Dynamics of cell packing and polar order in developing epithelia [Elektronische Ressource] / vorgelegt von Reza Farhadifar

Sujets

• Biologie

Informations

• Publié par: technische_universitat_dresden
• Publié le: 01 janvier 2009
• Nombre de lectures: 18
• Langue: English
• Poids de l'ouvrage: 10 Mo

Extrait

Institutfu¨rTheoretischePhysik
Fakulta¨t Mathematikund Naturwissenschaften
TechnischeUniversita¨tDresden
DynamicsofCellPackingandPolar
OrderinDeveloping Epithelia
Dissertation
zur ErlangungdesakademischenGrades
Doctor rerumnaturalium
vorgelegtvon
RezaFarhadifar
geborenam24. Mai 1982in Mashhad,Iran
Dresden 2009Eingereicht am 26.03.2009
1. Gutachter: Prof Dr Frank Jülicher
2. Gutachter: Prof Dr Karsten Kruse
3. Gutachter: Prof Dr Jens-Uwe Sommer
Verteidigt am 25.05.2009Abstract
During development, organs with different shape and functionality form from a
single fertilized egg cell. Mechanisms that control shape, size and morphology of
tissues pose challenges for developmental biology. These mechanisms are tightly
controlled by an underlying signaling system by which cells communicate to each
other. However, these signaling networks can affect tissue size and morphology
through limited processes such as cell proliferation, cell death and cell shape changes,
which are controlled by cell mechanics and cell adhesion. One example of such a
signaling system is the network of interacting proteins that control planar polariza-
tion of cells. These proteins distribute asymmetrically within cells and their distri-
bution in each cell determines of the polarity of the neighboring cells. These pro-
teins control the pattern of hairs in the adult Drosophila wing as well as hexagonal
repacking of wing cells during development. Planar polarity proteins also control
developmental processes such as convergent-extension. We present a theoretical
study of cell packing geometry in developing epithelia. We use a vertex model to
describe the packing geometry of tissues, for which forces are balanced throughout
the tissue. We introduce a cell division algorithm and show that repeated cell di-
vision results in the formation of a distinct pattern of cells, which is controlled by
cell mechanics and cell-cell interactions. We compare the vertex model with exper-
imental measurements in the wing disc of Drosophila and quantify for the first time
cell adhesion and perimeter contractility of cells. We also present a simple model
for the dynamics of polarity order in tissues. We identify a basic mechanism by
which long-range polarity order throughout the tissue can be established. In partic-
ular we study the role of shear deformations on polarity pattern and show that the
polarity of the tissue reorients during shear flow. Our simple mechanisms for order-
ing can account for the processes observed during development of the Drosophila
wing.Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1 Biophysics of Two-Dimensional Tissues . . . . . . . . . . . . . . . . . . . . . 7
1.2 Cell Packing and Tissue Morphology . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Planar Polarity of Epithelial Cells . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Wing Development of the Fruit Fly Drosophila . . . . . . . . . . . . . . . . . 16
2 Physical Description of Cell Packing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1 Cell Mechanics in Two-Dimensional Tissues . . . . . . . . . . . . . . . . . . . 22
2.2 Ground States of Cell Packing . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Ground State Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Shear and Bulk Modulus . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 Transition from Hexagonal to Soft Networks . . . . . . . . . . . . . . 27
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Dynamics of Tissue Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Cell Division in the Vertex Model . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Simulation of Tissue Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Statistics of Cell Packing Geometries . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Phase Transitions in Tissue Growth . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Junctional Remodeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.6 Tissue Relaxation due to Local Perturbations . . . . . . . . . . . . . . . . . . 39
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 Tissue Ordering and Remodeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 Internal Shear Generated by Remodeling . . . . . . . . . . . . . . . . . . . . . 46
4.1.1 Ordered Junctional Remodeling . . . . . . . . . . . . . . . . . . . . . 46
4.1.2 Cell Division without Growth . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Dynamics of Hexagonal Order . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.1 Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Contents 6
4.2.2 Shear Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3 Theory of Planar Cell Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.1 Planar Polarity in the Vertex Model . . . . . . . . . . . . . . . . . . . 55
4.3.2 Origin of Large-Scale Polarity . . . . . . . . . . . . . . . . . . . . . . 57
4.3.3 Reorientation of Polarity by Shear . . . . . . . . . . . . . . . . . . . . 60
4.3.4 Hydrodynamic Description of Tissue Polarity . . . . . . . . . . . . . . 61
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5 Compartment Boundaries: Interfaces in Epithelia . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1 Two-Population Tissue Growth . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2 Differential Adhesion in Two-Population Growth . . . . . . . . . . . . . . . . 67
5.3 Increased Interfacial Tension Results in Cell Sorting . . . . . . . . . . . . . . . 68
5.4 Shape and Roughness of Interfaces in Developing Tissues . . . . . . . . . . . . 70
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6 Comparison Between Theory and Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.1 Cell Shape and Cell Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.2 Displacements Upon Laser Ablation . . . . . . . . . . . . . . . . . . . . . . . 76
6.3 Morphology of Compartment Boundaries . . . . . . . . . . . . . . . . . . . . 81
6.4 Cell Clones in Growing Tissues . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
A Conjugate Gradient Mehod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
B Cell Packing Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
C Numerical Analysis of Phase Transitions in Tissue Growth . . . . . . . 97
D Displacements Upon Laser Ablation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
E Processing Epithelial Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1051 Introduction
1.1 Biophysics of Two-Dimensional Tissues
A B C
Figure 1.1: Examples of the epithelial junctional network. (A) Drosophila retina ommatidium
(adapted from [1]), (B) basilar papilla of chicken embryo (adapted from [2]), and
(C) Drosophila wing disc (adapted from [3]).
During development, organs with tremendous diversity in shape and functionality form from
a single fertilized egg cell. Mechanisms that control shape, size and morphology of tissues are
largely unknown. These mechanisms are tightly controlled by an underlying signaling system
by which cells communicate to each other. For example, morphogens, molecules secreted by
localized sources, spread in the tissue and guide the position dependent expression of genes
and control tissues final size and shape [4]. Although many molecules are involved in the
establishment of these signaling systems, the response of cells to such a flow of information
throughout the tissue is limited to processes such as cell division, cell death, cell growth, cell
migration and cell shape changes. All these processes are mainly governed by cell mechanics.
An important model system to study cell mechanics and cell adhesion is two-dimensional
sheets of cells, called epithelia. Epithelia are formed by repeated cell division from a small
group of cells, which have almost identical properties. Epithelial cells are packed in specific
morphologies via cell-cell adhesion. These cell packings are inherently dynamic structures
and remodel during development. However, biological tissues are structurally and functionally
stable in physiological environments [11]. These two contradictory properties of tissues as
active soft materials, have fascinated scientist for more than a century.1.1 Biophysics of Two-Dimensional Tissues 8
Epithelial cells assemble adhesive junctions with their neighbors in their apical region; the
adhesion molecules, Cadherin, and com