A geometric-surface PDE model for cell-nucleus translocation through confinement
Abstract
Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in migration through narrow pores or highly constrained spaces. In this work, we introduce a geometric surface partial differential equation (GS-PDE) model in which the cell plasma membrane and nuclear envelope are described as evolving energetic closed surfaces governed by force-balance equations. We replicate the results of a biophysical experiment, in which a microfluidic device is used to impose compressive stresses on cells by driving them through narrow microchannels under a controlled pressure gradient. The model is validated by reproducing cell entry into the microchannels. A parametric sensitivity analysis highlights the dominant influence of specific parameters, whose accurate estimation is essential to faithfully capture the experimental setup. We found that surface tension and confinement geometry emerge as key determinants of translocation efficiency. Although tailored to this specific setup for validation purposes, the framework is sufficiently general to be applied to a broad range of cell mechanics scenarios, providing a robust and flexible tool for investigating the interplay between cell mechanics and confinement. It also offers a solid foundation for future extensions integrating more complex biochemical processes such as active confined migration.
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BibTeX
@article{ballatore2026geometricsurface,
title = {{A geometric-surface PDE model for cell-nucleus translocation through confinement}},
author = {Francesca Ballatore and Anotida Madzvamuse and Cécile Jebane and Emmanuèle Helfer and Rachele Allena},
journal = {PLoS Computational Biology},
year = {2026},
month = jul,
doi = {10.1371/journal.pcbi.1014569},
url = {https://hal.science/hal-05708191v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A geometric-surface PDE model for cell-nucleus translocation through confinement
AU - Francesca Ballatore
AU - Anotida Madzvamuse
AU - Cécile Jebane
AU - Emmanuèle Helfer
AU - Rachele Allena
PY - 2026
DA - 2026/07/30
JO - PLoS Computational Biology
DO - 10.1371/journal.pcbi.1014569
UR - https://hal.science/hal-05708191v1
AB - Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in migration through narrow pores or highly constrained spaces. In this work, we introduce a geometric surface partial differential equation (GS-PDE) model in which the cell plasma membrane and nuclear envelope are described as evolving energetic closed surfaces governed by force-balance equations. We replicate the results of a biophysical experiment, in which a microfluidic device is used to impose compressive stresses on cells by driving them through narrow microchannels under a controlled pressure gradient. The model is validated by reproducing cell entry into the microchannels. A parametric sensitivity analysis highlights the dominant influence of specific parameters, whose accurate estimation is essential to faithfully capture the experimental setup. We found that surface tension and confinement geometry emerge as key determinants of translocation efficiency. Although tailored to this specific setup for validation purposes, the framework is sufficiently general to be applied to a broad range of cell mechanics scenarios, providing a robust and flexible tool for investigating the interplay between cell mechanics and confinement. It also offers a solid foundation for future extensions integrating more complex biochemical processes such as active confined migration.
SN - 1553-734X
SN - 1553-7358
ER -