AbstractMany important processes in cells are controlled by extracellular signals which are caused by many different chemical signals from their surrounding. Cells have the capability to react to signal transduction in an appropriate way, such as activate the response of intracellular molecules, which is mainly governed by proteins reacting with each other.
Intracellular signalling networks are mainly based on kinases and phosphatases, enzymes which control phosphorylation and dephosphorylation of other enzymes in the cellular surrounding to the nucleus.
In this thesis we present mathematical models for negative feedback signal transduction processes. Signal transduction pathways are often equipped with negative feedbacks. Negative feedback loops are important components that exhibit oscillations in concentrations of the substances involved, both temporally and spatially. These feedbacks constitute a major research for targeted therapies in cancer treatment, drug action and cause cross-activation of other pathways. Specifically, we investigate systematically how the negative feedback structure of the signal transduction network can transmit information despite noise in protein levels. In this thesis, we consider mathematical
models of the Hes1, Hes1-Stat3 and p53-Mdm2 pathways.
In chapter 3, we have undertaken a detailed study of the previous work done in the field. Building on this previous work, we derive mathematicalmodels (systems of partial differential equations) to capture the evolution in space and time of the key variables in the Hes1 and p53-Mdm2 systems. Computational simulations allow us to show that our reaction-diffusion models are able to produce sustained oscillations both spatially and temporally. The simulations of our models also allow us to calculate a diffusion coefficient range for the variables in each mRNA and protein, as well as ranges for other key parameters of the models. Also, we have carried out simulations under different
conditions such as considering a time delay in the protein diffusion process from nucleus to the cytoplasm, varying the thickness of the nucleus membrane which slows down diffusion in a cell. Our results have extended and generalized previous work in this area.
All the mathematical models in this thesis use the numerical analysis of nonlinear partial differential equations and computational simulations to obtain insight into the underlying biological systems. The systems of nonlinear partial differential equations were solved numerically using one of theMATLAB, COMSOL and URDME software packages.
|Date of Award||2014|
|Sponsors||Saudi Arabia Ministry of Higher Education|
|Supervisor||Mark Chaplain (Supervisor)|