Local Clustering and Global Spreading of Receptors for Optimal Spatial Gradient Sensing

Spatial information from cell-surface receptors is crucial for processes that require signal processing and sensing of the environment. Here, we investigate the optimal placement of such receptors through a theoretical model that minimizes uncertainty in gradient estimation. Without requiring a priori knowledge of the physical limits of sensing or biochemical processes, we reproduce the emergence of clusters that closely resemble those observed in real cells. On perfect spherical surfaces, optimally placed receptors spread uniformly. When perturbations break their symmetry, receptors cluster in regions of high curvature, massively reducing estimation uncertainty. This agrees in many scenarios with mechanistic models that minimize elastic preference discrepancies between receptors and cell membranes. We further extend our model to motile receptors responding to cell-shape changes and external fluid flow, demonstrating the biological relevance of our model. Our findings provide a simple and utilitarian explanation for receptor clustering at high-curvature regions when high sensing accuracy is paramount.