Stoichiometric Model for the Microtubule-mediated dynamics of centrosome and nucleus*

The Stoichiometric Model (S-model) for the interaction of centrosomes with cortically anchored pulling motors through their associated microtubules (MTs) has been applied to study key steps in cell division, such as spindle positioning and elongation. The S-model evolves the astral centrosome position, a probability field of cell-surface motor occupancy by centrosomal microtubules (under an assumption of stoichiometric binding), and free boundaries of unattached, growing microtubules. In this work, we apply the S-model to investigate the hydrodynamics of the centrosome/pronucleus (CP) complex inside a cell. Formulated as a fluid-structure interaction problem using the integral formulation, we use a highly accurate boundary integral code to simulate key dynamics of the centrosome/pronucleus complex, such as the separation of centrosomes around a nucleus, centering of the centrosome/pronucleus complex, and deformation of the pronucleus due to pulling forces from the centrosomes. Focusing on the enhanced permeability and reduced rigidity of a lamin-compromised pronucleus, we find that the CP complex may lose the centering stability and exhibit orbiting dynamics. In this talk, we first provide a comprehensive study of the morphology of a pronucleus in terms of membrane permeability and bending rigidity. We then quantify how deformation affects the centering stability of the CP complex. We further illustrate how the geometry of the cell affects the dynamics of CP complex.