Nuclear shapes are geometrically determined by lamina excess area

Abstract

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 the nucleus 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. Importantly, experimentally observed shapes can be predicted based on the geometric constraints alone, without modeling the elastic or viscoelastic properties of the cell and nucleus. This principle is demonstrated in 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 a slender micropost. 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.