预应力细胞骨架丝网络的离散到连续模型
Discrete-to-continuum models of pre-stressed cytoskeletal filament networks
AI总结：
本文提出离散到连续的细胞骨架力学模型，用于预测预应力蛋白丝网络的力学响应，并验证了模型在波形蛋白网络中的有效性，发现刚度随预应力和珠子尺寸呈特定标度关系。
摘要：
我们提出了一个用于真核细胞细胞骨架力学行为的数学模型。该离散模型涉及一个规则排列的预应力蛋白丝阵列，这些蛋白丝表现出对焓拉伸的阻力，并在交联点连接形成网络。假设交联点之间的距离远小于细胞的特征长度尺度，我们将离散力平衡升级为连续控制方程组，并推导出相应的宏观应力张量。我们使用这些离散和连续模型来分析放置在域中的珠子所受的强制位移，通过力-位移曲线表征细胞流变学。我们进一步推导了在小珠子半径极限下应力场和应变场的解析近似，预测了产生给定变形所需的净力，并阐明了其对丝微观特性的依赖。我们将这些模型应用于中间丝波形蛋白的网络，并展示了离散、连续和解析方法预测之间的良好一致性。特别是，我们的模型预测网络刚度随丝预应力的增加呈次线性增长，并随珠子尺寸呈对数尺度变化。
英文摘要：
We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at crosslinks to form a network. Assuming that the inter-crosslink distance is much shorter than the lengthscale of the cell, we upscale the discrete force balance to form a continuum system of governing equations and deduce the corresponding macroscopic stress tensor. We use these discrete and continuum models to analyse the imposed displacement of a bead placed in the domain, characterising the cell rheology through the force-displacement curve. We further derive an analytical approximation to the stress and strain fields in the limit of small bead radius, predicting the net force required to generate a given deformation and elucidating the dependency on the microscale properties of the filaments. We apply these models to networks of the intermediate filament vimentin and demonstrate good agreement between predictions of the discrete, continuum and analytical approaches. In particular, our model predicts that the network stiffness increases sublinearly with the filament pre-stress and scales logarithmically with the bead size.
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