Study of the genetic code adaptability by means of a genetic algorithm

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.

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.

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.

A multiobjective approach to the genetic code adaptability problem

BACKGROUND

The organization of the canonical code has intrigued researches since it was first described. If we consider all codes mapping the 64 codes into 20 amino acids and one stop codon, there are more than 1.51×10(84) possible genetic codes. The main question related to the organization of the genetic code is why exactly the canonical code was selected among this huge number of possible genetic codes. Many researchers argue that the organization of the canonical code is a product of natural selection and that the code's robustness against mutations would support this hypothesis. In order to investigate the natural selection hypothesis, some researches employ optimization algorithms to identify regions of the genetic code space where best codes, according to a given evaluation function, can be found (engineering approach). The optimization process uses only one objective to evaluate the codes, generally based on the robustness for an amino acid property. Only one objective is also employed in the statistical approach for the comparison of the canonical code with random codes. We propose a multiobjective approach where two or more objectives are considered simultaneously to evaluate the genetic codes.

RESULTS

In order to test our hypothesis that the multiobjective approach is useful for the analysis of the genetic code adaptability, we implemented a multiobjective optimization algorithm where two objectives are simultaneously optimized. Using as objectives the robustness against mutation with the amino acids properties polar requirement (objective 1) and robustness with respect to hydropathy index or molecular volume (objective 2), we found solutions closer to the canonical genetic code in terms of robustness, when compared with the results using only one objective reported by other authors.

CONCLUSIONS

Using more objectives, more optimal solutions are obtained and, as a consequence, more information can be used to investigate the adaptability of the genetic code. The multiobjective approach is also more natural, because more than one objective was adapted during the evolutionary process of the canonical genetic code. Our results suggest that the evaluation function employed to compare genetic codes should consider simultaneously more than one objective, in contrast to what has been done in the literature.

Simulated evolution applied to study the genetic code optimality using a model of codon reassignments

Background

As the canonical code is not universal, different theories about its origin and organization have appeared. The optimization or level of adaptation of the canonical genetic code was measured taking into account the harmful consequences resulting from point mutations leading to the replacement of one amino acid for another. There are two basic theories to measure the level of optimization: the statistical approach, which compares the canonical genetic code with many randomly generated alternative ones, and the engineering approach, which compares the canonical code with the best possible alternative.

Results

Here we used a genetic algorithm to search for better adapted hypothetical codes and as a method to guess the difficulty in finding such alternative codes, allowing to clearly situate the canonical code in the fitness landscape. This novel proposal of the use of evolutionary computing provides a new perspective in the open debate between the use of the statistical approach, which postulates that the genetic code conserves amino acid properties far better than expected from a random code, and the engineering approach, which tends to indicate that the canonical genetic code is still far from optimal. We used two models of hypothetical codes: one that reflects the known examples of codon reassignment and the model most used in the two approaches which reflects the current genetic code translation table. Although the standard code is far from a possible optimum considering both models, when the more realistic model of the codon reassignments was used, the evolutionary algorithm had more difficulty to overcome the efficiency of the canonical genetic code.

Conclusions

Simulated evolution clearly reveals that the canonical genetic code is far from optimal regarding its optimization. Nevertheless, the efficiency of the canonical code increases when mistranslations are taken into account with the two models, as indicated by the fact that the best possible codes show the patterns of the standard genetic code. Our results are in accordance with the postulates of the engineering approach and indicate that the main arguments of the statistical approach are not enough to its assertion of the extreme efficiency of the canonical genetic code.