Stability of the genetic code and optimal parameters of amino acids

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.

Local conditions for global stability in the space of codons of the genetic code

The polar requirement is an attribute of amino acids that is a major determinant of the structure and function of the proteins, and it plays a role in the flexibility and robustness of the genetic code. The viability of an organism depends on flexibility, which allows the exploration of new functions. However, robustness is necessary to protect the organism from deleterious changes derived from misreading errors and single-point mutations. Compared with random codes, the standard genetic code is one of the most robust against such errors. Here, using analytical and numerical calculations and the set of amino acid-encoding codons, we have proposed some local conditions that are necessary for the optimal robustness of the genetic code, and we explored the association between the local conditions and the robustness. The localness of the proposed conditions and the underlying evolutionary mechanism, which begins with a random code and progresses toward more efficient codes (e.g., the standard code), might be biologically plausible.

Probable relationship between partitions of the set of codons and the origin of the genetic code

Here we study the distribution of randomly generated partitions of the set of amino acid-coding codons. Some results are an application from a previous work, about the Stirling numbers of the second kind and triplet codes, both to the cases of triplet codes having four stop codons, as in mammalian mitochondrial genetic code, and hypothetical doublet codes. Extending previous results, in this work it is found that the most probable number of blocks of synonymous codons, in a genetic code, is similar to the number of amino acids when there are four stop codons, as well as it could be for a primigenious doublet code. Also it is studied the integer partitions associated to patterns of synonymous codons and it is shown, for the canonical code, that the standard deviation inside an integer partition is one of the most probable. We think that, in some early epoch, the genetic code might have had a maximum of the disorder or entropy, independent of the assignment between codons and amino acids, reaching a state similar to "code freeze" proposed by Francis Crick. In later stages, maybe deterministic rules have reassigned codons to amino acids, forming the natural codes, such as the canonical code, but keeping the numerical features describing the set partitions and the integer partitions, like a "fossil numbers"; both kinds of partitions about the set of amino acid-coding codons.