Optimality of the genetic code with respect to protein stability and amino-acid frequencies

Background

The genetic code is known to be efficient in limiting the effect of mistranslation errors. A misread codon often codes for the same amino acid or one with similar biochemical properties, so the structure and function of the coded protein remain relatively unaltered. Previous studies have attempted to address this question quantitatively, by estimating the fraction of randomly generated codes that do better than the genetic code in respect of overall robustness. We extended these results by investigating the role of amino-acid frequencies in the optimality of the genetic code.

Results

We found that taking the amino-acid frequency into account decreases the fraction of random codes that beat the natural code. This effect is particularly pronounced when more refined measures of the amino-acid substitution cost are used than hydrophobicity. To show this, we devised a new cost function by evaluating in silico the change in folding free energy caused by all possible point mutations in a set of protein structures. With this function, which measures protein stability while being unrelated to the code's structure, we estimated that around two random codes in a billion (10⁹) are fitter than the natural code. When alternative codes are restricted to those that interchange biosynthetically related amino acids, the genetic code appears even more optimal.

Conclusions

These results lead us to discuss the role of amino-acid frequencies and other parameters in the genetic code's evolution, in an attempt to propose a tentative picture of primitive life.     

A Realistic Model Under Which the Genetic Code is Optimal

The genetic code has a high level of error robustness. Using values of hydrophobicity scales as a proxy for amino acid character, and the mean square measure as a function quantifying error robustness, a value can be obtained for a genetic code which reflects the error robustness of that code. By comparing this value with a distribution of values belonging to codes generated by random permutations of amino acid assignments, the level of error robustness of a genetic code can be quantified. We present a calculation in which the standard genetic code is shown to be optimal. We obtain this result by (1) using recently updated values of polar requirement as input; (2) fixing seven assignments (Ile, Trp, His, Phe, Tyr, Arg, and Leu) based on aptamer considerations; and (3) using known biosynthetic relations of the 20 amino acids. This last point is reflected in an approach of subdivision (restricting the random reallocation of assignments to amino acid subgroups, the set of 20 being divided in four such subgroups). The three approaches to explain robustness of the code (specific selection for robustness, amino acid–RNA interactions leading to assignments, or a slow growth process of assignment patterns) are reexamined in light of our findings. We offer a comprehensive hypothesis, stressing the importance of biosynthetic relations, with the code evolving from an early stage with just glycine and alanine, via intermediate stages, towards 64 codons carrying todays meaning.     

An Alternative Look at Code Evolution: Using Non-canonical Codes to Evaluate Adaptive and Historic Models for the Origin of the Genetic Code

The canonical code has been shown many times to be highly robust against point mutations; that is, mutations that change a single nucleotide tend to result in similar amino acids more often than expected by chance. There are two major types of models for the origin of the code, which explain how this sophisticated structure evolved. Adaptive models state that the primitive code was specifically selected for error minimization, while historic models hypothesize that the robustness of the code is an artifact or by-product of the mechanism of code evolution. In this paper, we evaluated the levels of robustness in existing non-canonical codes as well as codes that differ in only one codon assignment from the standard code. We found that the level of robustness of many of these codes is comparable or better than that of the standard code. Although these results do not preclude an adaptive origin of the genetic code, they suggest that the code was not selected for minimizing the effects of point mutations.     

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.     

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.     

Some mathematical refinements concerning error minimization in the genetic code

The genetic code is known to have a high level of error robustness and has been shown to be very error robust compared to randomly selected codes, but to be significantly less error robust than a certain code found by a heuristic algorithm. We formulate this optimization problem as a Quadratic Assignment Problem and use this to formally verify that the code found by the heuristic algorithm is the global optimum. We also argue that it is strongly misleading to compare the genetic code only with codes sampled from the fixed block model, because the real code space is orders of magnitude larger. We thus enlarge the space from which random codes can be sampled from approximately 2.433 × 10(18) codes to approximately 5.908 × 10(45) codes. We do this by leaving the fixed block model, and using the wobble rules to formulate the characteristics acceptable for a genetic code. By relaxing more constraints, three larger spaces are also constructed. Using a modified error function, the genetic code is found to be more error robust compared to a background of randomly generated codes with increasing space size. We point out that these results do not necessarily imply that the code was optimized during evolution for error minimization, but that other mechanisms could be the reason for this error robustness.     

Stability of the genetic code and optimal parameters of amino acids

The standard genetic code is known to be much more efficient in minimizing adverse effects of misreading errors and one-point mutations in comparison with a random code having the same structure, i.e. the same number of codons coding for each particular amino acid. We study the inverse problem, how the code structure affects the optimal physico-chemical parameters of amino acids ensuring the highest stability of the genetic code. It is shown that the choice of two or more amino acids with given properties determines unambiguously all the others. In this sense the code structure determines strictly the optimal parameters of amino acids or the corresponding scales may be derived directly from the genetic code. In the code with the structure of the standard genetic code the resulting values for hydrophobicity obtained in the scheme “leave one out” and in the scheme with fixed maximum and minimum parameters correlate significantly with the natural scale. The comparison of the optimal and natural parameters allows assessing relative impact of physico-chemical and error-minimization factors during evolution of the genetic code. As the resulting optimal scale depends on the choice of amino acids with given parameters, the technique can also be applied to testing various scenarios of the code evolution with increasing number of codified amino acids. Our results indicate the co-evolution of the genetic code and physico-chemical properties of recruited amino acids.     

An Analysis of the Metabolic Theory of the Origin of the Genetic Code

A computer program was used to test Wong's coevolution theory of the genetic code. The codon correlations between the codons of biosynthetically related amino acids in the universal genetic code and in randomly generated genetic codes were compared. It was determined that many codon correlations are also present within random genetic codes and that among the random codes there are always several which have many more correlations than that found in the universal code. Although the number of correlations depends on the choice of biosynthetically related amino acids, the probability of choosing a random genetic code with the same or greater number of codon correlations as the universal genetic code was found to vary from 0.1% to 34% (with respect to a fairly complete listing of related amino acids). Thus, Wong's theory that the genetic code arose by coevolution with the biosynthetic pathways of amino acids, based on codon correlations between biosynthetically related amino acids, is statistical in nature. Received: 8 August 1996 / Accepted: 26 December 1996     

Genetic code development by stop codon takeover

A novel theoretical consideration of the origin and evolution of the genetic code is presented. Code development is viewed from the perspective of simultaneously evolving codons, anticodons and amino acids. Early code structure was determined primarily by thermodynamic stability considerations, requiring simplicity in primordial codes. More advanced coding stages could arise as biological systems became more complex and precise in their replication. To be consistent with these ideas, a model is described in which codons become permanently associated with amino acids only when a codon-anticodon pairing is strong enough to permit rapid translation. Hence all codons are essentially chain-termination or "stop" codons until tRNA adaptors evolve having the ability to bind tightly to them. This view, which draws support from several lines of evidence, differs from the prevalent thinking on code evolution which holds that codons specifying newer amino acids were derived from codons encoding older amino acids.     

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.     

Physico-chemical constraints connected with the coding properties of the genetic system

New insights on the origin of the genetic code, based on the analysis of the physico-chemical properties of its molecular constituents (RNA and amino acids), are reported in this paper. We point out a symmetry in the genetic code table and show that it can be explained by the nature of the anticodon-codon interaction. The importance of the strength of this interaction is examined and a correlation is found between the free-energy change (DeltaG(0)) of anticodon-codon association and the volume of the corresponding amino acids. This correlation is investigated in conjunction with the well-known one linking the hydrophobicity of the anticodons with that of the amino acids. We show that they can be considerated separately and that the energy vs. volume correlation may be explained by the process implicating the peptide bond formation between two successive amino acids during translation. This interpretation is supported by a statistical pattern of bases (purines or pyrimidines), observed in present coding genes, and by considerations involving the availability of the different kinds of amino acids. Finally, we try to explain the hydrophobicity correlation when reconstructing the events at the time of the so-called "RNA World". The whole of our investigation shows that the genetic code might be sufficiently robust to exist without the participation of pre-existing proteins, and that this robustness is a consequence of the physico-chemical properties of the four bases of the genetic system.     

Natural history and experimental evolution of the genetic code

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

Codon Usage Bias and Mutation Constraints Reduce the Level of ErrorMinimization of the Genetic Code

Studies on the origin of the genetic code compare measures of the degree of error minimization of the standard code with measures produced by random variant codes but do not take into account codon usage, which was probably highly biased during the origin of the code. Codon usage bias could play an important role in the minimization of the chemical distances between amino acids because the importance of errors depends also on the frequency of the different codons. Here I show that when codon usage is taken into account, the degree of error minimization of the standard code may be dramatically reduced, and shifting to alternative codes often increases the degree of error minimization. This is especially true with a high CG content, which was probably the case during the origin of the code. I also show that the frequency of codes that perform better than the standard code, in terms of relative efficiency, is much higher in the neighborhood of the standard code itself, even when not considering codon usage bias; therefore alternative codes that differ only slightly from the standard code are more likely to evolve than some previous analyses suggested. My conclusions are that the standard genetic code is far from being an optimum with respect to error minimization and must have arisen for reasons other than error minimization.[Reviewing Editor: Martin Kreitman]     

On the Evolution of Redundancy in Genetic Codes

We simulate a deterministic population genetic model for the coevolution of genetic codes and protein-coding genes. We use very simple assumptions about translation, mutation, and protein fitness to calculate mutation-selection equilibria of codon frequencies and fitness in a large asexual population with a given genetic code. We then compute the fitnesses of altered genetic codes that compete to invade the population by translating its genes with higher fitness. Codes and genes coevolve in a succession of stages, alternating between genetic equilibration and code invasion, from an initial wholly ambiguous coding state to a diversified frozen coding state. Our simulations almost always resulted in partially redundant frozen genetic codes. Also, the range of simulated physicochemical properties among encoded amino acids in frozen codes was always less than maximal. These results did not require the assumption of historical constraints on the number and type of amino acids available to codes nor on the complexity of proteins, stereochemical constraints on the translational apparatus, nor mechanistic constraints on genetic code change. Both the extent and timing of amino-acid diversification in genetic codes were strongly affected by the message mutation rate and strength of missense selection. Our results suggest that various omnipresent phenomena that distribute codons over sites with different selective requirements—such as the persistence of nonsynonymous mutations at equilibrium, the positive selection of the same codon in different types of sites, and translational ambiguity—predispose the evolution of redundancy and of reduced amino acid diversity in genetic codes. Received: 21 December 2000 / Accepted: 12 March 2001     

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.     

The most probable number of blocks for the partitions of the set of codons could have determined the number of standard amino acids

Given a genetic code formed by 64 codons, we calculate the number of partitions of the set of encoding amino acid codons. When there are 0-3 stop codons, the results indicate that the most probable number of partitions is 19 and/or 20. Then, assuming that in the early evolution the genetic code could have had random variations, we suggest that the most probable number of partitions of the set of encoding amino acid codons determined the actual number 20 of standard amino acids.     

Emergence of a Code in the Polymerization of Amino Acids along RNA Templates

The origin of the genetic code in the context of an RNA world is a major problem in the field of biophysical chemistry. In this paper, we describe how the polymerization of amino acids along RNA templates can be affected by the properties of both molecules. Considering a system without enzymes, in which the tRNAs (the translation adaptors) are not loaded selectively with amino acids, we show that an elementary translation governed by a Michaelis-Menten type of kinetics can follow different polymerization regimes: random polymerization, homopolymerization and coded polymerization. The regime under which the system is running is set by the relative concentrations of the amino acids and the kinetic constants involved. We point out that the coding regime can naturally occur under prebiotic conditions. It generates partially coded proteins through a mechanism which is remarkably robust against non-specific interactions (mismatches) between the adaptors and the RNA template. Features of the genetic code support the existence of this early translation system.     

Logic of the genetic code: Conservation of long-range interactions among amino acids as a prime factor

Any statement on the optimality of the existing code ought to imply that this code is ideal for conserving a certain hierarchy of properties while implying that other codes may have been better suited for conservation of other hierarchies of properties. We have evaluated the capability of mutations in the genetic code to convert one amino acid into another in relation to the consequent changes in physical properties of those amino acids. A rather surprising result emerging from this analysis is that the genetic code conserves long-range interactions among amino acids and not their short-range stereochemical attributes. This observation, based directly on the genetic code itself and the physical properties of the 20 amino acids, lends credibility to the idea that the genetic code has not originated by a frozen accident (the null hypothesis rejected by these studies) nor are stereochemical attributes particularly useful in our understanding of what makes the genetic code ‘tick’. While the argument that replacement of, say, an aspartate by a glutamate is less damaging than replacement by arginine makes sense, in order to subject such statements to rigorous statistical tests it is essential to define what constitutes a random sample for the genetic code. The present investigation describes one possible specification. In addition to obvious statistical considerations of testing hypotheses, this procedure points to the more exciting notion that alternative codes may have existed.