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.Author summary: The fitness landscape is a conceptual geometric structure that describes the relationship between genotypes and fitness (i.e., reproductive success). The evolutionary dynamics of a population can be viewed as an adaptive walk on the landscape toward a higher fitness region. Thus, by analyzing the landscape, one can infer how evolution has shaped current organisms, or which genotypes have high fitness. Here, we analyzed the fitness landscape of the genetic code, the rule by which codons encode amino acid. The standard genetic code (SGC), shared by almost all organisms, has an apparently non-random structure, implying that it has been subject to strong selection pressure. By applying multicanonical Monte Carlo, a numerical method developed in statistical physics, we visualized the genetic code fitness landscape. The landscape has four peaks, one of which contains the SGC, with the other three representing genetic codes that potentially could have been the current genetic code. Genetic algorithm analysis revealed that, in such a multimodal fitness landscape, evolution could be strongly biased toward narrower peaks, in an evolutionary pathway-dependent manner.