Computational design of fully overlapping coding schemes for protein pairs and triplets

Gene pairs that overlap in their coding regions are rare except in viruses. They may occur transiently in gene creation and are of biotechnological interest. We have examined the possibility to encode an arbitrary pair of protein domains as a dual gene, with the shorter coding sequence completely embedded in the longer one. For 500 × 500 domain pairs (X, Y), we computationally designed homologous pairs (X', Y') coded this way, using an algorithm that provably maximizes the sequence similarity between (X', Y') and (X, Y). Three schemes were considered, with X' and Y' coded on the same or complementary strands. For 16% of the pairs, an overlapping coding exists where the level of homology of X', Y' to the natural proteins represents an E-value of 10^-10 or better. Thus, for an arbitrary domain pair, it is surprisingly easy to design homologous sequences that can be encoded as a fully-overlapping gene pair. The algorithm is general and was used to design 200 triple genes, with three proteins encoded by the same DNA segment. The ease of design suggests overlapping genes may have occurred frequently in evolution and could be readily used to compress or constrain artificial genomes.