Introduction:: Nuclei have characteristic shapes depending on the cell type, and nuclear shape is critical to cell function. A deformed nuclear shape is commonly assumed to arise from a balance between cytoskeletal stresses and the elastic deformation of the nucleus from a spherical resting state. However, nuclei are not normally spherical; even in rounded cells, the nuclear lamina typically has surface folds and undulations that indicate a significantly larger surface area than needed for a sphere of the same volume. Geometrically, excess surface area permits a wide range of shape changes with for the same surface area and volume, and only when the nucleus becomes so deformed that the lamina becomes smoothed and tensed does it take on a limiting shape where further deformation requires areal expansion of the lamina or compression of the nuclear volume. Here we show mathematically that the geometric constraints of constant lamina area, cell volume, and nuclear volume are sufficient to fully determine limiting nuclear shapes that are observed in fully spread cells.
Materials and Methods:: We computed cell and nuclear shapes in a variety of contexts by computationally minimizing the cell cortex surface area under the constraints of constant cell volume, nuclear volume, and lamina surface area. The contexts various contexts, including in cells spread on a surface, in monolayers, on rectangles with various aspect ratios, confined to a well, or with nuclei indented by slender microposts. Computed cell and nuclear shapes were compared to the corresponding experimental shapes.
Results, Conclusions, and Discussions:: We found that experimentally observed cell and nuclear shapes in fully spread cells could be consistently predicted based on the geometric constraints alone, without modeling the elastic or viscoelastic properties of the cell and nucleus. This principle was consistently demonstrated in a wide range of contexts including a monolayer, cells confined to various micropatterned areas, and impinging against obstacles, as long as the nucleus was sufficiently deformed to smooth the lamina surface. We conclude that nuclear shapes in spread cells are primarily determined by geometry, not mechanics, and that lamina excess area is an essential parameter to consider when modeling nuclear deformation or inferring nuclear stress (and affected mechanosensitive cell signaling pathways) from the extent of nuclear deformation.
