In-silico rheology of microtubule asters

Asters are radiating arrays of microtubules associated with the centrosome organelle in dividing eukaryotic cells. These cytoskeletal structures play a critical role in the positioning and orientation of the mitotic spindle, pronuclear migration, and cell homeostasis [1-2]. During the cell cycle, cortical and cytoplasmatic forces create translational and rotational aster motions. Thus, determining the relationship between an applied force and the resulting aster motion is a central challenge. To this end, we develop a biophysical model that encapsulates important features of intracellular aster motion and conduct in-silico rheological experiments. We model the aster as a dense bed of thin, bendable, but inextensible fibers [3] attached to a rigid spherical core (the centrosome), immersed in the cytoplasm (assumed to be a linear Stokes fluid) and confined in a spherical shell mimicking the cell membrane. The system is simulated using an accurate and fast stabilized finite element method specially designed for such fluid-structure interactions. We study the response of a single aster under small amplitude oscillatory translations/rotations to quantify the aster translational/rotational relaxation time and the related storage and loss moduli. Using large amplitude oscillatory translations/rotations, we determine the translational/rotational drag force on the aster. For all cases, we examine the effect of fiber density, fiber branching, and confinement. Our detailed rheological characterization provides valuable information about the mechanical properties of cellular asters that could contribute to understanding cytoskeletal conformations during mitosis.

[1] Dutta, Sayantan, et al. Nature Physics (2024): 1-9.

[2] Sami, Abdullah Bashar, and Jesse C. Gatlin., Molecular Biology of the Cell 33.11 (2022): br20.

[3] Stein, David B., and Michael J. Shelley., Physical Review Fluids 4.7 (2019): 073302.