Document Detail

Generalized voronoi tessellation as a model of two-dimensional cell tissue dynamics.
MedLine Citation:
PMID:  20082148     Owner:  NLM     Status:  MEDLINE    
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however, so far only with flat hyper-surfaces 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.
Martin Bock; Amit Kumar Tyagi; Jan-Ulrich Kreft; Wolfgang Alt
Related Documents :
4064838 - Cell cycle analysis using numerical simulation of bivariate dna/bromodeoxyuridine distr...
25192698 - Abscisic acid and latd/nip modulate root elongation via reactive oxygen species in medi...
17113108 - Modulation of the reaction rate of regulating protein induces large morphological and m...
17261538 - Nuclear fragmentation and the number of particle tracks in tissue.
17327438 - No evidence for mouse pancreatic beta-cell epithelial-mesenchymal transition in vitro.
10704238 - Apoptosis during iron chelator-induced differentiation in f9 embryonal carcinoma cells.
Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't     Date:  2010-01-16
Journal Detail:
Title:  Bulletin of mathematical biology     Volume:  72     ISSN:  1522-9602     ISO Abbreviation:  Bull. Math. Biol.     Publication Date:  2010 Oct 
Date Detail:
Created Date:  2010-10-04     Completed Date:  2011-01-21     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  0401404     Medline TA:  Bull Math Biol     Country:  United States    
Other Details:
Languages:  eng     Pagination:  1696-731     Citation Subset:  IM    
IZMB, Theoretische Biologie, Universität Bonn, Bonn, Germany.
Export Citation:
APA/MLA Format     Download EndNote     Download BibTex
MeSH Terms
Cell Adhesion / physiology*
Computer Simulation
Cytoskeleton / physiology*
Models, Biological*

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine

Previous Document:  Simultaneous analysis of nine components in patch preparations of Ru-Yi-Jin-Huang-San by high-perfor...
Next Document:  An Improved Method for Determining Medium- and Long-Chain FAMEs Using Gas Chromatography.