Quantitative droplet FRAP based on physical principles

Fluorescence recovery after photobleaching (FRAP) is used to characterize a range of dynamic processes, for example binding kinetics and mobility of intracellular proteins, and recently liquid-liquid phase separation (LLPS) in vitro and in vivo.
To gain an understanding of the relevant molecular mechanisms, data analysis must be based on the underlying physics. Strikingly, for FRAP of phase-separated droplets, no physical model from first principles has been derived, which severely restricts data interpretation.
Here, we first derive a FRAP model from the physical principles underlying LLPS. Second, we use the full spatio-temporal imaging data within the droplet for fitting.
This results in the following improvements: we can (i) distinguish the time scales of exchange through the droplet interface (set by bulk diffusion and boundary kinetics) from diffusion inside the droplet, (ii) quantify the impact of the interface (iii) provide improved measurements for several biologically important proteins, and (iv) use our analysis framework to explore several multi-component scenarios. Finally, we provide experimental guidelines for highly quantitative in vitro FRAP, e.g. the necessity to perform a full bleach to allow robust analysis and routines to allow spatio-temporal fitting.