Comparison of different approaches and computer programs for progress curve analysis of enzyme kinetics

Enzyme kinetics by real-time quantitative NMR (qNMR) spectroscopy with progress curve analysis

This review article summarizes how the experimental data obtained using quantitative nuclear magnetic resonance (qNMR) spectroscopy can be combined with progress curve analysis to determine enzyme kinetic parameters. The qNMR approach enables following the enzymatic conversion of the substrate to the product in real-time by a continuous collection of spectra. The Lambert-W function, a closed-form solution to the time-dependent substrate/product kinetics of the rate equation, can estimate the Michaelis-Menten constant (K_M.) and the maximum velocity (V_max) from a single experiment. This article highlights how the qNMR data is well suited for analysis using the Lambert-W function with three different applications. Results from studies on acetylcholinesterase (acetylcholine to acetic acid and choline), β-Galactosidase (lactose to glucose and galactose), and invertase (sucrose to glucose and fructose) are presented. Furthermore, an additional example of how the progress curve analysis is applied to understand the inhibitory role of the artificial sweetener sucralose on sucrose's enzymatic conversion by invertase is discussed. With the wide availability of NMR spectrometers in academia and industries, including bench-top systems with permanent magnets, and the potential to enhance sensitivity using dynamic nuclear polarization in combination with ultrafast methods, the NMR-based enzyme kinetics could be considered a valuable tool for broader applications in the field of enzyme kinetics.

On the reproducibility of enzyme reactions and kinetic modelling

Enzyme reactions are highly dependent on reaction conditions. To ensure reproducibility of enzyme reaction parameters, experiments need to be carefully designed and kinetic modeling meticulously executed. Furthermore, to enable quality control of enzyme reaction parameters, the experimental conditions, the modeling process as well as the raw data need to be reported comprehensively. By taking these steps, enzyme reaction parameters can be open and FAIR (findable, accessible, interoperable, re-usable) as well as repeatable, replicable and reproducible. This review discusses these requirements and provides a practical guide to designing initial rate experiments for the determination of enzyme reaction parameters and gives an open, FAIR and re-editable example of the kinetic modeling of an enzyme reaction. Both the guide and example are scripted with Python in Jupyter Notebooks and are publicly available (https://fairdomhub.org/investigations/483/snapshots/1). Finally, the prerequisites of automated data analysis and machine learning algorithms are briefly discussed to provide further motivation for the comprehensive, open and FAIR reporting of enzyme reaction parameters.

The Removal of Time-Concentration Data Points from Progress Curves Improves the Determination of Km: The Example of Paraoxonase 1

Several approaches for determining an enzyme's kinetic parameter K_m (Michaelis constant) from progress curves have been developed in recent decades. In the present article, we compare different approaches on a set of experimental measurements of lactonase activity of paraoxonase 1 (PON1): (1) a differential-equation-based Michaelis-Menten (MM) reaction model in the program Dynafit; (2) an integrated MM rate equation, based on an approximation of the Lambert W function, in the program GraphPad Prism; (3) various techniques based on initial rates; and (4) the novel program "iFIT", based on a method that removes data points outside the area of maximum curvature from the progress curve, before analysis with the integrated MM rate equation. We concluded that the integrated MM rate equation alone does not determine kinetic parameters precisely enough; however, when coupled with a method that removes data points (e.g., iFIT), it is highly precise. The results of iFIT are comparable to the results of Dynafit and outperform those of the approach with initial rates or with fitting the entire progress curve in GraphPad Prism; however, iFIT is simpler to use and does not require inputting a reaction mechanism. Removing unnecessary points from progress curves and focusing on the area around the maximum curvature is highly advised for all researchers determining K_m values from progress curves.

Parameter Reliability and Understanding Enzyme Function

Knowledge of the Michaelis-Menten parameters and their meaning in different circumstances is an essential prerequisite to understanding enzyme function and behaviour. The published literature contains an abundance of values reported for many enzymes. The problem concerns assessing the appropriateness and validity of such material for the purpose to which it is to be applied. This review considers the evaluation of such data with particular emphasis on the assessment of its fitness for purpose.

Chemical Reaction Engineering to Understand Applied Kinetics in Free Enzyme Homogeneous Reactors

Chemical reaction engineering is interested in elucidating the reaction kinetics through the determination of the fundamental influencing variables. The understanding of enzyme kinetics is needed to implement the potential of enzymes to satisfy determined production targets and for the design of the reactor. The quantification of the enzyme kinetics is implemented by the elucidation and building of the kinetic model (it includes one or more kinetic equations). In the context of process development, the kinetic model is not only useful to identify feasibility and for optimizing reaction conditions but also, at an early stage of development it is very useful to anticipate implementation bottlenecks, and so guide reactor setup. In this chapter we describe theoretical and practical considerations to illustrate the methodological framework of kinetic analysis. We take as study cases four archetypal kinetic cases by using as example the hydrolysis of cellobiose catalyzed by a beta-glucosidase. We show the different experimental data that can be obtained by the monitoring of enzymatic reactions in different configuration of free enzyme homogeneous ideal reactors; we show step-by-step the visualization, treatment, and analysis of data to elucidate kinetic models and the procedure for the quantification of kinetic constants. Finally, the performance of different reactors is compared in the interplay with the enzyme kinetics. This book chapter aims at being useful for a broad multidisciplinary audience and different levels of academic development.

Framework of the kinetic analysis of O2-dependent oxidative biocatalysts for reaction intensification

A framework for kinetic modelling and evaluation of the reaction intensification of O2-dependent enzyme catalyzed reactions is built from measurements of consumption rates of the initially dissolved O2 in homogeneous liquid phase.

NMR based real-time enzyme kinetics on estimating the inhibitory effect of sucralose in the enzymatic conversion of sucrose

Sucralose, one of the popular non-caloric artificial sweeteners, has been known to influence the enzymatic conversion of sucrose to glucose and fructose by invertase. In continuing the use of real-time NMR experiments and reaction progress curve analysis to measure enzyme kinetics, here we investigate the role of sucralose as an inhibitor. NMR based kinetic experiments were performed as a function of the substrate concentration for a range of sucralose concentrations, and the results were analyzed by fitting the progress curve to the Lambert-W function. The Michaelis-Menten parameters were then used to estimate the inhibitory constant of sucralose. To estimate the extent of sucralose inhibition on the enzymatic production of glucose, control experiments were performed with lactose as the inhibitor under similar experimental conditions. The results show that sucralose is a much more potent inhibitor than lactose, inhibiting the enzymatic conversion at least seven times more.

Evaluation of the paraoxonase-1 kinetic parameters of the lactonase activity by nonlinear fit of progress curves

Although paraoxonase-1 (PON1) activity has been demonstrated to be a reliable biomarker of various diseases, clinical studies have been based only on relative comparison of specific enzyme activities, which capture differences mainly due to (usually unknown) PON1 concentration. Hence, the aim of this report is to present for the first time the simple evaluation method for determining autonomous kinetic parameter of PON1 that could be also associated with polymorphic forms and diseases; i.e. the Michaelis constant which is enzyme concentration independent quantity. This alternative approach significantly reduces the number of experiments needed, and it yields the results with great accuracy.

Derivation and identification of a mechanistic model for a branched enzyme-catalyzed carboligation

The kinetic description of enzyme-catalyzed reactions is a core task in biotechnology and biochemical engineering. In particular, mechanistic kinetic models help from the discovery of the biocatalyst throughout its application. Chemo- or enantioselective enzyme reactions often undergo two alternative pathways for the release of two different products from a central intermediate. For these types of reaction, no explicit reaction equations have been derived so far. To this end, we extend the commonly used Cleland's notation for branched reaction pathways and explicitly derive the rate expressions for two-coupled ordered bi-uni reactions. This mechanism also leads to a ping-pong bi-bi mechanism for a transfer reaction between the two products via the same central intermediate of the reaction system. Using the cross-ligation of benzaldehyde and propanal catalyzed by the thiamine diphosphate-dependent enzyme benzaldehyde lyase from Pseudomonas fluorescens yielding (R)-2-hydroxy-1-phenylbutan-1-one as a case study, we performed model-based experimental analysis to show that such a reaction mechanism can be modeled mechanistically and leads to reasonable kinetic parameters.

Direct determination of enzyme kinetic parameters from single reactions using a new progress curve analysis tool

With computer-based data-fitting methods becoming a standard tool in biochemistry, progress curve analysis of enzyme kinetics is a feasible, yet seldom used tool. Here we present a versatile Matlab-based tool (PCAT) to analyze catalysis progress curves with three complementary model approaches. The first two models are based on the known closed-form solution for this problem: the first describes the required Lambert W function with an analytical approximation and the second provides a numerical solution of the Lambert W function. The third model is a direct simulation of the enzyme kinetics. Depending on the chosen model, the tools excel in speed, accuracy or initial value requirements. Using simulated and experimental data, we show the strengths and pitfalls of the different fitting models. Direct simulation proves to have the highest level of accuracy, but it also requires reasonable initial values to converge. Finally, we propose a standard procedure to obtain optimized enzyme kinetic parameters from single progress curves.

High performance enzyme kinetics of turnover, activation and inhibition for translational drug discovery

INTRODUCTION

Enzymes are the macromolecular catalysts of many living processes and represent a sizable proportion of all druggable biological targets. Enzymology has been practiced just over a century during which much progress has been made in both the identification of new enzymes and the development of novel methodologies for enzyme kinetics. Areas covered: This review aims to address several key practical aspects in enzyme kinetics in reference to translational drug discovery research. The authors first define what constitutes a high performance enzyme kinetic assay. The authors then review the best practices for turnover, activation and inhibition kinetics to derive critical parameters guiding drug discovery. Notably, the authors recommend global progress curve analysis of dose/time dependence employing an integrated Michaelis-Menten equation and global curve fitting of dose/dose dependence. Expert opinion: The authors believe that in vivo enzyme and substrate abundance and their dynamics, binding modality, drug binding kinetics and enzyme's position in metabolic networks should be assessed to gauge the translational impact on drug efficacy and safety. Integrating these factors in a systems biology and systems pharmacology model should facilitate translational drug discovery.

Explicit analytic approximations for time-dependent solutions of the generalized integrated Michaelis-Menten equation

Various explicit reformulations of time-dependent solutions for the classical two-step irreversible Michaelis-Menten enzyme reaction model have been described recently. In the current study, I present further improvements in terms of a generalized integrated form of the Michaelis-Menten equation for computation of substrate or product concentrations as functions of time for more real-world, enzyme-catalyzed reactions affected by the product. The explicit equations presented here can be considered as a simpler and useful alternative to the exact solution for the generalized integrated Michaelis-Menten equation when fitted to time course data using standard curve-fitting software.