Résumé
Controlled motion and positioning of colloids and macromolecular complexes in a fluid, as well ascatalytic particles in active environments, are fundamental processes in physics, chemistry andbiology. Here we focus on an active biological system for which precise experimental results areavailable. Our work is fully inspired by studies of one of the most widespread and ancientmechanisms of liquid phase macromolecular segregation and positioning known in nature:bacterial DNA segregation systems. Efficient bacterial chromosome segregation typically requiresthe coordinated action of a three-component, fueled by adenosine triphosphate machinery calledthe partition complex. We can distinguish two steps: (i) a process of phase transition [2,3] tobuilt a membraneless region of high protein concentration (partition complex) (ii) the action ofmolecular 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 alsorelevant for the physics of catalytic particles in active environments. The model is obtained bycoupling simple linear reaction-diffusion equations with a volumetric chemophoresis force fieldthat arises from protein-protein interactions and provides a physically viable mechanism forcomplex translocation. This description captures experimental observations: dynamic oscillationsof complex components, complex separation and symmetrical positioning. The predictions of ourmodel 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 micrometricscales with a dynamical instability between static positioning and travelling wave regimestriggered by the dynamical spontaneous breaking of rotational symmetry. We also discuss thephase transition mechanism giving rise to macromolecular assembly of proteins. Our predictionsare 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., ParmeggianiA. 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. andPalmeri J., submitted to Phys. Rev. Lett. [arXiv/1811.09234] (2019).