A predictive unifying explanation for nuclear shapes based on a simple geometric principle

Nuclei have characteristic shapes dependent on cell type, which are critical for proper cell function, and nuclei lose their distinct shapes in multiple diseases including cancer, laminopathies, and progeria. Nuclear shapes result from deformations of the sub-nuclear components--nuclear lamina and chromatin. How these structures respond to cytoskeletal forces to form the nuclear shape remains unresolved. Although the mechanisms regulating nuclear shape in human tissues are not fully understood, it is known that different nuclear shapes arise from cumulative nuclear deformations post-mitosis, ranging from the rounded morphologies that develop immediately after mitosis to the various nuclear shapes that roughly correspond to cell shape (e.g., elongated nuclei in elongated cells, flat nuclei in flat cells). Here we establish a simple geometric principle of nuclear shaping: the excess surface area of the nucleus (relative to that of a sphere of the same volume) permits a wide range highly deformed nuclear shapes under the constraints of constant surface area and constant volume, and, when the lamina is smooth (tensed), the nuclear shape can be predicted entirely from these geometric constraints alone for a given cell shape. This principle explains why flattened nuclear shapes in fully spread cells are insensitive to the magnitude of the cytoskeletal forces. We demonstrate this principle by predicting limiting nuclear shapes (i.e. with smooth lamina) in various cell geometries, including isolated on a flat surface, on patterned rectangles and lines, within a monolayer, isolated in a well, or when the nucleus is impinging against a slender obstacle. We also show that the lamina surface tension and nuclear pressure can be estimated from the predicted cell and nuclear shapes when the cell cortical tension is known, and the predictions are consistent with measured forces. These results show that excess lamina surface area is the key determinant of nuclear shapes, and that nuclear shapes can be determined purely by the geometric constraints of constant (but excess) nuclear surface area and nuclear volume, not by the magnitude of the cytoskeletal forces involved.