Entropy-Induced Curvature: How Membrane-Anchored Proteins Shape Cell Geometry

Cell morphology plays a critical role in guiding protein pattern formation, thereby facilitating spatiotemporal self-organization in cells. Conversely, it has also been shown that proteins can locally induce shape deformations through various mechanisms. However, many of these mechanisms rely on specific protein properties, therefore limiting their general applicability to induce curvature. In this study, we propose a thermodynamically grounded and generic mechanism by which membrane-anchored proteins generate local spontaneous curvature. Using a continuum approach, we demonstrate how a finite distance between cell membrane and the cytosolic domain of a protein induces an effective spontaneous curvature. Notably, even in the absence of protein-protein interactions, we find that entropy alone is sufficient to induce a spontaneous curvature. Moreover, we show that nanometer-sized anchors can lead to spontaneous curvatures relevant for cells on the micrometer scale. Our theory offers to explore a generic mechanism how proteins induce shape deformations in living systems that can also be applied to non-equilibrium reaction-diffusion systems.