Theory of degenerate coding and informational parameters of protein coding genes

The theory of degenerate coding is presented in a way enabling further application to molecular biology. There are two kinds of redundancy of a degenerate code. The first is due to the excess in codon length and the second to the code degeneracy. If the code is asymmetrically degenerate, the second kind of redundancy can be profitable for control of error rate. This control can be performed just by selective synonymous codon usage. Utilisation of the genetic code is partially influenced by this theoretical possibility. In particular the degree of error protectivity is well correlated with deviation from equiprobability in synonymous codon usage. The biological significance of this fact is discussed.     

Evolution of the Genetic Triplet Code via Two Types of Doublet Codons

Explaining the apparent non-random codon distribution and the nature and number of amino acids in the ‘standard’ genetic code remains a challenge, despite the various hypotheses so far proposed. In this paper we propose a simple new hypothesis for code evolution involving a progression from singlet to doublet to triplet codons with a reading mechanism that moves three bases each step. We suggest that triplet codons gradually evolved from two types of ambiguous doublet codons, those in which the first two bases of each three-base window were read (‘prefix’ codons) and those in which the last two bases of each window were read (‘suffix’ codons). This hypothesis explains multiple features of the genetic code such as the origin of the pattern of four-fold degenerate and two-fold degenerate triplet codons, the origin of its error minimising properties, and why there are only 20 amino acids. Reviewing Editor: Dr. Laura Landweber An erratum to this article can be found at .     

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.     

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.     

The construction and evolution of DNA sequences having the same doublet ratios as those of non-satellite, mammalian DNA.

The doublet or nearest-neighbour ratios of the nucleotides in various computer-generated sequences of DNA have been counted to find out which sequences would have the same ratios as those measured for guinea-pig DNA by Russell et al. (1976). Their data shows that the ratio patterns for all nuclear DNA fractions except satellite, ribosomal and tRNA coding DNA are similar irrespective of G+C content and are characterised by the amount of the doublet CpG being less than 30% of that expected on a random basis. To construct and analyse such theoretical sequences, methods have been developed which allow to be counted the doublet frequencies that random DNA and the DNA expected to code for any amino acid (AA) sequence would have were they analysed experimentally. These methods permit the C+G content to be altered and the frequency of the doublet CpG to be lowered without affecting the information stored in the DNA. The former is achieved by selecting codons for a given AA that are high or low in G and C while the latter requires selecting against triplets that either contain CpG or will cause a CpG to occur between codons.The results show that no DNA sequence that we have been able to construct using the unrestricted genetic code has doublet ratios similar to those observed. However, the DNA expected to code for a group of 27 vertebrate proteins (5237 AAs) of diverse functions has doublet ratios virtually identical to those measured experimentally for the 47% G+C fraction, provided that 77·5 % of the CpG is eliminated. The data for the 34–43% G+C fractions are matched well by the protein sequence provided that codons low in G and C are selected and, again, that 77·5% of CpG is eliminated. We have been unable to match the data for the satellite DNA. A perhaps surprising result was that DNA with a random sequence of nucleotides but subjected to the removal of 80% of CpG had doublet ratios that were similar to the experimental data but matched them less well than the doublets of protein-coding DNA. This result probably does no more than emphasise that a significant part of the match of the pattern of doublet ratios of guinea-pig DNA derives from the elimination of CpG.The effect of evolution (random mutation) on the doublet ratios of protein-coding DNA has been investigated by assuming a mutation rate of 3·10^?9 per base per generation (the mutation rate of haemoglobin) and seeing how a great many generations of such mutation affect the doublet ratios. The results show that it will take ~1·5·10⁶ generations for the number of termination codons to double and ~2·10⁷ generations for the doublet ratios to become indistinguishable from those of random DNA. This seems to imply either that selection acts over the whole of the DNA or that the mutation rate of haemoglobin DNA is unusually high. The results, as a whole, support the view that, whether or not all non-satellite DNA actually codes for protein, its sequences are similar to those that would code for proteins.     

A New Classification Scheme of the Genetic Code

Since the early days of the discovery of the genetic code nonrandom patterns have been searched for in the code in the hope of providing information about its origin and early evolution. Here we present a new classification scheme of the genetic code that is based on a binary representation of the purines and pyrimidines. This scheme reveals known patterns more clearly than the common one, for instance, the classification of strong, mixed, and weak codons as well as the ordering of codon families. Furthermore, new patterns have been found that have not been described before: Nearly all quantitative amino acid properties, such as Woeses polarity and the specific volume, show a perfect correlation to Lagerkvists codon–anticodon binding strength. Our new scheme leads to new ideas about the evolution of the genetic code. It is hypothesized that it started with a binary doublet code and developed via a quaternary doublet code into the contemporary triplet code. Furthermore, arguments are presented against suggestions that a simpler code, where only the midbase was informational, was at the origin of the genetic code.     

A conformational rationale for the wobble behaviour of the first base of the anticodon triplet in tRNA

We present a conformational rationale for wobble behaviour of the first base in the anticodon triplet of tRNA and hence for the well-known degeneracy of the genetic code. The U-turn hydrogen bond plays an important role in the structure of the anticodon arm and particularly for the anticodon triplet to be in a geometry suitable for the process of recognition in the adaptor-mediated synthesis of proteins. This hydrogen bond in turn precludes a hydrogen bond between the first two sugars of the anticodon triplet, allowing the first base to wobble, while it facilitates one between the second and third sugars of the triplet, positioning these bases for the standard base-pairing with the codon. This neatly explains why there is a degeneracy in the code and why a RNA happens to be the adaptor for protein synthesis. Relevent conformational calculations are presented in support of the theory.     

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.     

Speculations on the evolution of the genetic code

An evolutionary scheme is postulated in which the bases enter the genetic code in a definite temporal sequence and the correlated amino acids are assigned definite functions in the evolving system.The scheme requires a singlet code (guanine coding for glycine) evolving into a doublet code (guanine-cytosine doublet coding for gly (GG), ala (GC), arg (CG), pro (CC)). The doublet code evolves into a triplet code. Polymerization of nucleotides is thought to have been by block polymerization rather than by a template mechanism. The proteins formed at first were simple structural peptides. No direct nucleotide-amino acid stereo-chemical interaction was required. Rather an adaptor-type indirect mechanism is thought to have been functioning since the origin.     

Speculations on the evolution of the genetic code.

An evolutionary scheme is postulated in which the bases enter the genetic code in a definite temporal sequence and the correlated amino acids are assigned definite functions in the evolving system. The scheme requires a singlet code (guanine coding for glycine) evolving into a doublet code (guanine-cytosine doublet coding for gly (GG), ala (GC), arg (CG), pro (CC). The doublet code evolves into a triplet code. Polymerization of nucleotides is thought to have been by block polymerization rather than by a template mechanism. The proteins formed at first were simple structural peptides. No direct nucleotide-amino acid stereo-chemical interaction was required. Rather an adaptor-type indirect mechanism is thought to have been functioning since the origin.     

A large-scale analysis of codon usage bias in 4868 bacterial genomes shows association of codon adaptation index with GC content,protein functional domains and bacterial phenotypes

Multiple synonymous codons code for the same amino acid, resulting in the degeneracy of the genetic code and in the preferred used of some codons called codon bias usage (CBU). We performed a large-scale analysis of codon usage bias analysing the distribution of the codon adaptation index (CAI) and the codon relative adaptiveness index (RA) in 4868 bacterial genomes. We found that CAI values differ significantly between protein functional domains and part of the protein outside domains and show how CAI, GC content and preferred usage of polymerase III alpha subunits are related. Additionally, we give evidence of the association between CAI and bacterial phenotypes.     

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]     

A diminutive and specific RNA binding site for L-tryptophan

Selection for amino acid affinity by elution of RNAs from tryptophan–Sepharose using free L-tryptophan evokes one sequence predominantly (K_D = 12 µM), a symmetrical internal loop of 3 nt per side. Though we have also isolated larger sequences with affinity for tryptophan, successively squeezed selection in randomized tracts of 70, 60, 40, 20 and 17 nt show that this internal loop is the simplest sequence that can meet the column affinity selection. From sequence variation in ~50 independent isolates, only 26 bits of information are required to describe this loop (equivalent to only 13 fully conserved nucleotides). Thus, it is among the simplest amino acid binding sites known, as well as selective among hydrophobic side chains. Among site sequences defined as essential to affinity by conservation, protection and modification-interference, there is a recurring CCA sequence (a tryptophan anticodon triplet) which apparently forms one side of the binding site. Such conserved juxtaposition of tryptophan with a cognate coding triplet supports a stereochemical origin for the genetic code.     

Codon Size Reduction as the Origin of the Triplet Genetic Code

The genetic code appears to be optimized in its robustness to missense errors and frameshift errors. In addition, the genetic code is near-optimal in terms of its ability to carry information in addition to the sequences of encoded proteins. As evolution has no foresight, optimality of the modern genetic code suggests that it evolved from less optimal code variants. The length of codons in the genetic code is also optimal, as three is the minimal nucleotide combination that can encode the twenty standard amino acids. The apparent impossibility of transitions between codon sizes in a discontinuous manner during evolution has resulted in an unbending view that the genetic code was always triplet. Yet, recent experimental evidence on quadruplet decoding, as well as the discovery of organisms with ambiguous and dual decoding, suggest that the possibility of the evolution of triplet decoding from living systems with non-triplet decoding merits reconsideration and further exploration. To explore this possibility we designed a mathematical model of the evolution of primitive digital coding systems which can decode nucleotide sequences into protein sequences. These coding systems can evolve their nucleotide sequences via genetic events of Darwinian evolution, such as point-mutations. The replication rates of such coding systems depend on the accuracy of the generated protein sequences. Computer simulations based on our model show that decoding systems with codons of length greater than three spontaneously evolve into predominantly triplet decoding systems. Our findings suggest a plausible scenario for the evolution of the triplet genetic code in a continuous manner. This scenario suggests an explanation of how protein synthesis could be accomplished by means of long RNA-RNA interactions prior to the emergence of the complex decoding machinery, such as the ribosome, that is required for stabilization and discrimination of otherwise weak triplet codon-anticodon interactions.     

On the information content of the genetic code

In living organisms 20 amino acids along with the terminator value(s) are encoded by 64 codons giving a degeneracy of the codons as described by the genetic code. A basic theoretical problem of genetic codes is to explain the particular distribution of degeneracies of partitions involved in the codes. In this work the degeneracy problem is considered in the framework of information theory. It is shown by direct numerical evaluation of a certain degeneracy information function associated with the genetic code that the degeneracy of the codes is observed to be related to the optimization of this function.     

氨基酸的分子结构与遗传密码简并及二维集合分类

根据氨基酸遗传密码子的简并程度,可将64个遗传密码子分为高简并度类（3,4,6度简并组）和低简并度类（1,2度简并组）两大类。高简并度类有9个氨基酸,其分子量比较小,等电点的分布比较集中。低简并度类有11个氨基酸,其分子结构比较复杂,参考Taylor对氨基酸特性的分类图,本文提出以分子量（M）及等电点（P）作为氨基酸的化学特性坐标,作出其二维集合MP分类图,MP分类图可以反映出氨基酸的各种属性,如分子量的大小,简并度的高低,极性与非极性、带电荷或不带电荷,疏水性与亲水性,以及氨基酸残基的种类等。根据氨基酸的分类分析,可以认为：高简并度氨基酸多数是脂烃类和羟脂烃类的氨基酸,分子量比较小,分子结构比较简单,大部分为疏子性,主要组成跨膜结构或蛋白质的结构域,可能是出现较早的氨基酸;而低简并度的氨基酸,分子结构比较复杂,分子量比较大,多数是和蛋白质功能有密切联系的基团,可能是进化出现较晚的结构。     

The multiple codes of nucleotide sequences

Nucleotide sequences carry genetic information of many different kinds, not just instructions for protein synthesis (triplet code). Several codes of nucleotide sequences are discussed including: (1) the translation framing code, responsible for correct triplet counting by the ribosome during protein synthesis; (2) the chromatin code, which provides instructions on appropriate placement of nucleosomes along the DNA molecules and their spatial arrangement; (3) a putative loop code for single-stranded RNA-protein interactions. The codes are degenerate and corresponding messages are not only interspersed but actually overlap, so that some nucleotides belong to several messages simultaneously. Tandemly repeated sequences frequently considered as functionless “junk” are found to be grouped into certain classes of repeat unit lengths. This indicates some functional involvement of these sequences. A hypothesis is formulated according to which the tandem repeats are given the role of weak enhancer-silencers that modulate, in a copy number-dependent way, the expression of proximal genes. Fast amplification and elimination of the repeats provides an attractive mechanism of species adaptation to a rapidly changing environment.