Biphasic curvature dependence of cell migration: Persistent randomness versus directionality

Xiaoyu Yu; Haiqin Wang; Mingxi Xie; Fangfu Ye; Zhiqi Shen; Xiaochen Wang; Qihui Fan; Xinpeng Xu

doi:10.1016/j.bpj.2025.10.003

Biphasic curvature dependence of cell migration: Persistent randomness versus directionality

Biophys J. 2025 Oct 9:S0006-3495(25)00654-X. doi: 10.1016/j.bpj.2025.10.003. Online ahead of print.

Authors

Xiaoyu Yu¹, Haiqin Wang², Mingxi Xie³, Fangfu Ye⁴, Zhiqi Shen⁵, Xiaochen Wang⁶, Qihui Fan⁷, Xinpeng Xu⁸

Affiliations

¹ School of Mechanical Engineering & Automation, Beihang University, Beijing, China; Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China.
² Department of Physics and MATEC Key Lab, Guangdong Technion - Israel Institute of Technology, Shantou, Guangdong, China; Department of Physics, Technion - Israel Institute of Technology, Haifa, Israel.
³ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
⁴ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China; Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang, China; Oujiang Laboratory (Zhejiang Lab for Regenerative Medicine, Vision and Brain Health), Wenzhou, Zhejiang, China.
⁵ Department of Physics and MATEC Key Lab, Guangdong Technion - Israel Institute of Technology, Shantou, Guangdong, China; Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen, China.
⁶ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China; Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang, China; Joint Centre of Translational Medicine, The First Affiliated Hospital of Wenzhou Medical University, Wenzhou, China. Electronic address: wangxiaochendaisy@ucas.ac.cn.
⁷ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China. Electronic address: fanqh@iphy.ac.cn.
⁸ Department of Physics and MATEC Key Lab, Guangdong Technion - Israel Institute of Technology, Shantou, Guangdong, China; Department of Physics, Technion - Israel Institute of Technology, Haifa, Israel. Electronic address: xu.xinpeng@gtiit.edu.cn.

PMID: 41063455
DOI: 10.1016/j.bpj.2025.10.003

Abstract

Cell-scale curvature is a key regulator of cell migration, yet its quantitative effects and underlying mechanisms remain elusive. Here, we combine controlled in vitro experiments with a phenomenological theoretical framework to investigate the migration of fibroblasts (NIH3T3) and epithelial cells (MCF10A) on the inner concave surfaces of polydimethylsiloxane microcylinders across a wide range of cell-scale curvatures (∼0.01 per micrometer). We find that migration persistence positively correlates with mean speed across all curvatures, consistent with the universal speed-persistence coupling relation previously observed for cells migrating on 1D and 2D planar substrates, as well as for cells embedded in 3D environments. Cell migration inside microcylinders is stochastic and anisotropic, as quantified by the nematic order parameter, and exhibits a biphasic dependence on curvature. At small curvatures, cells remain fully adhered to the surface, with anisotropy and speed both increasing while persistence decreases. When curvature exceeds a threshold of approximately 1/75 per micrometer, cells detach by forming stress-fiber chords, leading to reduced anisotropy and speed but increased persistence. This adhered-to-chord transition is followed by a shift in preferred orientation: migration initially favors the lateral direction and progressively aligns toward the axis at larger curvatures. These findings demonstrate that cells can actively reorient their stress fibers and migration in response to local cell-scale curvature sensed by the entire cell, even on cylindrical surfaces with constant mean curvature and vanishing Gaussian curvature. A modified persistent random walk model, incorporating persistent randomness and curvature-dependent directionality via bending and adhesion energetics, quantitatively captures these behaviors and predicts the transition threshold in close agreement with experiments. Together, this work establishes a quantitative framework for biphasic, curvature-dependent migration and provides new insight into how local geometry regulates mesenchymal motility.