A constitutive model deciphers the viscoelastic mechanics of metaphase spindle positioning

The precise positioning and orientation of mitotic spindles are critical for ensuring accurate segregation of daughter cells during tissue development. Spindle positioning machinery-composed of astral microtubules and motor proteins-must withstand diverse mechanical forces, requiring robust mechanical properties. However, due to the difficulty in experimental measurements, the viscoelastic properties of this machinery remain poorly understood. Here, we develop a three-dimensional model to systematically investigate the dynamic mechanical responses of spindle positioning machinery. Our simulations reveal that this machinery exhibits distinct viscoelastic behavior in response to stepwise force and displacement loadings. Building upon these observations, we propose a minimal constitutive model comprising three parallel branches: 1) cytoplasmic drag (purely viscous branch), 2) microtubule elasticity (spring branch), and 3) motor-mediated stress dissipation (a Maxwell branch, i.e., spring-dashpot in series). Through parametric analysis, we demonstrate that increased microtubule rescue/growth rates enhance spindle positioning stability by strengthening microtubule-mediated elastic restoration-specifically through an increase in the spring branch's elastic coefficient. Conversely, elevated dynein motor turnover destabilizes positioning via two synergistic mechanisms: reducing effective stiffness (decreased spring coefficient) and accelerating motor-driven stress relaxation (shortened Maxwell relaxation time). Overall, the proposed constitutive model has the potential to replace complex simulations and provide more insightful predictions, thus advancing our understanding of spindle positioning mechanisms.