Quantitative Theory for the Diffusive Exchange Dynamics of Liquid Condensates

To unravel the biological function of phase-separated condensates it is key to develop a quantitative understanding of the physics governing the droplet dynamics. A key property of droplets is their ability to exchange material with their environment via diffusion. To date we lack a physics-based framework for the dynamics of labeled components inside and outside of liquid droplets. Using the theory of phase separation we derive a framework that quantitatively captures the diffusive transport of labeled droplet components. Based on our framework, we analyse FRAP experiments and show that diffusion coefficients inside liquid droplets can be precisely determined by combining experimentally measured concentrations at the droplet interface with the governing equation inside of liquid droplets. We proof the accuracy of this method by considering space and time resolved FRAP data of PGL-3 droplets as well as two different coacervate systems. Strikingly, without explicitly measuring the outside dynamics, we can also determine the outside diffusion coefficient or the partitioning. Thus, by combining the theory of phase separation and dynamic measurements of concentration fields, we provide a framework to characterize physical properties highly relevant to understand condensate functions.