Beyond static geometry: dynamic curvature in mechanobiology

Living tissues are continuously reshaped by dynamic changes in geometry generated during development, physiology and disease. Yet, although curvature is increasingly recognized as a regulator of mechanotransduction, it is still largely viewed as a static geometric property. Here, we argue that the spatiotemporal evolution of curvature constitutes an independent physical variable whose biological effects arise not only from curvature magnitude and sign but also from its rate of change, frequency, persistence and temporal history. Rather than reviewing curvature as a geometric constraint, we propose a geometry–force–time framework in which curvature dynamics act as a distinct form of mechanical information coordinating membrane remodelling, cytoskeletal organization, nuclear mechanotransduction, collective tissue behaviour and mechanical memory across biological scales. We discuss emerging experimental evidences supporting this concept, highlight recent advances in biomaterials and engineered platforms that now enable precise control of curvature dynamics, and identify the key challenges that must be overcome to establish causal relationships between geometry and biological functions. By establishing dynamic curvature as a controllable physical variable rather than a static geometric descriptor, this framework expands the conceptual foundations of mechanobiology and opens new opportunities for developmental biology, disease modelling, organ-on-chip technologies, regenerative medicine and mechanomedicine.