Testing for the Shape of a 'Polyhedral' Cellular Inclusion

• Activity Number: 187
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Sukantadev Bag*+ and Kingshuk Roy Choudhury and Mingzhi Liang and Michael Prentice
• Companies: University College Cork and University College Cork and University College Cork and University College Cork
• Keywords: Cryo-electron tomography ; shape analysis ; polyhedron ; principal component analysis

Abstract

We consider the problem of identifying the shape of a type of cellular inclusion, called metabolosome, newly identified in E. coli cells from 3d reconstructions obtained via cryo-electron tomography. Due to limited angle tomography, the reconstructions are of uneven resolution, with a missing wedge at the top and bottom of the reconstruction. Most reconstructed slices appear to have convex polygonal shapes, suggesting a convex polyhedral shape for the 3d object. Naturally occurring objects such as viruses have previously been noted to possess symmetric polyhedral shapes. However, principal component analysis of a collection of metabolosomes reveals variation and a significant departure from symmetry. To test the hypothesis that the observed objects may be deformed Archimedean solids, we use the edge profile statistic, which is a vector of the number of edges of polygons in successive slices of the object. This statistic is invariant under shear transformations and uniquely identifies Archimedean solids. Resulting tests can be applied under missing data. Our tests reveal significant departures from all Archimedean solids.