Decoupling diffusion, turnover, and advection in long-term FRAP

Intracellular molecular turnover is a dynamic process governed by diffusion, biochemical reactions, and intracellular transport dynamics. While fluorescence recovery after photobleaching (FRAP) has been widely used to quantify fluorescence recovery mechanisms, conventional models primarily focus on diffusion and reaction kinetics, often overlooking the influence of intracellular advection. However, in cytoskeletal structures such as stress fibers, myosin-driven actin retrograde flow generates a significant advective component, which complicates the interpretation of FRAP data, particularly in long-term observations where advective effects become sufficiently pronounced. Here, we develop an analytical framework that extends FRAP modeling to incorporate the coupled effects of diffusion, turnover, and intracellular advection within the photobleached region of interest. By deriving exact solutions to a reaction-diffusion-advection system, we identify three key dimensionless parameters that govern fluorescence recovery dynamics: the turnover-to-diffusion ratio, the monomer-to-filament ratio, and the advection magnitude. Our results demonstrate that, even in the absence of biochemical reactions, fluorescence recovery in a fixed region can occur due to advection, leading to potential misinterpretations of molecular exchange rates. The model provides a theoretical foundation for distinguishing these effects and offers a practical tool for long-term FRAP analysis, where the interplay of diffusion, turnover, and advection becomes increasingly relevant over extended timescales. By systematically characterizing the interplay between molecular diffusion, reaction kinetics, and intracellular transport, our framework provides deeper insight into protein turnover in complex biological environments.