Dynamic deformation and positioning of nucleus

We investigate the coupled dynamics of centrosomes and the cell nucleus under microtubule-mediated pulling within a viscous cytoplasmic environment. A coarse-grained, stoichiometric framework is developed to capture the interactions between microtubules and force generators (FGs) distributed on the nuclear envelope and cortex. The model integrates hydrodynamic coupling, nuclear envelope elasticity, FG transport along the nuclear envelope, and FG binding kinetics, enabling quantitative predictions of force balance and shape evolution. Using a boundary-integral formulation benchmarked against analytical limits, we examine how envelope stiffness, permeability, and FG mobility control the stability and positioning of the centrosome–nucleus complex. Simulations in spherical and spheroidal geometries reveal that enhanced FG mobility or weakened envelope stiffness amplifies nuclear deformation and destabilizes centrosomal organization—conditions reminiscent of pathological nuclear softening. Parameter sweeps across FG number and mechanical moduli delineate the transition from stable to misaligned configurations. This framework establishes a unified mechanical description linking molecular-scale force transduction to mesoscale nuclear morphology, providing mechanistic insight into how cytoskeletal dysregulation and envelope integrity jointly govern centrosome–nucleus coupling.