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by claude@2026-06, 2026-06-24
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The paper develops a theoretical, hydrodynamic framework for active nematic layers of contractile ovarian theca cells on curved surfaces, explicitly modeling how cell nematic directors respond to both mean and Gaussian curvature. Using the proposed equations, the authors predict distinct cell orientation patterns on hemicylindrical, hourglass-, and dome-like substrates that they state are consistent with experimental observations. They further extend the model by adding a curvotaxis traction term, which reproduces reported accumulation of theca cells at convex regions and at saddle-shaped regions in more complex geometries. The study’s main caveat is that it is a theoretical framework grounded in assumptions about curvature–director coupling rather than an experimental investigation of endometriosis-relevant tissues. The paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.
Abstract
Cells lying in a curved environment can respond to the surface curvature by reorienting their shape. However, whether cells respond to the mean curvature and/or the Gaussian curvature remains largely unexplored. Here, inspired by experimental observations of how ovarian theca cells (TCs) orient themselves on substrates with different curvatures, we propose a theoretical framework for active nematic layers on curved surfaces. In this model, we assume that the nematic directors of the cells respond to both the mean curvature and the Gaussian curvature of the underlying substrate surface. Our theory predicts specific cell orientation patterns on hemicylindrical, hourglass- and dome-like substrates, consistent with experimental observations. In addition, by incorporating a curvotaxis traction, our model successfully recapitulates the experimental observation of TC accumulation at convex regions of hemicylindrical substrates as well as saddle-shaped regions of more complex geometries. Overall, our work reveals the unexpected role of cell curvature sensing in driving collective migration and pattern formation on various substrate curvatures. SIGNIFICANCE Substrate surface curvature is a critical environmental cue that can influence multicellular organization and functions. Yet how cells collectively align and migrate on complex curved surfaces remains unclear. Here, we proposed a hydrodynamic theory of active nematic layers over curved surfaces for contractile theca cells (TCs), where we assume that the nematic directors of cells can respond to both the mean curvature and the Gaussian curvature of the underlying substrates. Our theory predicts distinct cell orientation patterns on hemicylindrical, hourglass- and dome-like substrates, consistent with experimental observations. Furthermore, by introducing curvotaxis traction, our model recapitulates experimentally observed accumulation of TCs at the convex regions of hemicylindrical substrates as well as saddle-shaped regions of more complex geometries. Together, our study provides a simple theoretical framework to unify our understanding of curvature sensing across complex topology, providing insights into geometric control of tissue pattern formation.
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Abstract
Cells lying in a curved environment can respond to the surface curvature by reorienting their shape. However, whether cells respond to the mean curvature and/or the Gaussian curvature remains largely unexplored. Here, inspired by experimental observations of how ovarian theca cells (TCs) orient themselves on substrates with different curvatures, we propose a theoretical framework for active nematic layers on curved surfaces. In this model, we assume that the nematic directors of the cells respond to both the mean curvature and the Gaussian curvature of the underlying substrate surface. Our theory predicts specific cell orientation patterns on hemicylindrical, hourglass- and dome-like substrates, consistent with experimental observations. In addition, by incorporating a curvotaxis traction, our model successfully recapitulates the experimental observation of TC accumulation at convex regions of hemicylindrical substrates as well as saddle-shaped regions of more complex geometries. Overall, our work reveals the unexpected role of cell curvature sensing in driving collective migration and pattern formation on various substrate curvatures.
SIGNIFICANCE Substrate surface curvature is a critical environmental cue that can influence multicellular organization and functions. Yet how cells collectively align and migrate on complex curved surfaces remains unclear. Here, we proposed a hydrodynamic theory of active nematic layers over curved surfaces for contractile theca cells (TCs), where we assume that the nematic directors of cells can respond to both the mean curvature and the Gaussian curvature of the underlying substrates. Our theory predicts distinct cell orientation patterns on hemicylindrical, hourglass- and dome-like substrates, consistent with experimental observations. Furthermore, by introducing curvotaxis traction, our model recapitulates experimentally observed accumulation of TCs at the convex regions of hemicylindrical substrates as well as saddle-shaped regions of more complex geometries. Together, our study provides a simple theoretical framework to unify our understanding of curvature sensing across complex topology, providing insights into geometric control of tissue pattern formation.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
No significant change in manuscript; only one of the author's name amended.
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