A Kinetic Analysis of Coupled (or Auxiliary) Enzyme Reactions

Activity assays for flavoprotein oxidases: an overview

Flavoprotein oxidases have found many biotechnological applications. For identifying and improving their characteristics, it is essential to have reliable and robust assay methodology available. The methodologies used to monitor their activity seem to be scattered in the literature and seem often selected based on convenience. Due to the diversity of reactions catalyzed by flavoprotein oxidases, it is virtually impossible to recommend a single activity assay. A literature analysis of 60 recent papers describing flavoprotein oxidases revealed that continuous spectrophotometric assays, in particular colorimetric assays, are the preferred choice, as they are facile, scalable and allow for better interpretation of data than discontinuous assays. Colorimetric assays typically rely on the extinction coefficient of a monitored chromogenic product, which can be highly variable depending on the experimental conditions. Therefore, it is important to determine the extinction coefficient under the specific experimental conditions used, rather than taking it directly from the literature. To provide a guideline and assist in standardization, this review describes the most commonly utilized activity assays for flavoprotein oxidases, along with their respective merits and limitations. KEY POINTS: • Researchers should be more aware of limitations of activity assays. • Extinction coefficients should be determined for the appropriate experimental setup. • New robust activity assays are desired.

Natural Parameter Conditions for Singular Perturbations of Chemical and Biochemical Reaction Networks

We consider reaction networks that admit a singular perturbation reduction in a certain parameter range. The focus of this paper is on deriving "small parameters" (briefly for small perturbation parameters), to gauge the accuracy of the reduction, in a manner that is consistent, amenable to computation and permits an interpretation in chemical or biochemical terms. Our work is based on local timescale estimates via ratios of the real parts of eigenvalues of the Jacobian near critical manifolds. This approach modifies the one introduced by Segel and Slemrod and is familiar from computational singular perturbation theory. While parameters derived by this method cannot provide universal quantitative estimates for the accuracy of a reduction, they represent a critical first step toward this end. Working directly with eigenvalues is generally unfeasible, and at best cumbersome. Therefore we focus on the coefficients of the characteristic polynomial to derive parameters, and relate them to timescales. Thus, we obtain distinguished parameters for systems of arbitrary dimension, with particular emphasis on reduction to dimension one. As a first application, we discuss the Michaelis-Menten reaction mechanism system in various settings, with new and perhaps surprising results. We proceed to investigate more complex enzyme catalyzed reaction mechanisms (uncompetitive, competitive inhibition and cooperativity) of dimension three, with reductions to dimension one and two. The distinguished parameters we derive for these three-dimensional systems are new. In fact, no rigorous derivation of small parameters seems to exist in the literature so far. Numerical simulations are included to illustrate the efficacy of the parameters obtained, but also to show that certain limitations must be observed.

"Switching On" Enzyme Substrate Specificity Analysis with a Fluorescent Competitive Inhibitor

Enzymatically driven change to the spectroscopic properties of a chemical substrate or product has been a linchpin in the development of continuous enzyme kinetics assays. These assays inherently necessitate substrates or products that naturally comply with the constraints of the spectroscopic technique being used, or they require structural changes to the molecules involved to make them observable. Here we demonstrate a new analytical kinetics approach with enzyme histidine triad nucleotide binding protein 1 (HINT1) that allows us to extract both useful k_cat values and a rank-ordered list of substrate specificities without the need to track substrates or products directly. Instead, this is accomplished indirectly using a "switch on" competitive inhibitor that fluoresces maximally only when bound to the HINT1 enzyme active site. Kinetic information is extracted from the duration of the diminished fluorescence when the monitorable inhibitor-bound enzyme is challenged with saturating concentrations of a nonfluorescent substrate. We refer to the loss of fluorescence, while the substrate competes for the fluorescent probe in the active site, as the substrate's residence transit time (RTT). The ability to assess k_cat values and substrate specificity by monitoring the RTTs for a set of substrates with a competitive "switch on" inhibitor should be broadly applicable to other enzymatic reactions in which the "switch on" inhibitor has sufficient binding affinity over the enzymatic product.

Using singular perturbation theory to determine kinetic parameters in a non-standard coupled enzyme assay

We investigate how to characterize the kinetic parameters of an aminotransaminase using a non-standard coupled (or auxiliary) enzyme assay, where the peculiarity arises for two reasons. First, one of the products of the auxiliary enzyme is a substrate for the primary enzyme and, second, we explicitly account for the reversibility of the auxiliary enzyme reaction. Using singular perturbation theory, we characterize the two distinguished asymptotic limits in terms of the strength of the reverse reaction, which allows us to determine how to deduce the kinetic parameters of the primary enzyme for a characterized auxiliary enzyme. This establishes a parameter-estimation algorithm that is applicable more generally to similar reaction networks. We demonstrate the applicability of our theory by performing enzyme assays to characterize a novel putative aminotransaminase enzyme, CnAptA (UniProtKB Q0KEZ8) from Cupriavidus necator H16, for two different omega-amino acid substrates.

Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics

Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions, it is often overlooked that the characteristic timescales used for the scaling the rate equations are not ideal for determining when concentrations and reaction rates reach their maximum values. In this work, we first illustrate this point by considering the classic example of the single-enzyme, single-substrate Michaelis-Menten reaction mechanism. We then extend this analysis to a more complicated reaction mechanism, the auxiliary enzyme reaction, in which a substrate is converted to product in two sequential enzyme-catalyzed reactions. In this case, depending on the ordering of the relevant timescales, several dynamic regimes can emerge. In addition to the characteristic timescales for these regimes, we derive matching timescales that determine (approximately) when the transitions from transient to quasi-steady-state kinetics occurs. The approach presented here is applicable to a wide range of singular perturbation problems in nonlinear dynamical systems.

Phase-plane geometries in coupled enzyme assays

The determination of a substrate or enzyme activity by coupling one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course expressions valid under the quasi-steady-state and reactant stationary state assumptions. In this paper, the dynamical behavior of coupled enzyme catalyzed reaction mechanisms is studied by analysis of the phase-plane. We analyze two types of time-dependent slow manifolds - Sisyphus and Laelaps manifolds - that occur in the asymptotically autonomous vector fields that arise from enzyme coupled reactions. Projection onto slow manifolds yields various reduced models, and we present a geometric interpretation of the slow/fast dynamics that occur in the phase-planes of these reactions.