Substitution-Mutation Rate Ratio (c/µ) As Molecular Adaptation Test Beyond Ka/Ks: A SARS-COV-2 Case Study

The Ka/Ks ratio test, which assesses nonsynonymous versus synonymous substitution rates in Translated Region (TR) of a genome, is widely used to quantify fitness changes due to mutations but its critical limits are to be addressed. Ka/Ks can categorize the total fitness change as neutral (Ka/Ks = 1), beneficial (Ka/Ks > 1), or deleterious (Ka/Ks < 1), only if synonymous mutations are neutral. Otherwise, Ka/Ks only provides the fitness change due to protein sequence change. This neutrality assumption also renders this test inapplicable to sites in non-protein-coding UnTranslated Region (UTR). Our previous work introduced a substitution-mutation rate ratio (c/µ) per nucleotide site test (c: substitution rate in UTR/TR or a mean value of Ka and Ks in TR; and µ: mutation rate) as a generalized alternative to detect selection pressure, offering a broader application without forementioned presumptions. This paper derives a general equation linking c/µ with weighted Ks/µ and Ka/µ (c/µ = Ps*(Ks/μ) + Pa*(Ka/μ), Ps and Pa: proportions of synonymous and nonsynonymous sites under a mutation model and a codon table), demonstrating that Ka/Ks infers the same fitness change as c/µ does only if synonymous mutations are neutral (i.e. Ks/µ = 1). Otherwise, Ka/Ks might provide a different assignment from the c/µ test. Indeed, our comparative analysis of the c/µ and Ka/Ks tests across 25 proteins of SARS-COV-2 using three independent genomic sequence datasets shows that Ka/Ks inaccurately reports the type of fitness change for 7 proteins. Our findings advocate for the c/µ test to complement traditional Ka/Ks test to detect the selection pressure at a nucleotide site in a genome.