Spatial patterning through coupled phase separation and reaction diffusion processes

Control and regulation of protein assemblies across space and time are critical for function in cells and tissues. Important examples include morphogen gradients in developing embryos and bio-condensates like stress granules, which are responsible for rapid response to external stressors. Chemical activity is typically the non-equilibrium driving force in producing well-regulated spatial patterns. In this work, we couple chemical driving, through a reaction-diffusion model, to the simplest paradigm for assembly: a phase-separating scalar field. We aim to study the effects of such reaction-diffusion systems, which show Turing patterns, on the phase-separation behaviour of a condensate. We model the condensate with standard Model-B dynamics and couple it to the Brusselator reaction-diffusion system, which shows a variety of static patterns, including spots and stripes. We find that for a weak coupling strength, phase-separation can be arrested, leading to multiple stable droplets at steady state. Upon further increasing the coupling strength, the system exhibits a secondary instability and develops patterns within the dense region of the condensate, leading to superlattices and higher-order structures. Our work provides an alternative mechanism by which proteins in biological systems might adaptively organize across multiple length scales.