use transition/transversion (κ) ratio test to detect functional polypeptide

"To confirm our results using an independent nucleotide-based approach (as opposed to the codon-based test described earlier), we applied the transition/transversion (κ) ratio test to make inferences about biological significance of ARFs. The test is based on the following reasoning: in most standard protein-coding regions (with only one reading frame), κ at the third codon position (κ3) is significantly different (higher) than at the first and second codon positions (κ12), so that κ12 < κ3 [15]. This is because most substitutions at the third codon position are synonymous, whereas in the first codon position all but eight substitutions are nonsynonymous, and all substitutions in the second codon position are nonsynonymous. By contrast, in overlapping reading frames, codon positions are codependent. For example, in a +1 ARF, the third codon positions correspond to the first codon positions of the canonical frame. Thus, almost every change in the third codon position of the ARF is guaranteed to change amino acids encoded in the canonical frame. However, if the ARF encodes a truly functional product, purifying selection would resist such changes, and the condition κ12 < κ3 would not hold. This gives us the opportunity to test functionality of ARF in our dataset by contrasting two hypotheses: H₀: κ₁₂ = κ₃ (ARF does encode functional polypeptide) and H_A: κ₁₂ < κ₃ (ARF does not encode functional polypeptide). To perform this test, we used a maximum likelihood framework to test κ₁₂ and κ₃ for equality [16]. Application of the test to our list of dual-coding genes identified 18 candidates" PLoS Computational Biology - A First Look at ARFome: Dual-Coding Genes in Mammalian Genomes