Abstract
Kinetic models provide the means to understand and predict the dynamic behaviour of enzymes upon different perturbations. Despite their obvious advantages, classical parameterizations require large amounts of data to fit their parameters. Particularly, enzymes displaying complex reaction and regulatory (allosteric) mechanisms require a great number of parameters and are therefore often represented by approximate formulae, thereby facilitating the fitting but ignoring many real kinetic behaviours. Here, we show that full exploration of the plausible kinetic space for any enzyme can be achieved using sampling strategies provided a thermodynamically feasible parameterization is used. To this end, we developed a General Reaction Assembly and Sampling Platform (GRASP) capable of consistently parameterizing and sampling accurate kinetic models using minimal reference data. The former integrates the generalized MWC model and the elementary reaction formalism. By formulating the appropriate thermodynamic constraints, our framework enables parameterization of any oligomeric enzyme kinetics without sacrificing complexity or using simplifying assumptions. This thermodynamically safe parameterization relies on the definition of a reference state upon which feasible parameter sets can be efficiently sampled. Uniform sampling of the kinetics space enabled dissecting enzyme catalysis and revealing the impact of thermodynamics on reaction kinetics. Our analysis distinguished three reaction elasticity regions for common biochemical reactions: a steep linear region (0> ΔGr >-2 kJ/mol), a transition region (-2> ΔGr >-20 kJ/mol) and a constant elasticity region (ΔGr <-20 kJ/mol). We also applied this framework to model more complex kinetic behaviours such as the monomeric cooperativity of the mammalian glucokinase and the ultrasensitive response of the phosphoenolpyruvate carboxylase of Escherichia coli. In both cases, our approach described appropriately not only the kinetic behaviour of these enzymes, but it also provided insights about the particular features underpinning the observed kinetics. Overall, this framework will enable systematic parameterization and sampling of enzymatic reactions.
Highlights
Since the seminal work of Michaelis and Menten [1], enzyme kinetics theory has been developed for most catalytic mechanisms, captured as a series of elementary reactions representing events at molecular level, i.e. binding and release of reactants from enzyme intermediates and catalysis
Here we present a novel framework General Reaction Assembly and Sampling Platform (GRASP) for exploring the kinetic behaviour of enzymatic reactions under uncertainty based on parameter sampling
By formulating the appropriate thermodynamic constraints and using minimal biochemical reference data, our framework is capable of parameterizing the kinetics of any oligomeric enzyme without sacrificing complexity
Summary
Since the seminal work of Michaelis and Menten [1], enzyme kinetics theory has been developed for most catalytic mechanisms, captured as a series of elementary reactions representing events at molecular level, i.e. binding and release of reactants from enzyme intermediates and catalysis. The particular catalytic pattern of the enzyme dictates its mathematical representation, which can be obtained by solving equations for the enzyme intermediate concentrations [2]. A quasi-steady-state assumption for these intermediates is commonly employed to this end [3], yielding a final expression function of microscopic rate constants and reactant concentrations. Some of the rate constants are related to the apparent equilibrium constant of the overall reaction by the Haldane relationships, directly linking kinetics with thermodynamics [5]. The rate constants can be converted into macroscopic kinetic constants [6], which can be measured and estimated from subsequent enzymatic assays
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