Mathematical models of tissue development
File(s)
Author(s)
Hecht, Sophie
Type
Thesis
Abstract
How tissues develop and regulate their growth is a key question in biology. Studies of developing tissue have identified possible regulators of growth such, as chemical signalling and mechanical forces. This thesis aims to understand the influence of mechanical feedback on the development of the imaginal of Drosophila. In particular, we focus on understanding the mechanisms by which an organ knows when it has reached its adult size and shape and stops growing. As mechanical forces can influence the development at different scales, going from the compression of a single cell to the whole tissue stretching, this thesis is separated in two part.
In the first part, the influence of the structure of the imaginal disc of Drosophila on growth regulation is studied. This study leads to the development of continuous two-populations models with segregation constraints. The asymptotic limits of the partial differential equation (PDE) models, related to the two populations model, into a Hele-Shaw free boundary model are shown. The new models developed are used to study the impact of local stresses on the development of the imaginal disc of Drosophila.
The second part considers the influence of crowding in the imaginal disc of Drosophila and the effect of nuclear movement on growth regulation in dense tissue. We develop an individual-based model for the interkinetic nuclear movement in pseudostratified epithelia, founded upon a minimisation framework. The new model is tuned to study the influence of crowding in the specific case of the imaginal disc of Drosophila through biological data. In particular, we consider the effect of the crowding on the cell cycle and propose a mechanism to explain some of its phase transition.
In the first part, the influence of the structure of the imaginal disc of Drosophila on growth regulation is studied. This study leads to the development of continuous two-populations models with segregation constraints. The asymptotic limits of the partial differential equation (PDE) models, related to the two populations model, into a Hele-Shaw free boundary model are shown. The new models developed are used to study the impact of local stresses on the development of the imaginal disc of Drosophila.
The second part considers the influence of crowding in the imaginal disc of Drosophila and the effect of nuclear movement on growth regulation in dense tissue. We develop an individual-based model for the interkinetic nuclear movement in pseudostratified epithelia, founded upon a minimisation framework. The new model is tuned to study the influence of crowding in the specific case of the imaginal disc of Drosophila through biological data. In particular, we consider the effect of the crowding on the cell cycle and propose a mechanism to explain some of its phase transition.
Version
Open Access
Date Issued
2019-07
Date Awarded
2019-11
Copyright Statement
Creative Commons Attribution NonCommercial NoDerivatives Licence
Advisor
Degond, Pierre
Sponsor
Imperial College London
Publisher Department
Mathematics, Francis Crick Institute
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)