George, Uduak Zenas (2012) A numerical approach to studying cell dynamics. Doctoral thesis (DPhil), University of Sussex.
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The focus of this thesis is to propose and implement a highly efficient numerical
method to study cell dynamics. Three key phases are covered: mathematical
modelling, linear stability analytical theory and numerical simulations
using the moving grid finite element method. This aim is to study cell
deformation and cell movement by considering both the mechanical and biochemical
properties of the cortical network of actin filaments and its concentration.
These deformations are assumed to be a result of the cortical actin
dynamics through its interaction with a protein known as myosin II in the cell
The mathematical model that we consider is a continuum model that couples
the mechanics of the network of actin filaments with its bio-chemical dynamics.
Numerical treatment of the model is carried out using the moving grid
finite element method. By assuming slow deformations of the cell boundary,
we verify the numerical simulation results using linear stability theory close
to bifurcation points. Far from bifurcation points, we show that the model
is able to describe the deformation of cells as a function of the contractile
tonicity of the complex formed by the association of actin filaments with the
myosin II motor proteins. Our results show complex cell deformations and
cell movements such as cell expansion, contraction, translation and protrusions
in accordance with experimental observations.
The migratory behaviour of cells plays a crucial role in many biological
events such as immune response, wound healing, development of tissues, embryogenesis,
inflammation and the formation of tumours.
|Item Type:||Thesis (Doctoral)|
|Schools and Departments:||School of Mathematical and Physical Sciences > Mathematics|
|Subjects:||Q Science > QH Natural history > QH0301 Biology > QH0426 Genetics > QH0438.4 Special aspects of the subject as a whole, A-Z > QH0438.4.M33 Mathematics|
|Depositing User:||Library Cataloguing|
|Date Deposited:||07 Feb 2012 14:55|
|Last Modified:||24 Aug 2015 14:52|