Modelling Enzyme-Driven pH Control and Dynamic Behaviour in Compartmentalised Enzymatic Networks

This thesis uses numerical simulations based on ordinary differential equations to investigate enzymatic pH control within lipid vesicles. These membrane-bound compartments are widely used in synthetic cell research and offer controllable environments with potential applications in drug delivery, synthetic biology, and dynamic materials. Despite their widespread use, the mechanistic behaviour and interactions of encapsulated enzyme networks present outstanding questions, limiting the interpretation of experimental trends and the design of predictable systems. Chapters 1-3 establish the context of this work, reviewing relevant literature, developing the modelling framework, and presenting baseline models of urease-driven pH modulation that underpin subsequent analyses. Chapter 4 demonstrates a tunable urease–glucose oxidase oscillator that operates within physiological pH ranges and remains dampened but functional when confined to vesicles, offering a design roadmap for synthetic biological timers. Chapter 5 moves to more realistic systems and examines the influence of membrane transport and electrochemical gradients on feedback mechanisms, uncovering counterintuitive effects of membrane thickness and identifying conditions where ionic transport and membrane potential shape system behaviour. Chapter 6 explores applications in metabolite-responsive drug release, demonstrating how enzymatic pH modulation can be used to pre-program the timing and extent of vesicle release and identifying regimes where chemical control dominates over passive dissolution or diffusion. Collectively, the studies establish general principles linking enzyme kinetics, transport, and compartmentalisation, highlighting the power of mechanistic modelling to guide the design and experimental implementation of dynamic chemical networks in compartmentalised systems