Hawkins Rhoda J, Tindemans Simon H, Mulder Bela M
FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jul;82(1 Pt 1):011911. doi: 10.1103/PhysRevE.82.011911. Epub 2010 Jul 19.
The plant microtubule cortical array is a striking feature of all growing plant cells. It consists of a more or less homogeneously distributed array of highly aligned microtubules connected to the inner side of the plasma membrane and oriented transversely to the cell growth axis. Here, we formulate a continuum model to describe the origin of orientational order in such confined arrays of dynamical microtubules. The model is based on recent experimental observations that show that a growing cortical microtubule can interact through angle dependent collisions with pre-existing microtubules that can lead either to co-alignment of the growth, retraction through catastrophe induction or crossing over the encountered microtubule. We identify a single control parameter, which is fully determined by the nucleation rate and intrinsic dynamics of individual microtubules. We solve the model analytically in the stationary isotropic phase, discuss the limits of stability of this isotropic phase, and explicitly solve for the ordered stationary states in a simplified version of the model.
植物微管皮质阵列是所有正在生长的植物细胞的一个显著特征。它由或多或少均匀分布的高度排列的微管阵列组成，这些微管连接到质膜内侧，并与细胞生长轴横向排列。在这里，我们建立了一个连续介质模型来描述这种动态微管受限阵列中取向有序性的起源。该模型基于最近的实验观察结果，这些结果表明，正在生长的皮质微管可以通过与预先存在的微管发生角度依赖性碰撞进行相互作用，这可能导致生长的共排列、通过灾难诱导而回缩或越过遇到的微管。我们确定了一个单一的控制参数，它完全由单个微管的成核速率和内在动力学决定。我们在静态各向同性相中对模型进行了解析求解，讨论了该各向同性相稳定性的极限，并在模型的简化版本中明确求解了有序静态状态。
