Wang Yifan, Gong Jinghai, Wirtz Denis, Schafer Benjamin W
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
J Mech Behav Biomed Mater. 2017 Aug;72:52-65. doi: 10.1016/j.jmbbm.2017.04.015. Epub 2017 Apr 20.
Actin filaments and cross-linkers are main components of cytoskeletal networks in eukaryotic cells, and they support bending moments and axial forces respectively. A three-dimensional form-finding model is proposed in this work to investigate affine and non-affine deformations in cytoskeletal networks. In recent studies, modeling of cytoskeletal networks turns out to be a key piece in the cell mechanics puzzle. We used form-finding analysis to compute and analyze cytoskeletal models. A three-dimensional model is much more flexible and contains more elements than a two-dimensional model, and non-linear finite element analysis is difficult to converge. Thus, vector form intrinsic finite element analysis is employed here for valid results. The three-dimensional model reveals new behaviors beyond earlier two-dimensional models and better aligns with available data. Relative density of actin filaments and height of the form-finding model both play important roles in determining cytoskeletal stiffness, positively and negatively, respectively. Real cytoskeletal networks are quite mixed in terms of affine and non-affine deformations, which are quantified by internal strain energy in actin filaments and cross-linkers. Results are also influenced by actin filament relative density and height of the model. The three-dimensional form-finding model does provide much more room for intensive studies on cytoskeletal networks. In our future study, microtubules, fluidics, viscoelastic-plastic cross-linkers and even the whole cell model may be taken into account gradually to improve the cytoskeletal form-finding model.
肌动蛋白丝和交联蛋白是真核细胞细胞骨架网络的主要组成部分，它们分别支撑弯矩和轴向力。本文提出了一种三维找形模型，以研究细胞骨架网络中的仿射和非仿射变形。在最近的研究中，细胞骨架网络的建模成为细胞力学难题中的关键一环。我们使用找形分析来计算和分析细胞骨架模型。三维模型比二维模型更加灵活且包含更多元素，非线性有限元分析难以收敛。因此，这里采用向量形式固有有限元分析以获得有效的结果。三维模型揭示了超越早期二维模型的新行为，并且与现有数据更好地吻合。肌动蛋白丝的相对密度和找形模型的高度在分别正向和负向决定细胞骨架刚度方面都起着重要作用。真实的细胞骨架网络在仿射和非仿射变形方面相当复杂，这通过肌动蛋白丝和交联蛋白中的内应变能来量化。结果也受肌动蛋白丝相对密度和模型高度的影响。三维找形模型确实为细胞骨架网络的深入研究提供了更多空间。在我们未来的研究中，可能会逐步考虑微管、流体力学、粘弹塑性交联蛋白甚至整个细胞模型，以改进细胞骨架找形模型。
