(1/7) The lastest #popgen piece (now accepted) from the Payne-McCandlish-Stoltzfus collaboration features work of Bryan Gitschlag and Alejandro Cano
Mutation rates (u) matter so, rather than a distribution of fitness effects (DFE), we focus on a joint dist of u and s, exploring how it changes going from an underlying nominal dist of possibilities, to a de novo dist of mutations, to a fixed distribution
tagging @JoannaMasel @PeterALind
The de novo is simply the nominal weighted by u and, under a simple model of beneficial changes, the fixed is the de novo weighted proportional to s
In this example, u and s are exponentially distributed and uncorrelated. Weighting by u increases the density rightwards, and weighting by s increases it upwards
Even with no correlation in the nominal, there is a negative association in the de novo, and a stronger negative association in the fixed
Why is that interesting?
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Our initial focus was on apparent induced (i.e., non-causal) associations that we saw in the literature
Left, the rate of driver muts identified in tumors shows a negative relation with growth rate (from https://ncbi.nlm.nih.gov/pubmed/30647454)
Middle, same kind of thing in regard to clonal haematopoesis (from http://biorxiv.org/content/early/2022/05/09/2022.05.07.491016.abstract)
Right, I replotted the same data to make the negative association clear
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Recent studies have revealed the mutational signatures underlying the somatic evolution of cancer, and the prevalences of associated somatic genetic variants. Here we estimate the intensity of positive selection that drives mutations to high frequency in tumors, yielding higher prevalences than expe …
This kind of negative correlation could emerge even if u and s are uncorrelated in the nominal, bc variants that achieve clinical prevalence in spite of lower u will tend to have higher s, and vice versa. It's like Berkson's paradox (https://en.wikipedia.org/wiki/Berkson's_paradox)
That was our initial motivation
What did we find?
It's complicated! Also fundamental
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We found that, depending on the exact shape of the nominal, covariance(u,s) can have any pattern of signs going from nominal to de novo to fixed! This non-intuitive aspect emerges from a dependence on higher mixed moments
Theory says anything can happen so...
we looked to real examples to see what's likely
In the case of TP53, we can define a nominal from mut signatures (u) and results of deep mut scanning (s),
and we can use clinical prevalence of driver muts for the fixed dist
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For single-nt muts in TP53, we find a positive correlation in the fixed dist
We also compared single- to multi-nt changes, which happen maybe 100X less, but are covered by deep-mut-scanning studies, and are sometimes found clinically as drivers
We found that multi-nt TP53 muts found clinically in tumors are quite rare but tend to have enhanced s (relative to the nominal), as if to compensate for their lower u
(the most fun result for me as a fan of Berkson's paradox)
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We argue that, in nature, negative correlations in the fixed dist are more likely (but not inevitable)
Finally, we point out that the mathematical theory also applies directly to 2 higher dists with important meanings: the contribution to adaptation (i.e., to increase in fitness), and the contribution to parallel adaptation
Thanks to you for following along, to my collaborators, and to Deepa Agashe for inviting this symposium contribution
https://biorxiv.org/content/10.1101/2023.02.13.528299v1
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Arlin Stoltzfus