Aster swarming by symmetry breaking of cortical dynein transport and coupling kinesins

Wave-like oscillations of clamped microtubules driven by collective dynein transport

Microtubules (MTs) are observed to move and buckle driven by ATP-dependent molecular motors in both mitotic and interphasic eukaryotic cells as well as in specialized structures such as flagella and cilia with a stereotypical geometry. In previous work, clamped MTs driven by a few kinesin motors were seen to buckle and occasionally flap in what was referred to as flagella-like motion. Theoretical models of active-filament dynamics and a following force have predicted that, with sufficient force and binding-unbinding, such clamped filaments should spontaneously undergo periodic buckling oscillations. However, a systematic experimental test of the theory and reconciliation to a model was lacking. Here, we have engineered a minimal system of MTs clamped at their plus ends and transported by a sheet of dynein motors that demonstrate the emergence of spontaneous traveling-wave oscillations along single filaments. The frequencies of tip oscillations are in the millihertz range and are statistically indistinguishable in the onset and recovery phases. We develop a 2D computational model of clamped MTs binding and unbinding stochastically to motors in a "gliding-assay" geometry. The simulated MTs oscillate with a frequency comparable to experiment. The model predicts the effect of MT length and motor density on qualitative transitions between distinct phases of flapping, regular oscillations, and looping. We develop an effective "order parameter" based on the relative deflection along the filament and orthogonal to it. The transitions predicted in simulations are validated by experimental data. These results demonstrate a role for geometry, MT buckling, and collective molecular motor activity in the emergence of oscillatory dynamics.

Evolutionary divergence of anaphase spindle mechanics in nematode embryos constrained by antagonistic pulling and viscous forces

Cellular functions like cell division are remarkably conserved across phyla. However the evolutionary principles of cellular organization that drive it are less well explored. Thus, an essential question remains: to what extent cellular parameters evolve without altering the basic function they sustain? Here we have observed 6 different nematode species for which the mitotic spindle is positioned asymmetrically during the first embryonic division. Whereas the C. elegans spindle undergoes oscillations during its displacement, the spindle elongates without oscillations in other species. We asked which evolutionary changes in biophysical parameters could explain differences in spindle motion while maintaining a constant output. Using laser microsurgery of the spindle we revealed that all species are subjected to cortical pulling forces, of varying magnitudes. Using a viscoelastic model to fit the recoil trajectories and with an independent measurement of cytoplasmic viscosity, we extracted the values of cytoplasmic drag, cortical pulling forces and spindle elasticity for all species. We found large variations in cytoplasmic viscosity whereas cortical pulling forces and elasticity were often more constrained. In agreement with previous simulations, we found that increased viscosity correlates with decreased oscillation speeds across species. However, the absence of oscillations despite low viscosity in some species, can only be explained by smaller pulling forces. Consequently, we find that spindle mobility across the species analyzed here is characterized by a tradeoff between cytoplasmic viscosity and pulling forces normalized by the size of the embryo. Our work provides a framework for understanding mechanical constraints on evolutionary diversification of spindle mobility.

Self-organized optimal packing of kinesin-5-driven microtubule asters scales with cell size

Radial microtubule (MT) arrays or asters determine cell geometry in animal cells. Multiple asters interacting with motors, such as those in syncytia, form intracellular patterns, but the mechanical principles behind this are not clear. Here, we report that oocytes of the marine ascidian Phallusia mammillata treated with the drug BI-D1870 spontaneously form cytoplasmic MT asters, or cytasters. These asters form steady state segregation patterns in a shell just under the membrane. Cytaster centers tessellate the oocyte cytoplasm, that is divide it into polygonal structures, dominated by hexagons, in a kinesin-5-dependent manner, while inter-aster MTs form 'mini-spindles'. A computational model of multiple asters interacting with kinesin-5 can reproduce both tessellation patterns and mini-spindles in a manner specific to the number of MTs per aster, MT lengths and kinesin-5 density. Simulations predict that the hexagonal tessellation patterns scale with increasing cell size, when the packing fraction of asters in cells is ∼1.6. This self-organized in vivo tessellation by cytasters is comparable to the 'circle packing problem', suggesting that there is an intrinsic mechanical pattern-forming module that is potentially relevant to understanding the role of collective mechanics of cytoskeletal elements in embryogenesis. This article has an associated First Person interview with the first author of the paper.