A computational platform for biomechanics problems in the cell

Polymer filament and motor-protein assemblies are major structural components of biological cells. Filaments' nonlinear deformation and hydrodynamic interactions with the other immersed structures lead to complicated flows that have important mechanical and transport properties. I will review our computational platform for the large-scale three-dimensional simulations of flexible filaments, motor proteins and rigid bodies in a Stokesian fluid. We use non-local slender body theory for the fluid-structure interactions of the filaments and a second-kind boundary integral formulation for rigid bodies and the confining boundary. We also incorporate the key biophysical elements such as the filaments' (de)polymerization kinetics and motor proteins. I will discuss recent applications of this platform: the orientation and positioning of the mitotic spindle (the organelle that orchestrates the division of chromosomes); swirling flows induced by the interaction of motor proteins and thousands of microtubules attached to a cortex, as observed in early development of the Drosophila oocyte; and the dynamics of microtubule arrays in large cells driven by streaming flows created by moving motor-proteins, as has been proposed as the basis for centering of spindles in large embryos.