Multiscale Modeling of Motor-Driven Microtubules

Microtubules are key components of force transmission in cells, and play a role in cell locomotion, transport, and mitosis. At the length scales of mammalian cells, microtubules behave as semi-flexible filaments and can be coarse-grained using the Kirchoff theory for elastic rods. We have supplemented the Kirchoff model with the stochastic growth and collapse of microtubules (the dynamic instability), and by a model for dynein generated forces. I will present recent results for the dynamics of a microtubular network driven by polymerization forces and dynein motors.

I will first describe our implementation of the Kirchoff model, which is based on a symplectic integration of Hamiltonian equations of motion for a continuous filament [1]. The advantage of this approach is that long-term energy conservation is guaranteed. The model reproduces the non-linear bending and buckling of a single filament with second order spatial accuracy. We incorporate dynein motors using a viscoelastic model for the force generation [2]. Interestingly, motor-driven microtubules show the characteristic short-wavelength buckling observed in cells [3]. Finally, I will present simulations of the dynamics of the centrosome, driven by the motion of ~ 100 microtubules. We compare the dynamics with and without dynein motors. The simulations span time scales of about 14 orders of magnitude, using a projection method [4] combined with parallelization to speed up the simulations.

[1] A. J. C. Ladd and G. Misra, J. Chem. Phys. 130:124909, 2009. [2] R. B. Dickinson, Private Communication, 2010. [3] C. P. Brangwynne et al., J. Cell. Biol., 173:733, 2006. [4] I. G. Kevrekidis, C. W. Gear and G. Hummer, AIChE J. 50:1346, 2004.