Quantitative analysis of the time courses of enzyme-catalyzed reactions

Optimizing Trilobatin Production via Screening and Modification of Glycosyltransferases

Trilobatin (TBL) is a key sweet compound from the traditional Chinese sweet tea plant (Rubus suavissimus S. Lee). Because of its intense sweetness, superior taste profile, and minimal caloric value, it serves as an exemplary natural dihydrochalcone sweetener. It also has various health benefits, including anti-inflammatory and glucose-lowering effects. It is primarily produced through botanical extraction, which impedes its scalability and cost-effectiveness. In a novel biotechnological approach, phloretin is used as a precursor that is transformed into TBL by the glycosyltransferase enzyme ph-4'-OGT. However, this enzyme's low catalytic efficiency and by-product formation limit the large-scale synthesis of TBL. In our study, the enzyme Mdph-4'-OGT was used to screen 17 sequences across species for TBL synthesis, of which seven exhibited catalytic activity. Notably, PT577 exhibited an unparalleled 97.3% conversion yield within 3 h. We then optimized the reaction conditions of PT577, attaining a peak TBL bioproduction of 163.3 mg/L. By employing virtual screening, we identified 25 mutation sites for PT577, thereby creating mutant strains that reduced by-products by up to 50%. This research enhances the enzymatic precision for TBL biosynthesis and offers a robust foundation for its industrial-scale production, with broader implications for the engineering and in silico analysis of glycosyltransferases.

Sources of bias and limitations of thrombinography: inner filter effect and substrate depletion at the edge of failure algorithm

BACKGROUND

Fluorogenic thrombin generation (TG) is a global hemostasis assay that provides an overall representation of hemostasis potential. However, the accurate detection of thrombin activity in plasma may be affected by artifacts inherent to the assay-associated fluorogenic substrate. The significance of the fluorogenic artifacts or their corrections has not been studied in hemophilia treatment applications.

METHODS

We sought to investigate TG in hemophilia plasma samples under typical and worst-case fluorogenic artifact conditions and assess the performance of artifact correction algorithms. Severe hemophilic plasma with or without added Factor VIII (FVIII) was evaluated using commercially available and in-house TG reagents, instruments, and software packages. The inner filter effect (IFE) was induced by spiking elevated amounts of fluorophore 7-amino-4-methylcoumarin (AMC) into plasma prior to the TG experiment. Substrate consumption was modeled by adding decreasing amounts of Z-Gly-Gly-Arg-AMC (ZGGR-AMC) to plasma or performing TG in antithrombin deficient plasma.

RESULTS

All algorithms corrected the AMC-induced IFE and antithrombin-deficiency induced substrate consumption up to a certain level of either artifact (edge of failure) upon which TG results were not returned or overestimated. TG values in FVIII deficient (FVIII-DP) or supplemented plasma were affected similarly. Normalization of FVIII-DP resulted in a more accurate correction of substrate artifacts than algorithmic methods.

CONCLUSIONS

Correction algorithms may be effective in situations of moderate fluorogenic substrate artifacts inherent to highly procoagulant samples, but correction may not be required under typical conditions for hemophilia treatment studies if TG parameters can be normalized to a reference plasma sample.

Substrate-dependent inactivation of recombinant paraoxonase 1 during catalytic dihydrocoumarin turnover and the protective properties of surfactants

Human paraoxonase-1 (PON1) is the most studied member of the paraoxonases (PONs) family and catalyzes the hydrolysis of various substrates (lactones, aryl esters, and paraoxon). Numerous studies link PON1 to oxidative stress-related diseases such as cardiovascular disease, diabetes, HIV infection, autism, Parkinson's, and Alzheimer's, where the kinetic behavior of an enzyme is characterized by initial rates or by modern methods that obtain enzyme kinetic parameters by fitting the computed curves over the entire time-courses of product formation (progress curves). In the analysis of progress curves, the behavior of PON1 during hydrolytically catalyzed turnover cycles is unknown. Hence, progress curves for enzyme-catalyzed hydrolysis of the lactone substrate dihydrocoumarin (DHC) by recombinant PON1 (rePON1) were analyzed to investigate the effect of catalytic DHC turnover on the stability of rePON1. Although rePON1 was significantly inactivated during the catalytic DHC turnover, its activity was not lost due to the product inhibition or spontaneous inactivation of rePON1 in the sample buffers. Examination of the progress curves of DHC hydrolysis by rePON1 led to the conclusion that rePON1 inactivates itself during catalytic DHC turnover hydrolysis. Moreover, human serum albumin or surfactants protected rePON1 from inactivation during this catalytic process, which is significant because the activity of PON1 in clinical samples is measured in the presence of albumin.

Estimating and Assessing Differential Equation Models with Time-Course Data

Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This Article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations, time-course data are often noisy, and some components of the system may not be observed. Furthermore, the computational demands of numerical integration have hindered the widespread adoption of time-course analysis using ODEs. To address these challenges, we explore the efficacy of the recently developed MAGI (MAnifold-constrained Gaussian process Inference) method for ODE inference. First, via a range of examples we show that MAGI is capable of inferring the parameters and system trajectories, including unobserved components, with appropriate uncertainty quantification. Second, we illustrate how MAGI can be used to assess and select different ODE models with time-course data based on MAGI's efficient computation of model predictions. Overall, we believe MAGI is a useful method for the analysis of time-course data in the context of ODE models, which bypasses the need for any numerical integration.

Hybrid Nucleic Acid-Quantum Dot Assemblies as Multiplexed Reporter Platforms for Cell-Free Transcription Translation-Based Biosensors

Cell-free synthetic biology has emerged as a valuable tool for the development of rapid, portable biosensors that can be readily transported in the freeze-dried form to the point of need eliminating cold chain requirements. One of the challenges associated with cell-free sensors is the ability to simultaneously detect multiple analytes within a single reaction due to the availability of a limited set of fluorescent and colorimetric reporters. To potentially provide multiplexing capabilities to cell-free biosensors, we designed a modular semiconductor quantum dot (QD)-based reporter platform that is plugged in downstream of the transcription-translation functionality in the cell-free reaction and which converts enzymatic activity in the reaction into distinct optical signals. We demonstrate proof of concept by converting restriction enzyme activity, utilized as our prototypical sensing output, into optical changes across several distinct spectral output channels that all use a common excitation wavelength. These hybrid Förster resonance energy transfer (FRET)-based QD peptide PNA-DNA-Dye reporters (QD-PDDs) are completely self-assembled and consist of differentially emissive QD donors paired to a dye-acceptor displayed on a unique DNA encoding a given enzyme's cleavage site. Three QD-based PDDs, independently activated by the enzymes BamHI, EcoRI, and NcoI, were prototyped in mixed enzyme assays where all three demonstrated the ability to convert enzymatic activity into fluorescent output. Simultaneous monitoring of each of the three paired QD-donor dye-acceptor spectral channels in cell-free biosensing reactions supplemented with added linear genes encoding each enzyme confirmed robust multiplexing capabilities for at least two enzymes when co-expressed. The modular QD-PDDs are easily adapted to respond to other restriction enzymes or even proteases if desired.

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.

Kinetic and structural studies on the inhibition of acetylcholinesterase and butyrylcholinesterase by a series of multitarget-directed galantamine-peptide derivatives

Complex neurological disorders, including Alzheimer's disease, are one of the major therapeutic areas to which multitarget drug discovery strategies have been applied in the last twenty years. Due to the complex multifactorial etiopathogenesis of Alzheimer's disease, it has been proposed that to be successful the pharmaceutical agents should act on multiple targets in order to restore the complex disease network and to provide disease modifying effects. Here we report on the synthesis and the anticholinergic activity profiles of seven multitarget anti-Alzheimer compounds designed by combining galantamine, a well-known acetylcholinesterase inhibitor, with different peptide fragments endowed with inhibitory activity against BACE-1. A complementary approach based on molecular docking simulations of the galantamine-peptide derivatives in the active sites of acetylcholinesterase and of the related butyrylcholinesterase, as well as on inhibition kinetics, by global fitting of the reaction progress curves, allowed to gain insights into the enzyme-inhibitor mechanism of interaction. The resulting structure-activity relationships pave the way towards the design of more effective pharmacodynamic/pharmacokinetic multitarget inhibitors.

Kinetic Modeling of Time-Dependent Enzyme Inhibition by Pre-Steady-State Analysis of Progress Curves: The Case Study of the Anti-Alzheimer's Drug Galantamine

The Michaelis–Menten model of enzyme kinetic assumes the free ligand approximation, the steady-state approximation and the rapid equilibrium approximation. Analytical methods to model slow-binding inhibitors by the analysis of initial velocities have been developed but, due to their inherent complexity, they are seldom employed. In order to circumvent the complications that arise from the violation of the rapid equilibrium assumption, inhibition is commonly evaluated by pre-incubating the enzyme and the inhibitors so that, even for slow inhibitors, the binding equilibrium is established before the reaction is started. Here, we show that for long drug-target residence time inhibitors, the conventional analysis of initial velocities by the linear regression of double-reciprocal plots fails to provide a correct description of the inhibition mechanism. As a case study, the inhibition of acetylcholinesterase by galantamine, a drug approved for the symptomatic treatment of Alzheimer’s disease, is reported. For over 50 years, analysis based on the conventional steady-state model has overlooked the time-dependent nature of galantamine inhibition, leading to an erroneous assessment of the drug potency and, hence, to discrepancies between biochemical data and the pharmacological evidence. Re-examination of acetylcholinesterase inhibition by pre-steady state analysis of the reaction progress curves showed that the potency of galantamine has indeed been underestimated by a factor of ~100.

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.

Implementing Multi-Enzyme Biocatalytic Systems Using Nanoparticle Scaffolds

Interest in multi-enzyme synthesis outside of cells (in vitro) is becoming far more prevalent as the field of cell-free synthetic biology grows exponentially. Such synthesis would allow for complex chemical transformations based on the exquisite specificity of enzymes in a "greener" manner as compared to organic chemical transformations. Here, we describe how nanoparticles, and in this specific case-semiconductor quantum dots, can be used to both stabilize enzymes and further allow them to self-assemble into nanocomplexes that facilitate high-efficiency channeling phenomena. Pertinent protocol information is provided on enzyme expression, choice of nanoparticulate material, confirmation of enzyme attachment to nanoparticles, assay format and tracking, data analysis, and optimization of assay formats to draw the best analytical information from the underlying processes.

A guide to the Michaelis-Menten equation: steady state and beyond

The modern definition of enzymology is synonymous with the Michaelis-Menten equation instituted by Leonor Michaelis and Maud Menten. Most textbooks, or chapters within, discussing enzymology start with the derivation of the equation under the assumption of rapid equilibrium (as done by Michaelis-Menten) or steady state (as modified by Briggs and Haldane) conditions to highlight the importance of this equation as the bedrock on which interpretation of enzyme kinetic results is dependent. However, few textbooks or monographs take the effort of placing the equation within its right historical context and discuss the assumptions that have gone into its institution. This guide will dwell on these in substantial detail. Further, this guide will attempt to instil a sense of appreciation for the mathematical curve rectangular hyperbola, its unique attributes and how ubiquitous the curve is in biological systems. To conclude, this guide will discuss the limitations of the equation, and the method it embodies, and trace the journey of how investigators are attempting to move beyond the steady-state approach and the Michaelis-Menten equation into full progress curve, pre-steady state and single-turnover kinetic analysis to obtain greater insights into enzyme kinetics and catalysis.

Explicit Treatment of Non-Michaelis-Menten and Atypical Kinetics in Early Drug Discovery*

Biological systems are highly regulated. They are also highly resistant to sudden perturbations enabling them to maintain the dynamic equilibrium essential to sustain life. This robustness is conferred by regulatory mechanisms that influence the activity of enzymes/proteins within their cellular context to adapt to changing environmental conditions. However, the initial rules governing the study of enzyme kinetics were mostly tested and implemented for cytosolic enzyme systems that were easy to isolate and/or recombinantly express. Moreover, these enzymes lacked complex regulatory modalities. Now, with academic labs and pharmaceutical companies turning their attention to more-complex systems (for instance, multiprotein complexes, oligomeric assemblies, membrane proteins and post-translationally modified proteins), the initial axioms defined by Michaelis-Menten (MM) kinetics are rendered inadequate, and the development of a new kind of kinetic analysis to study these systems is required. This review strives to present an overview of enzyme kinetic mechanisms that are atypical and, oftentimes, do not conform to the classical MM kinetics. Further, it presents initial ideas on the design and analysis of experiments in early drug-discovery for such systems, to enable effective screening and characterisation of small-molecule inhibitors with desirable physiological outcomes.

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.

interferENZY: A Web-Based Tool for Enzymatic Assay Validation and Standardized Kinetic Analysis

Enzymatic assays are widely employed to characterize important allosteric and enzyme modulation effects. The high sensitivity of these assays can represent a serious problem if the occurrence of experimental errors surreptitiously affects the reliability of enzyme kinetics results. We have addressed this problem and found that hidden assay interferences can be unveiled by the graphical representation of progress curves in modified reaction coordinates. To render this analysis accessible to users across all levels of expertise, we have developed a webserver, interferENZY, that allows (i) an unprecedented tight quality control of experimental data, (ii) the automated identification of small and major assay interferences, and (iii) the estimation of bias-free kinetic parameters. By eliminating the subjectivity factor in kinetic data reporting, interferENZY will contribute to solving the "reproducibility crisis" that currently challenges experimental molecular biology. The interferENZY webserver is freely available (no login required) at https://interferenzy.i3s.up.pt.

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.

Considerations when Measuring Biocatalyst Performance

As biocatalysis matures, it becomes increasingly important to establish methods with which to measure biocatalyst performance. Such measurements are important to assess immobilization strategies, different operating modes, and reactor configurations, aside from comparing protein engineered variants and benchmarking against economic targets. While conventional measurement techniques focus on a single performance metric (such as the total turnover number), here, it is argued that three metrics (achievable product concentration, productivity, and enzyme stability) are required for an accurate assessment of scalability.

Assessing the impact of product inhibition in a chromogenic assay

Chromogenic substrates (CS) are synthetic substrates used to monitor the activity of a target enzyme. It has been reported that some CSs display competitive product inhibition with their target enzyme. Thus, in assays where enzyme activity is continuously monitored over long periods of time, the product inhibition may significantly interfere with the reactions being monitored. Despite this knowledge, it is rare for CSs to be directly incorporated into mathematical models that simulate these assays. This devalues the predictive power of the models. In this study, we examined the interactions between a single enzyme, coagulation factor Xa, and its chromogenic substrate. We developed, and experimentally validated, a mathematical model of a chromogenic assay for factor Xa that explicitly included product inhibition from the CS. We employed Bayesian inference, in the form of Markov-Chain Monte Carlo, to estimate the strength of the product inhibition and other sources of uncertainty such as pipetting error and kinetic rate constants. Our model, together with carefully calibrated biochemistry experiments, allowed for full characterization of the strength and impact of product inhibition in the assay. The effect of CS product inhibition in more complex reaction mixtures was further explored using mathematical models.

Small Surface, Big Effects, and Big Challenges: Toward Understanding Enzymatic Activity at the Inorganic Nanoparticle-Substrate Interface

Enzymes are important biomarkers for molecular diagnostics and targets for the action of drugs. In turn, inorganic nanoparticles (NPs) are of interest as materials for biological assays, biosensors, cellular and in vivo imaging probes, and vectors for drug delivery and theranostics. So how does an enzyme interact with a NP, and what are the outcomes of multivalent conjugation of its substrate to a NP? This invited feature article addresses the current state of the art in answering this question. Using gold nanoparticles (Au NPs) and semiconductor quantum dots (QDs) as illustrative materials, we discuss aspects of enzyme structure-function and the properties of NP interfaces and surface chemistry that determine enzyme-NP interactions. These aspects render the substrate-on-NP configurations far more complex and heterogeneous than the conventional turnover of discrete substrate molecules in bulk solution. Special attention is also given to the limitations of a standard kinetic analysis of the enzymatic turnover of these configurations, the need for a well-defined model of turnover, and whether a "hopping" model can account for behaviors such as the apparent acceleration of enzyme activity. A detailed and predictive understanding of how enzymes turn over multivalent NP-substrate conjugates will require a convergence of many concepts and tools from biochemistry, materials, and interface science. In turn, this understanding will help to enable rational, optimized, and value-added designs of NP bioconjugates for biomedical and clinical applications.

Modeling Starch Digestograms: Computational Characteristics of Kinetic Models for in vitro Starch Digestion in Food Research

Starch digestion is mostly investigated with in vitro techniques, and time-course measurements are common. These yield digestograms that are modeled by theoretical, semitheoretical, and empirical kinetic equations, many of which are reviewed here. The Duggleby model has Michaelis-Menten functions, and its dependent variable is on both sides of the equation with no apparent parameter for maximum digestible starch (D_∞ ). The Gaouar and Peleg models are equivalent. They predict both the initial digestible starch (D₀ ) and D_∞ , and an average digestion rate, but they can reveal "biratial" digestions. The first-order kinetic model exhibits diverse predictabilities and, when linearized, D_∞ is sometimes equated to 100 g/100 g dry starch (100%), it yields an average rate of digestion and can predict negative D₀ . The log of slope (LOS) model is unique in revealing the rapid-to-slow digestion rate phenomenon, but without guidelines to identify such. The LOS model does not sometimes use all the digestogram data, can predict D_∞ greater than 100%, and returns zero digestion rate for some digestograms. However, some starchy materials exhibit a slow-to-rapid digestion rate phenomenon, as demonstrated with an example. The modified first-order kinetic model uses all the digestogram data with practical constraints (D₀  ≥ 0 g/100 g dry starch; D_∞  ≤ 100 g/100 g dry starch), describes all digestograms, and yields an average digestion rate, but it can also be used for "biratial" digestions. In addition, the logistic and Weibull models are discussed. Using some published data, the computational characteristics of these commonly used models are presented with objective parameters to guide choices.

Pursuing the Promise of Enzymatic Enhancement with Nanoparticle Assemblies

The growing emphasis on green chemistry, renewable resources, synthetic biology, regio-/stereospecific chemical transformations, and nanotechnology for providing new biological products and therapeutics is reinvigorating research into enzymatic catalysis. Although the promise is profound, many complex issues remain to be addressed before this effort will have a significant impact. Prime among these is to combat the degradation of enzymes frequently seen in ex vivo formats following immobilization to stabilize the enzymes for long-term application and to find ways of enhancing their activity. One promising avenue for progress on these issues is via nanoparticle (NP) display, which has been found in a number of cases to enhance enzyme activity while also improving long-term stability. In this feature article, we discuss the phenomenon of enhanced enzymatic activity at NP interfaces with an emphasis on our own work in this area. Important factors such as NP surface chemistry, bioconjugation approaches, and assay formats are first discussed because they can critically affect the observed enhancement. Examples are given of improved performance for enzymes such as phosphotriesterase, alkaline phosphatase, trypsin, horseradish peroxidase, and β-galactosidase and in configurations with either the enzyme or the substrate attached to the NP. The putative mechanisms that give rise to the performance boost are discussed along with how detailed kinetic modeling can contribute to their understanding. Given the importance of biosensing, we also highlight how this configuration is already making a significant contribution to NP-based enzymatic sensors. Finally, a perspective is provided on how this field may develop and how NP-based enzymatic enhancement can be extended to coupled systems and multienzyme cascades.

Beyond the Michaelis-Menten equation: Accurate and efficient estimation of enzyme kinetic parameters

Examining enzyme kinetics is critical for understanding cellular systems and for using enzymes in industry. The Michaelis-Menten equation has been widely used for over a century to estimate the enzyme kinetic parameters from reaction progress curves of substrates, which is known as the progress curve assay. However, this canonical approach works in limited conditions, such as when there is a large excess of substrate over enzyme. Even when this condition is satisfied, the identifiability of parameters is not always guaranteed, and often not verifiable in practice. To overcome such limitations of the canonical approach for the progress curve assay, here we propose a Bayesian approach based on an equation derived with the total quasi-steady-state approximation. In contrast to the canonical approach, estimates obtained with this proposed approach exhibit little bias for any combination of enzyme and substrate concentrations. Importantly, unlike the canonical approach, an optimal experiment to identify parameters with certainty can be easily designed without any prior information. Indeed, with this proposed design, the kinetic parameters of diverse enzymes with disparate catalytic efficiencies, such as chymotrypsin, fumarase, and urease, can be accurately and precisely estimated from a minimal amount of timecourse data. A publicly accessible computational package performing such accurate and efficient Bayesian inference for enzyme kinetics is provided.

Extracting Kinetic Isotope Effects From a Global Analysis of Reaction Progress Curves

Enzyme reaction progress curves, or time course datasets, are often rich in information, yet their analysis typically reduces their information content to a single parameter, the initial velocity. An alternative approach is described here, where the time course is described by a model constructed from rate equations. In combination with global nonlinear regression, intrinsic rate and/or equilibrium constants can be directly obtained by fitting these data. This method can be greatly enhanced when combined with the measurement of (usually deuterium) isotope effects, which selectively perturb individual step(s) within the reaction, allowing better separation of fitted parameters and more robust model testing. This chapter focuses on practical considerations when using analytical and/or numerically integrated rate equations to model enzyme reactions. The emphasis is on the underlying methodology, which is demonstrated with specific examples alongside recommendations of suitable software.

Elucidating Surface Ligand-Dependent Kinetic Enhancement of Proteolytic Activity at Surface-Modified Quantum Dots

Combining biomolecules such as enzymes with nanoparticles has much to offer for creating next generation synergistically functional bionanomaterials. However, almost nothing is known about how these two disparate components interact at this critical biomolecular-materials interface to give rise to improved activity and emergent properties. Here we examine how the nanoparticle surface can influence and increase localized enzyme activity using a designer experimental system consisting of trypsin proteolysis acting on peptide-substrates displayed around semiconductor quantum dots (QDs). To minimize the complexity of analyzing this system, only the chemical nature of the QD surface functionalizing ligands were modified. This was accomplished by synthesizing a series of QD ligands that were either positively or negatively charged, zwitterionic, neutral, and with differing lengths. The QDs were then assembled with different ratios of dye-labeled peptide substrates and exposed to trypsin giving rise to progress curves that were monitored by Förster resonance energy transfer (FRET). The resulting trypsin activity profiles were analyzed in the context of detailed molecular dynamics simulations of key interactions occurring at this interface. Overall, we find that a combination of factors can give rise to a localized activity that was 35-fold higher than comparable freely diffusing enzyme-substrate interactions. Contributing factors include the peptide substrate being prominently displayed extending from the QD surface and not sterically hindered by the longer surface ligands in conjunction with the presence of electrostatic and other productive attractive forces between the enzyme and the QD surface. An intimate understanding of such critical interactions at this interface can produce a set of guidelines that will allow the rational design of next generation high-activity bionanocomposites and theranostics.

Utilization of gel electrophoreses for the quantitative estimation of digestive enzyme papain

SDS-PAGE densitometric method for analysis of papain in pharmaceutical formulations was developed and validated for the first time. Standard and samples were mixed with SDS sample buffer and denatured at 95 °C for 5 min and the gel was run at 20 mA and 200 V for 30–40 min in SDS-PAGE buffer. Gels were stained in Coomassie blue solution and distained by 5% methanol and 10% acetic acid. Destained gels were imaged and analyzed using the ChemiDoc™ XRS+ System. Bands of papain appeared at R_f value 0.78 ± 0.03 corresponding to molecular weight 23406 Da between proteins with molecular weight 31,000 and 21,500 Da of the broad range protein standard. The generated calibration curve was used for quantitative estimation of papain in pharmaceutical formulations. The developed method was validated for precision, accuracy, specificity and robustness as described by the ICH guidelines. The proposed method gives an alternative approach for enzymes and protein analysis.

Pop-it beads to introduce catalysis of reaction rate and substrate depletion effects

A kinesthetic classroom activity was designed to help students understand enzyme activity and catalysis of reaction rate. Students served the role of enzymes by manipulating Pop-It Beads as the catalytic event. This activity illuminates the relationship between reaction rate and reaction progress by allowing students to experience first-hand the effect of substrate depletion on catalyzed reaction rate. Preliminary findings based on survey results and exam performance suggest the activity could prove beneficial to students in the targeted learning outcomes. Unique to previous kinesthetic approaches that model Michaelis-Menten kinetics, this activity models the effects of substrate depletion on catalyzed reaction rate. Therefore, it could prove beneficial for conveying the reasoning behind the initial rate simplification used in Michaelis-Menten kinetics. © 2016 by The International Union of Biochemistry and Molecular Biology, 45(2):179-183, 2017.

The anti-inflammatory compound palmitoylethanolamide inhibits prostaglandin and hydroxyeicosatetraenoic acid production by a macrophage cell line

The anti‐inflammatory agent palmitoylethanolamide (PEA) reduces cyclooxygenase (COX) activity in vivo in a model of inflammatory pain. It is not known whether the compound reduces prostaglandin production in RAW264.7 cells, whether such an action is affected by compounds preventing the breakdown of endogenous PEA, whether other oxylipins are affected, or whether PEA produces direct effects upon the COX‐2 enzyme. RAW264.7 cells were treated with lipopolysaccharide and interferon‐γ to induce COX‐2. At the level of mRNA, COX‐2 was induced >1000‐fold following 24 h of the treatment. Coincubation with PEA (10 μmol/L) did not affect the levels of COX‐2, but reduced the levels of prostaglandins D₂ and E₂ as well as 11‐ and 15‐hydroxyeicosatetraenoic acid, which can also be synthesised by a COX‐2 pathway in macrophages. These effects were retained when hydrolysis of PEA to palmitic acid was blocked. Linoleic acid‐derived oxylipin levels were not affected by PEA. No direct effects of PEA upon the oxygenation of either arachidonic acid or 2‐arachidonoylglycerol by COX‐2 were found. It is concluded that in lipopolysaccharide and interferon‐γ‐stimulated RAW264.7 cells, PEA reduces the production of COX‐2‐derived oxylipins in a manner that is retained when its metabolism to palmitic acid is inhibited.

Derivation of a valid momentary first-order rate constant for kinetic and energetic analyses of enzymatic reactions

To analyze enzymatic reactions energetically for comparison with non-enzymatic reactions (first order) under the same dimension, a method to derive valid momentary first-order rate constants for enzymatic reactions was developed. The momentary first-order rate constant, k _enz0 = k _cat[E'S']_e,0/[S]₀, was derived for an enzymatic reaction under a certain condition. It was shown that this rate constant is applicable for a wide range of enzymatic reactions. Utilizing this constant, one can conduct reliable kinetic and energetic analyses of enzymatic reactions.

Enzyme inhibition studies by integrated Michaelis-Menten equation considering simultaneous presence of two inhibitors when one of them is a reaction product

To determine initial velocities of enzyme catalyzed reactions without theoretical errors it is necessary to consider the use of the integrated Michaelis-Menten equation. When the reaction product is an inhibitor, this approach is particularly important. Nevertheless, kinetic studies usually involved the evaluation of other inhibitors beyond the reaction product. The occurrence of these situations emphasizes the importance of extending the integrated Michaelis-Menten equation, assuming the simultaneous presence of more than one inhibitor because reaction product is always present. This methodology is illustrated with the reaction catalyzed by alkaline phosphatase inhibited by phosphate (reaction product, inhibitor 1) and urea (inhibitor 2). The approach is explained in a step by step manner using an Excel spreadsheet (available as a template in Appendix). Curve fitting by nonlinear regression was performed with the Solver add-in (Microsoft Office Excel). Discrimination of the kinetic models was carried out based on Akaike information criterion. This work presents a methodology that can be used to develop an automated process, to discriminate in real time the inhibition type and kinetic constants as data (product vs. time) are achieved by the spectrophotometer.

Ubiquitin-Mediated Degradation of Aurora Kinases

The Aurora kinases are essential regulators of mitosis in eukaryotes. In somatic cell divisions of higher eukaryotes, the paralogs Aurora kinase A (AurA) and Aurora kinase B (AurB) play non-overlapping roles that depend on their distinct spatiotemporal activities. These mitotic roles of Aurora kinases depend on their interactions with different partners that direct them to different mitotic destinations and different substrates: AurB is a component of the chromosome passenger complex that orchestrates the tasks of chromosome segregation and cytokinesis, while AurA has many known binding partners and mitotic roles, including a well-characterized interaction with TPX2 that mediates its role in mitotic spindle assembly. Beyond the spatial control conferred by different binding partners, Aurora kinases are subject to temporal control of their activation and inactivation. Ubiquitin-mediated proteolysis is a critical route to irreversible inactivation of these kinases, which must occur for ordered transition from mitosis back to interphase. Both AurA and AurB undergo targeted proteolysis after anaphase onset as substrates of the anaphase-promoting complex/cyclosome (APC/C) ubiquitin ligase, even while they continue to regulate steps during mitotic exit. Temporal control of Aurora kinase destruction ensures that AurB remains active at the midbody during cytokinesis long after AurA activity has been largely eliminated from the cell. Differential destruction of Aurora kinases is achieved despite the fact that they are targeted at the same time and by the same ubiquitin ligase, making these substrates an interesting case study for investigating molecular determinants of ubiquitin-mediated proteolysis in higher eukaryotes. The prevalence of Aurora overexpression in cancers and their potential as therapeutic targets add importance to the task of understanding the molecular determinants of Aurora kinase stability. Here, we review what is known about ubiquitin-mediated targeting of these critical mitotic regulators and discuss the different factors that contribute to proteolytic control of Aurora kinase activity in the cell.

Quantitative measurement of proteolytic rates with quantum dot-peptide substrate conjugates and Förster resonance energy transfer

An important challenge in biology is the development of probes for visualizing and quantitatively tracking enzyme activity. Proteases are an important class of enzyme with value as both diagnostic and therapeutic targets. In this chapter, we describe the preparation of quantum dot (QD)-peptide substrate conjugates as probes for measuring proteolytic activity. QDs have several highly advantageous optical properties that make these materials especially well suited for applications in bioanalysis and bioimaging. Further, peptide substrates for proteases can be controllably self-assembled to QDs and this capability, in combination with Förster resonance energy transfer (FRET), enables the design of quantitative in vitro assays capable of directly reporting on proteolytic activity. We present a detailed method for the preparation, calibration, and application of such QD probes, along with methods of analysis to generate progress curves for the proteolytic digestion of substrate. Representative data are illustrated for two different proteases and two different QD-fluorescent dye FRET pairs. The general methodology is likely to be applicable with other hydrolytic enzymes in addition to proteases. Overall, the method is straightforward to implement with commercially available materials and does not require specialized expertise.

Assays for S-adenosylmethionine (AdoMet/SAM)-dependent methyltransferases

Modification of small molecules and proteins by methyltransferases impacts a wide range of biological processes. Here we report two methods for measuring methyltransferase activity. First we describe an enzyme-coupled continuous spectrophotometric assay used to quantitatively characterize S-adenosyl-L-methionine (AdoMet or SAM)-dependent methyltransferase activity. In this assay, S-adenosyl-L-homocysteine (AdoHcy or SAH), the transmethylation product of AdoMet-dependent methyltransferase, is hydrolyzed to S-ribohomocysteine and adenine by recombinant AdoHcy nucleosidase. Subsequently, the adenine generated from AdoHcy is further hydrolyzed to homoxanthine and ammonia by recombinant adenine deaminase. This deamination is associated with a decrease in absorbance at 265 nm that can be monitored continuously. Secondly, we describe a discontinuous assay that follows radiolabel incorporation into the methyl receptor. An advantage of both assays is the destruction of AdoHcy by AdoHcy nucleosidase, which alleviates AdoHcy product feedback inhibition of S-adenosylmethionine-dependent methyltransferases. Importantly both methods are inexpensive, robust, and amenable to high throughput.

Utilization of integrated Michaelis-Menten equations for enzyme inhibition diagnosis and determination of kinetic constants using Solver supplement of Microsoft Office Excel

Enzyme kinetic parameters are usually determined from initial rates nevertheless, laboratory instruments only measure substrate or product concentration versus reaction time (progress curves). To overcome this problem we present a methodology which uses integrated models based on Michaelis-Menten equation. The most severe practical limitation of progress curve analysis occurs when the enzyme shows a loss of activity under the chosen assay conditions. To avoid this problem it is possible to work with the same experimental points utilized for initial rates determination. This methodology is illustrated by the use of integrated kinetic equations with the well-known reaction catalyzed by alkaline phosphatase enzyme. In this work nonlinear regression was performed with the Solver supplement (Microsoft Office Excel). It is easy to work with and track graphically the convergence of SSE (sum of square errors). The diagnosis of enzyme inhibition was performed according to Akaike information criterion.

Multiplexed tracking of protease activity using a single color of quantum dot vector and a time-gated Förster resonance energy transfer relay

Semiconductor quantum dots (QDs) are attractive probes for optical sensing and imaging due to their unique photophysical attributes and nanoscale size. In particular, the development of assays and biosensors based on QDs and Förster resonance energy transfer (FRET) continues to be a prominent focus of research. Here, we demonstrate the application of QDs as simultaneous donors and acceptors in a time-gated FRET relay for the multiplexed detection of protease activity. In contrast to the current state-of-the-art, which uses multiple colors of QDs, multiplexing was achieved using only a single color of QD. The other constituents of the FRET relay, a luminescent terbium complex and fluorescent dye, were assembled to QDs via peptides that were selected as substrates for the model proteases trypsin and chymotrypsin. Loss of prompt FRET between the QD and dye signaled the activity of chymotrypsin; loss of time-gated FRET between the terbium and QD signaled the activity of trypsin. We applied the FRET relay in a series of quantitative, real-time kinetic assays of increasing biochemical complexity, including multiplexed sensing, measuring inhibition in a multiplexed format, and tracking the proteolytic activation of an inactive pro-protease to its active form in a coupled, multienzyme system. These capabilities were derived from a ratiometric analysis of the two FRET pathways in the relay and permitted extraction of initial reaction rates, enzyme specificity constants, and apparent inhibition constants. This work adds to the growing body of research on multifunctional nanoparticles and introduces multiplexed sensing as a novel capability for a single nanoparticle vector. Furthermore, the ability to track both enzymes within a coupled biological system using one vector represents a significant advancement for nanoparticle-based biosensing. Prospective applications in biochemical research, applied diagnostics, and drug discovery are discussed.

Improved inhibitor screening experiments by comparative analysis of simulated enzyme progress curves

A difficulty associated with high throughput screening for enzyme inhibitors is to establish reaction conditions that maximize the sensitivity and resolution of the assay. Deduction of information from end-point assays at single concentrations requires a detailed understanding of the time progress of the enzymatic reaction, an essential but often difficult process to model. A tool to simulate the time progress of enzyme catalyzed reactions and allows adjustment of reactant concentrations and parameters (initial concentrations, K_m, k_cat, K_i values, enzyme half-life, product•enzyme dissociation constant, and the rate constant for the reversed reaction) has been developed. This tool provides comparison of the progress of uninhibited versus inhibited reactions for common inhibitory mechanisms, and guides the tuning of reaction conditions. Possible applications include: analysis of substrate turnover, identification of the point of maximum difference in product concentration (Δ_max[P]) between inhibited and uninhibited reactions, determination of an optimal observation window unbiased for inhibitor mechanisms or potency, and interpretation of observed inhibition in terms of true inhibition. An important observation that can be utilized to improve assay signal strength and resolution is that Δ_max[P] occurs at a high degree of substrate consumption (commonly >75%) and that observation close to this point does not adversely affect observed inhibition or IC₅₀ values.

Proteolytic activity at quantum dot-conjugates: kinetic analysis reveals enhanced enzyme activity and localized interfacial "hopping"

Recent studies show that polyvalent, ligand-modified nanoparticles provide significantly enhanced binding characteristics compared to isolated ligands. Here, we assess the ability of substrate-modified nanoparticles to provide enhanced enzymatic activity. Energy transfer assays allowed quantitative, real-time measurement of proteolytic digestion at polyvalent quantum dot-peptide conjugates. Enzymatic progress curves were analyzed using an integrated Michaelis-Menten (MM) formalism, revealing mechanistic details, including deviations from classic MM-behavior. A "hopping" mode of proteolysis at the nanoparticle was identified, confirming enhanced activity.