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

Radial microtubule (MT) arrays or asters determine cell geometry in animal cells. Multiple asters interacting with motors such as in syncytia form intracellular patterns, but the mechanical principles are not clear. Here, we report oocytes of the marine ascidian Phallusia mammillata treated with a 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, i.e. 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 MTs per aster, MT lengths and kinesin-5 density. Simulations predict the hexagonal tessellation patterns scale with increasing cell size, when the packing fraction of asters in cells∼1.6. This self-organized in vivo tessellation by cytasters is comparable to the 'circle packing problem', suggesting an intrinsic mechanical pattern forming module potentially relevant to understand the role of collective mechanics of cytoskeletal elements in embryogenesis.