Résumé
Controlled motion and positioning of colloids and macromolecular complexes in a fluid, as well as catalytic particles in active environments, are fundamental processes in physics, chemistry and biology. Here we focus on an active biological system for which precise experimental results are available. Our work is fully inspired by studies of one of the most widespread and ancient mechanisms of liquid phase macromolecular segregation and positioning known in nature: bacterial DNA segregation systems. Efficient bacterial chromosome segregation typically requires the coordinated action of a three-component, fueled by adenosine triphosphate machinery called the partition complex. We can distinguish two steps: (i) a process of phase transition [2,3] to built a membraneless region of high protein concentration (partition complex) (ii) the action of molecular motor action upon the complex to create a chemical force. We present a phenomenological model [1] accounting for the dynamics of this system that is also relevant for the physics of catalytic particles in active environments. The model is obtained by coupling simple linear reaction-diffusion equations with a volumetric chemophoresis force field that arises from protein-protein interactions and provides a physically viable mechanism for complex translocation. This description captures experimental observations: dynamic oscillations of complex components, complex separation and symmetrical positioning. The predictions of our model are in agreement with and provide substantial insight into recent experiments. From a non-linear physics view point, this system explores the active separation of matter at micrometric scales with a dynamical instability between static positioning and travelling wave regimes triggered by the dynamical spontaneous breaking of rotational symmetry. We also discuss the phase transition mechanism giving rise to macromolecular assembly of proteins. Our predictions are compared to Super Resolution microscopy and microbiology experiments [1,2,3].[1] Walter J.-C., Dorignac J., Lorman V., Rech J., Bouet J.-Y., Nollmann M., Palmeri J., Parmeggiani A. and Geniet F., Phys. Rev. Lett. 119, 028101 (2017).[2] Debaugny R., Sanchez A., Rech J., Labourdette D., Dorignac J., Geniet F., Palmeri J., Parmeggiani A., Boudsocq, Leberre V., Walter* J.-C. and Bouet* J.-Y Mol. Syst. Biol. 14, e8516 (2018)[3] David G., Walter J.-C., Broedersz C., Dorignac J., Geniet F., Parmeggiani A., Walliser N.-O. and Palmeri J., submitted to Phys. Rev. Lett. [arXiv/1811.09234] (2019).