Unlocking Deeper Insights into Viral Evolution: Why the New c/µ Test Matters
- Ray Sullivan
- Jul 25
- 4 min read
For decades, evolutionary biologists have used the Ka/Ks ratio test to explore how genes adapt and change over time. This traditional test compares the rate of nonsynonymous (amino acid-changing) substitutions (Ka) to synonymous (silent) substitutions (Ks) in protein-coding regions. A Ka/Ks ratio equal to 1 suggests neutral changes, a ratio greater than 1 indicates beneficial (adaptive) changes, and less than 1 points to deleterious (purifying) selection.
However, this method has a significant limitation: it fundamentally assumes that synonymous mutations are effectively neutral (Ks = µ = constant). This assumption limits its application to protein-coding regions (Translated Regions, TR) and renders it inapplicable to Untranslated Regions (UTRs), which were often mistakenly considered neutral from a protein-centric perspective. Growing evidence, however, reveals that both synonymous sites in TR and regulatory sites in UTRs are indeed under natural selection, playing crucial roles in gene expression and protein folding.
To address these limitations, Chun Wu’s Lab from Rowan University proposed a new framework called the substitution-mutation rate ratio (c/µ) test in 2023 (see citation below). This test measures the ratio of the substitution rate (c) to the mutation rate (µ) per nucleotide site, providing a more generalized and robust way to detect selection pressure.
The 2023 paper first proposed the c/µ test, establishing its foundation and demonstrating its initial ability to quantify selection pressure on any genomic region, including UTRs and both synonymous and nonsynonymous sites in TR, using empirical sequence data. This initial study of SARS-CoV-2 revealed an unexpected L-shaped distribution of relative substitution rates, which was inconsistent with existing evolutionary theories but supported a new Near-Neutral Balanced Selectionist Theory (NNBST). The 2023 paper also noted that Ka/Ks was not applicable to non-coding regions like UTRs and Transcriptional Regulatory Sequences (TRSs), while these functionally important regions were likely under non-neutral selection.
With their most recent work (see citation below), Wu, et al. significantly expand upon this foundational work, offering further detailed insights and validations of the c/µ framework. Here's how it progresses:
The 2023 paper approximated the mutation rate (µ) using the genomic substitution rate. The 2025 paper refines this estimate and, crucially, validates the in vivo inferred mutation rate (µ) from SARS-CoV-2 sequence data by comparing it with experimentally determined in vitro cell-based and cell-free substitution rates from published literature. This external validation strengthens the reliability of the µ value used in the c/µ test.
A major advancement in the 2025 paper is the derivation of a novel general equation that formally links the overall fitness change (c/µ) with the contributions from synonymous (Ks/µ) and nonsynonymous (Ka/µ) mutations. This equation demonstrates that the Ka/Ks test infers the same fitness change as c/µ only if synonymous mutations are truly neutral (i.e., Ks/µ = 1). If Ks/µ is not equal to 1, then Ka/Ks provides only the fitness change due to protein sequence alteration, while c/µ provides the complete fitness effects from nucleic acid sequence changes.
The 2025 study provides a more detailed assessment of the c/µ framework against the traditional Ka/Ks method across 25 proteins, 11 UTRs, and 9 TRSs of SARS-CoV-2.
It definitively found that all UTRs and TRSs (except Orf1ab 5'UTR) are not effectively neutral, indicating they are under selective pressure.
None of the 25 proteins exhibited Ks/µ = 1. This strongly suggests that most synonymous mutations in these proteins are not effectively neutral, directly contradicting a fundamental assumption of the Ka/Ks test.
While c/µ and Ka/Ks reported the same type of fitness change for 18 out of 25 proteins, Ka/Ks inaccurately reported the type of fitness change for 7 proteins because it overlooks the fitness change attributed to synonymous mutations (Ks/µ).
The paper also highlights that Ka/Ks can lead to undefined values or false positives when Ks approaches zero, a technical error that the c/µ test avoids due to its well-defined, non-zero mutation rate (µ) as a reference.
Broader Applicability and Higher Resolution: The 2025 paper reinforces that c/µ is applicable to any genomic region, including non-protein-coding UTRs, without the neutrality assumption of synonymous sites. It also reiterates c/µ's ability to provide the highest-resolution analysis at the nucleotide (NT) level, facilitating more accurate identification of adaptive mutations.
In essence, the 2025 paper deepens the theoretical and empirical validation of the c/µ test, demonstrating its superior comprehensiveness and accuracy compared to Ka/Ks, especially for non-coding regions and silent mutations. It solidifies the argument for c/µ as a crucial tool to unlock deeper insights into evolutionary dynamics and contribute to resolving long-standing debates in evolutionary biology. While currently optimized for simple haploid systems like RNA viruses, future research aims to broaden its application to more complex organisms by relaxing assumptions about mutation rate constancy.
Wu C, Paradis NJ, Lakernick PM, Hryb M. L-shaped distribution of the relative substitution rate (c/μ) observed for SARS-COV-2's genome, inconsistent with the selectionist theory, the neutral theory and the nearly neutral theory but a near-neutral balanced selection theory: Implication on "neutralist-selectionist" debate. Comput Biol Med. 2023 Feb;153:106522. doi: 10.1016/j.compbiomed.2022.106522. Epub 2023 Jan 5. PMID: 36638615; PMCID: PMC9814386.
Wu C, Paradis NJ, Jain K. Substitution-Mutation Rate Ratio (c/µ) As Molecular Adaptation Test Beyond Ka/Ks: A SARS-COV-2 Case Study. J Mol Evol. 2025 Jun;93(3):322-349. doi: 10.1007/s00239-025-10248-6. Epub 2025 May 3. PMID: 40319123; PMCID: PMC12198311.
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