DNA supercoiling in bacteria: state of play and challenges from a modeling viewpoint

DNA supercoiling is central to fundamental processes of living organisms. Its average level along the chromosome and over time reflects the dynamic equilibrium of opposite activities of topoisomerases, which are required to relax mechanical stresses that are inevitably produced during DNA replication and gene transcription. Supercoiling affects all scales of the spatio-temporal organization of bacterial DNA, from the base pair to the large scale chromosome conformation. Highlighted {\it in vitro} and {\it in vivo} in the 1960s and 1970s, respectively, the first physical models were proposed concomitantly in order to predict the deformation properties of the double helix. About fifteen years later, polymer physics models demonstrated on larger scales the plectonemic nature and the tree-like organization of supercoiled DNA. Since then, many works have tried to establish a better understanding of the multiple structuring and physiological properties of bacterial DNA in thermodynamic equilibrium and out of equilibrium. The purpose of this essay is to discuss upcoming challenges by discussing the relevance, the predictive capacity and the limitations of current physical models, focusing on structural properties above the scale of the double helix. We discuss more particularly four fundamental aspects: gene transcription, DNA replication, nucleoid formation and the large-scale structure of chromosomes. The review being intended for both biologists and physicists, we have tried to reduce the respective jargon to a minimum.