3D time series analysis of cell shape using Laplacian approaches

Background: Fundamental cellular processes such as cell movement, division or food uptake critically depend on cells being able to change shape. Fast acquisition of three-dimensional image time series has now become possible, but we lack efficient tools for analysing shape deformations in order to understand the real three-dimensional nature of shape changes. Results: We present a framework for 3D+time cell shape analysis. The main contribution is three-fold: First, we develop a fast, automatic random walker method for cell segmentation. Second, a novel topology fixing method is proposed to fix segmented binary volumes without spherical topology. Third, we show that algorithms used for each individual step of the analysis pipeline (cell segmentation, topology fixing, spherical parameterization, and shape representation) are closely related to the Laplacian operator. The framework is applied to the shape analysis of neutrophil cells. Conclusions: The method we propose for cell segmentation is faster than the traditional random walker method or the level set method, and performs better on 3D time-series of neutrophil cells, which are comparatively noisy as stacks have to be acquired fast enough to account for cell motion. Our method for topology fixing outperforms the tools provided by SPHARM-MAT and SPHARM-PDM in terms of their successful fixing rates. The different tasks in the presented pipeline for 3D+time shape analysis of cells can be solved using Laplacian approaches, opening the possibility of eventually combining individual steps in order to speed up computations

Reversibility of Red blood Cell deformation

The ability of cells to undergo reversible shape changes is often crucial to their survival. For Red Blood Cells (RBCs), irreversible alteration of the cell shape and flexibility often causes anemia. Here we show theoretically that RBCs may react irreversibly to mechanical perturbations because of tensile stress in their cytoskeleton. The transient polymerization of protein fibers inside the cell seen in sickle cell anemia or a transient external force can trigger the formation of a cytoskeleton-free membrane protrusion of micrometer dimensions. The complex relaxation kinetics of the cell shape is shown to be responsible for selecting the final state once the perturbation is removed, thereby controlling the reversibility of the deformation. In some case, tubular protrusion are expected to relax via a peculiar "pearling instability".Comment: 4 pages, 3 figure

PAR-dependent and geometry-dependent mechanisms of spindle positioning.

During intrinsically asymmetric division, the spindle is oriented onto a polarized axis specified by a group of conserved PAR proteins. Extrinsic geometric asymmetry generated by cell shape also affects spindle orientation in some systems, but how intrinsic and extrinsic mechanisms coexist without interfering with each other is unknown. In some asymmetrically dividing cells of the wild-type Caenorhabditis elegans embryo, nuclear rotation directed toward the anterior cortex orients the forming spindle. We find that in such cells, a PAR-dependent mechanism dominates and causes rotation onto the polarized axis, regardless of cell shape. However, when geometric asymmetry is removed, free nuclear rotation in the center of the cell is observed, indicating that the anterior-directed nature of rotation in unaltered embryos is an effect of cell shape. This free rotation is inconsistent with the prevailing model for nuclear rotation, the specialized cortical site model. In contrast, in par-3 mutant embryos, a geometry-dependent mechanism becomes active and causes directed nuclear rotation. These results lead to the model that in wild-type embryos both PAR-3 and PAR-2 are essential for nuclear rotation in asymmetrically dividing cells, but that PAR-3 inhibits geometry-dependent rotation in nonpolarized cells, thus preventing cell shape from interfering with spindle orientation

The effect of flotation cell shape on deinking behaviour

Studies were undertaken to investigate the deinking behaviour of different shaped deinking cells of the same volume. For comparative purposes, most oprational variables were kept constant, and the same injector was used throughout the study. The position of the injector, however, was varied in some cases to go along with the particular cell shape being studied. Three types of cell shapes were studied, (1) cylindrical with tangential air injection, (2) rectanular with vertical injection, and (3) rectangular with horizontal injection. Eucalyptus/toner slurries and news/mag wastepaper slurries were deinked. Flow patterns in the cells and the corresponding deinking efficiencies were measured. It was found that strong and excessive re-circulatory flows within the cells could under certain conditions be a major factor in reducing brightness lift. Vertical injection into a rectangular cell gave stable flow patterns, non-wavy froth removal and sustained brightness lift for a wide range of feed and airflow rates. Horizontal injection into a similar rectangular shaped cell exhibited quite different characteristics. High brightness lift was possible for certain conditions and not for others. Wavy froth and excessive recirculation flow patterns varied with feed and airflow. The cylindrical cell with tangential injection gave stable circulatory flow and stable froth removal at low flow rates but was unable to deink at high flows

Shear band formation in granular media as a variational problem

Strain in sheared dense granular material is often localized in a narrow region called shear band. Recent experiments in a modified Couette cell provided localized shear flow in the bulk away from the confining walls. The non-trivial shape of the shear band was measured as the function of the cell geometry. First we present a geometric argument for narrow shear bands which connects the function of their surface position with the shape in the bulk. Assuming a simple dissipation mechanism we show that the principle of minimum dissipation of energy provides a good description of the shape function. Furthermore, we discuss the possibility and behavior of shear bands which are detached from the free surface and are entirely covered in the bulk.Comment: 4 pages, 5 figures; minor changes, typos and journal-ref adde