Abstract
The cellular cytoplasm is organized into compartments. Phase separation is a simple manner to create membraneless 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.