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. © 2007 International Society for Analytical Cytology

[1]  G. Borisy,et al.  Improved silencing vector co-expressing GFP and small hairpin RNA. , 2004, BioTechniques.

[2]  Alain Trouvé,et al.  Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms , 2005, International Journal of Computer Vision.

[3]  R. Eils,et al.  Computational imaging in cell biology , 2003, The Journal of cell biology.

[4]  J. Krause,et al.  Investigation of cell size and nuclear clefts as prognostic parameters in chronic lymphocytic leukemia , 1986, Cancer.

[5]  Alejandro F Frangi,et al.  Automatic construction of 3-D statistical deformation models of the brain using nonrigid registration , 2003, IEEE Transactions on Medical Imaging.

[6]  Robert F. Murphy,et al.  From imaging to understanding: Frontiers in Live Cell Imaging, Bethesda, MD, April 19–21, 2006 , 2006, The Journal of cell biology.

[7]  Michael I. Miller,et al.  Deformable templates using large deformation kinematics , 1996, IEEE Trans. Image Process..

[8]  L. Younes,et al.  On the metrics and euler-lagrange equations of computational anatomy. , 2002, Annual review of biomedical engineering.

[9]  Ting Zhao,et al.  Automated learning of generative models for subcellular location: Building blocks for systems biology , 2007, Cytometry. Part A : the journal of the International Society for Analytical Cytology.

[10]  Anand Rangarajan,et al.  Unsupervised learning of an Atlas from unlabeled point-sets , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Guido Gerig,et al.  Unbiased diffeomorphic atlas construction for computational anatomy , 2004, NeuroImage.

[12]  M L Mendelsohn,et al.  THE ANALYSIS OF CELL IMAGES * , 1966, Annals of the New York Academy of Sciences.

[13]  U. Grenander,et al.  Computational anatomy: an emerging discipline , 1998 .

[14]  P. Thomas Fletcher,et al.  Principal geodesic analysis for the study of nonlinear statistics of shape , 2004, IEEE Transactions on Medical Imaging.

[15]  P. McCullagh.  Tensor Methods in Statistics , 1987 .

[16]  Rikard Berthilsson,et al.  A Statistical Theory of Shape , 1998, SSPR/SPR.

[17]  Zachary Pincus,et al.  Emergence of Large-Scale Cell Morphology and Movement from Local Actin Filament Growth Dynamics , 2007, PLoS biology.

[18]  M. Miller.  Computational anatomy: shape, growth, and atrophy comparison via diffeomorphisms , 2004, NeuroImage.

[19]  Z. P. I N C U S,et al.  Comparison of quantitative methods for cell-shape analysis , 2007 .

[20]  G. Dunn,et al.  Alignment of fibroblasts on grooved surfaces described by a simple geometric transformation. , 1986, Journal of cell science.

[21]  Leslie M Loew,et al.  The Virtual Cell project. , 2002, Novartis Foundation symposium.

[22]  Robert F. Murphy,et al.  A neural network classifier capable of recognizing the patterns of all major subcellular structures in fluorescence microscope images of HeLa cells , 2001, Bioinform..

[23]  M V Boland,et al.  Automated recognition of patterns characteristic of subcellular structures in fluorescence microscopy images. , 1998, Cytometry.

[24]  D'arcy W. Thompson,et al.  On Growth and Form , 1917, Nature.

[25]  H. Blum.  Biological shape and visual science. I. , 1973, Journal of theoretical biology.

[26]  D R Soll,et al.  A computer-assisted system for reconstructing and interpreting the dynamic three-dimensional relationships of the outer surface, nucleus and pseudopods of crawling cells. , 1998, Cell motility and the cytoskeleton.

[27]  Pius J. Egbelu,et al.  Virtual cell formation , 2003 .

[28]  F. Bruggeman,et al.  Introduction to systems biology. , 2007, EXS.

[29]  M. Raphaël,et al.  Two statistical approaches to nuclei shape and size in a morphometric description of lymph node sections in non-Hodgkin's lymphoma. , 1989, Cytometry.

[30]  H. Blum.  Biological shape and visual science (part I) , 1973 .

[31]  D. Kendall.  SHAPE MANIFOLDS, PROCRUSTEAN METRICS, AND COMPLEX PROJECTIVE SPACES , 1984 .

[32]  Kilian Q. Weinberger,et al.  Spectral Methods for Dimensionality Reduction , 2006, Semi-Supervised Learning.

[33]  Daniele Zink,et al.  Nuclear structure in cancer cells , 2004, Nature Reviews Cancer.

[34]  F. Bookstein.  Size and Shape Spaces for Landmark Data in Two Dimensions , 1986 .

[35]  J. Gee,et al.  Geodesic estimation for large deformation anatomical shape averaging and interpolation , 2004, NeuroImage.

[36]  Meel Velliste,et al.  Automated interpretation of subcellular patterns in fluorescence microscope images for location proteomics , 2006, Cytometry. Part A : the journal of the International Society for Analytical Cytology.

[37]  Haishan Wu,et al.  Image analysis and morphometry in the diagnosis of breast cancer , 2002, Microscopy research and technique.

[38]  Yosef Gruenbaum,et al.  Accumulation of mutant lamin A causes progressive changes in nuclear architecture in Hutchinson–Gilford progeria syndrome , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[39]  J. Prewitt,et al.  Computer analysis of cell images. , 1965, Postgraduate medicine.

[40]  Kevin E. Healy,et al.  Engineering gene expression and protein synthesis by modulation of nuclear shape , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[41]  Tom Misteli,et al.  Distinct structural and mechanical properties of the nuclear lamina in Hutchinson–Gilford progeria syndrome , 2006, Proceedings of the National Academy of Sciences.

[42]  Karl Rohr,et al.  Non-rigid Registration of 3D Multi-channel Microscopy Images of Cell Nuclei , 2006, MICCAI.

[43]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[44]  Michael T. Heath,et al.  Scientific Computing: An Introductory Survey , 1996 .

[45]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.