number of all binary collisions to the number of homogeneous binary collisions in a mixture of different molecules, may be the new other “entropy” which represents informational properties of the mixture not represented by thermodynamic entropy of mixing. Both functions (G and M) have maxima when all random variables are equal and they are multiplicative in nature in contrast to entropy which is additive. The multiplicativity of the function G may contribute to the enormous informational capacity of genes.     

Study of the genetic code adaptability by means of a genetic algorithm

We used simulated evolution to study the adaptability level of the canonical genetic code. An adapted genetic algorithm (GA) searches for optimal hypothetical codes. Adaptability is measured as the average variation of the hydrophobicity that the encoded amino acids undergo when errors or mutations are present in the codons of the hypothetical codes. Different types of mutations and point mutation rates that depend on codon base number are considered in this study. Previous works have used statistical approaches based on randomly generated alternative codes or have used local search techniques to determine an optimum value. In this work, we emphasize what can be concluded from the use of simulated evolution considering the results of previous works. The GA provides more information about the difficulty of the evolution of codes, without contradicting previous studies using statistical or engineering approaches. The GA also shows that, within the coevolution theory, the third base clearly improves the adaptability of the current genetic code.     

简并性还是多态性?——遗传密码子设定的进化特点的剖析(英文)

遗传密码子的设定表现出令人困惑的多态性特点 :不同氨基酸拥有的密码子的数目 ,除 5个外 ,从 1个到 6个都有 .这种特点显示出密码子无论在翻译行为还是进化轨迹上 ,都存在诸多的异质性 .因此 ,简并性一词的收敛含义 ,并不能表征这种多态性的进化内涵 .没有同义密码子的AUG(Met)和UGG (Trp)并无简并现象 .其余的密码子则可分为两大类 :一类是 ,4个同义密码子为 1组 ,具有相同的第 1、2位碱基 ,并遵循“3中读 2”的读出规则 .同组的 4个同义密码子 ,不过是来自同一个双字母原始密码子 (XYN)的孑遗物 ,从这个意义上讲 ,也不宜视为简并现象 ;另一类则主要是 ,2个同义密码子为一组 ,并遵循“3中读 3”读出规则 .它们是由编码 2个氨基酸的双义原始密码子 ,第 3位的未定碱基N进一步设定形成 .至于有 6个同义密码子的 ,特别令人困感不解的组别 ,实际上是 4 + 2个 ,这启示它们可能源于上述两大类 .遗传密码子多态性的起源 ,可能始于最初阶段 ,氨基酸同某类寡核苷酸的起始二联体的相互作用 ,而完成于所有的双义原始密码子的第 3位碱基的分化 .这种进化轨迹被传统的简并性一词所模糊 ,并导致鉴定各有关理论可信性的坚实依据和令不同观点取得共识的基础被掩盖起来 .这可能就是在遗传密码子起源领域里 ,长期存在着众     

Possible evolutionary steps in the genetic code

In mammalian mitochondrial codes, fourfold codons wobble-pair with UNN anticodons so that U wobbles with U, C, A and G. Twofold pyrimidine-terminated codons pair with GNN and twofold purine-terminated codons pair with UNN. These properties enable a prediction to be made for evolution of the universal genetic code. It was postulated (1) that an archetypal code of 16 quartets coded for 15 amino acids. If this code used UNN anticodons, then duplication of tRNA genes, followed by mutations in the anticodons and aminoacylation sites, would give rise to the present universal code.     

Sequence similarity is more relevant than species specificity in probabilistic backtranslation

Background  

Backtranslation is the process of decoding a sequence of amino acids into the corresponding codons. All synthetic gene design systems include a backtranslation module. The degeneracy of the genetic code makes backtranslation potentially ambiguous since most amino acids are encoded by multiple codons. The common approach to overcome this difficulty is based on imitation of codon usage within the target species.     

The evolutionary change of the genetic code as restricted by the anticodon and identity of transfer RNA

The discovery of non-universal genetic codes in several mitochondria and nuclear systems during the past ten years has necessitated a reconsideration of the concept that the genetic code is universal and frozen, as was once believed. Here, the flexibility of the relationship between codons and amino acids is discussed on the basis of the distribution of non-universal genetic codes in various organisms insofar as has been observed to date. Judging from the result of recent investigations into tRNA identity, it would appear that the non-participation of the anticodon in recognition by aminoacyl-tRNA synthetase has significantly influenced the variability of codons.     

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.     

Noise immunity of the genetic code

Error detection and correction properties are fundamental for informative codes. Hamming's distance allows us to study this noise resistance. We present codes characterized by the resistance optimization to nonsense mutational effects. The calculation of the cumulated Hamming's distance allowing to determine the number of optimal codes and their structure can be detailed. The principle of these laws of optimization of resistance consists of choosing constituent codons connected by mutational neighbouring in such a way that random application of mutations on such a code minimize the occurrence of nonsense n-uplets or terminators. New coding symmetries are then described and screened using Galois's polynomials properties and Baudot's code. Such a study can be applied to any length of the codons. Here we present the principles of this optimization for the most simple doublet codes. Another constraint is discussed: the distribution of optimal subcodes for synonymity and the frequencies of utilization of the different codons.We compare these results to those of the present genetic code, and we observe that all coded amino acids (except the particular case of SER) are using optimal sub-codes of synonymity.This work suggests that the appearance of the genetic code was provoked by mutations while optimizing on several levels its resistance to their effects. Thus genetic coding would have been the best automata that could be produced in prebiotic conditions.     

Characterisation of a non-canonical genetic code in the oxymonad Streblomastix strix

The genetic code is one of the most highly conserved characters in living organisms. Only a small number of genomes have evolved slight variations on the code, and these non-canonical codes are instrumental in understanding the selective pressures maintaining the code. Here, we describe a new case of a non-canonical genetic code from the oxymonad flagellate Streblomastix strix. We have sequenced four protein-coding genes from S.strix and found that the canonical stop codons TAA and TAG encode the amino acid glutamine. These codons are retained in S.strix mRNAs, and the legitimate termination codons of all genes examined were found to be TGA, supporting the prediction that this should be the only true stop codon in this genome. Only four other lineages of eukaryotes are known to have evolved non-canonical nuclear genetic codes, and our phylogenetic analyses of alpha-tubulin, beta-tubulin, elongation factor-1 alpha (EF-1 alpha), heat-shock protein 90 (HSP90), and small subunit rRNA all confirm that the variant code in S.strix evolved independently of any other known variant. The independent origin of each of these codes is particularly interesting because the code found in S.strix, where TAA and TAG encode glutamine, has evolved in three of the four other nuclear lineages with variant codes, but this code has never evolved in a prokaryote or a prokaryote-derived organelle. The distribution of non-canonical codes is probably the result of a combination of differences in translation termination, tRNAs, and tRNA synthetases, such that the eukaryotic machinery preferentially allows changes involving TAA and TAG.     

On the Evolution of the Standard Genetic Code: Vestiges of Critical Scale Invariance from the RNA World in Current Prokaryote Genomes

Herein two genetic codes from which the primeval RNA code could have originated the standard genetic code (SGC) are derived. One of them, called extended RNA code type I, consists of all codons of the type RNY (purine-any base-pyrimidine) plus codons obtained by considering the RNA code but in the second (NYR type) and third (YRN type) reading frames. The extended RNA code type II, comprises all codons of the type RNY plus codons that arise from transversions of the RNA code in the first (YNY type) and third (RNR) nucleotide bases. In order to test if putative nucleotide sequences in the RNA World and in both extended RNA codes, share the same scaling and statistical properties to those encountered in current prokaryotes, we used the genomes of four Eubacteria and three Archaeas. For each prokaryote, we obtained their respective genomes obeying the RNA code or the extended RNA codes types I and II. In each case, we estimated the scaling properties of triplet sequences via a renormalization group approach, and we calculated the frequency distributions of distances for each codon. Remarkably, the scaling properties of the distance series of some codons from the RNA code and most codons from both extended RNA codes turned out to be identical or very close to the scaling properties of codons of the SGC. To test for the robustness of these results, we show, via computer simulation experiments, that random mutations of current genomes, at the rates of 10⁻¹⁰ per site per year during three billions of years, were not enough for destroying the observed patterns. Therefore, we conclude that most current prokaryotes may still contain relics of the primeval RNA World and that both extended RNA codes may well represent two plausible evolutionary paths between the RNA code and the current SGC.     

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.