Daae, Elisabeth Bull; (1999) Mathematical modelling of biochemical pathways. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The primary objective of this thesis is to develop a framework for mathematical modelling of biochemical reactions in Streptomyces bacteria grown in batch fermentations. Secondly, the thesis investigates and applies mathematical methods in the modelling of biochemical pathways of different complexity and relation. The models enhance the understanding of the biochemical system in question and have the ability to predict certain systemic events; thus illustrating the power of mathematics applied to complex biochemical reaction systems. The thesis investigates two metabolic systems, the primary metabolism in Streptomyces lividans and a genetically engineered pathway for the production of biodegradable plastics in plants. Mathematical modelling of the primary metabolic network illustrates the application of linear algebra to large biochemical systems, providing a flexible and powerful analytical tool. A cybernetic model, a special form of structured models, was also developed to illustrate the dynamics of glucose uptake in Streptomyces lividans. The genetically engineered pathway has non-linear properties related to the kinetics of the various enzymes in the pathway. The mathematical complexity of this problem requires an alternative approach where ordinary differential equations are central to solving the problem. Powerful algorithms are used to execute the model and to generate predictive data. A mathematical framework for the analysis and modelling of biochemical fluxes in the primary metabolic pathways of Streptomyces lividans is presented. The model aided in the identification of strain specific parameters and enhanced the understanding of metabolic mechanisms such as organic acids secretion, providing insight into its causes and conditions. The cybernetic model is designed to mimic a proposed metabolic mechanism. The kinetic model of the genetically engineered pathway provided the answers to whether quality plastic could be produced efficiently in plants.

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