Mechanics and Hydrodynamics of Cellular Assemblies

Courant Institute of Mathematical Sciences

New York University

Proper positioning and orientation of spindle is crucial for asymmetric cell division and generating cell diversity during development. We study the mechanics and hydrodynamics of pronuclear centering and rotation of the first cell division in C-elegans using theory and direct simulation. This study, to our knowledge, is the first to explicitly include long-ranged hydrodynamic interactions between microtubules (MTs). This is made possible through the use of highly efficient numerical methods for simulating many-body interactions and flexible microstructure in low Reynolds number flows. Through simulating different conditions, we show that including detailed hydrodynamic interactions between MTs and the cell cortex is essential for determining the dynamics of and requisite forces upon the pronuclear complex (PNC).We consider three different models for PNC centering: (1) "cortical pushing" in which growing astral MTs push against cortex; (2) "cytoplasmic pulling" where minus-end directed dynein motors bound to cytoplasmic organelles bind and translocate along MTs; and (3) "cortical pulling" where pulling forces are applied by cortically-bound dyneins upon MTs. We find that all three models can induce centering and rotation, and we use the ratio of rotation to centering times, λ , and the generated cytoplasmic flows as two physical measures to differentiate between them. Our results show that the cortical pushing model yields values of λ that are much larger than those experimentally observed. While cortical and cytoplasmic pulling can both yield reasonable values of λ, they have very different flow signatures due to the differing nature of the applied forces.