Why Mutant Allele Frequencies in Oncogenes Peak Around 0.40 and Rapidly Decrease?

TL;DR

This paper explains the peak and decline of mutant allele frequencies in oncogenes using a mathematical model based on population genetics and the inverse function theorem, validated across various cancer types.

Contribution

It introduces a general formula for natural selection under complete dominance applicable at all allele frequencies, extending existing models.

Findings

Selection function fits a gamma distribution curve.

Selection exhibits linear behavior at all times.

Selection behaves like a power-law at low dominant allele frequencies.

Abstract

The mutant allele frequencies in oncogenes peak around 0.40 and rapidly decrease. In this article, we explain why this is the case. Invoking a key result from mathematical analysis in our model, namely, the inverse function theorem, we estimate the selection pressures of the mutations as a function of germline allele frequencies. Under complete dominance of oncogenic mutations, this selection function is expected to be linearly correlated with the distribution of the mutant alleles. We demonstrate that this is the case by investigating the allele frequencies of mutations in oncogenes across various cancer types, validating our model for mean effective selection. Consistent with the population genetics model of fitness, the selection function fits a gamma distribution curve that accurately describes the trend of the mutant allele frequencies. While existing equations for selection explain evolution at low allele frequencies, our equations are general formulas for natural selection under complete dominance operating at all frequencies. We show that selection exhibits linear behavior at all times, favoring dominant alleles with respect to the change in recessive allele frequency. Also, these equations show, selection behaves like power-law against the recessive alleles at low dominant allele frequency.