Biophysical modeling of membrane curvature generation and curvature sensing by the glycocalyx

Abstract

Generation of membrane curvature is fundamental to cellular function. Recent studies have established that the glycocalyx, a sugar-rich polymer layer at the cell surface, can generate membrane curvature. While there have been some theoretical efforts to understand the interplay between the glycocalyx and membrane bending, there remain open questions about how the properties of the glycocalyx affect membrane bending. For example, the relationship between membrane curvature and the density of glycosylated proteins on its surface remains unclear. In this work, we use polymer brush theory to develop a detailed biophysical model of the energetic interactions of the glycocalyx with the membrane. Using this model, we identify the conditions under which the glycocalyx can both generate and sense curvature. Our model predicts that the extent of membrane curvature generated depends on the grafting density of the glycocalyx and the length of the polymers constituting the glycocalyx. Furthermore, when coupled with the intrinsic membrane properties such as spontaneous curvature and a line tension along the membrane, the curvature generation properties of the glycocalyx are enhanced. These predictions were tested experimentally by examining the propensity of glycosylated transmembrane proteins to drive the assembly of highly-curved filopodial protrusions at the plasma membrane of adherent mammalian cells. Our model also predicts that the glycocalyx has curvature sensing capabilities, in agreement with the results of our experiments. Thus, our study develops a quantitative framework for mapping the properties of the glycocalyx to the curvature generation capability of the membrane. Significance StatementThe glycocalyx is a dense layer of glycosylated transmembrane proteins and lipids distributed on the extracellular surface of eukaryotic cells. It is known to mediate cell-cell interactions and protect cells from invasion by pathogens. However, recently it has been found to play a role in generating membrane curvature, which is essential to diverse cellular functions spanning from endocytosis to cell division. Experiments have revealed that different membrane shapes: spherical vesicles, pearls, and tubes are regulated by the glycocalyx. However, currently, we lack a quantitative physical explanation of how glycocalyx properties determine membrane geometries. Here we develop a polymer brush theory-based model, which suggests that the interplay between glycocalyx polymers and membrane bending captures the wide variety of membrane shapes from spherical buds to elongated pearl-like shapes found in previously published experiments. We predict that the physical properties of glycocalyx polymers, line tension, and membrane elastic parameters play significant roles in regulating membrane morphologies. We find that the glycocalyx prefers higher local membrane curvature indicating that the glycocalyx can sense local curvature.