Mathematical models for the kinetics of some carbohydrate enzymes

Abstract

In this thesis, some mathematical models for the mechanism of action of carbohydrate enzymes are developed and analysed.

Chapter 1 provides a general introduction to enzymes and their applications. In Chapter 2, mathematical preliminaries required for the subsequent analysis are introduced and discussed. This chapter also describes the Python software employed in the thesis.

In Chapter 3, a mathematical model for the degradation of hyaluronan by Streptococcus pneumoniae hyaluronate lyase is developed and analysed. The model results were found to agree well with experimental data. A Sobol global sensitivity analysis was implemented to identify the key model parameters. Some practical applications of the model are also indicated.

Chapter 4 considers a mathematical model that describes the phosphorylation of glucose by human hexokinase I. Numerical simulations of the model produce results that are consistent with the experimentally observed behaviour. A global sensitivity analysis of the model was implemented to help identify the key mechanisms of hexokinase I regulation. The sensitivity analysis also enabled the development of a simpler model that produces output close to that of the full model.

The model developed in Chapter 4 is too complex to obtain simple analytic expressions for the rate of product formation. It is also difficult to obtain simple qualitative insights into the enzyme behaviour from this model. In an effort to overcome those deficiencies, two simpler related models are developed in Chapter 5. The first model focuses on the mechanism of competitive product inhibition only, while the second model considers allosteric inhibition only. Some practical applications of the models are also indicated.

In Chapter 6, a brief discussion of the work presented in the thesis is given, and some possible directions for refinement and expansion of the models are also indicated.