Molecular Cell Biomechanics Laboratory, Department of Bioengineering, University of California, Berkeley, California, United States of America.
PLoS One. 2011;6(10):e25627. doi: 10.1371/journal.pone.0025627. Epub 2011 Oct 5.
Quantitative description of cell mechanics has challenged biological scientists for the past two decades. Various structural models have been attempted to analyze the structure of the cytoskeleton. One important aspect that has been largely ignored in all these modeling approaches is related to the flexural and buckling behavior of microtubular filaments. The objective of this paper is to explore the influence of this flexural and buckling behavior in cytoskeletal mechanics.In vitro the microtubules are observed to buckle in the first mode, reminiscent of a free, simply-supported beam. In vivo images of microtubules, however, indicate that the buckling mostly occurs in higher modes. This buckling mode switch takes place mostly because of the lateral support of microtubules via their connections to actin and intermediate filaments. These lateral loads are exerted throughout the microtubule length and yield a considerable bending behavior that, unless properly accounted for, would produce erroneous results in the modeling and analysis of the cytoskeletal mechanics.One of the promising attempts towards mechanical modeling of the cytoskeleton is the tensegrity model, which simplifies the complex network of cytoskeletal filaments into a combination merely of tension-bearing actin filaments and compression-bearing microtubules. Interestingly, this discrete model can qualitatively explain many experimental observations in cell mechanics. However, evidence suggests that the simplicity of this model may undermine the accuracy of its predictions, given the model's underlying assumption that "every single member bears solely either tensile or compressive behavior," i.e. neglecting the flexural behavior of the microtubule filaments. We invoke an anisotropic continuum model for microtubules and compare the bending energy stored in a single microtubule with its axial strain energy at the verge of buckling. Our results suggest that the bending energy can exceed the axial energy of microtubules by 40 folds. A modification to tensegrity model is, therefore, proved necessary in order to take into account the flexural response of microtubules. The concept of "bendo-tensegrity" is proposed as a modification to contemporary cytoskeletal tensegrity models.
细胞力学的定量描述在过去的二十年里一直是生物学家面临的挑战。已经尝试了各种结构模型来分析细胞骨架的结构。在所有这些建模方法中，一个重要的方面在很大程度上被忽视了，那就是与微管丝的弯曲和屈曲行为有关。本文的目的是探讨这种弯曲和屈曲行为对细胞骨架力学的影响。在体外，微管被观察到在第一模态下屈曲，类似于自由的、简支梁。然而，体内微管的图像表明，屈曲主要发生在更高的模态。这种屈曲模式的切换主要是由于微管通过与肌动蛋白和中间丝的连接而产生的侧向支撑。这些侧向载荷作用于整个微管长度，并产生相当大的弯曲行为，如果不加以适当考虑，在细胞骨架力学的建模和分析中会产生错误的结果。细胞骨架力学的机械建模的一个有前途的尝试是张紧结构模型，它将细胞骨架纤维的复杂网络简化为仅仅由承受张力的肌动蛋白纤维和承受压缩的微管的组合。有趣的是，这个离散模型可以定性地解释细胞力学中的许多实验观察结果。然而，有证据表明，鉴于该模型的基本假设是“每个单独的成员仅承受拉伸或压缩行为”，即忽略微管丝的弯曲行为，该模型的简单性可能会破坏其预测的准确性。我们为微管引入了各向异性连续体模型，并将单个微管中储存的弯曲能与屈曲边缘处的轴向应变能进行比较。我们的结果表明，弯曲能可以超过微管的轴向能量 40 倍。因此，为了考虑微管的弯曲响应，有必要对张紧结构模型进行修正。因此，提出了“弯曲张紧结构”的概念，作为对当代细胞骨架张紧结构模型的修正。
