On the antisymmetry of the amino acid code table

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.

Horizontal transfer of code fragments between protocells can explain the origins of the genetic code without vertical descent

Theories of the origin of the genetic code typically appeal to natural selection and/or mutation of hereditable traits to explain its regularities and error robustness, yet the present translation system presupposes high-fidelity replication. Woese's solution to this bootstrapping problem was to assume that code optimization had played a key role in reducing the effect of errors caused by the early translation system. He further conjectured that initially evolution was dominated by horizontal exchange of cellular components among loosely organized protocells ("progenotes"), rather than by vertical transmission of genes. Here we simulated such communal evolution based on horizontal transfer of code fragments, possibly involving pairs of tRNAs and their cognate aminoacyl tRNA synthetases or a precursor tRNA ribozyme capable of catalysing its own aminoacylation, by using an iterated learning model. This is the first model to confirm Woese's conjecture that regularity, optimality, and (near) universality could have emerged via horizontal interactions alone.

Fundamental amino acid mass distributions and entropy costs in proteomes

We examine whether the frequency of amino acids across an organism's proteome is primarily determined by optimization to function or other factors, such as the structure of the genetic code. Considering all available proteins together, we first point out that the frequency of an amino acid in a proteome negatively correlates with its mass, suggesting that the genome preserves a fundamental distribution ruled by simple energetics. Given the universality of such distributions, one can use outliers, cysteine and leucine, to identify amino acids that deviate from this simple rule for functional purposes and examine those functions. We quantify the strength of such selection as the entropic cost outliers pay to defy the mass-frequency relation. Codon degeneracy of an amino acid partially explains the correlation between mass and frequency: light amino acids being typically encoded by highly degenerate codon families, with the exception of arginine. While degeneracy may be a factor in hard wiring the relationship between mass and frequency in proteomes, it does not provide a complete explanation. By examining extremophiles, we are able to show that this law weakens with temperature, likely due to protein stability considerations, thus the environment is essential.

Numeral series hidden in the distribution of atomic mass of amino acids to codon domains in the genetic code

The distribution of codons in the nearly universal genetic code is a long discussed issue. At the atomic level, the numeral series 2x(2) (x=5-0) lies behind electron shells and orbitals. Numeral series appear in formulas for spectral lines of hydrogen. The question here was if some similar scheme could be found in the genetic code. A table of 24 codons was constructed (synonyms counted as one) for 20 amino acids, four of which have two different codons. An atomic mass analysis was performed, built on common isotopes. It was found that a numeral series 5 to 0 with exponent 2/3 times 10(2) revealed detailed congruency with codon-grouped amino acid side-chains, simultaneously with the division on atom kinds, further with main 3rd base groups, backbone chains and with codon-grouped amino acids in relation to their origin from glycolysis or the citrate cycle. Hence, it is proposed that this series in a dynamic way may have guided the selection of amino acids into codon domains. Series with simpler exponents also showed noteworthy correlations with the atomic mass distribution on main codon domains; especially the 2x(2)-series times a factor 16 appeared as a conceivable underlying level, both for the atomic mass and charge distribution. Furthermore, it was found that atomic mass transformations between numeral systems, possibly interpretable as dimension degree steps, connected the atomic mass of codon bases with codon-grouped amino acids and with the exponent 2/3-series in several astonishing ways. Thus, it is suggested that they may be part of a deeper reference system.

Extreme nearly neutral evolution in mitochondrial genomes of laboratory mouse strains

Relaxation of the selective constraint during the domestication process is known. In this study, we report unexpected closeness to neutral evolution of mitochondrial genomes of laboratory mouse strains: estimated non-synonymous/synonymous rate ratio being very close to 1 (ω^=1.32). Probably it is due to the extreme inbreeding extending over 100 years as well as to their recent origin (middle of the last millennium). There is no rate difference observed among three codon positions as well as ribosomal RNA and control regions. However, the amino acid substitutions occurred not randomly, and substitutions were more frequent between physico-chemically similar amino acids than between dissimilar ones. Probably this is inevitable consequence caused by the codon table itself, but not by selections. This implies that a large portion of the new mutations are conservative, and most of them are slightly deleterious and not lethal. It seems that, even though the selection pressures do not hold normally, the function of genes may not be impaired in most cases.

The origin of the genetic code in the ocean abysses: new comparisons confirm old observations

I have analysed the amino acid substitution pattern between two pairs of nonbarophilic-barophilic organisms in order to confirm previous results. Indeed, the pattern deriving from a different pair of such organisms led to establish that the origin of the genetic code might have occurred in the ocean abysses. The hydrostatic pressure asymmetry indices computable from these matrices of amino acid substitutions confirm the correlation previously observed, even when differences in GC content are accounted for. As the three substitution matrices are independent between them, the old conclusion that the genetic code originated in the ocean abysses is considerably strengthened.

On the organizational dynamics of the genetic code

The organization of the canonical genetic code needs to be thoroughly illuminated. Here we reorder the four nucleotides—adenine, thymine, guanine and cytosine—according to their emergence in evolution, and apply the organizational rules to devising an algebraic representation for the canonical genetic code. Under a framework of the devised code, we quantify codon and amino acid usages from a large collection of 917 prokaryotic genome sequences, and associate the usages with its intrinsic structure and classification schemes as well as amino acid physicochemical properties. Our results show that the algebraic representation of the code is structurally equivalent to a content-centric organization of the code and that codon and amino acid usages under different classification schemes were correlated closely with GC content, implying a set of rules governing composition dynamics across a wide variety of prokaryotic genome sequences. These results also indicate that codons and amino acids are not randomly allocated in the code, where the six-fold degenerate codons and their amino acids have important balancing roles for error minimization. Therefore, the content-centric code is of great usefulness in deciphering its hitherto unknown regularities as well as the dynamics of nucleotide, codon, and amino acid compositions.

Origin and evolution of the genetic code: the universal enigma

The genetic code is nearly universal, and the arrangement of the codons in the standard codon table is highly nonrandom. The three main concepts on the origin and evolution of the code are the stereochemical theory, according to which codon assignments are dictated by physicochemical affinity between amino acids and the cognate codons (anticodons); the coevolution theory, which posits that the code structure coevolved with amino acid biosynthesis pathways; and the error minimization theory under which selection to minimize the adverse effect of point mutations and translation errors was the principal factor of the code's evolution. These theories are not mutually exclusive and are also compatible with the frozen accident hypothesis, that is, the notion that the standard code might have no special properties but was fixed simply because all extant life forms share a common ancestor, with subsequent changes to the code, mostly, precluded by the deleterious effect of codon reassignment. Mathematical analysis of the structure and possible evolutionary trajectories of the code shows that it is highly robust to translational misreading but there are numerous more robust codes, so the standard code potentially could evolve from a random code via a short sequence of codon series reassignments. Thus, much of the evolution that led to the standard code could be a combination of frozen accident with selection for error minimization although contributions from coevolution of the code with metabolic pathways and weak affinities between amino acids and nucleotide triplets cannot be ruled out. However, such scenarios for the code evolution are based on formal schemes whose relevance to the actual primordial evolution is uncertain. A real understanding of the code origin and evolution is likely to be attainable only in conjunction with a credible scenario for the evolution of the coding principle itself and the translation system.

Evolution of the genetic code: partial optimization of a random code for robustness to translation error in a rugged fitness landscape

Background

The standard genetic code table has a distinctly non-random structure, with similar amino acids often encoded by codons series that differ by a single nucleotide substitution, typically, in the third or the first position of the codon. It has been repeatedly argued that this structure of the code results from selective optimization for robustness to translation errors such that translational misreading has the minimal adverse effect. Indeed, it has been shown in several studies that the standard code is more robust than a substantial majority of random codes. However, it remains unclear how much evolution the standard code underwent, what is the level of optimization, and what is the likely starting point.

Results

We explored possible evolutionary trajectories of the genetic code within a limited domain of the vast space of possible codes. Only those codes were analyzed for robustness to translation error that possess the same block structure and the same degree of degeneracy as the standard code. This choice of a small part of the vast space of possible codes is based on the notion that the block structure of the standard code is a consequence of the structure of the complex between the cognate tRNA and the codon in mRNA where the third base of the codon plays a minimum role as a specificity determinant. Within this part of the fitness landscape, a simple evolutionary algorithm, with elementary evolutionary steps comprising swaps of four-codon or two-codon series, was employed to investigate the optimization of codes for the maximum attainable robustness. The properties of the standard code were compared to the properties of four sets of codes, namely, purely random codes, random codes that are more robust than the standard code, and two sets of codes that resulted from optimization of the first two sets. The comparison of these sets of codes with the standard code and its locally optimized version showed that, on average, optimization of random codes yielded evolutionary trajectories that converged at the same level of robustness to translation errors as the optimization path of the standard code; however, the standard code required considerably fewer steps to reach that level than an average random code. When evolution starts from random codes whose fitness is comparable to that of the standard code, they typically reach much higher level of optimization than the standard code, i.e., the standard code is much closer to its local minimum (fitness peak) than most of the random codes with similar levels of robustness. Thus, the standard genetic code appears to be a point on an evolutionary trajectory from a random point (code) about half the way to the summit of the local peak. The fitness landscape of code evolution appears to be extremely rugged, containing numerous peaks with a broad distribution of heights, and the standard code is relatively unremarkable, being located on the slope of a moderate-height peak.

Conclusion

The standard code appears to be the result of partial optimization of a random code for robustness to errors of translation. The reason the code is not fully optimized could be the trade-off between the beneficial effect of increasing robustness to translation errors and the deleterious effect of codon series reassignment that becomes increasingly severe with growing complexity of the evolving system. Thus, evolution of the code can be represented as a combination of adaptation and frozen accident.

Reviewers

This article was reviewed by David Ardell, Allan Drummond (nominated by Laura Landweber), and Rob Knight.

Open Peer Review

This article was reviewed by David Ardell, Allan Drummond (nominated by Laura Landweber), and Rob Knight.

The genetic code is nearly optimal for allowing additional information within protein-coding sequences

DNA sequences that code for proteins need to convey, in addition to the protein-coding information, several different signals at the same time. These "parallel codes" include binding sequences for regulatory and structural proteins, signals for splicing, and RNA secondary structure. Here, we show that the universal genetic code can efficiently carry arbitrary parallel codes much better than the vast majority of other possible genetic codes. This property is related to the identity of the stop codons. We find that the ability to support parallel codes is strongly tied to another useful property of the genetic code--minimization of the effects of frame-shift translation errors. Whereas many of the known regulatory codes reside in nontranslated regions of the genome, the present findings suggest that protein-coding regions can readily carry abundant additional information.

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 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 Woese's polarity and the specific volume, show a perfect correlation to Lagerkvist's 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 comparison of proteins from Pyrococcus furiosus and Pyrococcus abyssi: barophily in the physicochemical properties of amino acids and in the genetic code

A comparison is made between orthologous proteins from a nonbarophile (Pyrococcus furiosus) and a barophile (Pyrococcus abyssi) organism. The pattern of asymmetries in the amino acid substitution process identifies the amino acids arginine, serine, glycine, valine and aspartic acid as those having the most barophilic behaviour, and tyrosine and glutamine as the least barophilic. The construction of a hydrostatic pressure asymmetry index (PAI) which orders the amino acids from the most barophilic to the least barophilic makes it possible to visualise the amino acid properties that best explain barophily. The polarity of amino acids is positively correlated to the PAI values, i.e., on average, the more polar amino acids possess a higher PAI value, that is to say they are more barophilic. Moreover, the "size" of amino acids (molecular weight) is negatively correlated to the PAI value, that is to say that, on average, high PAI values are associated to "small" amino acids which are therefore more barophilic than "larger" ones. These two amino acid properties are the same ones that are known for having been important in affecting the origin of genetic code organisation. All the above, as well as the significant and positive correlation between the number of codons attributed to the amino acids in the genetic code and the PAI values, seem to favour the hypothesis that genetic code structuring took place under high hydrostatic pressure.

The ocean abysses witnessed the origin of the genetic code

The comparison of proteins from a non-barophilous and a barophilous organism makes it possible to define the barophily ranks of amino acids. The correlation of these ranks with the number of codons attributed to amino acids in the genetic code, together with another straightforward argument based on an optimisation percentage of a barophily index (BI) (easily defined by barophily ranks) which can be associated to the genetic code table, suggest that the genetic code originated under high hydrostatic pressure. Moreover, as the BI value can be calculated for the sequence of any protein, it also makes it possible to define the BI for the genetic code if the number of 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, sampling the BI variable between many non-barophile organisms and from many proteins of a single non-barophile organism leads to the conclusion that the BI value of the genetic code is not typical of these organisms. Whereas, since the genetic code BI value is statistically higher than that of these non-barophile organisms, it supports the hypothesis that genetic code structuring took place under high hydrostatic pressure.

The origin of the genetic code: theories and their relationships, a review

A review of the main theories proposed to explain the origin of the genetic code is presented. I analyze arguments and data in favour of different theories proposed to explain the origin of the organization of the genetic code. It is possible to suggest a mechanism that makes compatible the different theories of the origin of the code, even if these are based on a historical or physicochemical determinism and thus appear incompatible by definition. Finally, I discuss the question of why a given number of synonymous codons was attributed to the amino acids in the genetic code.

The case for an error minimizing standard genetic code

Since discovering the pattern by which amino acids are assigned to codons within the standard genetic code, investigators have explored the idea that natural selection placed biochemically similar amino acids near to one another in coding space so as to minimize the impact of mutations and/or mistranslations. The analytical evidence to support this theory has grown in sophistication and strength over the years, and counterclaims questioning its plausibility and quantitative support have yet to transcend some significant weaknesses in their approach. These weaknesses are illustrated here by means of a simple simulation model for adaptive genetic code evolution. There remain ill explored facets of the 'error minimizing' code hypothesis, however, including the mechanism and pathway by which an adaptive pattern of codon assignments emerged, the extent to which natural selection created synonym redundancy, its role in shaping the amino acid and nucleotide languages, and even the correct interpretation of the adaptive codon assignment pattern: these represent fertile areas for future research.

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.

A common periodic table of codons and amino acids

A periodic table of codons has been designed where the codons are in regular locations. The table has four fields (16 places in each) one with each of the four nucleotides (A, U, G, C) in the central codon position. Thus, AAA (lysine), UUU (phenylalanine), GGG (glycine), and CCC (proline) were placed into the corners of the fields as the main codons (and amino acids) of the fields. They were connected to each other by six axes. The resulting nucleic acid periodic table showed perfect axial symmetry for codons. The corresponding amino acid table also displaced periodicity regarding the biochemical properties (charge and hydropathy) of the 20 amino acids and the position of the stop signals. The table emphasizes the importance of the central nucleotide in the codons and predicts that purines control the charge while pyrimidines determine the polarity of the amino acids. This prediction was experimentally tested.

The late stage of genetic code structuring took place at a high temperature

The correlation between the optimal growth temperature of organisms and a thermophily index based on the propensity of amino acids to enter more frequently into (hyper)thermophile proteins is used to conduct an analysis aiming to establish whether genetic code structuring took place at a low or a high temperature. If the number of codons attributed to the various amino acids in the genetic code constitutes an estimate of the mean amino acid composition of proteins produced when the genetic code was definitively structured, then the thermophily index can also be associated to the genetic code. This value and the sampling of the variable thermophily index of different alignments of protein sequences from mesophile, thermophile and hyperthermophile species make it possible to establish, with an extremely high statistical confidence, that the late stage of genetic code structuring took place in a hyperthermophile (or thermophile) 'organism'. Moreover the 95% confidence interval of the temperature at which the genetic code was fixed turned out to be 91+/-24 degrees C. These observations seem to support the hypothesis that the origin of life might have taken place at a high temperature.

Protein evolution drives the evolution of the genetic code and vice versa

A model for the developmental pathway of the genetic code, grounded on group theory and the thermodynamics of codon-anticodon interaction is presented. At variance with previous models, it takes into account not only the optimization with respect to amino acid attributes but, also physicochemical constraints and initial conditions. A 'simple-first' rule is introduced after ranking the amino acids with respect to two current measures of chemical complexity. It is shown that a primeval code of only seven amino acids is enough to build functional proteins. It is assumed that these proteins drive the further expansion of the code. The proposed primeval code is compared with surrogate codes randomly generated and with another proposal for primeval code found in the literature. The departures from the 'universal' code, observed in many organisms and cellular compartments, fit naturally in the proposed evolutionary scheme. A strong correlation is found between, on one side, the two classes of aminoacyl-tRNA synthetases, and on the other, the amino acids grouped by end-atom-type and by codon type. An inverse of Davydov's rules, to associate the amino acid end atoms (O/N and non-O/non-N) of 18 amino acids with codons containing a weak base (A/U), extended to the 20 amino acids, is derived.

Evolution of the genetic code

Comparative path lengths in amino acid biosynthesis and other molecular indicators of the timing of codon assignment were examined to reconstruct the main stages of code evolution. The codon tree obtained was rooted in the 4 N-fixing amino acids (Asp, Glu, Asn, Gln) and 16 triplets of the NAN set. This small, locally phased (commaless) code evidently arose from ambiguous translation on a poly(A) collector strand, in a surface reaction network. Copolymerisation of these amino acids yields polyanionic peptide chains, which could anchor uncharged amide residues to a positively charged mineral surface. From RNA virus structure and replication in vitro, the first genes seemed to be RNA segments spliced into tRNA. Expansion of the code reduced the risk of mutation to an unreadable codon. This step was conditional on initiation at the 5'-codon of a translated sequence. Incorporation of increasingly hydrophobic amino acids accompanied expansion. As codons of the NUN set were assigned most slowly, they received the most nonpolar amino acids. The origin of ferredoxin and Gln synthetase was traced to mid-expansion phase. Surface metabolism ceased by the end of code expansion, as cells bounded by a proteo-phospholipid membrane, with a protoATPase, had emerged. Incorporation of positively charged and aromatic amino acids followed. They entered the post-expansion code by codon capture. Synthesis of efficient enzymes with acid-base catalysis was then possible. Both types of aminoacyl-tRNA synthetases were attributed to this stage. tRNA sequence diversity and error rates in RNA replication indicate the code evolved within 20 million yr in the preIsuan era. These findings on the genetic code provide empirical evidence, from a contemporaneous source, that a surface reaction network, centred on C-fixing autocatalytic cycles, rapidly led to cellular life on Earth.

Chou-Fasman conformational amino acid parameters and the genetic code

It was found that the distribution of Chou-Fasman P alpha conformational parameters within the genetic code (arranged into the one-step mutation ring) may be described by a quite simple trigonometric function of mutational angle. The mutational angle is defined as k pi/32, where k is a number of codons count from i under consideration to k. The principal eight-codon periodicity defines the P alpha-genetic code correspondence, but the other perioditicies seem also to modulate the principal function. The eight-codon periodicity finds the explanation in the regular changes of third bases of successive codons. These changes appear in the order; C,U,A,G,G,A,U,C, assigning eight maxima and eight minima of P alpha curve. The experimental P alpha values fit well the dependence found, except proline, the amino acid which breaks the regular eight-codon P alpha periodicity. The analysis of dependence obtained suggest that, in agreement with the hypothesis of Jukes (1973), arginine CGR and AGR codons could be in an earlier genetic code used for coding of ornithine.

The informational context of the third base in amino acid codons

It is shown that in the pairs of amino acids coded by the codons possesing identical bases in the first and second positions, the amino acids with R in the third position are of higher structural importance (which is reflected by higher values of (P alpha + P beta) sums of Chou-Fasman conformational parameters), and of stronger helix forming potentials (reflected by the differences (P alpha - P beta)), than the amino acids coded with Y. The same structural factors seem to be of importance for the codon choice in the case of amino acids coded by more than two codons. The amino acids which prefer alpha-helical over the beta-sheet conformation favour the codons with R in their third position, and those which favour the beta-sheet conformation favour the codons with Y in this position.

Periodical changes of amino acid reactivity within the genetic code

Enthalpies (delta H++) and entropies (delta S++) of activation for the reaction of 18 N'-hydroxysuccinimide esters of N-protected proteinaceous amino acids with p-anisidine were measured and free enthalpies of activation (delta G++) at 25 degrees C were calculated on this basis. A regular correlation between delta G++s and the corresponding amino acid codons was found. To obtain this correlation all the codons had to be arranged in a closed ring in which the consecutive codons were connected by one-step mutational changes. One-step mutations appeared as a regular series: 2,3,3,3,1,3,3,3,1,3,3,3,1,3,3,3,2,3,3,3. (the numbers denote a codon position in which a change took place). There were three such 'one-step mutation periods' in the ring, each containing 20 codons (in each block of 16 codons with A, U and C, in the central position and 4 codons containing G in the central position). The end of the third period (UG) and the beginning of the first period were bridged by the four codons of glycine with G in the second position. The values of delta G++ change similarly in each period, increasing upon approaching Lys, Pro, and Ile. The periodical relation between the chemical reactivities of the coded amino acids (reflected by delta G++s) and the structure of their codons could be of importance for the origin of the genetic code i.e. for selection of proper codons for the definite amino acids.

On the informational content of viral DNA

This paper is concerned primarily with how information is stored in viral DNA. The general problem of defining information content is discussed and a procedure for analysis extended from that of Gatlin (1972) is developed. Long range correlations in base sequences are analyzed for several viral genomes. The relationship of these correlations to the existence of strong codon biases is examined and the consequences discussed.

A thermodynamic theory of codon bias in viral genes

The relationship between degeneracy in the genetic code and the occurrence of a strong codon bias is examined, with particular reference to a group of viral genomes. The present paper shows how codon bias may have been imposed by thermodynamic considerations at the time the primitive DNA first formed in the primordial soup. Using a four-state Ising-like model with stacking interactions between successive base pairs, we show how primeval periodic DNA polymers could have arisen the remnants of which are still observed in codon biases today.

A model for the development of genetic translation

Several models have been advanced, both in this journal and others, for the development of the genetic code and translation apparatus. Eigen in particular has put forward a detailed model based on the hypercycle. This paper uses some of these previous ideas to develop a new model of the code and translation in which the pairs AU and GC play complementary roles, and in which tRNAs develop from a molecule with two loops which stacks in repetitive patterns without the need for a messenger RNA. Thus a bridge is provided between random, (or autocatalytic) polymerization, and coded translation. In addition, alternative postulates to several of Eigen's ideas are tested by computer simulation.