A Theorem for Overlapping Genes

A theorem is formulated for genes belonging to one RNA chain and overlapping in pairs. In the theorem a solution of the inverse problem is obtained: to compute all the nucleotide sequences (n.s.'s) corresponding to two protein sequences with sections on which their genes overlap. It is proved that this problem has unique solution if protein sequences do not contain leucine and argine. Due to presence of Leu and Arg Ambiguous points may occur in corresponding positions. These positions are determined by specific properties of local overlaps for codon collections of leucine (L-positions) and arginine (R-positions). Overlapping genes are analyzed, which were found in the genomes of some viruses, for example, BSMV, PAMV, OO174, G4, HIV-1, HIV-2, SIV_MAC, STLV-III_AGM, HBV, GSHV, WHV, ASHV. Among them there are the genomes with more than 50