Effective long range interactions generated by polymer fluctuations induce bound particle phase separation

The confinement of chemical species within the cytoplasm is mandatory for the spatio-temporal organization of chemical activities in the cell. Cells indeed compartmentalize the intracellular space using either membrane-bound vesicles or membrane-less organelles. For the latter, cells may employ phase separation of chemical species in order to create localized high density regions in which specific reactions may occur. Such biological phase separation mechanisms often need polymeric scaffolds such as RNA or DNA to bind the chemical species. We propose a general theoretical 3D framework for such polymer-bound particles from which we derive an effective 1D lattice gas model with both nearest neighbor and long range interactions, the latter arising from polymer fluctuations. We argue that 1D phase transitions exist in such system for both Gaussian and self-avoiding polymers and, using a variational method that goes beyond mean field theory, we obtain the mean occupation/temperature phase diagram. To illustrate this model, we apply it to the biologically relevant case of the ParABS system, a prevalent bacterial DNA segregation system, to study the formation of ParBS complexes on DNA.