A Framework for Modeling Enzyme Kinetics via Dynamic Regimes Theory

Thesis Abstract

Enzyme kinetics remain central to understanding metabolic regulation and industrial biocatalysis, yet classical models often inadequately capture transitions between kinetic regimes observed under fluctuating cellular and process conditions. This study addresses the gap by developing a Dynamic Regimes Theory (DRT) framework that integrates regime-switching behavior into enzymatic rate laws, enabling robust prediction of reaction velocity across substrate concentrations, cofactor states, and environmental perturbations. The aim is to formulate a mathematically tractable framework that identifies distinct kinetic regimes, characterizes transition criteria, and estimates regime-specific parameters from empirical data. Specific objectives include (i) deriving a multi-regime kinetic model that accommodates allosteric effects, substrate inhibition, and cofactor-dependent switching, (ii) establishing statistical and dynamical criteria for regime delineation using a combination of hidden Markov models and regime-switching autoregressive processes, (iii) validating the framework against experimentally generated enzyme velocity data across multiple enzymes (e.g., lactate dehydrogenase, hexokinase, and lysozyme variants) under varying pH, temperature, and substrate flux, and (iv) evaluating predictive performance against classical Michaelis–Menten and Hill formalisms using cross-validation and information-theoretic metrics. The methodology employs a mixed-methods design that combines quantitative modeling with targeted calibration experiments. The population comprises kinetic datasets reported in peer-reviewed sources and newly conducted microplate assays for representative enzymes. A purposive sample of 12–15 enzyme systems with publicly available turnover data and 3–4 in-house experiments is planned. Data collection instruments include high-throughput spectrophotometric assays, stopped-flow measurements for rapid kinetics, and microfluidic platforms to impose controlled environmental perturbations, supplemented by published kinetic datasets from open repositories. Instrument validity is addressed through calibration curves, standard curves for each substrate, and inter-assay repeatability checks, while reliability is ensured by triplicate measurements and blinded duplicate assays. Data analysis proceeds in stages (i) preprocessing to normalize velocity data and align regime labels, (ii) estimation of regime-specific parameters via a hierarchical Bayesian framework with Markov-switching priors, (iii) model comparison with conventional kinetic models using Akaike and Bayesian information criteria, (iv) sensitivity analysis to identify influential regime boundaries, and (v) out-of-sample validation using withheld datasets. The analytical core integrates dynamic systems theory with statistical learning regime transitions are modeled through a hidden Markov model that governs piecewise kinetic laws, while parameter estimation relies on particle filtering and variational Bayes to cope with sparse data within regime windows. The expected findings include (a) a parsimonious set of regime indicators corresponding to substrate-saturation, allosteric activation, and substrate-inhibition states, (b) enhanced predictive accuracy for velocity profiles under complex perturbations relative to Michaelis–Menten and Hill equations, as evidenced by reductions in RMSE by 15–30% and improved AUC for regime classification, and (c) elucidation of the dependence of regime stability on temperature and pH, providing mechanistic insights into dynamic regulatory controls. The study contributes to knowledge by offering a unified, testable framework that reconciles steady-state kinetics with dynamic regime shifts, enabling more faithful modeling of enzyme behavior in physiological and industrial contexts. The theoretical contribution includes formalization of Dynamic Regimes Theory as an extension of piecewise-smooth dynamical systems to enzyme catalysis, along with a methodological toolkit combining Bayesian regime estimation, regime-switching regression, and information-criterion-guided model selection. Practically, the framework supports improved parameterization of kinetic models in metabolic engineering, drug design, and bioprocess optimization by delivering regime-aware predictions and interpretable transition cues. The conclusion anticipates that incorporating regime dynamics will reduce predictive uncertainty in enzyme kinetics under fluctuating environments and will prompt revisions of standard kinetic modeling practices. Recommendations emphasize extending the framework to networks of coupled enzymes, integrating thermal and molecular chaperone effects, and adapting the approach for real-time process control in biomanufacturing settings.