Endocytosis optimizes the dynamic localization of membrane proteins that regulate cortical polarity

Diverse cell types require the ability to maintain dynamically polarized membrane-protein distributions through balancing transport and diffusion. However, design principles underlying dynamically maintained cortical polarity are not well understood. Here we constructed a mathematical model for characterizing the morphology of dynamically polarized protein distributions. We developed analytical approaches for measuring all model parameters from single-cell experiments. We applied our methods to a well-characterized system for studying polarized membrane proteins: budding yeast cells expressing activated Cdc42. We found that a balance of diffusion, directed transport, and endocytosis was sufficient for accurately describing polarization morphologies. Surprisingly, the model predicts that polarized regions are defined with a precision that is nearly optimal for measured endocytosis rates and that polarity can be dynamically stabilized through positive feedback with directed transport. Our approach provides a step toward understanding how biological systems shape spatially precise, unambiguous cortical polarity domains using dynamic processes.