DNA supercoiling acts as a global transcriptional regulator in bacteria, that plays an important role in adapting their expression programme to environmental changes, but for which no quantitative or even qualitative regulatory model is available. Here, we focus on spatial supercoiling heterogeneities caused by the transcription process itself, which strongly contribute to this regulation mode. We propose a new mechanistic modeling of the transcription-supercoiling dynamical coupling along a genome, which allows simulating and quantitatively reproducing in vitro and in vivo transcription assays, and highlights the role of genes' local orientation in their su-percoiling sensitivity. Consistently with predictions, we show that chromosomal relaxation artificially induced by gyrase inhibitors selectively activates con-vergent genes in several enterobacteria, while conversely , an increase in DNA supercoiling naturally selected in a long-term evolution experiment with Escherichia coli favours divergent genes. Simulations show that these global expression responses to changes in DNA supercoiling result from fundamental mechanical constraints imposed by transcription, independently from more specific regulation of each promoter. These constraints underpin a significant and predictable contribution to the complex rules by which bacteria use DNA supercoiling as a global but fine-tuned transcriptional regulator.