60 research outputs found
Cell shape analysis of random tessellations based on Minkowski tensors
To which degree are shape indices of individual cells of a tessellation
characteristic for the stochastic process that generates them? Within the
context of stochastic geometry and the physics of disordered materials, this
corresponds to the question of relationships between different stochastic
models. In the context of image analysis of synthetic and biological materials,
this question is central to the problem of inferring information about
formation processes from spatial measurements of resulting random structures.
We address this question by a theory-based simulation study of shape indices
derived from Minkowski tensors for a variety of tessellation models. We focus
on the relationship between two indices: an isoperimetric ratio of the
empirical averages of cell volume and area and the cell elongation quantified
by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for
these quantities, as well as for distributions thereof and for correlations of
cell shape and volume, are presented for Voronoi mosaics of the Poisson point
process, determinantal and permanental point processes, and Gibbs hard-core and
random sequential absorption processes as well as for Laguerre tessellations of
polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data
are complemented by mechanically stable crystalline sphere and disordered
ellipsoid packings and area-minimising foam models. We find that shape indices
of individual cells are not sufficient to unambiguously identify the generating
process even amongst this limited set of processes. However, we identify
significant differences of the shape indices between many of these tessellation
models. Given a realization of a tessellation, these shape indices can narrow
the choice of possible generating processes, providing a powerful tool which
can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their
Applications in Stochastic Geometry and Imaging" in Lecture Notes in
Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense
Cadherin-Dependent Cell Morphology in an Epithelium: Constructing a Quantitative Dynamical Model
Cells in the Drosophila retina have well-defined morphologies that are attained during tissue morphogenesis. We present a computer simulation of the epithelial tissue in which the global interfacial energy between cells is minimized. Experimental data for both normal cells and mutant cells either lacking or misexpressing the adhesion protein N-cadherin can be explained by a simple model incorporating salient features of morphogenesis that include the timing of N-cadherin expression in cells and its temporal relationship to the remodeling of cell-cell contacts. The simulations reproduce the geometries of wild-type and mutant cells, distinguish features of cadherin dynamics, and emphasize the importance of adhesion protein biogenesis and its timing with respect to cell remodeling. The simulations also indicate that N-cadherin protein is recycled from inactive interfaces to active interfaces, thereby modulating adhesion strengths between cells
Comparative study of non-invasive force and stress inference methods in tissue
In the course of animal development, the shape of tissue emerges in part from
mechanical and biochemical interactions between cells. Measuring stress in
tissue is essential for studying morphogenesis and its physical constraints.
Experimental measurements of stress reported thus far have been invasive,
indirect, or local. One theoretical approach is force inference from cell
shapes and connectivity, which is non-invasive, can provide a space-time map of
stress and relies on prefactors. Here, to validate force- inference methods, we
performed a comparative study of them. Three force-inference methods, which
differ in their approach of treating indefiniteness in an inverse problem
between cell shapes and forces, were tested by using two artificial and two
experimental data sets. Our results using different datasets consistently
indicate that our Bayesian force inference, by which cell-junction tensions and
cell pressures are simultaneously estimated, performs best in terms of accuracy
and robustness. Moreover, by measuring the stress anisotropy and relaxation, we
cross-validated the force inference and the global annular ablation of tissue,
each of which relies on different prefactors. A practical choice of
force-inference methods in distinct systems of interest is discussed.Comment: 12 pages, 8 figures, EPJ E: Topical issue on "Physical constraints on
morphogenesis and evolution
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