1,005 research outputs found
Membrane simulation analysis using Voronoi tessellation (Conference Abstract)
Lukat G, Sommer B, Krüger J. Membrane simulation analysis using Voronoi tessellation (Conference Abstract). In: Journal of Cheminformatics. Journal of Cheminformatics. Vol 6. Springer Science and Business Media LLC; 2014
Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics
Voronoi tessellations have been used to model the geometric arrangement of
cells in morphogenetic or cancerous tissues, however so far only with flat
hypersurfaces as cell-cell contact borders. In order to reproduce the
experimentally observed piecewise spherical boundary shapes, we develop a
consistent theoretical framework of multiplicatively weighted distance
functions, defining generalized finite Voronoi neighborhoods around cell bodies
of varying radius, which serve as heterogeneous generators of the resulting
model tissue. The interactions between cells are represented by adhesive and
repelling force densities on the cell contact borders. In addition, protrusive
locomotion forces are implemented along the cell boundaries at the tissue
margin, and stochastic perturbations allow for non-deterministic motility
effects. Simulations of the emerging system of stochastic differential
equations for position and velocity of cell centers show the feasibility of
this Voronoi method generating realistic cell shapes. In the limiting case of a
single cell pair in brief contact, the dynamical nonlinear Ornstein-Uhlenbeck
process is analytically investigated. In general, topologically distinct tissue
conformations are observed, exhibiting stability on different time scales, and
tissue coherence is quantified by suitable characteristics. Finally, an
argument is derived pointing to a tradeoff in natural tissues between cell size
heterogeneity and the extension of cellular lamellae.Comment: v1: 34 pages, 19 figures v2: reformatted 43 pages, 21 figures, 1
table; minor clarifications, extended supplementary materia
InferenceMAP: Mapping of Single-Molecule Dynamics with Bayesian Inference
Single-particle tracking (SPT) grants unprecedented insight into cellular
function at the molecular scale [1]. Throughout the cell, the movement of
single-molecules is generally heterogeneous and complex. Hence, there is an
imperative to understand the multi-scale nature of single-molecule dynamics in
biological systems. We have previously shown that with high-density SPT,
spatial maps of the parameters that dictate molecule motion can be generated to
intricately describe cellular environments [2,3,4]. To date, however, there
exist no publically available tools that reconcile trajectory data to generate
the aforementioned maps. We address this void in the SPT community with
InferenceMAP: an interactive software package that uses a powerful Bayesian
method to map the dynamic cellular space experienced by individual
biomolecules.Comment: 56 page
Statistical Laws and Mechanics of Voronoi Random Lattices
We investigate random lattices where the connectivities are determined by the
Voronoi construction, while the location of the points are the dynamic degrees
of freedom. The Voronoi random lattices with an associated energy are immersed
in a heat bath and investigated using a Monte Carlo simulation algorithm. In
thermodynamic equilibrium we measure coordination number distributions and test
the Aboav-Weaire and Lewis laws.Comment: 14 pages (figures not included), LaTeX, HLRZ-26/9
An integrative computational model for intestinal tissue renewal
Objectives\ud
\ud
The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation.\ud
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Methods\ud
\ud
At the subcellular level, deterministic models characterise molecular networks, such as cell-cycle control and Wnt signalling. The output of these models determines the behaviour of each epithelial cell in response to intra-, inter- and extracellular cues. The modular nature of the model enables us to easily modify individual assumptions and analyse their effects on the system as a whole.\ud
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Results\ud
\ud
We perform virtual microdissection and labelling-index experiments, evaluate the impact of various model extensions, obtain new insight into clonal expansion in the crypt, and compare our predictions with recent mitochondrial DNA mutation data. \ud
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Conclusions\ud
\ud
We demonstrate that relaxing the assumption that stem-cell positions are fixed enables clonal expansion and niche succession to occur. We also predict that the presence of extracellular factors near the base of the crypt alone suffices to explain the observed spatial variation in nuclear beta-catenin levels along the crypt axis
Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web
We study the topology of the Megaparsec Cosmic Web in terms of the
scale-dependent Betti numbers, which formalize the topological information
content of the cosmic mass distribution. While the Betti numbers do not fully
quantify topology, they extend the information beyond conventional cosmological
studies of topology in terms of genus and Euler characteristic. The richer
information content of Betti numbers goes along the availability of fast
algorithms to compute them.
For continuous density fields, we determine the scale-dependence of Betti
numbers by invoking the cosmologically familiar filtration of sublevel or
superlevel sets defined by density thresholds. For the discrete galaxy
distribution, however, the analysis is based on the alpha shapes of the
particles. These simplicial complexes constitute an ordered sequence of nested
subsets of the Delaunay tessellation, a filtration defined by the scale
parameter, . As they are homotopy equivalent to the sublevel sets of
the distance field, they are an excellent tool for assessing the topological
structure of a discrete point distribution. In order to develop an intuitive
understanding for the behavior of Betti numbers as a function of , and
their relation to the morphological patterns in the Cosmic Web, we first study
them within the context of simple heuristic Voronoi clustering models.
Subsequently, we address the topology of structures emerging in the standard
LCDM scenario and in cosmological scenarios with alternative dark energy
content. The evolution and scale-dependence of the Betti numbers is shown to
reflect the hierarchical evolution of the Cosmic Web and yields a promising
measure of cosmological parameters. We also discuss the expected Betti numbers
as a function of the density threshold for superlevel sets of a Gaussian random
field.Comment: 42 pages, 14 figure
Tessellations and Pattern Formation in Plant Growth and Development
The shoot apical meristem (SAM) is a dome-shaped collection of cells at the
apex of growing plants from which all above-ground tissue ultimately derives.
In Arabidopsis thaliana (thale cress), a small flowering weed of the
Brassicaceae family (related to mustard and cabbage), the SAM typically
contains some three to five hundred cells that range from five to ten microns
in diameter. These cells are organized into several distinct zones that
maintain their topological and functional relationships throughout the life of
the plant. As the plant grows, organs (primordia) form on its surface flanks in
a phyllotactic pattern that develop into new shoots, leaves, and flowers.
Cross-sections through the meristem reveal a pattern of polygonal tessellation
that is suggestive of Voronoi diagrams derived from the centroids of cellular
nuclei. In this chapter we explore some of the properties of these patterns
within the meristem and explore the applicability of simple, standard
mathematical models of their geometry.Comment: Originally presented at: "The World is a Jigsaw: Tessellations in the
Sciences," Lorentz Center, Leiden, The Netherlands, March 200
Motility-driven glass and jamming transitions in biological tissues
Cell motion inside dense tissues governs many biological processes, including
embryonic development and cancer metastasis, and recent experiments suggest
that these tissues exhibit collective glassy behavior. To make quantitative
predictions about glass transitions in tissues, we study a self-propelled
Voronoi (SPV) model that simultaneously captures polarized cell motility and
multi-body cell-cell interactions in a confluent tissue, where there are no
gaps between cells. We demonstrate that the model exhibits a jamming transition
from a solid-like state to a fluid-like state that is controlled by three
parameters: the single-cell motile speed, the persistence time of single-cell
tracks, and a target shape index that characterizes the competition between
cell-cell adhesion and cortical tension. In contrast to traditional particulate
glasses, we are able to identify an experimentally accessible structural order
parameter that specifies the entire jamming surface as a function of model
parameters. We demonstrate that a continuum Soft Glassy Rheology model
precisely captures this transition in the limit of small persistence times, and
explain how it fails in the limit of large persistence times. These results
provide a framework for understanding the collective solid-to-liquid
transitions that have been observed in embryonic development and cancer
progression, which may be associated with Epithelial-to-Mesenchymal transition
in these tissues.Comment: accepted for publication in Physical Review X, 201
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