On combinatorial and biofunctional symmetries hidden in polynucleotide sequences

Various types of symmetry of polynucleotide sequences and methods of their algebraic description are considered. Among the methods of description, the main attention is paid to the application of semigroup theory (in particular, group theory). For convenience, all symmetry is divided into types. Combinatorial symmetry, first of all, it is associated with the explicit and hidden periodicity of the arrangement of identical nucleotides in subsequences. The above is generalized to the case of color symmetry, when different types of nucleotides or their associations can transform into each other upon shift. Fractal symmetry can also be added to this. Biofunctional symmetry means the presence of sequence factors of different nature (and size), which can be interchanged (swap places) solely due to their biological equivalence in the strand. A number of issues that are indirectly related to symmetry are also touched upon, for example, the presence of closed loops in polynucleotide (or polypeptide) chains and some physicochemical aspects.