| Summary: | The main interest of this work is the application of mathematical programming and optimisation methodologies to problems of biological nature. Biological data forms the basis for modelling, simulation and optimisation - techniques developed and matured successfully within the Process Systems Engineering community - to be carried out in systems like biological networks, metabolic pathways or proteins. Mathematical programming techniques have not yet extensively been applied to such systems. In the first part of the thesis, optimisation methods for the analysis of biological networks are developed. Metabolic pathway distances and their correlations with genome distance and enzyme function for E. coli small molecule metabolism are examined through the use of a linear programming algorithm. The same technique is also applied to the study of the robustness of the p53 cell cycle and apoptotic control network. The p53 network is found to be robust against mutational perturbation, but vulnerable to directed assault against its hubs from tumour-inducing viruses, which act as "biological hackers" to attack the system. The second part studies protein folding using lattice models. A mixed integer linear programming framework is developed, to implement a successful three-step solution strategy for reading the 3D structure of proteins from only the knowledge of the amino acid sequence and the contact energies among amino acids. The methodology is validated by its application on model proteins designed to fold in a cubical lattice. Finally, the third part presents mathematical models for the concurrent synthesis of optimal peptide tags and purification steps for protein downstream processing in biochemical processes. In particular, a mixed integer non-linear programming model for the solution of the problem is proposed. A mixed integer linear programming model is then developed by modifying the process synthesis constraints and applying linear approximations of the non-linear functions. The applicability of the models is demonstrated by examples that rely on experimental data.
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