Ohm's Law for increasing fitness gene expression with selection pressure

Natural selection relies on genotypic and phenotypic adaptation in response to fluctuating environmental conditions and is the key to predicting and preventing drug resistance. Whereas classic persistence is all-or-nothing, here we show for the first time that an antibiotic resistance gene displays linear dose-responsive selection for increased expression in proportion to rising antibiotic concentration in E. coli. Furthermore, we observe the general nature of an instantaneous phenotypic selection process upon bactericidal and bacteriostatic antibiotic treatment, as well as an amino acid synthesis pathway enzyme under a range of auxotrophic conditions. To explain this phenomenon, we propose an analogy to Ohms law in electricity (V=IR) where fitness pressure acts similarly to voltage (V), gene expression to current (I), and resistance (R) to cellular machinery constraints. Lastly, mathematical modelling approaches reveal that the emergent gene expression mechanism requires variation in mRNA and protein production within an isogenic population, and cell memory from positive feedbacks between growth and expression of any fitness-inducing gene.