Phase separation of polymer-bound particles induced by loop-mediated one dimensional effective long-range interactions

G. David,J.-C. Walter,J. Dorignac,F. Geniet,C. P. Broedersz,J. Palmeri,N.-O. Walliser,A. Parmeggiani

doi:10.1103/physrevresearch.2.033377

Abstract

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.

Highlights

The confinement of chemical species, such as Ribonucleic acid (RNA) or proteins, within the cytoplasm is mandatory for the spatiotemporal organization of chemical activities in the cell [1]
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
We have proposed a general theoretical framework for the physics of particles interacting on a polymer fluctuating in 3D that leads naturally to an effective 1D long-range lattice gas (LRLG) model

Summary

Introduction

The confinement of chemical species, such as RNA or proteins, within the cytoplasm is mandatory for the spatiotemporal organization of chemical activities in the cell [1]. Cells compartmentalize the intracellular space using either membrane vesicles or membraneless 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 [2,3]. Cells may employ phase separation of chemical species in order to create localized high-density regions in which specific reactions may occur [2,3] Such biological phase separation mechanisms often involve polymeric scaffolds like Ribonucleic acid (RNA) or Deoxyribonucleic acid (DNA) to bind the chemical species [4,5,6,7,8,9]. The interaction between a fluctuating polymer in a good solvent and smaller associating particles is a general problem that goes beyond biology. There are important industrial applications that exploit the possibility of fine-tuning such systems to induce polymer-surfactant aggregation at low surfactant concentration [16]

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