Phase separation of polymer-bound particles induced by loop-mediated 1D effective long-range interactions

• Published in: arXiv.org 2018-11
• Main Authors: David, G, J -C Walter, Broedersz, C P, Dorignac, J, Geniet, F, Parmeggiani, A, N -O Walliser, Palmeri, J
• Format: Article
• Language: English
• Subjects: Compartments; Cytoplasm; Deoxyribonucleic acid; DNA; Mean field theory; Phase diagrams; Phase separation; Phase transitions; Polymers
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1811.09234

The cellular cytoplasm is organized into compartments. Phase separation is a simple manner to create membrane-less compartments in order to confine and localize particles like proteins. In many cases these particles are bound to fluctuating polymers like DNA or RNA. We propose a general theoretical framework for such polymer-bound particles and derive an effective 1D lattice gas model with both nearest-neighbor and emergent long-range interactions arising from looped configurations of the fluctuating polymer. We argue that 1D phase transitions exist in such systems for both Gaussian and self-avoiding polymers and, using a variational method that goes beyond mean-field theory, we obtain the complete mean occupation-temperature phase diagram. To illustrate this model we apply it to the biologically relevant case of ParABS, a prevalent bacterial DNA segregation system.