Bock, Martin: Beyond whole-cell motion : reactive interpenetrating flow and elliptic Voronoi tessellation in two dimensions. - Bonn, 2013. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-31765
@phdthesis{handle:20.500.11811/5661,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-31765,
author = {{Martin Bock}},
title = {Beyond whole-cell motion : reactive interpenetrating flow and elliptic Voronoi tessellation in two dimensions},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2013,
month = apr,

note = {A crucial property of higher-developed living beings is the ability to continuously exchange and renew their body. This is achieved by division and redistribution of cells, the micron-sized and autonomous "atoms" of life. In the skin and during embryogenesis, these cells undergo directed motion to arrive at their native place within dedicated tissue environments. Only few molecular players essentially determine the involved physical force balances, namely actin, integrin, cadherin and myosin.
The intracellular dynamics of actin network polymerisation, transport and the interstitial flow of the aqueous cytosol can be described by a two-component hydrodynamical continuum theory called the Reactive Interpenetrating Flow. The central underlying assumption in this theory is, that the cytoplasm is essentially an incompressible fluid, consisting of the dynamic actin network and the aqueous cytosol. The force balances in the fluid are dominated by friction and involve both active and passive isotropic stresses. Passive stresses arise from the presence of two fluid components, leading to network swelling and friction due to viscosity and fluid permeation. Active stresses in the fluid relate to the presence of myosin motor proteins that induce contractions in the actin network.
Including the adhesion of the cell towards the substrate by means of integrin molecules, one can construct a one-dimensional model cell that exhibits two characteristic dynamical cell states: 1. in the symmetric resting state, traction from front and back balances so that the cell adheres to the substratum without moving, and 2. in the polarized migrating state, an asymmetry in traction drives persistent cell locomotion. These two steady states are rather stable and autonomous in the sense that they do not need any out-of-model regulation prescribing front and back of the cell. A simplified two-dimensional model exhibits the characteristic correlation features from trajectories of human epidermal keratinocyte cells as determined in experiments.
The shapes of individual interacting cells in a monolayer can be mathematicaly quantified by means of a novel type of Voronoi tessellation, which involves ellipses as so-called generators. These generator ellipses are prescribed and encode the positions of the cells, their preferred size and orientation. To every point in the plane each generator attributes a certain power, given by the center distance divided by the colinear local radius of the ellipse. From these point powers, the proposed Voronoi tessellation constructs explicit neighbor relations and the shape of the cell-cell contacts within groups of model cells. By taking cell nuclei from fluorescence micrographs as model input for the generator ellipses, the resulting Voronoi tesselation is able to recapitulate the corresponding cell-cell contacts as observed simultaneously in the experiment.
Central to cell-cell adhesion in groups and tissue are cadherin receptors on the exterior cell membranes, providing for a force link between cells in contact. Employing the Voronoi tesselation as cell geometry model, one can construct compatible in-tissue force balances and thereby elucidate the interactions of cells in groups. The explicit consideration of size variation and stochastic forces leads to several relatively stable topological cell arrangements in small groups. The cohesion of the model tissue crucially depends on the relative lamella width and the homogeneity of the cell size distribution, both of which are geometric quantities accessible in phase-contrast microscopy. As observed in cell extracts from embryos, the model is able to slowly sort mixed cells into matching groups by attributing differential cadherin expression levels to the individual cells. Finally, the so-called convergent extension during the development of the Drosophila fly relies on topological rearrangements induced by only small anisotropies in the cellular interaction force.},

url = {https://hdl.handle.net/20.500.11811/5661}
}

The following license files are associated with this item:

InCopyright