A model of cytoplasmically driven microtubule-based motion in the single-celled Caenorhabditis elegans embryo

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.