Form, Force, and Fate: The Biological Language of Curvature.

Across scales and dimensions, curvature is an intrinsic feature of living systems that regulates cellular behavior in both health and disease. Recent advances in mechanobiology have established curvature as a bioactive physical cue capable of driving cellular functions and linking form, force, and fate. In this perspective, we highlight how curvature manifests across biological length scales and shapes key cellular processes such as migration and differentiation. We discuss emerging mechanisms of curvature sensing and transduction, outlining open questions regarding their integration within native and engineered environments. Finally, we reflect on current and future advances in curvature-guided biomaterial design, their impact on tissue engineering, and the potential of curvature as a biophysical marker in physiological and pathological contexts.