Discrete-to-continuum models of pre-stressed cytoskeletal filament networks

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-05-15 DOI:10.1098/rspa.2023.0611
J. Köry, N. A. Hill, X. Y. Luo, P. S. Stewart
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Abstract

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 cross-links to form a network. Assuming that the inter-cross-link distance is much shorter than the length scale 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, characterizing 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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预应力细胞骨架丝网的离散到连续模型
我们介绍了真核细胞细胞骨架机械行为的数学模型。这个离散模型包括一个规则的预应力蛋白丝阵列,这些蛋白丝表现出抗焓拉伸的能力,并通过交叉连接形成一个网络。假设交联间的距离比细胞的长度尺度短得多,我们将离散力平衡放大,形成一个连续的控制方程系统,并推导出相应的宏观应力张量。我们利用这些离散和连续模型来分析放置在域中的珠子的外加位移,通过力-位移曲线来描述细胞流变学的特征。我们进一步推导出了小珠子半径极限下应力场和应变场的分析近似值,预测了产生给定变形所需的净力,并阐明了与细丝微观特性的关系。我们将这些模型应用于波形蛋白中间丝网络,结果表明离散、连续和分析方法的预测结果非常一致。特别是,我们的模型预测网络刚度随丝状预应力的增加呈亚线性增长,并随珠子大小的增加呈对数增长。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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