Evolutionary symmetries of the genetic code and their implications for natural computing

The genetic code, viewed as the simplest abstract description of the complex process of translation, is characterized by various symmetries. These symmetries are not mere mathematical peculiarities but are deeply intertwined with the molecular mechanisms governing gene expression and the faithful decoding of genetic information. The emergence and evolutionary path of these molecular mechanisms are intrinsically linked to the origin and evolution of the standard genetic code in the progenotic stages of life, indicating that certain symmetries can be evolutionarily very distant. Despite the considerable uncertainty and complexity surrounding primordial evolution, it can be considered as a consensus view that the genetic code has evolved from a rudimentary, imprecise form to its current advanced, highly accurate state. This evolution, encompassing the transcription and translation machinery and the organization of genetic information itself, could have left traces in the transition of symmetry from the dinucleotide to the trinucleotide (codon) level. While dinucleotides determine the most prominent symmetry of the genetic code in the form of bipartition associated with its degeneracy (redundancy), codons are essential for the precise specification of all proteinogenic amino acids. This code redundancy is crucial not only for minimizing translational errors but also for enabling other “regulatory codes”. Within certain proteincoding regions, synonymous codon preference is often influenced by factors beyond protein structure, such as transcription factor binding. This overlap of the genetic code and other regulatory codes related to transcription, chromatin organization, mRNA splicing, cotranslational folding, etc., is considered to be partly manifested in constrained codon choice, more precisely defined through codon and codon-pair usage bias, phenomena directly linked to dinucleotide bias. Remarkably, this hierarchical organization of the genetic code and its numerous symmetries are describable through arithmetic regularities in nucleon numbers of its constituents. Given that some of these symmetries likely originated in different evolutionary epochs, nucleon number balancing may represent a fundamental, underlying mechanism influencing the organization of living matter. We further propose that these phenomena are relevant to natural computing.