Biophysical model of self-organized spindle formation patterns without centrosomes and kinetochores

Eukaryotic cell division and chromosome segregation depend crucially on the mitotic spindle pattern formation. The usual pathway for spindle production involves microtubule polymerization from two centrosomes. However, experiments using Xenopus extracts with micrometer-sized chromatin-coated beads found, remarkably, that spindle patterns can form in the absence of centrosomes, kinetochores, and duplicated chromosomes. Here we introduce a previously undescribed biophysical model inspired by the heuristic interpretations of the experiments that provides a quantitative explanation and constraints for this type of experiment. The model involves plus-directed (chromokinesin and Eg5) and minus-directed (cytoplasmic dynein oligomers) motors walking on microtubules and the boundary conditions caused by the chromatin-coated spheres. This model combines the effects of the plus-directed cross-linking motor Eg5 and any chromokinesin on the chromatin-covered beads, reflecting current uncertainties in the division of function between the two kinds of motors. The model can nucleate dynamically a variety of self-organized spindle patterns over a wide range of biological parameter values. Our calculations show that spindles will form over a wide range of parameter values. Some parameter values cause a monaster to form instead of a bipolar spindle. Varying the processivity and the dynein microtubule attachment and detachment rates, we find stability parameters for spindle formations. These results not only constrain the possible parameter values, but they point toward the proper division of function between Eg5 and chromokinesin in this spindle formation pathway. The model results suggest experiments that would further enhance our understanding of the basic elements needed for spindle pattern formation in this pathway.