Hydrodynamic modeling of protein transport in lipid membranes

Lateral transport of membrane proteins is governed by the hydrodynamics of lipid bilayers and their coupling to the surrounding fluids. Protein mobility determines its diffusion rate, which can regulate important cellular functions such as cell signaling, especially when diffusion is the rate limiting process. Classic theories, such as the Saffman-Delbrück model, established the foundation for understanding protein mobility in membranes. Saffman-Delbrück theory has since been extended in many ways to understand and model the observations and measurements in living and reconstituted systems. In this review, we focus on hydrodynamic models that treat the membrane as a two-dimensional fluid continuum with embedded proteins, enabling quantitative predictions of protein mobility, correlated motion, and transport across planar and curved membranes. We summarize theoretical and computational advances for free-standing and supported membranes, discuss the role of hydrodynamic interactions in crowded systems, and discuss the extensions to active and passive protein assemblies. In tandem we also discuss the experimental studies that verified these theories or motivated their extensions. Recent advances in the rate and accuracy of acquiring microscopy data have made many of these hydrodynamic predictions experimentally accessible, highlighting the growing role of hydrodynamic modeling in connecting membrane mechanics to protein transport in cells and reconstituted systems.