A Darwinian evolutionary system. II. Experiments on protein evolution and evolutionary aspects of the genetic code

On the basis of the principles of Darwinian evolutionary systems laid out earlier, a system is constructed which simulates protein evolution. Two types of situations are studied: adaptation to highest possible alkalinity (“alkalinity model”), and adaptation to an arbitrary sequence (“sequence model”). No restrictions in adaptability were found for the (comparably special) alkalinity model, but severe restrictions were found for the sequence model. Approximately 15% of all possible evolutionary paths from one amino acid to another turned out to be impossible, in the sense that no chain of intermediate steps exists which leads to a higher fitness level, in this case an increased chemical similarity of the two amino acids.The evolutionary efficiency of the natural genetic code was also investigated by comparing it with two classes of artificially constructed codes: semi-random and random codes. It was found that the natural code possesses the highest evolutionary efficiency, given by the mean number of generations required to reach identity in 5 of 10 sites, if originally all 10 were different. Closest to the natural code in evolutionary efficiency were the random codes, next, the semi-random codes.This pattern could be explained by a theoretical measure, called the code efficiency. The most important component of the code efficiency is the percentage of impossible paths. The natural code is far superior to the other code types in this respect. However, the random codes are superior to the natural code with respect to the mean shortest path length of the possible paths, the other important component of the code efficiency.It is suggested that the natural genetic code might have arisen from a semi-random code during a process of optimizing several of its features, of which the evolutionary efficiency is a very important one; or that the natural code is the most efficient edition of a large variety of semi-random codes which originated by chance.     

Load minimization of the genetic code: history does not explain the pattern

The average effect of errors acting on a genetic code (the change in amino-acid meaning resulting from point mutation and mistranslation) may be quantified as its ''load''. The natural genetic code shows a clear property of minimizing this load when compared against randomly generated variant codes. Two hypotheses may be considered to explain this property. First, it is possible that the natural code is the result of selection to minimize this load. Second, it is possible that the property is an historical artefact. It has previously been reported that amino acids that have been assigned to codons starting with the same base come from the same biosynthetic pathway. This probably reflects the manner in which the code evolved from a simpler code, and says more about the physicochemical mechanisms of code assembly than about selection. The apparent load minimization of the code may therefore follow as a consequence of the fact that the code could not have evolved any other way than to allow biochemically related amino acids to have related codons. Here then, we ask whether this ''historical'' force alone can explain the efficiency of the natural code in minimizing the effects of error. We therefore compare the error-minimizing ability of the natural code with that of alternative codes which, rather than being a random selection, are restricted such that amino acids from the same biochemical pathway all share the same first base. We find that although on average the restricted set of codes show a slightly higher efficiency than random ones, the real code remains extremely efficient relative to this subset P = 0.0003. This indicates that for the most part historical features do not explain the load- minimization property of the natural code. The importance of selection is further supported by the finding that the natural code''s efficiency improves relative to that of historically related codes after allowance is made for realistic mutational and mistranslational biases. Once mistranslational biases have been considered, fewer than four per 100,000 alternative codes are better than the natural code.     

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.     

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.     

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     

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.     

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.     

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]     

The Historical Factor: The Biosynthetic Relationships Between Amino Acids and Their Physicochemical Properties in the Origin of the Genetic Code

Two forces are in general, hypothesized to have influenced the origin of the organization of the genetic code: the physicochemical properties of amino acids and their biosynthetic relationships. In view of this, we have considered a model incorporating these two forces. In particular, we have studied the optimization level of the physicochemical properties of amino acids in the set of amino acid permutation codes that respects the biosynthetic relationships between amino acids. Where the properties of amino acids are represented by polarity and molecular volume we obtain indetermination percentages in the organization of the genetic code of approximately 40%. This indicates that the contingent factor played a significant role in structuring the genetic code. Furthermore, this result is in agreement with the genetic code coevolution hypothesis, which attributes a merely ancillary role to the properties of amino acids while it suggests that it was their biosynthetic relationships that organized the code. Furthermore, this result does not favor the stereochemical models proposed to explain the origin of the genetic code. On the other hand, where the properties of amino acids are represented by polarity alone, we obtain an indetermination percentage of at least 21.5%. This might suggest that the polarity distances played an important role and would therefore provide evidence in favor of the physicochemical hypothesis of genetic code origin. Although, overall, the analysis might have given stronger support to the latter hypothesis, this did not actually occur. The results are therefore discussed in the context of the different theories proposed to explain the origin of the genetic code. Received: 10 September 1996 / Accepted: 3 March 1997     

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.     

Selection, history and chemistry: the three faces of the genetic code.

The genetic code might be a historical accident that was fixed in the last common ancestor of modern organisms. 'Adaptive', 'historical' and 'chemical' arguments, however, challenge such a 'frozen accident' model. These arguments propose that the current code is somehow optimal, reflects the expansion of a more primitive code to include more amino acids, or is a consequence of direct chemical interactions between RNA and amino acids, respectively. Such models are not mutually exclusive, however. They can be reconciled by an evolutionary model whereby stereochemical interactions shaped the initial code, which subsequently expanded through biosynthetic modification of encoded amino acids and, finally, was optimized through codon reassignment. Alternatively, all three forces might have acted in concert to assign the 20 'natural' amino acids to their present positions in the genetic code.     

A quantitative measure of error minimization in the genetic code

Summary We have calculated the average effect of changing a codon by a single base for all possible single-base changes in the genetic code and for changes in the first, second, and third codon positions separately. Such values were calculated for an amino acid's polar requirement, hydropathy, molecular volume, and isoelectric point. For each attribute the average effect of single-base changes was also calculated for a large number of randomly generated codes that retained the same level of redundancy as the natural code. Amino acids whose codons differed by a single base in the first and third codon positions were very similar with respect to polar requirement and hydropathy. The major differences between amino acids were specified by the second codon position. Codons with U in the second position are hydrophobic, whereas most codons with A in the second position are hydrophilic. This accounts for the observation of complementary hydropathy. Single-base changes in the natural code had a smaller average effect on polar requirement than all but 0.02% of random codes. This result is most easily explained by selection to minimize deleterious effects of translation errors during the early evolution of the code.     

Short Barcodes for Next Generation Sequencing

We consider the design and evaluation of short barcodes, with a length between six and eight nucleotides, used for parallel sequencing on platforms where substitution errors dominate. Such codes should have not only good error correction properties but also the code words should fulfil certain biological constraints (experimental parameters). We compare published barcodes with codes obtained by two new constructions methods, one based on the currently best known linear codes and a simple randomized construction method. The evaluation done is with respect to the error correction capabilities, barcode size and their experimental parameters and fundamental bounds on the code size and their distance properties. We provide a list of codes for lengths between six and eight nucleotides, where for length eight, two substitution errors can be corrected. In fact, no code with larger minimum distance can exist.     

A hardware interpretation of the evolution of the genetic code

A quantitative rationale for the evolution of the genetic code is developed considering the principle of minimal hardware. This principle defines an optimal code as one that minimizes for a given amount of information encoded, the product of the number of physical devices used by the average complexity of each device. By identifying the number of different amino acids, number of nucleotide positions per codon and number of base types that can occupy each such position with, respectively, the amount of information, number of devices and the complexity, we show that optimal codes occur for 3, 7 and 20 amino acids with codons having a single, two and three base positions per codon, respectively. The advantage of a code of exactly 4 symbols is deduced, as well as a plausible evolutionary pathway from a code of doublets to triplets. The present day code of 20 amino acids encoded by 64 codons is shown to be the most optimal in an absolute sense. Using a tetraplet code further evolution to a code in which there would be 55 amino acids is in principle possible, but such a code would deviate slightly more than the present day code from the minimal hardware configuration. The change from a triplet code to a tetraplet code would occur at about 32 amino acids. Our conclusions are independent of, but consistent with, the observed physico-chemical properties of the amino acids and codon structures. These correlations could have evolved within the constrains imposed by the minimal hardware principle.     

Physicochemical Optimization in the Genetic Code Origin as the Number of Codified Amino Acids Increases

We have assumed that the coevolution theory of genetic code origin (Wong JT, Proc Natl Acad Sci USA 72:1909–1912, 1975) is essentially correct. This theory makes it possible to identify at least 10 evolutionary stages through which genetic code organization might have passed prior to reaching its current form. The calculation of the minimization level of all these evolutionary stages leads to the following conclusions. (1) The minimization percentages increased linearly with the number of amino acids codified in the codes of the various evolutionary stages when only the sense changes are considered in the analysis. This seems to favor the physicochemical theory of genetic code origin even if, as discussed in the paper, this observation is also compatible with the coevolution theory. (2) For the first seven evolutionary stages of the genetic code, this trend is less clear and indeed is inverted when we consider the global optimisation of the codes due to both sense changes and synonymous changes. This inverse correlation between minimization percentages and the number of amino acids codified in the codes of the intermediate stages seems to favor neither the physicochemical nor the stereochemical theories of genetic code origin, as it is in the early and intermediate stages of code development that these theories would expect minimization to have played a crucial role, and this does not seem to be the case. However, these results are in agreement with the coevolution theory, which attributes a role to the physicochemical properties of amino acids that, while important, is nevertheless subordinate to the mechanism which concedes codons from the precursor amino acids to the product amino acids as the primary factor determining the evolutionary structuring of the genetic code. The results are therefore discussed in the context of the various theories proposed to explain genetic code origin. Received: 25 October 1998 / Accepted: 19 February 1999     

Dwell time symmetry in random walks and molecular motors

The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result, theoretical results for cycle completion in enzyme kinetics do not apply to stepping data. To allow correct parameter estimation, and to guide data analysis and experiment design, a theoretical treatment is needed that takes this observation into account. In this article, we model the distribution of dwell times and number of forward and backward steps using first passage processes, based on the assumption that forward and backward steps correspond to different directions of the same transition. We extend recent results for systems with a single cycle and consider the full dwell time distributions as well as models with multiple pathways, detectable substeps, and detachments. Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle. We demonstrate our results by analyzing recent stepping data for a bacterial flagellar motor, and discuss the implications for the efficiency and reversibility of the force-generating subunits.     

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.     

A Novel Theory on the Origin of the Genetic Code: A GNC-SNS Hypothesis

We have previously proposed an SNS hypothesis on the origin of the genetic code (Ikehara and Yoshida 1998). The hypothesis predicts that the universal genetic code originated from the SNS code composed of 16 codons and 10 amino acids (S and N mean G or C and either of four bases, respectively). But, it must have been very difficult to create the SNS code at one stroke in the beginning. Therefore, we searched for a simpler code than the SNS code, which could still encode water-soluble globular proteins with appropriate three-dimensional structures at a high probability using four conditions for globular protein formation (hydropathy, α-helix, β-sheet, and β-turn formations). Four amino acids (Gly [G], Ala [A], Asp [D], and Val [V]) encoded by the GNC code satisfied the four structural conditions well, but other codes in rows and columns in the universal genetic code table do not, except for the GNG code, a slightly modified form of the GNC code. Three three-amino acid systems ([D], Leu and Tyr; [D], Tyr and Met; Glu, Pro and Ile) also satisfied the above four conditions. But, some amino acids in the three systems are far more complex than those encoded by the GNC code. In addition, the amino acids in the three-amino acid systems are scattered in the universal genetic code table. Thus, we concluded that the universal genetic code originated not from a three-amino acid system but from a four-amino acid system, the GNC code encoding [GADV]-proteins, as the most primitive genetic code. Received: 11 June 2001 / Accepted: 11 October 2001