A Model for Enzymatic Reaction Dynamics in Metabolic Pathways

Thesis Abstract

Understanding the dynamic behavior of enzymatic reactions within metabolic pathways is essential for advancing biochemical knowledge and optimizing biomedical and biotechnological applications. Despite extensive experimental investigations, a comprehensive theoretical framework capable of accurately modeling enzyme-catalyzed reaction kinetics at a systems level remains underdeveloped. This study aims to develop a robust mathematical model to describe enzymatic reaction dynamics, integrating enzyme kinetics, substrate interactions, and allosteric regulation, with the purpose of improving the predictive understanding of metabolic fluxes. The specific objectives include formulating a nonlinear dynamical model based on Michaelis-Menten kinetics extended to account for enzyme cooperativity and feedback inhibition, validating the model through empirical data, and analyzing the influence of key regulatory parameters on pathway behavior. The research adopts a mixed-methods approach combining theoretical modeling with empirical validation. The theoretical component involves constructing a system of differential equations derived from established biochemical principles, such as the Briggs-Haldane and Hill equations, to simulate enzyme-substrate interactions within a specified metabolic pathway—namely glycolysis. Refinements are made to incorporate allosteric effects, substrate saturation, and product feedback mechanisms. For empirical validation, data are collected from enzymatic assays performed on liver cell cultures derived from a sample of 150 human donors, representing variations in enzyme activity due to genetic and environmental factors. Enzyme activity levels and metabolite concentrations are measured using spectrophotometry and mass spectrometry techniques, respectively. The model parameters are estimated via nonlinear regression analysis employing iterative least squares algorithms, and sensitivity analyses are performed to identify parameters with the greatest influence on system dynamics. Expected key findings include the identification of critical regulatory points within the pathway, elucidation of how enzyme cooperativity influences overall flux, and the development of a predictive model capable of simulating enzymatic responses to various perturbations such as drug inhibition or substrate overload. It is anticipated that the model will reveal nonlinear behaviors, such as bifurcations or oscillations, under specific regulatory conditions, thereby offering insight into pathway resilience and susceptibility to dysregulation. This study contributes to the body of knowledge by advancing the theoretical understanding of enzymatic dynamics, integrating biochemical kinetics with systems modeling, and providing a platform for predictive simulations in metabolic regulation. The developed model serves as a foundational tool for exploring therapeutic interventions targeting enzyme activities and for optimizing metabolic engineering strategies. Furthermore, the research demonstrates the applicability of dynamical systems theory, particularly the use of bifurcation analysis and stability theory, in elucidating complex biochemical processes. In conclusion, this research underscores the importance of a systems-level approach to enzyme kinetics, providing a validated and adaptable model that enhances predictive capabilities for metabolic pathway behavior. It recommends further research to extend the model to include spatial heterogeneity and to incorporate stochastic effects for more comprehensive simulations. Future studies should explore the integration of the model with multi-omics data to facilitate personalized medicine approaches and to improve understanding of metabolic diseases. Overall, the findings will have significant implications for biochemical research, clinical diagnostics, and metabolic engineering, enabling more precise modulation of enzymatic activity within complex biological systems.