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bioRxiv · 10.64898/2025.12.18.695144

A geometric-surface PDE model for cell-nucleus translocation through confinement

Ballatore, F.·Madzvamuse, A.·Jebane, C.·Helfer, E.·Allena, R.
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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. Author summaryCells often migrate through very narrow spaces in tissues, a process critical for cancer invasion, immune surveillance, and tissue development. In particular, the stiffness of the nucleus, the largest and most rigid organelle, can limit migration through tight pores. In this study, we present a mathematical model describing the motion of a cell and its nucleus through a microchannel during cell translocation, using a geometric formulation based on surface partial differential equations. The model is general and applicable to a variety of scenarios involving confined cell transport. The model is validated by reproducing key experiments on cell translocation through narrow microchannels. The framework incorporates essential surface features, including mechanical responses, bending rigidity, and surface tension. Sensitivity analysis highlights surface tension and channel geometry as the parameters that most strongly influence translocation. Overall, the model provides new insights into the mechanics of confined cell transport, grants access to cellular quantities that are difficult to measure experimentally, such as cell and nucleus areas, perimeters, and stresses, and establishes a foundation for future extensions incorporating more complex biochemical processes.

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Ballatore, F., Madzvamuse, A., Jebane, C., Helfer, E., Allena, R.. 2025-12-20. A geometric-surface PDE model for cell-nucleus translocation through confinement. https://doi.org/10.64898/2025.12.18.695144

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