McEvoy Eóin, Deshpande Vikram S, McGarry Patrick
Biomedical Engineering, National University of Ireland Galway, Galway, Ireland.
Department of Engineering, University of Cambridge, U.K..
J Mech Behav Biomed Mater. 2017 Oct;74:283-295. doi: 10.1016/j.jmbbm.2017.06.006. Epub 2017 Jun 7.
In this study we present a steady-state adaptation of the thermodynamically motivated stress fiber (SF) model of Vigliotti et al. (2015). We implement this steady-state formulation in a non-local finite element setting where we also consider global conservation of the total number of cytoskeletal proteins within the cell, global conservation of the number of binding integrins on the cell membrane, and adhesion limiting ligand density on the substrate surface. We present a number of simulations of cell spreading in which we consider a limited subset of the possible deformed spread-states assumed by the cell in order to examine the hypothesis that free energy minimization drives the process of cell spreading. Simulations suggest that cell spreading can be viewed as a competition between (i) decreasing cytoskeletal free energy due to strain induced assembly of cytoskeletal proteins into contractile SFs, and (ii) increasing elastic free energy due to stretching of the mechanically passive components of the cell. The computed minimum free energy spread area is shown to be lower for a cell on a compliant substrate than on a rigid substrate. Furthermore, a low substrate ligand density is found to limit cell spreading. The predicted dependence of cell spread area on substrate stiffness and ligand density is in agreement with the experiments of Engler et al. (2003). We also simulate the experiments of Théry et al. (2006), whereby initially circular cells deform and adhere to "V-shaped" and "Y-shaped" ligand patches. Analysis of a number of different spread states reveals that deformed configurations with the lowest free energy exhibit a SF distribution that corresponds to experimental observations, i.e. a high concentration of highly aligned SFs occurs along free edges, with lower SF concentrations in the interior of the cell. In summary, the results of this study suggest that cell spreading is driven by free energy minimization based on a competition between decreasing cytoskeletal free energy and increasing passive elastic free energy.
在本研究中，我们提出了Vigliotti等人（2015年）基于热力学原理的应力纤维（SF）模型的稳态适应性模型。我们在非局部有限元设置中实现了这种稳态公式，其中我们还考虑了细胞内细胞骨架蛋白总数的全局守恒、细胞膜上结合整合素数量的全局守恒以及底物表面上的粘附限制配体密度。我们进行了一些细胞铺展模拟，其中我们考虑了细胞假设的可能变形铺展状态的有限子集，以检验自由能最小化驱动细胞铺展过程的假设。模拟表明，细胞铺展可以被视为以下两者之间的竞争：（i）由于细胞骨架蛋白应变诱导组装成收缩性应力纤维而导致的细胞骨架自由能降低，以及（ii）由于细胞机械被动成分的拉伸而导致的弹性自由能增加。计算结果表明，与刚性底物上的细胞相比，顺应性底物上的细胞的计算最小自由能铺展面积更低。此外，发现低底物配体密度会限制细胞铺展。预测的细胞铺展面积对底物刚度和配体密度的依赖性与Engler等人（2003年）的实验结果一致。我们还模拟了Théry等人（2006年）的实验，即最初呈圆形的细胞变形并粘附到“V形”和“Y形”配体斑块上。对许多不同铺展状态的分析表明，具有最低自由能的变形构型表现出与实验观察结果相对应的应力纤维分布，即沿着自由边缘出现高浓度的高度排列的应力纤维，而细胞内部的应力纤维浓度较低。总之，本研究结果表明，细胞铺展是由基于细胞骨架自由能降低和被动弹性自由能增加之间竞争的自由能最小化驱动的。
