Geometric Limits of Mitotic Pressure Under Confinement

Abstract

Cells often divide under mechanical confinement, where surrounding structures restrict shape changes during cytokinesis. Although forces generated during confined division have been measured experimentally, it remains unclear how confinement geometry and mechanics determine the transmitted force. Here we develop a minimal mechanical theory of cell division under confinement. Modeling the cell as an incompressible volume bounded by an interface with effective isotropic tension, we show that confinement restricts the set of mechanically admissible furrow shapes. As the furrow radius decreases, it reaches it reaches a confinement-induced minimum. Beyond this point, further ingression does not alter the interface shape, and both pressure and axial force saturate. We analyze force and pressure in rigid, soft, and strong three-dimensional confinement and demonstrate that a single geometric mechanism underlies these distinct cases. After rescaling force and length by the appropriate geometric scale, cells of different size and surface tension collapse onto a single universal curve. The relevant length scale is the cell size for rigid and soft confinement, and the confinement size in fully enclosing three-dimensional confinement. In soft confinement, environmental stiffness and spindle-generated axial forces determine the operating force and pressure, while the geometric constraint fixes the maximal attainable levels. In summary, our results show that mitotic force transmission and mitotic pressure during cytokinesis are bounded by confinement geometry, with material properties and active forces selecting the operating point within these geometry-imposed limits.