Phase separation driven by production of architectural RNA transcripts

We here use an extension of the Flory-Huggins theory to predict that the phase separation is driven by the production of architectural RNA (arcRNA) at a DNA locus with a constant rate. The arcRNA molecules diffuse in the nucleoplasm and show attractive interactions via proteins that are bound to the arcRNA. Our theory predicts that when the Flory interaction parameter is larger than the value at the critical point, the volume fraction of arcRNA jumps between the two values, corresponding to the volume fraction of the two coexisting phases in the equilibrium, at a distance from the DNA locus due to the local equilibrium condition. The distance defines the radius of the condensate that is assembled by the phase separation. When the interaction parameter is large, the volume of the condensates is proportional to the production rate of arcRNA and inversely proportional to the degradation rate of arcRNA. These results imply that most arcRNA molecules are degraded before it diffuses out from the condensates due to the strong segregation of arcRNA.