Theory and Application of the Relationship Between Steady-State Isotope Effects on Enzyme Intermediate Concentrations and Net Rate Constants

Measurement of Net Rate Constants from Enzyme Progress Curves without Curve Fitting

A method is described whereby net rate constants can be directly inferred from the progress curves of enzyme intermediates without the need for model specification, numerical analysis, curve fitting, or the steady-state approximation. Specifically, if an enzyme intermediate in an ultimately irreversible serial subsequence is perturbed from and returns back to its equilibrium state as the substrate is consumed, then its net rate constant is given by the ratio of the total substrate consumed and the area under the progress curve for the enzyme intermediate. A rigorous analysis demonstrates this result to hold independent of the complete enzymatic reaction in which the subsequence is embedded, making it broadly applicable to a very wide range of kinetic mechanisms, including those complicated by inhibition. As a theoretical consequence, it is shown that traditionally steady-state parameters such as k_cat, k_cat/K_M, and net rate constants can be expressed as limiting ratios of averages without requiring the steady-state hypothesis. Finally, a mock data set is generated for a system of contemporary interest that can serve as both an example of how the methodology would be used in practice and a proof of concept.

Changes in Regioselectivity of H Atom Abstraction during the Hydroxylation and Cyclization Reactions Catalyzed by Hyoscyamine 6β-Hydroxylase

Hyoscyamine 6β-hydroxylase (H6H) is an αKG-dependent nonheme iron oxidase that catalyzes the oxidation of hyoscyamine to scopolamine via two separate reactions: hydroxylation followed by oxidative cyclization. Both of these reactions are expected to involve H atom abstraction from each of two adjacent carbon centers (C6 vs C7) in the substrate. During hydroxylation, there is a roughly 85:1 preference for H atom abstraction from C6 versus C7; however, this inverts to a 1:16 preference during cyclization. Furthermore, ¹⁸O incorporation experiments in the presence of deuterated substrate are consistent with the catalytic iron(IV)-oxo complex being able to support the coordination of an additional ligand during hydroxylation. These observations suggest that subtle differences in the substrate binding configuration can have significant consequences for the catalytic cycle of H6H.