Department of Mathematical Modeling, Moscow Institute of Electronics and Mathematics, Moscow, Russia.
Biophys J. 2010 Nov 3;99(9):2831-40. doi: 10.1016/j.bpj.2010.09.017.
Many cell cytoskeletons include an aster of microtubules, with the centrosome serving as the focal point. The position of the centrosome within the cell is important in such directional activities as wound closure and interactions of immune cells. Here we analyzed the centrosome positioning as it is dictated by microtubule elasticity alone in a mechanical model of an intrinsically fully symmetric microtubule aster. We demonstrate that the symmetry and the central position of the centrosome are unstable. The equilibrium deviation of the centrosome from the center is approximately proportional to the difference of the microtubule length and cell radius. The proportionality coefficient is 1 in flat cells and 2 in three-dimensional cells. The loss of symmetry is irreversible, and in general, the equilibrium form of the aster exhibits memory of past perturbations. The equilibrium position of the centrosome as a function of the microtubule length exhibits hysteresis, and the history of the length variation is reflected in the aster form. These properties of the simple aster of elastic microtubules must be taken into account in the analysis of more comprehensive theoretical models, and in the design and interpretation of experiments addressing the complex process of cytoskeleton morphogenesis.
许多细胞骨架包括一个微管星状体，其中中心体作为焦点。中心体在细胞内的位置对于诸如伤口闭合和免疫细胞相互作用等定向活动非常重要。在这里，我们分析了在一个内在完全对称的微管星状体的力学模型中，仅由微管弹性决定的中心体定位。我们证明了中心体的对称性和中心位置是不稳定的。中心体从中心的平衡偏差与微管长度和细胞半径的差值大致成比例。在平面细胞中比例系数为 1，在三维细胞中比例系数为 2。对称性的丧失是不可逆的，通常情况下，星状体的平衡形式会记住过去的干扰。作为微管长度函数的中心体的平衡位置表现出滞后现象，长度变化的历史反映在星状体的形态上。在分析更全面的理论模型时，以及在设计和解释涉及细胞骨架形态发生的复杂过程的实验时，必须考虑到这些弹性微管简单星状体的特性。
