Cell shape modulates mitotic spindle positioning forces via intracellular hydrodynamics.

The regulation of mitotic spindle positioning and orientation is central to the morphogenesis of developing embryos and tissues.^1,2,3,4,5 In many multicellular contexts, cell geometry has been shown to have a major influence on spindle positioning, with spindles that commonly align along the longest cell shape axis.^{6,7,8,9,10,11,12,13,14} To date, however, we still lack an understanding of how the nature and amplitude of intracellular forces that position, orient, or hold mitotic spindles depend on cell geometry. Here, we used in vivo magnetic tweezers to directly measure the forces that maintain the mitotic spindle in the center of sea urchin cells that adopt different shapes during early embryo development. We found that spindles are held by viscoelastic forces that progressively increase in amplitude as cells become more elongated during early development. By coupling direct cell shape manipulations in microfabricated chambers with in vivo force measurements, we establish how spindle-associated forces increase in dose dependence with cell shape anisotropy. Cytoplasm flow analysis and hydrodynamic simulations suggest that this geometry-dependent mechanical enhancement results from a stronger hydrodynamic coupling between the spindle and cell boundaries, which dampens cytoplasm flows and spindle mobility as cells become more elongated. These findings establish how cell shape affects spindle-associated forces and suggest a novel mechanism for shape sensing and division positioning mediated by intracellular hydrodynamics with functional implications for early embryo morphogenesis.