Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.
Proc Natl Acad Sci U S A. 2011 Jun 28;108(26):10508-13. doi: 10.1073/pnas.1017369108. Epub 2011 Jun 13.
We present a model of cytoplasmically driven microtubule-based pronuclear motion in the single-celled Caenorhabditis elegans embryo. In this model, a centrosome pair at the male pronucleus initiates stochastic microtubule (MT) growth. These MTs encounter motor proteins, distributed throughout the cytoplasm, that attach and exert a pulling force. The consequent MT-length-dependent pulling forces drag the pronucleus through the cytoplasm. On physical grounds, we assume that the motor proteins also exert equal and opposite forces on the surrounding viscous cytoplasm, here modeled as an incompressible Newtonian fluid constrained within an ellipsoidal eggshell. This naturally leads to streaming flows along the MTs. Our computational method is based on an immersed boundary formulation that allows for the simultaneous treatment of fluid flow and the dynamics of structures immersed within. Our simulations demonstrate that the balance of MT pulling forces and viscous nuclear drag is sufficient to move the pronucleus, while simultaneously generating minus-end directed flows along MTs that are similar to the observed movement of yolk granules toward the center of asters. Our simulations show pronuclear migration, and moreover, a robust pronuclear centration and rotation very similar to that observed in vivo. We find also that the confinement provided by the eggshell significantly affects the internal dynamics of the cytoplasm, increasing by an order of magnitude the forces necessary to translocate and center the pronucleus.
我们提出了一个基于微管的细胞质驱动的原核运动模型，该模型存在于单细胞秀丽隐杆线虫胚胎中。在这个模型中，位于雄性原核的一对中心体启动随机微管（MT）生长。这些 MT 遇到分布在细胞质中的马达蛋白，这些蛋白附着并施加拉力。由此产生的 MT 长度依赖性拉力将原核通过细胞质拖曳。根据物理原理，我们假设马达蛋白也对周围的粘性细胞质施加相等且相反的力，在这里将细胞质模拟为限制在椭圆形卵壳内的不可压缩牛顿流体。这自然会导致沿着 MT 产生流动。我们的计算方法基于浸入边界公式，可以同时处理流体流动和浸入其中的结构的动力学。我们的模拟表明，MT 拉力和粘性核阻力的平衡足以移动原核，同时沿着 MT 产生指向负端的流动，类似于观察到的卵黄颗粒向星状体中心的运动。我们的模拟表明原核迁移，并且还显示出与体内观察到的非常相似的原核定位和旋转。我们还发现卵壳提供的限制显著影响了细胞质的内部动力学，使平移和中心定位原核所需的力增加了一个数量级。
