Cell migration is fundamental for the immune response, development, and morphogenesis. For navigation through complex and ever-changing environments, migrating cells require a balance between a stable leading-edge, which is necessary for directional migration, and some unstable features to enable the required dynamic behaviors. The leading edge is often composed of actin-driven protrusions including lamellipodia and ruffles with continuously changing membrane curvature. Whether their membrane topography affects the cell's leading edge and motion persistence in complex environments remains unknown. To study this, we combined a theoretical analysis with machine learning-based segmentation for time-resolved TIRF microscopy, membrane topography analysis from electron microscopy images and microfluidics. We discovered that cell motion persistence and directionality, in both freely moving and environmentally-constrained cells, strongly depend on the curvature-sensing protein Snx33. Specifically, Snx33 promotes leading edge instabilities by locally inhibiting WAVE2- driven actin polymerization in a curvature-dependent manner. Snx33 knockout cells migrate faster and are more persistent during unobstructed migration, but fail when a change in direction is required. Thus, Snx33 is key for steering cell motility in complex environments by facilitating contact inhibition of locomotion and promoting efficient turning. These results identify cell surface topography as an organizing principle at the cell periphery that directs cell migration.

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