Biomolecular condensates and biogeomorphological systems exhibit a phase-separation behavior unified by a mass-conserving model

Recent research in biogeomorphology has shown that many macroscale systems exhibit spatiotemporal self-organized patterns with coarsening behaviors and also phase separation behaviors, successfully described by a mass-conserving dynamical model. Also recently, macromolecules, such as nucleic acids and proteins, have been found to assemble mesoscale biomolecular condensates inside living cells. Despite their significance, the fundamental biophysical properties of these biomolecular condensates remain poorly understood. Here, we selected DNA and the human transcription factor p53 as a model system to form a specific type of biomolecular condensate, DNA-protein interactive co-condensates (DPICs). We developed a mass-conserving dynamical model, with all parameters derived from direct experimental measurements. This model successfully reproduces the spatiotemporal dynamics of DPICs. Our findings reveal that both mesoscale biomolecular condensates and macroscale biogeomorphological systems exhibit cross-scale spatiotemporal self-organized patterns with coarsening behaviors, and cross-scale phase separation behavior. Both systems also exhibit emergent properties. Our theoretical framework offers a deeper understanding of the mechanisms underlying these phase-separation systems.