Question

DN/dS is often used as a measure of the intensity of selective pressure on a mutation or gene, but I'm curious about how it can be written as a function of the selection coefficient. I'm specifically interested in the scenario of somatic mutations in human cells; suppose there's a gene, and all non-silent mutations in the gene are equivalent (such as if they're all loss of function mutations). The mutation rate is μ mutations per bp per cell division and once both alleles are (nonsilently) mutated, there's no fitness gain (or loss) from additional mutations. The selection coefficient for mutations in the gene for homozygous mutations is:

w_hom = 1 + s
and for heterozygous:

w_het = 1 + hs
How would one derive the expected dN/dS ratio (where the selection coefficient of a silent mutation is 0)? I realize there are a few questions for which answers must be assumed to begin to answer this question, such as:

Is population static, or growing?
Is dN/dS only including clonal/fixed mutations, or perhaps all mutations with a frequency in the population greater than or equal to some value?
I'd be interested in what the relationship with dN/dS is even under the simplest assumptions, e.g. h = 1, only considering clonal mutations, and static population. I've found one paper that posits such a formula, citing a finding from another paper, but I don't think either shows all the math.

Answer 1

To derive the expected dN/dS ratio in the scenario of somatic mutations in human cells, you can use the selection coefficients provided for homozygous and heterozygous mutations in the gene. The dN/dS ratio is the ratio of the number of non-synonymous (dN) substitutions to the number of synonymous (dS) substitutions.

Step-by-step explanation:

To derive the expected dN/dS ratio in the scenario of somatic mutations in human cells, you can use the selection coefficients provided for homozygous and heterozygous mutations in the gene. The dN/dS ratio is the ratio of the number of non-synonymous (dN) substitutions to the number of synonymous (dS) substitutions. In this case, the selection coefficient (s) represents the fitness advantage or disadvantage of a mutation. Assuming a static population and only considering clonal mutations, you can determine the expected dN/dS ratio by calculating the expected number of non-synonymous and synonymous mutations based on the selection coefficients and mutation rate.

For instance, if the selection coefficient for homozygous mutations (w_hom) is 1 + s and for heterozygous mutations (w_het) is 1 + hs, the expected number of non-synonymous mutations can be calculated as the product of the mutation rate (μ) and the selection coefficients, while the expected number of synonymous mutations is simply the mutation rate multiplied by the frequency of silent mutations (0). Dividing the expected number of non-synonymous mutations by the expected number of synonymous mutations gives you the dN/dS ratio.