膜张力与细胞–细胞核力学耦合调控受限细胞迁移的几何表面偏微分方程模型
Membrane tension and cell–nucleus mechanical coupling regulate confined cell migration
一个基于几何表面偏微分方程（GS-PDEs）的无量纲生物物理模型再现了受限细胞迁移的实验观测模式，并用演化表面有限元方法（ESFEM）求解，将质膜与核膜建模为有能量的几何膜以实现降维。模型复现了脂质库耗竭与核–核纤层解折叠限制质膜和核膜表面积、阻断细胞通过狭窄通道，以及核速度在穿出孔道时达到峰值、核运动在牵拉与推挤之间交替等现象。模型进一步预测：穿出孔道时的速度峰值源于核膜后缘以膜张力形式储存的曲率弹性能释放；质膜–核膜力学耦合会阻碍细胞位移，因为部分运动能量被用于核定位。该模型可量化膜张力、弯曲能、渗透压、质膜–核膜弹性与接触力等实验难以获取的力，为检验受限迁移的机制假设提供可解释平台。
来源：PLOS Computational Biology · journals.plos.org
by David Hernandez-Aristizabal, Anotida Madzvamuse, Rachele Allena
Cell migration is a fundamental physiological process essential from embryogenesis to cancer metastasis. It is primarily governed by the coupled mechanics of the plasma membrane (PM) and the nucleus, together with cytoskeletal dynamics. Being the largest and stiffest organelle, the nucleus is considered a rate-limiting factor in confined migration. However, nuclear positioning varies across cell types and migration modes, and the forces orchestrating its mechanical coupling with the PM are not completely understood. In recent decades, mathematical modelling has gained relevance to support cell migration research, yet models face the fundamental challenge of balancing mechanistic detail with computational efficiency. Here, we develop a dimensionless, biophysically grounded model based on geometric surface partial differential equations (GS-PDEs) for cell migration. This approach benefits from dimensional reduction—the PM and the nuclear envelope (NE) are modelled as energetic geometric membranes—and is solved using the evolving surface finite element method (ESFEM), balancing mechanistic detail with computational feasibility. The model reproduces experimentally observed migration patterns: exhaustion of lipid reservoirs and nuclear–lamina unfolding limit PM and NE surface area, blocking cell passage through constrictions; nuclear velocity peaks upon pore exit; and nuclear movement alternates between pulling and pushing regimes. Moreover, the modelling approach makes key predictions: the velocity peak upon nuclear pore exit is driven by the release of the curvature-elastic energy stored as membrane tension at the NE rear, and PM–NE mechanical coupling can hinder cell translocation, since part of the locomotion energy is invested in nuclear positioning. The model quantifies forces that are not easily experimentally accessible, including membrane tension, bending energy, osmotic pressure, PM–NE elasticity, and contact forces, offering an interpretable platform to test and propose mechanistic hypotheses on confined cell migration.