How multiscale curvature couples forces to cellular functions

Among the physicochemical cues in the cellular microenvironment that orchestrate cell processes, the different levels of curvature in the extracellular matrix and intrinsic to the tissues play a pivotal role in the spatiotemporal control of key cellular functions. Curvature influences multicellular organization and contributes to the onset of specific human diseases. This Review outlines how physical parameters used to describe the balance of forces in cells and tissues shed light on the mechanism of curvature sensing of cells across different length scales. We provide a summary of progress in delineating the fundamental mechanobiological characteristics of curvature sensing across various scales, emphasizing key challenges in the field. Additionally, we explore the potential of vertex model approaches to uncover critical physical elements involved in the mechanical regulation of curved tissues and the construction of functional architectures at the collective level. Finally, we examine how changes in curvature can influence transcriptional regulation through a reorganization of cytoskeletal forces acting on the nucleus, thereby facilitating the development of specific human diseases.