Generalized Voronoi Tessellation as a Model of Twodimensional Cell Tissue Dynamics
Abstract
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 cellcell 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 nondeterministic 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 OrnsteinUhlenbeck 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2009
 arXiv:
 arXiv:0901.4469
 Bibcode:
 2009arXiv0901.4469B
 Keywords:

 Physics  Biological Physics;
 Physics  Computational Physics;
 Quantitative Biology  Tissues and Organs
 EPrint:
 v1: 34 pages, 19 figures v2: reformatted 43 pages, 21 figures, 1 table