由粘弹性细胞骨架介导的熵驱动起始和细胞摄取：基于昂萨格变分原理的动力学相图
Entropy-Driven Initiation and Cellular Uptake Mediated by Viscoelastic Cytoskeleton: A Kinetic Phase Diagram from Onsager Variational Principle
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中文总结 AI 辅助
研究受体介导内吞作用中配体和受体靠近的初始驱动力问题，基于昂萨格变分原理开发连续介质模型，纳入多种因素，通过动力学相图预测相关参数，为细胞摄取提供变分基础，对多领域有重要意义。
中文摘要 AI 辅助
受体介导的内吞作用中一个基本问题仍未得到解答：是什么初始驱动力使配体和受体靠近？以往模型假设已有接触而忽略了起始问题，本文提出拥挤细胞环境中纳米级生物分子的熵力提供了关键驱动机制。我们基于昂萨格变分原理开发了一个统一的连续介质模型，其中吞噬深度为广义坐标，驱动力来自熵、结合、膜和细胞骨架贡献的自由能景观。该框架自然纳入了：（i）熵驱动粘附作为起始；（ii）配体-受体结合作为维持力；（iii）通过赫尔弗里希-卡纳姆哈密顿量进行膜变形；（iv）通过弹性-粘弹性对应原理考虑细胞骨架粘弹性。动力学相图预测了起始的关键生物分子浓度、完全吞噬的配体密度下限、可吞噬颗粒的有限尺寸窗口以及随结合能增加而减小的30-60nm最佳病毒半径。昂萨格溶解度条件自然产生相边界。该模型在大颗粒平面极限下与经典朝仓-大泽结果具有渐近一致性。更硬的细胞导致更长的吞噬时间和更窄的尺寸窗口。惊人的是，在生理现实参数下最佳尺寸与HIV-1尺寸匹配。这项工作为细胞摄取提供了一个变分基础，对病毒学、纳米技术和药物递送具有重要意义。
英文摘要
A fundamental question in receptor-mediated endocytosis remains unanswered: what initial driving force brings ligands and receptors into close proximity? While previous models assume pre-existing contact and overlook this initiation problem, we propose that entropic forces from nanoscale biomolecules in crowded cellular environments provide the essential driving mechanism. We develop a unified continuum model rooted in the Onsager variational principle, where engulfment depth serves as the generalized coordinate and the driving force derives from a free energy landscape of entropic, binding, membrane, and cytoskeleton contributions. The framework naturally incorporates: (i) entropy-driven adhesion as initiation; (ii) ligand-receptor binding as the sustaining force; (iii) membrane deformation via the Helfrich-Canham Hamiltonian; and (iv) cytoskeleton viscoelasticity through the elastic-viscoelastic correspondence principle. The kinetic phase diagram predicts a critical biomolecule concentration for initiation, a lower bound of ligand density for complete engulfment, a finite size window for engulfable particles, and an optimal virus radius of 30--60 nm that decreases with increasing binding energy. The Onsager solubility condition naturally yields the phase boundaries. The model exhibits asymptotic consistency with the classic Asakura-Oosawa result in the large-particle flat-surface limit. Stiffer cells lead to longer engulfment times and narrower size windows. Strikingly, the optimal size matches HIV-1 dimensions under physiologically realistic parameters. This work provides a variational foundation for cellular uptake with implications for virology, nanotechnology, and drug delivery.
