Substrate curvature and stiffness equivalence in governing cell mechanosensing

Mechanosensing enables cells to perceive and interpret their mechanical microenvironment, including forces, stiffness and topography. Although focal adhesions (FAs) are central to this process, their structural adaptation to mechanical stimuli remains poorly understood. Here, we uncover FA tilting - the inclination of the FA plane relative to the substrate - as a mechanically regulated architectural feature. Using reverse cell imprinting and atomic force microscopy, we reveal a strong inverse correlation between FA tilting angle and substrate stiffness. A two-dimensional clutch model shows that tilting emerges from force distribution across the FA–substrate interface and contributes to cell mechanosensing. By engineering rigid substrates with defined curvatures, we impose specific tilting angles independently of stiffness and modulate the cellular mechanostate, revealing a curvature–stiffness mechanical equivalence principle. This enables the construction of a correlation map linking curvature values to equivalent stiffness levels. Together, our results identify FA tilting as a geometrical and mechanical transducer and a powerful design parameter for instructive biomaterials in physio-pathological tissue engineering. This study reveals how cells translate substrate stiffness and curvature into biological responses through focal adhesion tilting, uncovering a mechanical equivalence that opens new routes for designing cell-instructive biomaterials.