Ripening and synchronization of biomolecular condensates in a heterogeneous elastic medium

Biomolecular condensates play a crucial role in regulating gene expression, but their behavior in chromatin remains poorly understood. Classical theories of phase separation are limited to thermal equilibrium, and traditional methods can only simulate a limited number of condensates. In this paper, we introduce a novel mean-field-like method that allows us to simulate millions of condensates in a heterogeneous elastic medium to model the dynamics of transcriptional condensates in chromatin. Using this method, we unveil an elastic ripening process in which the average condensate radius exhibits a unique temporal scaling, [<]R[>] [~] t1/5, different from the classical Ostwald ripening, and we theoretically derive the exponent based on energy conservation and scale invariance. We also introduce active dissolution to model the degradation of transcriptional condensates upon RNA accumulation. Surprisingly, three different kinetics of condensate growth emerge, corresponding to constitutively expressed, transcriptional-bursting, and silenced genes. Notably, multiple distributions of transcriptional-bursting kinetics from simulations, e.g., the burst frequency, agree with transcriptome-wide experimental data. Furthermore, the timing of growth initiation can be synchronized among bursting condensates, with power-law scaling between the synchronization period and dissolution rate. Our results shed light on the complex interplay between biomolecular condensates and the elastic medium, with important implications for gene expression regulation.