A Conserved Geometric Code: Extracellular Matrix Curvature Directs Cell Migration Strategy via Nuclear Mechanosensing

Cells navigate complex tissue microenvironments defined by intricate physical cues, yet how they interpret the three-dimensional geometry of the extracellular matrix (ECM) remains an open question. Current models often fail to account for the tortuous architectures found in physiological tissues. Here, we demonstrate that ECM curvature functions as a tissue-specific geometric code read by the cell nucleus. By mapping collagen architectures across cancers and tissues, we find unique curvature fingerprints preserved during metastasis. Using micro-engineered substrates, we show that high curvature imposes localized nuclear bending stress, triggering a Lamin A/C-cPLA2-Ca2+ mechanotransductive cascade. This sensor rewires the cytoskeleton from longitudinal stress fibers to a cortical actomyosin network, driving a sharp transition from fast mesenchymal migration to a slower, exploratory amoeboid phenotype. We term this "nuclear curvotaxis", establishing a physical principle linking static geometry to dynamic strategy, with implications for predicting metastatic risk, understanding immune exclusion, and designing bio-instructive scaffolds for tissue engineering. ### Competing Interest Statement The authors have declared no competing interest. National Natural Science Foundation of China, 12572352, 12225208, 12432015 Surface Project (Key Grant) of Chinese Medicine Education Assciation, 2024KTZ037 Technology Innovation Leading Program of Shaanxi, 2024QCY-KXJ069 Scientific Research Program Funded by Education Department of Shaanxi Provincial Government, 24JP160