Theory of Cytoskeletal Reorganization during Cross-Linker-Mediated Mitotic Spindle Assembly

Abstract

Cells grow, move, and respond to outside stimuli by large-scale cytoskeletal reorganization. A prototypical example of cytoskeletal remodeling is mitotic spindle assembly, during which microtubules nucleate, undergo dynamic instability, bundle, and organize into a bipolar spindle. Key mechanisms of this process include regulated filament polymerization, cross-linking, and motor-protein activity. Remarkably, using passive cross-linkers, fission yeast can assemble a bipolar spindle in the absence of motor proteins. We develop a torque-balance model that describes this reorganization because of dynamic microtubule bundles, spindle-pole bodies, the nuclear envelope, and passive cross-linkers to predict spindle-assembly dynamics. We compare these results to those obtained with kinetic Monte Carlo-Brownian dynamics simulations, which include cross-linker-binding kinetics and other stochastic effects. Our results show that rapid cross-linker reorganization to microtubule overlaps facilitates cross-linker-driven spindle assembly, a testable prediction for future experiments. Combining these two modeling techniques, we illustrate a general method for studying cytoskeletal network reorganization.

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

“…Because chromosomes are not bioriented on the spindle during initial SPB separation, they do not exert significant inward force. This result is consistent with our previous work, which demonstrated that initial bipolar spindle assembly can occur in a model lacking chromosomes [63,65,66].…”

“…Most spindle models have started with a bipolar structure or separated spindle poles, and most previous chromosome models have begun with chromosomes attached to the spindle or near a pre-formed spindle. Because we seek to model simultaneous spindle assembly and chromosome alignment with few imposed constraints, we developed a new model, building on previous work on spindle assembly in the absence of chromosomes and kinetochore-microtubule attachments [63,65,66].…”

“…However, constraining SPBs to a fixed radius alters force balance on the spindle and may alter spindle length. Therefore, we tested a model of a soft nuclear envelope by allowing the SPBs to move radially in a potential that mimics the energy required to deform the nuclear envelope [65,66] (Methods, Appendix A). The results show that a soft nuclear envelope leads to slightly longer spindles ( Figure 3D, Video S3), but for a physically realistic nuclear envelope force of around 17 pN, spindle length remains near 3 µm, as measured experimentally.…”

“…Our group has developed a simulation framework for microtubule-motor active matter and mitotic spindle self-assembly [52,62,63,65,66]. The computational scheme alternates between Brownian dynamics (BD) and kinetic Monte Carlo (kMC) steps to evolve the system forward in time.…”

“…To better understand the key mechanistic requirements for chromosome biorientation and how kinetochore number and attachment affect spindle length stability, we developed a computational model of fission-yeast mitosis. Schizosaccharomyces pombe cells are amenable to genetic manipulation and quantitative experiments [59][60][61][62][63] and the spindles are small enough that full 3D simulations are computationally tractable [59,[63][64][65]. We were motivated by previous work modeling spindle function and chromosome segregation [3,4].…”