Abstract：
Cells can sense the physical properties of the extracellular matrices (ECMs), such as stiffness and ligand density, through cell adhesions to actively regulate their behaviors. Recent studies have shown that varying ligand spacing of ECMs can influence adhesion size, cell spreading, and even stem cell differentiation, indicating that cells have the spatial sensing ability of ECM ligands. However, the mechanism of the cells\' spatial sensing remains unclear. In this study, we have developed a lattice-spring motor-clutch model by integrating cell membrane deformation, the talin unfolding mechanism, and the lattice spring for substrate ligand distribution to explore how the spatial distribution of integrin ligands and substrate stiffness influence cell spreading and adhesion dynamics. By applying the Gillespie algorithm, we found that large ligand spacing reduces the superposition effect of the substrate\'s displacement fields generated by pulling force from motor-clutch units, increasing the effective stiffness probed by the force-sensitive receptors; this finding explains a series of previous experiments. Furthermore, using the mean-field theory, we obtain the effective stiffness sensed by bound clutches analytically; our analysis shows that the bound clutch number and ligand spacing are the two key factors that affect the superposition effects of deformation fields and, hence, the effective stiffness. Overall, our study reveals the mechanism of cells\' spatial sensing, i.e., ligand spacing changes the effective stiffness sensed by cells due to the superposition effect of deformation fields, which provides a physical clue for designing and developing biological materials that effectively control cell behavior and function.
摘要：
细胞可以感知细胞外基质（ECM）的物理特性，如刚度和配体密度，通过细胞粘附来积极调节自己的行为。最近的研究表明，ECM的不同配体间距可以影响粘附大小，细胞扩散,甚至干细胞分化，表明细胞具有ECM配体的空间感知能力。然而,细胞空间感知的机制尚不清楚。在这项研究中,我们通过整合细胞膜变形，开发了一种晶格弹簧电机离合器模型，塔林展开机构，和基质配体分布的晶格弹簧，以探讨整合素配体和基质刚度的空间分布如何影响细胞扩散和粘附动力学。通过应用Gillespie算法,我们发现，大的配体间距减少了由来自电机离合器单元的拉力产生的基板的位移场的叠加效应，增加力敏受体探测的有效刚度；这一发现解释了一系列先前的实验。此外，使用平均场理论，我们通过分析获得了约束离合器的有效刚度；我们的分析表明，约束离合器数量和配体间距是影响变形场叠加效应的两个关键因素，因此，有效刚度。总的来说,我们的研究揭示了细胞空间感知的机制，即，由于变形场的叠加效应，配体间距改变了细胞感知的有效刚度，这为设计和开发有效控制细胞行为和功能的生物材料提供了物理线索。
