The role of crossover operator in evolutionary-based approach to the problem of genetic code optimization

Theories of the origin of the genetic code: Strong corroboration for the coevolution theory

I analyzed all the theories and models of the origin of the genetic code, and over the years, I have considered the main suggestions that could explain this origin. The conclusion of this analysis is that the coevolution theory of the origin of the genetic code is the theory that best captures the majority of observations concerning the organization of the genetic code. In other words, the biosynthetic relationships between amino acids would have heavily influenced the origin of the organization of the genetic code, as supported by the coevolution theory. Instead, the presence in the genetic code of physicochemical properties of amino acids, which have also been linked to the physicochemical properties of anticodons or codons or bases by stereochemical and physicochemical theories, would simply be the result of natural selection. More explicitly, I maintain that these correlations between codons, anticodons or bases and amino acids are in fact the result not of a real correlation between amino acids and codons, for example, but are only the effect of the intervention of natural selection. Specifically, in the genetic code table we expect, for example, that the most similar codons - that is, those that differ by only one base - will have more similar physicochemical properties. Therefore, the 64 codons of the genetic code table ordered in a certain way would also represent an ordering of some of their physicochemical properties. Now, a study aimed at clarifying which physicochemical property of amino acids has influenced the allocation of amino acids in the genetic code has established that the partition energy of amino acids has played a role decisive in this. Indeed, under some conditions, the genetic code was found to be approximately 98% optimized on its columns. In this same work, it was shown that this was most likely the result of the action of natural selection. If natural selection had truly allocated the amino acids in the genetic code in such a way that similar amino acids also have similar codons - this, not through a mechanism of physicochemical interaction between, for example, codons and amino acids - then it might turn out that even different physicochemical properties of codons (or anticodons or bases) show some correlation with the physicochemical properties of amino acids, simply because the partition energy of amino acids is correlated with other physicochemical properties of amino acids. It is very likely that this would inevitably lead to a correlation between codons (or anticodons or bases) and amino acids. In other words, since the codons (anticodons or bases) are ordered in the genetic code, that is to say, some of their physicochemical properties should also be ordered by a similar order, and given that the amino acids would also appear to have been ordered in the genetic code by selection natural, then it should inevitably turn out that there is a correlation between, for example, the hydrophobicity of anticodons and that of amino acids. Instead, the intervention of natural selection in organizing the genetic code would appear to be highly compatible with the main mechanism of structuring the genetic code as supported by the coevolution theory. This would make the coevolution theory the only plausible explanation for the origin of the genetic code.

Rare-event sampling analysis uncovers the fitness landscape of the genetic code

The genetic code refers to a rule that maps 64 codons to 20 amino acids. Nearly all organisms, with few exceptions, share the same genetic code, the standard genetic code (SGC). While it remains unclear why this universal code has arisen and been maintained during evolution, it may have been preserved under selection pressure. Theoretical studies comparing the SGC and numerically created hypothetical random genetic codes have suggested that the SGC has been subject to strong selection pressure for being robust against translation errors. However, these prior studies have searched for random genetic codes in only a small subspace of the possible code space due to limitations in computation time. Thus, how the genetic code has evolved, and the characteristics of the genetic code fitness landscape, remain unclear. By applying multicanonical Monte Carlo, an efficient rare-event sampling method, we efficiently sampled random codes from a much broader random ensemble of genetic codes than in previous studies, estimating that only one out of every 1020 random codes is more robust than the SGC. This estimate is significantly smaller than the previous estimate, one in a million. We also characterized the fitness landscape of the genetic code that has four major fitness peaks, one of which includes the SGC. Furthermore, genetic algorithm analysis revealed that evolution under such a multi-peaked fitness landscape could be strongly biased toward a narrow peak, in an evolutionary path-dependent manner.

The Influence of the Selection at the Amino Acid Level on Synonymous Codon Usage from the Viewpoint of Alternative Genetic Codes

Synonymous codon usage can be influenced by mutations and/or selection, e.g., for speed of protein translation and correct folding. However, this codon bias can also be affected by a general selection at the amino acid level due to differences in the acceptance of the loss and generation of these codons. To assess the importance of this effect, we constructed a mutation-selection model model, in which we generated almost 90,000 stationary nucleotide distributions produced by mutational processes and applied a selection based on differences in physicochemical properties of amino acids. Under these conditions, we calculated the usage of fourfold degenerated (4FD) codons and compared it with the usage characteristic of the pure mutations. We considered both the standard genetic code (SGC) and alternative genetic codes (AGCs). The analyses showed that a majority of AGCs produced a greater 4FD codon bias than the SGC. The mutations producing more thymine or adenine than guanine and cytosine increased the differences in usage. On the other hand, the mutational pressures generating a lot of cytosine or guanine with a low content of adenine and thymine decreased this bias because the nucleotide content of most 4FD codons stayed in the compositional equilibrium with these pressures. The comparison of the theoretical results with those for real protein coding sequences showed that the influence of selection at the amino acid level on the synonymous codon usage cannot be neglected. The analyses indicate that the effect of amino acid selection cannot be disregarded and that it can interfere with other selection factors influencing codon usage, especially in AT-rich genomes, in which AGCs are usually used.

The structure of the genetic code as an optimal graph clustering problem

The standard genetic code (SGC) is the set of rules by which genetic information is translated into proteins, from codons, i.e. triplets of nucleotides, to amino acids. The questions about the origin and the main factor responsible for the present structure of the code are still under a hot debate. Various methodologies have been used to study the features of the code and assess the level of its potential optimality. Here, we introduced a new general approach to evaluate the quality of the genetic code structure. This methodology comes from graph theory and allows us to describe new properties of the genetic code in terms of conductance. This parameter measures the robustness of codon groups against the potential changes in translation of the protein-coding sequences generated by single nucleotide substitutions. We described the genetic code as a partition of an undirected and unweighted graph, which makes the model general and universal. Using this approach, we showed that the structure of the genetic code is a solution to the graph clustering problem. We presented and discussed the structure of the codes that are optimal according to the conductance. Despite the fact that the standard genetic code is far from being optimal according to the conductance, its structure is characterised by many codon groups reaching the minimum conductance for their size. The SGC represents most likely a local minimum in terms of errors occurring in protein-coding sequences and their translation.

Model of Genetic Code Structure Evolution under Various Types of Codon Reading

The standard genetic code (SGC) is a set of rules according to which 64 codons are assigned to 20 canonical amino acids and stop coding signal. As a consequence, the SGC is redundant because there is a greater number of codons than the number of encoded labels. This redundancy implies the existence of codons that encode the same genetic information. The size and organization of such synonymous codon blocks are important characteristics of the SGC structure whose evolution is still unclear. Therefore, we studied possible evolutionary mechanisms of the codon block structure. We conducted computer simulations assuming that coding systems at early stages of the SGC evolution were sets of ambiguous codon assignments with high entropy. We included three types of reading systems characterized by different inaccuracy and pattern of codon recognition. In contrast to the previous study, we allowed for evolution of the reading systems and their competition. The simulations performed under minimization of translational errors and reduction of coding ambiguity produced the coding system resistant to these errors. The reading system similar to that present in the SGC dominated the others very quickly. The survived system was also characterized by low entropy and possessed properties similar to that in the SGC. Our simulation show that the unambiguous SGC could emerged from a code with a lower level of ambiguity and the number of tRNAs increased during the evolution.

Average and Standard Deviation of the Error Function for Random Genetic Codes with Standard Stop Codons

The origin of the genetic code has been attributed in part to an accidental assignment of codons to amino acids. Although several lines of evidence indicate the subsequent expansion and improvement of the genetic code, the hypothesis of Francis Crick concerning a frozen accident occurring at the early stage of genetic code evolution is still widely accepted. Considering Crick's hypothesis, mathematical descriptions of hypothetical scenarios involving a huge number of possible coexisting random genetic codes could be very important to explain the origin and evolution of a selected genetic code. This work aims to contribute in this regard, that is, it provides a theoretical framework in which statistical parameters of error functions are calculated. Given a genetic code and an amino acid property, the functional code robustness is estimated by means of a known error function. In this work, using analytical calculations, general expressions for the average and standard deviation of the error function distributions of completely random codes with standard stop codons were obtained. As a possible biological application of these results, any set of amino acids and any pure or mixed amino acid properties can be used in the calculations, such that, in case of having to select a set of amino acids to create a genetic code, possible advantages of natural selection of the genetic codes could be discussed.

On the Origin of Frameshift-Robustness of the Standard Genetic Code

The standard genetic code (SGC) has been extensively analyzed for the biological ramifications of its nonrandom structure. For instance, mismatch errors due to point mutation or mistranslation have an overall smaller effect on the amino acid polar requirement under the SGC than under random genetic codes (RGCs). A similar observation was recently made for frameshift errors, prompting the assertion that the SGC has been shaped by natural selection for frameshift-robustness-conservation of certain amino acid properties upon a frameshift mutation or translational frameshift. However, frameshift-robustness confers no benefit because frameshifts usually create premature stop codons that cause nonsense-mediated mRNA decay or production of nonfunctional truncated proteins. We here propose that the frameshift-robustness of the SGC is a byproduct of its mismatch-robustness. Of 564 amino acid properties considered, the SGC exhibits mismatch-robustness in 93-133 properties and frameshift-robustness in 55 properties, respectively, and that the latter is largely a subset of the former. For each of the 564 real and 564 randomly constructed fake properties of amino acids, there is a positive correlation between mismatch-robustness and frameshift-robustness across one million RGCs; this correlation arises because most amino acid changes resulting from a frameshift are also achievable by a mismatch error. Importantly, the SGC does not show significantly higher frameshift-robustness in any of the 55 properties than RGCs of comparable mismatch-robustness. These findings support that the frameshift-robustness of the SGC need not originate through direct selection and can instead be a site effect of its mismatch-robustness.

Models of genetic code structure evolution with variable number of coded labels

It is assumed that at the early stage of cell evolution its translation machinery was characterized by high noise, i.e. ambiguous assignment of codons to amino acids in the genetic code, which initially encoded only few amino acids. Next, during its evolution new amino acids were added to this code. Taking into account this facts, we investigated theoretical models of genetic code's structure, which evolved from a set of ambiguous codons assignments into a coding system with a low level of uncertainty. We considered three types of translational inaccuracies assuming a different number of fixed codon positions. We applied a modified version of evolutionary algorithm for finding the genetic codes that the most effectively reduced the initial uncertainty in the assignment of codons to encoded labels, i.e. amino acids and a stop translation signal. We examined codes with the number of labels from four to 22. Our results indicated that the quality of genetic code structure is strongly dependent on the number of encoded labels as well as the type of translational mechanism. The more strict assignments of codon to the labels was preferred by the codes encoding more number of labels. The results showed that a smaller degeneracy of codes evolved from a more tolerant coding with the stepwise addition of coded amino acids to the genetic code. The distribution of codon groups in the standard genetic code corresponds well to the translation model assuming two fixed codon positions, whereas the six-codon groups can be relics form previous stages of evolution when the code characterized by a greater uncertainty.

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.

Basic principles of the genetic code extension

Compounds including non-canonical amino acids (ncAAs) or other artificially designed molecules can find a lot of applications in medicine, industry and biotechnology. They can be produced thanks to the modification or extension of the standard genetic code (SGC). Such peptides or proteins including the ncAAs can be constantly delivered in a stable way by organisms with the customized genetic code. Among several methods of engineering the code, using non-canonical base pairs is especially promising, because it enables generating many new codons, which can be used to encode any new amino acid. Since even one pair of new bases can extend the SGC up to 216 codons generated by a six-letter nucleotide alphabet, the extension of the SGC can be achieved in many ways. Here, we proposed a stepwise procedure of the SGC extension with one pair of non-canonical bases to minimize the consequences of point mutations. We reported relationships between codons in the framework of graph theory. All 216 codons were represented as nodes of the graph, whereas its edges were induced by all possible single nucleotide mutations occurring between codons. Therefore, every set of canonical and newly added codons induces a specific subgraph. We characterized the properties of the induced subgraphs generated by selected sets of codons. Thanks to that, we were able to describe a procedure for incremental addition of the set of meaningful codons up to the full coding system consisting of three pairs of bases. The procedure of gradual extension of the SGC makes the whole system robust to changing genetic information due to mutations and is compatible with the views assuming that codons and amino acids were added successively to the primordial SGC, which evolved minimizing harmful consequences of mutations or mistranslations of encoded proteins.

Genetic codes optimized as a traveling salesman problem

The Standard Genetic Code (SGC) is robust to mutational errors such that frequently occurring mutations minimally alter the physio-chemistry of amino acids. The apparent correlation between the evolutionary distances among codons and the physio-chemical distances among their cognate amino acids suggests an early co-diversification between the codons and amino acids. Here we formulated the co-minimization of evolutionary distances between codons and physio-chemical distances between amino acids as a Traveling Salesman Problem (TSP) and solved it with a Hopfield neural network. In this unsupervised learning algorithm, macromolecules (e.g., tRNAs and aminoacyl-tRNA synthetases) associating codons with amino acids were considered biological analogs of Hopfield neurons associating "tour cities" with "tour positions". The Hopfield network efficiently yielded an abundance of genetic codes that were more error-minimizing than SGC and could thus be used to design artificial genetic codes. We further argue that as a self-optimization algorithm, the Hopfield neural network provides a model of origin of SGC and other adaptive molecular systems through evolutionary learning.

The influence of different types of translational inaccuracies on the genetic code structure

BACKGROUND

The standard genetic code is a recipe for assigning unambiguously 21 labels, i.e. amino acids and stop translation signal, to 64 codons. However, at early stages of the translational machinery development, the codons did not have to be read unambiguously and the early genetic codes could have contained some ambiguous assignments of codons to amino acids. Therefore, the goal of this work was to obtain the genetic code structures which could have evolved assuming different types of inaccuracy of the translational machinery starting from unambiguous assignments of codons to amino acids.

RESULTS

We developed a theoretical model assuming that the level of uncertainty of codon assignments can gradually decrease during the simulations. Since it is postulated that the standard code has evolved to be robust against point mutations and mistranslations, we developed three simulation scenarios assuming that such errors can influence one, two or three codon positions. The simulated codes were selected using the evolutionary algorithm methodology to decrease coding ambiguity and increase their robustness against mistranslation.

CONCLUSIONS

The results indicate that the typical codon block structure of the genetic code could have evolved to decrease the ambiguity of amino acid to codon assignments and to increase the fidelity of reading the genetic information. However, the robustness to errors was not the decisive factor that influenced the genetic code evolution because it is possible to find theoretical codes that minimize the reading errors better than the standard genetic code.

The optimality of the standard genetic code assessed by an eight-objective evolutionary algorithm

BACKGROUND

The standard genetic code (SGC) is a unique set of rules which assign amino acids to codons. Similar amino acids tend to have similar codons indicating that the code evolved to minimize the costs of amino acid replacements in proteins, caused by mutations or translational errors. However, if such optimization in fact occurred, many different properties of amino acids must have been taken into account during the code evolution. Therefore, this problem can be reformulated as a multi-objective optimization task, in which the selection constraints are represented by measures based on various amino acid properties.

RESULTS

To study the optimality of the SGC we applied a multi-objective evolutionary algorithm and we used the representatives of eight clusters, which grouped over 500 indices describing various physicochemical properties of amino acids. Thanks to that we avoided an arbitrary choice of amino acid features as optimization criteria. As a consequence, we were able to conduct a more general study on the properties of the SGC than the ones presented so far in other papers on this topic. We considered two models of the genetic code, one preserving the characteristic codon blocks structure of the SGC and the other without this restriction. The results revealed that the SGC could be significantly improved in terms of error minimization, hereby it is not fully optimized. Its structure differs significantly from the structure of the codes optimized to minimize the costs of amino acid replacements. On the other hand, using newly defined quality measures that placed the SGC in the global space of theoretical genetic codes, we showed that the SGC is definitely closer to the codes that minimize the costs of amino acids replacements than those maximizing them.

CONCLUSIONS

The standard genetic code represents most likely only partially optimized systems, which emerged under the influence of many different factors. Our findings can be useful to researchers involved in modifying the genetic code of the living organisms and designing artificial ones.

Optimization of the standard genetic code according to three codon positions using an evolutionary algorithm

Many biological systems are typically examined from the point of view of adaptation to certain conditions or requirements. One such system is the standard genetic code (SGC), which generally minimizes the cost of amino acid replacements resulting from mutations or mistranslations. However, no full consensus has been reached on the factors that caused the evolution of this feature. One of the hypotheses suggests that code optimality was directly selected as an advantage to preserve information about encoded proteins. An important feature that should be considered when studying the SGC is the different roles of the three codon positions. Therefore, we investigated the robustness of this code regarding the cost of amino acid replacements resulting from substitutions in these positions separately and the sum of these costs. We applied a modified evolutionary algorithm and included four models of the genetic code assuming various restrictions on its structure. The SGC was compared both with the codes that minimize the objective function and those that maximize it. This approach allowed us to place the SGC in the global space of possible codes, which is a more appropriate and unbiased comparison than that with randomly generated codes because they are characterized by relatively uniform amino acid assignments to codons. The SGC appeared to be well optimized at the global scale, but its individual positions were not fully optimized because there were codes that were optimized for only one codon position and simultaneously outperformed the SGC at the other positions. We also found that different code structures may lead to the same optimality and that random codes can show a tendency to minimize costs under some of the genetic code models. Our results suggest that the optimality of SGC could be a by-product of other processes.

Bijective codon transformations show genetic code symmetries centered on cytosine's coding properties

Homology of some RNAs with template DNA requires systematic exchanges between nucleotides. Such exchanges produce 'swinger' RNA along 23 bijective transformations (nine symmetric, X ↔ Y; and 14 asymmetric, X → Y → Z → X, for example A ↔ C and A → C → G → A, respectively). Here, analyses compare amino acids coded by swinger-transformed codons to those coded by untransformed codons, defining coding invariance after transformations. Swinger transformations cluster according to coding invariance in four groups characterized by transformations into cytosine (C = C, T → C, A → C, and G → C). C's central mutational coding role shows that swinger transformations constrained genetic code genesis. Coding invariance post-transformations correlate positively/negatively with mitochondrial swinger transcription/lepidosaurian body temperature. Presumably, low/high temperatures stabilize/revert rare swinger polymerization modes, producing long swinger sequences/point mutations, respectively. Coding invariance after swinger transformations might compensate effects of swinger polymerizations in species with low body temperatures. Hypothetically, swinger transcription increased coding potential of RNA self-replicating protolife systems under heating/cooling cycles.

Genetic Code Optimization for Cotranslational Protein Folding: Codon Directional Asymmetry Correlates with Antiparallel Betasheets, tRNA Synthetase Classes

A new codon property, codon directional asymmetry in nucleotide content (CDA), reveals a biologically meaningful genetic code dimension: palindromic codons (first and last nucleotides identical, codon structure XZX) are symmetric (CDA = 0), codons with structures ZXX/XXZ are 5'/3' asymmetric (CDA = - 1/1; CDA = - 0.5/0.5 if Z and X are both purines or both pyrimidines, assigning negative/positive (-/+) signs is an arbitrary convention). Negative/positive CDAs associate with (a) Fujimoto's tetrahedral codon stereo-table; (b) tRNA synthetase class I/II (aminoacylate the 2'/3' hydroxyl group of the tRNA's last ribose, respectively); and (c) high/low antiparallel (not parallel) betasheet conformation parameters. Preliminary results suggest CDA-whole organism associations (body temperature, developmental stability, lifespan). Presumably, CDA impacts spatial kinetics of codon-anticodon interactions, affecting cotranslational protein folding. Some synonymous codons have opposite CDA sign (alanine, leucine, serine, and valine), putatively explaining how synonymous mutations sometimes affect protein function. Correlations between CDA and tRNA synthetase classes are weaker than between CDA and antiparallel betasheet conformation parameters. This effect is stronger for mitochondrial genetic codes, and potentially drives mitochondrial codon-amino acid reassignments. CDA reveals information ruling nucleotide-protein relations embedded in reversed (not reverse-complement) sequences (5'-ZXX-3'/5'-XXZ-3').

Optimization of amino acid replacement costs by mutational pressure in bacterial genomes

Mutations are considered a spontaneous and random process, which is important component of evolution because it generates genetic variation. On the other hand, mutations are deleterious leading to non-functional genes and energetically costly repairs. Therefore, one can expect that the mutational pressure is optimized to simultaneously generate genetic diversity and preserve genetic information. To check if empirical mutational pressures are optimized in these ways, we compared matrices of nucleotide mutation rates derived from bacterial genomes with their best possible alternatives that minimized or maximized costs of amino acid replacements associated with differences in their physicochemical properties (e.g. hydropathy and polarity). It should be noted that the studied empirical nucleotide substitution matrices and the costs of amino acid replacements are independent because these matrices were derived from sites free of selection on amino acid properties and the amino acid costs assumed only amino acid physicochemical properties without any information about mutation at the nucleotide level. Obtained results indicate that the empirical mutational matrices show a tendency to minimize costs of amino acid replacements. It implies that bacterial mutational pressures can evolve to decrease consequences of amino acid substitutions. However, the optimization is not full, which enables generation of some genetic variability.

Inclusion of the fitness sharing technique in an evolutionary algorithm to analyze the fitness landscape of the genetic code adaptability

Background

The canonical code, although prevailing in complex genomes, is not universal. It was shown the canonical genetic code superior robustness compared to random codes, but it is not clearly determined how it evolved towards its current form.

The error minimization theory considers the minimization of point mutation adverse effect as the main selection factor in the evolution of the code. We have used simulated evolution in a computer to search for optimized codes, which helps to obtain information about the optimization level of the canonical code in its evolution.

A genetic algorithm searches for efficient codes in a fitness landscape that corresponds with the adaptability of possible hypothetical genetic codes. The lower the effects of errors or mutations in the codon bases of a hypothetical code, the more efficient or optimal is that code.

The inclusion of the fitness sharing technique in the evolutionary algorithm allows the extent to which the canonical genetic code is in an area corresponding to a deep local minimum to be easily determined, even in the high dimensional spaces considered.

Results

The analyses show that the canonical code is not in a deep local minimum and that the fitness landscape is not a multimodal fitness landscape with deep and separated peaks. Moreover, the canonical code is clearly far away from the areas of higher fitness in the landscape.

Conclusions

Given the non-presence of deep local minima in the landscape, although the code could evolve and different forces could shape its structure, the fitness landscape nature considered in the error minimization theory does not explain why the canonical code ended its evolution in a location which is not an area of a localized deep minimum of the huge fitness landscape.