Deformation-based nuclear morphometry: capturing nuclear shape variation in HeLa cells.

The empirical characterization of nuclear shape distributions is an important unsolved problem with many applications in biology and medicine. Numerous genetic diseases and cancers have alterations in nuclear morphology, and methods for characterization of morphology could aid in both diagnoses and fundamental understanding of these disorders. Automated approaches have been used to measure features related to the size and shape of the cell nucleus, and statistical analysis of these features has often been performed assuming an underlying Euclidean (linear) vector space. We discuss the difficulties associated with the analysis of nuclear shape in light of the fact that shape spaces are nonlinear, and demonstrate methods for characterizing nuclear shapes and shape distributions based on spatial transformations that map one nucleus to another. By combining large deformation metric mapping with multidimensional scaling we offer a flexible approach for elucidating the intrinsic nonlinear degrees of freedom of a distribution of nuclear shapes. More specifically, we demonstrate approaches for nuclear shape interpolation and computation of mean nuclear shape. We also provide a method for estimating the number of free parameters that contribute to shape as well as an approach for visualizing most representative shape variations within a distribution of nuclei. The proposed methodology can be completely automated, is independent of the dimensionality of the images, and can handle complex shapes. Results obtained by analyzing two sets of images of HeLa cells are shown. In addition to identifying the modes of variation in normal HeLa nuclei, the effects of lamin A/C on nuclear morphology are quantitatively described.