NEMO: A Framework for Nematic and Morphological Analysis of Curved and Multi-layered Biological Surfaces
Abstract
Across biological scales, from cytoskeletal networks to whole tissues, orientational order and topological defects arise within complex three-dimensional geometries. However, quantifying nematic order orientational order with head-to-tail symmetry remains challenging: 2D projections introduce geometric distortions, while current 3D methods often struggle to resolve distinct nematic fields within curved or multilayer structures. Here, we introduce NEMO, a modular Python framework for the depth-resolved quantification of tangential nematic order and surface morphology. By reconstructing biological surfaces as triangulated meshes, NEMO projects curved intensity layers, extracts local nematic directors, and computes locally averaged nematic tensors within the tangent plane. The pipeline identifies topological defects and computes their topological charge by accounting for the Gaussian curvature of the underlying surface. Furthermore, NEMO quantifies tissue morphology through inter-surface distance and surface-fitted estimates of Gaussian and mean curvatures. We show the capacities of this framework using a synthetic nematic film on a vesicle and experimental actin organisation in Hydra. By combining customisable projections with surface-constrained analysis, NEMO provides a unified framework for quantifying the interplay between orientational order and geometry across scales.
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BibTeX
@misc{andreadis2026nemo,
title = {{NEMO: A Framework for Nematic and Morphological Analysis of Curved and Multi-layered Biological Surfaces}},
author = {Konstantinos Andreadis and Oriol Mañé-Benach and Claire A. Dessalles and Lodovico Mazzei and Aurélien Roux and Guillaume Salbreux},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12906},
eprint = {2609.12906},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12906},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - NEMO: A Framework for Nematic and Morphological Analysis of Curved and Multi-layered Biological Surfaces
AU - Konstantinos Andreadis
AU - Oriol Mañé-Benach
AU - Claire A. Dessalles
AU - Lodovico Mazzei
AU - Aurélien Roux
AU - Guillaume Salbreux
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12906
UR - https://arxiv.org/abs/2609.12906
AB - Across biological scales, from cytoskeletal networks to whole tissues, orientational order and topological defects arise within complex three-dimensional geometries. However, quantifying nematic order orientational order with head-to-tail symmetry remains challenging: 2D projections introduce geometric distortions, while current 3D methods often struggle to resolve distinct nematic fields within curved or multilayer structures. Here, we introduce NEMO, a modular Python framework for the depth-resolved quantification of tangential nematic order and surface morphology. By reconstructing biological surfaces as triangulated meshes, NEMO projects curved intensity layers, extracts local nematic directors, and computes locally averaged nematic tensors within the tangent plane. The pipeline identifies topological defects and computes their topological charge by accounting for the Gaussian curvature of the underlying surface. Furthermore, NEMO quantifies tissue morphology through inter-surface distance and surface-fitted estimates of Gaussian and mean curvatures. We show the capacities of this framework using a synthetic nematic film on a vesicle and experimental actin organisation in Hydra. By combining customisable projections with surface-constrained analysis, NEMO provides a unified framework for quantifying the interplay between orientational order and geometry across scales.
ER -