An Analytical Framework for Phenotypic Selection of Fitness-Conferring Genes.

Phenotypic selection can cause the transient, selective upregulation of fitness-conferring genes in isogenic cell populations under stress, producing selective enrichment of the fitness gene relative to a neutral reference gene. While computational models have shown that such enrichment requires noisy gene expression and a cellular memory linking growth rate to gene expression (Ciechonska et al. 2022), the precise mechanistic requirements and the analytical principles governing enrichment have remained unclear. Here, we present an exact analytical framework that unifies enrichment mechanisms across both growth-driven and death-driven selection regimes. By analysing a stochastic model of explicit mRNA and protein dynamics, we prove that when selection acts via cell division, the fitness advantage of faster growth is exactly cancelled by the penalty of faster protein dilution. We show that this cancellation is bypassed by translational feedback but not by transcriptional feedback alone; for genes with regulated (switching) promoters, the promoter-state memory provides an independent route to enrichment without translational feedback. Conversely, when selection acts via cell death, this exact cancellation is bypassed, allowing selective enrichment to emerge from baseline gene expression noise without any assumptions about growth-related feedback loops or regulated vs constitutive expression. We derive an exact fluctuation-response relation demonstrating that, in all cases, enrichment scales with the super-Poissonian component of unperturbed protein noise times the relevant memory timescale. All analytical predictions are corroborated by stochastic simulations of a finite-population Moran model. These results have implications for the emergence of drug resistance: by transiently enriching survival-conferring phenotypes, phenotypic selection can extend the window during which cell division occurs under stress, increasing the opportunity for permanent genetic mutations to arise.