Exploring phenylketonuria through mathematical models: enzyme kinetics and genetic probabilities
摘要
Phenylketonuria (PKU) represents a paradigmatic monogenic metabolic disorder requiring precise, individualized therapeutic interventions. Current clinical approaches often compartmentalize enzyme dysfunction, metabolic dysregulation, and genetic risk assessment, thereby constraining opportunities for truly predictive, personalized medicine. This study presents an integrated mathematical framework that unifies enzyme kinetics, metabolic modeling, and population genetics, enabling the quantitative prediction and optimization of PKU management strategies. We employ Michaelis-Menten kinetics to characterize phenylalanine hydroxylase (PAH) mutations, develop ordinary differential equations to simulate phenylalanine-tyrosine dynamics, and apply Hardy-Weinberg equilibrium principles to estimate disease burden. Our model accurately predicts catalytic efficiency across diverse PAH mutations, demonstrating that BH4-responsive variants achieve 40% improvement in phenylalanine clearance under optimal cofactor supplementation. Simulations reveal that pegvaliase therapy reduces phenylalanine below neurotoxic thresholds even with standard dietary intake in severe PKU. Population-level integration yields 95% accuracy in predicting PKU incidence across diverse ethnic populations. This comprehensive framework offers quantitative tools for treatment optimization, establishing a template for modeling other monogenic disorders and advancing PKU management from a reactive to a predictive paradigm.