الفهرس 
Biological BackgroundOnly 14 pages are availabe for public view
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Abstract
Genes carry the genetic information and traits of the human. A gene is a distinct portion of a cell’s DNA. A gene corresponds to a sequence of micro-molecules along one or more regions of a DNA. Each gene codes for a specific protein by specifying the order in which amino acids must be joined together. These proteins are then the regulators of all cell’s and tissue functions. Gene expression refers to the activity of the gene, whether a gene is on or off. During the activity of a gene, a special type of molecules is synthesised called mRNA. Hence, the state of the gene is hitched to this mRNA, an active or suppressed gene is covalent to the abundance of mRNA molecules.
Non-coding RNAs are the seminal molecules in the mechanisms that is yet another layer of control of the cell’s gene expression over the already existing complex gene expression system These mechanisms are tethered to small non-coding RNA called small interfering RNA (siRNA) and microRNA (miRNA). The siRNA and miRNA impose a biological process of mRNA destabilization or translation inhibition
This thesis is particularly interested in the regulators of mRNA, the regulators of ncRNA and mRNA-ncRNA interactions on the temporal and spatial concentrations of mRNA and hence the gene activity and gene expression.
A better understanding of cancer requires a thorough consideration of the regulators of cancer. This understanding is the crux for discovering effective methods for the prognosis, diagnosis and treatment to various types and stages of cancer. Genes play an eminent role in synthesising proteins that regulates tumorigenic cell growth. Moreover, cells have age and a cell cycle. The activity of certain genes whether translation or suppression may alter and cause disruption to the cell’s ages or its functions; normal cells can undergo a process of tumorigenesis. To modulate the temporal and spatial concentrations of the mRNAs covalent to cancer opens the horizon for the treatment and prognosis of the disease.
The foremost aim of this work consists in continuously approximating the temporal expression profile of genes in a tissue in a two-dimensional spatial domain for the transition states before converging to the stationary state. by a system of coupled partial differential equations.
The system of partial differential equations penalises the mRNA-ncRNA interactions that plays a crucial role in the gene regulation. We differentiate between the two non-coding RNA species gene regulation mechanism. Small interfering RNA regulates genes by causing degradation to the mRNA and hence is modelled by a system of coupled partial differential equations. However, micro-RNA regulates genes by inhibiting translation but eventually causes degradation. The gene regulation mechanism of the miRNA is rather modelled by a system of coupled delay partial differential equations. Moreover, the molecular movement potency of mRNA and the two species of non-coding RNA within the tissue is modelled by a diffusion paradigm.
There are several seminal properties related to our model. Firstly, we provide a quantitively continuous approximation to the experimental data that conveys the biological gene regulatory system. Secondly, we introduce a qualitative counter-part approximation for the expression profile of experimental data.
To date and to our knowledge, the studies dealt only with gene regulations of tissues displaying sharp interface between high mRNA concentrations and low mRNA concentrations. We introduce a novel quantitative continuous time approximation to the experimental data and qualitative approximation for the expression profile, for genes with substantially different initial distributions.
Moreover, in higher multicellular organisms, the epigenetic DNA methylation is appealing in the proliferation and transcription abundance of genes. Although the DNA methylation were broadly discussed, to our knowledge they have not been systematically analysed in a system of partial differential equations. An epigenetic mRNA transcription rate is assembled into the system of partial differential equations.
This thesis concerns an efficient approximation to the dynamics of genes in a tissue for the transition states before converging to the steady state. This research is structured as follows: Chapter Two introduces the Biological nature of the research. Chapter Three deals with clustering and Dempster-Shafer theory. In Chapter Four we discuss the mathematical model building. We present the computational results and qualitative analysis in chapter Five. Chapter Six summarises the conclusions and future work.