Computational and mathematical models of cellular processes promise great benets in important elds such as molecular biology and medicine. Increasingly, researchers are incorporating the fundamentally discrete and stochastic nature of biochemical processes into the mathematical models that are intended to represent them. This has led to the formulation of models for genetic networks as continuous-time, discrete state, Markov processes, giving rise to the so-called Chemical Master Equation (CME), which is a discrete, partial dierential equation, that governs the evolution of the associated probability distribution function (PDF). While promising many insights, the CME is computationally challenging, especially as the dimension of the model grows. In this thesis, novel methods are developed for computing the PDF of the Master Equation. The problems associated with the high-dimensional nature of the Chemical Master Equation are addressed by adapting Krylov methods, in combination with Finite State Projection methods, to derive algorithms well-suited to the Master Equation. Variations of the approach that incorporate the Strang splitting and a stochastic analogue of the total quasi-steady-state approximation are also derived for chemical systems with disparate rates. Monte Carlo approaches, such as the Stochastic Simulation Algorithm, that simulate trajectories of the process governed by the CME have been a very popular approach and we compare these with the PDF approaches developed in this thesis. The thesis concludes with a discussion of various implementation issues along with numerical results for important applications in systems biology, including the gene toggle, the Goldbeter-Koshland switch and the Mitogen-Activated Protein Kinase Cascade.

Computational and mathematical models of cellular processes promise great benets in important elds such as molecular biology and medicine. Increasingly, researchers are incorporating the fundamentally discrete and stochastic nature of biochemical processes into the mathematical models that are intended to represent them. This has led to the formulation of models for genetic networks as continuous-time, discrete state, Markov processes, giving rise to the so-called Chemical Master Equation (CME), which is a discrete, partial dierential equation, that governs the evolution of the associated probability distribution function (PDF). While promising many insights, the CME is computationally challenging, especially as the dimension of the model grows. In this thesis, novel methods are developed for computing the PDF of the Master Equation. The problems associated with the high-dimensional nature of the Chemical Master Equation are addressed by adapting Krylov methods, in combination with Finite State Projection methods, to derive algorithms well-suited to the Master Equation. Variations of the approach that incorporate the Strang splitting and a stochastic analogue of the total quasi-steady-state approximation are also derived for chemical systems with disparate rates. Monte Carlo approaches, such as the Stochastic Simulation Algorithm, that simulate trajectories of the process governed by the CME have been a very popular approach and we compare these with the PDF approaches developed in this thesis. The thesis concludes with a discussion of various implementation issues along with numerical results for important applications in systems biology, including the gene toggle, the Goldbeter-Koshland switch and the Mitogen-Activated Protein Kinase Cascade.

Thesis (Ph.D.)--Drexel University, 2005. / Includes abstract and vita. Includes bibliographical references (leaves 91-98).

Berlin, Humboldt-University, Diss., 2006.

Thesis (Ph. D.)--University of Sydney, 2007. / Title from title screen (viewed 25th October, 2007). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to Work & Organisational Studies, Faculty of Economics and Business, University of Sydney. Degree awarded 2007. Includes bibliographical references. Also issued in print.

Research Project (M.B.A.) - Simon Fraser University, 2006. / Theses (Faculty of Business Administration) / Simon Fraser University. Senior supervisor : Dr. Jennifer C. Chang. MBA-MKTG Specialist Program.

Thesis (M. Ed.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 90-93).

Thesis (M.Ed.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 90-93). Also available in print.

Thesis (Ed. D.)--Illinois State University, 1992. / Title from title page screen, viewed February 6, 2006. Dissertation Committee: Larry D. Kennedy (chair), G. Thomas Baer, Barbara S. Heyl, Jeanne B. Morris. Includes bibliographical references (leaves 249-265) and abstract. Also available in print.

Thesis (Ph. D.)--Drexel University, 2005. / Includes abstract and vita. Includes bibliographical references (leaves 91-98).