Abstract: Phase separation of intracellular biological macromolecules plays a crucial role in physiology and disease pathogenesis. In this study, we developed a dynamic phase-separation theory for RNA and RNA-binding proteins (RBPs) within cells based on diffusion dynamics and Hill kinetics. Using a diffusion dynamics model, we characterized the multiphase separation between RNA and RBPs, encompassing multiple phases and multi-component phases. Our findings reveal that the dynamic multiphase separation mechanism of RNA and RBPs within cells is primarily governed by biochemical interactions between them and their specific diffusivity properties. In these biochemical interactions, RNA and RBP bind to each other through binding domains, causing RNA and RBP with rapid diffusion to aggregate and form RNA-RBD complexes with slower diffusion. The diffusion correlation is a result of the biochemical reactions to the formation of multiple condensed phases of RNA and RBP. Additionally, our investigation uncovered periodic oscillations in the biochemical reactions involving RNA-RNA complexes as well as RBP-condensed phase formation and phase separation phenomena. Furthermore, through integration with the mean-field theory, we established a correspondence between the diffusion coefficients and Flory interaction parameters, providing profound insights into the relationship be-tween various interactions and diffusivity in the system, while comprehensively elucidating the physical essence of multiphase separation between RNA and RBPs. These findings highlight the dissipative structural characteristics associated with condensates formed by periodic oscillations in biochemical reactions involving RNA-RBP complexes. Importantly, it can be predicted that, apart from diffusion effects or changes in solubility, phase separation between RNA and RBPs may also occur owing to periodic changes in their biochemical reactions. These results are consistent with the experimental results of important factors contributing to intracellular phase separation, and provide a valuable reference for subsequent research endeavors.

Key words: non-equilibrium, multiphase separation, di?usion dynamics, mean-?eld theory, dissipative structure