Nuclear deformation regulates YAP dynamics in cancer associated fibroblasts

Cells cultured on stiff 2D substrates exert high intracellular force, resulting in mechanical deformation of their nuclei. This nuclear deformation (ND) plays a crucial role in the transport of Yes Associated Protein (YAP) from the cytoplasm to the nucleus. However, cells in vivo are in soft 3D environment with potentially much lower intracellular forces. Whether and how cells may deform their nuclei in 3D for YAP localization remains unclear. Here, by culturing human colon cancer associated fibroblasts (CAFs) on 2D, 2.5D, and 3D substrates, we differentiated the effects of stiffness, force, and ND on YAP localization. We found that nuclear translocation of YAP depends on the degree of ND irrespective of dimensionality, stiffness and total force. ND induced by the perinuclear force, not the total force, and nuclear membrane curvature correlate strongly with YAP activation. Immunostained slices of human tumors further sup-ported the association between ND and YAP nuclear localization, suggesting ND as a potential biomarker for YAP activation in tumors. Additionally, we conducted quantitative analysis of the force dynamics of CAFs on 2D substrates to construct a stochastic model of YAP kinetics. This model revealed that the probability of YAP nuclear translocation, as well as the residence time in the nucleus follow a power law. This study provides valuable insights into the regulatory mechanisms governing YAP dynamics and highlights the significance of threshold activation in YAP localization.