Genes are the fundamental units of biological organisms. Genes encode proteins which carryout various functions required for the maintenance of life. Gene regulation is a complex process that begins with a DNA sequence for a given gene. The process from DNA through many intermediates to functional proteins involves transcription, translation, transport, degradation, bio-chemical modification, and many other mechanisms. In this thesis, we studied the stability analysis of gene regulatory networks in the context of Lyapunov second method of gene regulatory networks under various constraints such as time-delay and stochastic perturbations. First we establish a mathematical framework of genetic regulatory model, and workedout the details of its components. Later, we studied the stability analysis of the fundamental gene regulatory model. We extended this fundamnetal model to incorporate time delays in transcription, translation, and translocation processes and establish the stability of this system. Finally, we investigated the stochastic nature of the intercellular, extracellular and environmental fluctuations and studied the noise effects on stability of such fundamental gene regulatory network systems.
|Commitee:||Busby, Michael, Ganesan, Kothandaraman, Scheick, Sandra|
|School:||Tennessee State University|
|Department:||Physics & Mathematics|
|School Location:||United States -- Tennessee|
|Source:||MAI 52/03M(E), Masters Abstracts International|
|Subjects:||Applied Mathematics, Genetics, Mathematics|
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