DNA supercoiling, the level of under- or overwinding of the DNA polymer around itself, is widely recognized as an ancestral regulation mechanism of gene expression in bacteria. Higher levels of negative supercoiling facilitate the opening of the DNA double helix at gene promoters and thereby increase gene transcription rates. Different levels of supercoiling have been measured in bacteria exposed to different environments, leading to the hypothesis that variations in supercoiling could be a response to changes in the environment. Moreover, DNA transcription has been shown to generate local variations in the supercoiling level and, therefore, to impact the transcription rate of neighboring genes. In this work, we study the coupled dynamics of DNA supercoiling and transcription at the genome scale. We implement a genome-wide model of gene expression based on the transcription-supercoiling coupling. We show that, in this model, a simple change in global DNA supercoiling is sufficient to trigger differentiated responses in gene expression levels via the transcription-supercoiling coupling. Then, studying our model in the light of evolution, we demonstrate that this non-linear response to different environments, mediated by the transcription-supercoiling coupling, can serve as the basis for the evolution of specialized phenotypes.