Polymer brush inspired by ribosomal RNA transcription

Pre-ribosomal RNAs are synthesized during the transcription by RNA polymerase I molecules localized at the surfaces of a nucleolus subcompartment. Inspired by the ribosomal RNA transcription, we here develop a scaling theory of a brush of polymers, where monomers are added to their grafted ends in the steady state. Our theory predicts that monomers newly added to the polymers stay at the vicinity of the surface due to the slow dynamics of the polymers and thus the polymer volume fraction increases with increasing the polymerization rate. The excluded volume interaction between polymers and reactant monomers suppresses the diffusion of reactant monomers and thus decreases the polymerization rate. The extent of the suppression of monomer diffusion increases with increasing the polymerization rate because the diffusion length decreases, rather than the condensation of polymers due to their slow dynamics.