Predicting mechanical properties of mitotic spindles with a minimal constitutive model

The mitotic spindle, crucial for precise chromosome segregation and cytoplasmic partitioning during cell division, demands stability against forces arising from chromosomal movements and thermal fluctuations. Despite its central role, the mechanical properties of spindles remain largely elusive. In this study, we delve into the mechanical properties of spindles through a comprehensive model encompassing interactions among centrosomes, microtubules, chromosomes, and molecular motors. Our model successfully reproduces the 3D self–assembly of spindles and their responses to mechanical forces. We find that the spindle exhibits viscoelastic properties, responding distinctively to stretch and compression. Rapid stretch induces transient softening of the spindle, while compression leads to temporary hardening. Based on the viscoelastic responses of spindles under constant–force and constant–displacement loadings, we propose a minimal constitutive model for the spindle structure. This constitutive model can not only accurately recapture the viscoelastic responses of spindles under stretch and compression but also predict the mechanical behaviors of spindles under constant–rate loadings and cyclic loadings, which are further verified by simulations. Therefore, our validated constitutive model can replace complex simulations, providing more interesting predictions and guidance for future experiments.