Determining enzyme kinetics for systems biology with nuclear magnetic resonance spectroscopy

Bottom-up parameterization of enzyme rate constants: Reconciling inconsistent data

Kinetic models of metabolism are promising platforms for studying complex metabolic systems and designing production strains. Given the availability of enzyme kinetic data from historical experiments and machine learning estimation tools, a straightforward modeling approach is to assemble kinetic data enzyme by enzyme until a desired scale is reached. However, this type of 'bottom up' parameterization of kinetic models has been difficult due to a number of issues including gaps in kinetic parameters, the complexity of enzyme mechanisms, inconsistencies between parameters obtained from different sources, and in vitro-in vivo differences. Here, we present a computational workflow for the robust estimation of kinetic parameters for detailed mass action enzyme models while taking into account parameter uncertainty. The resulting software package, termed MASSef (the Mass Action Stoichiometry Simulation Enzyme Fitting package), can handle standard 'macroscopic' kinetic parameters, including Km, kcat, Ki, Keq, and nh, as well as diverse reaction mechanisms defined in terms of mass action reactions and 'microscopic' rate constants. We provide three enzyme case studies demonstrating that this approach can identify and reconcile inconsistent data either within in vitro experiments or between in vitro and in vivo enzyme function. We further demonstrate how parameterized enzyme modules can be used to assemble pathway-scale kinetic models consistent with in vivo behavior. This work builds on the legacy of knowledge on kinetic behavior of enzymes by enabling robust parameterization of enzyme kinetic models at scale utilizing the abundance of historical literature data and machine learning parameter estimates.

Analysis of enzyme reactions using NMR techniques: A case study with α-methylacyl-CoA racemase (AMACR)

α-Methylacyl-CoA racemase (AMACR; P504S) catalyzes the conversion of R-2-methylacyl-CoA esters into their corresponding S-2-methylacyl-CoA epimers enabling their degradation by β-oxidation. The enzyme also catalyzes the key epimerization reaction in the pharmacological activation pathway of ibuprofen and related drugs. AMACR protein levels and enzymatic activity are increased in prostate cancer, and the enzyme is a recognized drug target. Key to the development of novel treatments based on AMACR inhibition is the development of functional assays. Synthesis of substrates and purification of recombinant human AMACR are described. Incubation of R- or S-2-methylacyl-CoA esters with AMACR in vitro resulted in formation of epimers (at a near 1-1 ratio at equilibrium) via removal of their α-protons to form an enolate intermediate followed by reprotonation. Conversion can be conveniently followed by incubation in buffer containing 2H2O followed by 1H NMR analysis to monitor conversion of the α-methyl doublet to a single peak upon deuterium incorporation. Incubation of 2-methylacyl-CoA esters containing leaving groups results in an elimination reaction, which was also characterized by 1H NMR. The synthesis of substrates, including a double labeled substrate for mechanistic studies, and subsequent analysis is also described.

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.

2D and 3D maximum-quantum NMR and diffusion spectroscopy for the characterization of enzymatic reaction mixtures

Using MaxQ-NMR, we characterized enzymatic reaction mixtures containing several compounds (substrate, final product, and various intermediates). This approach enables, in a first analytical step, the counting of the molecules present in the samples.

A mixing microfluidic chip for real-time NMR monitoring of macromolecular reaction

NMR spectroscopy permits real-time monitoring of reactions that involve changes in the spectra of reactants. MICCS (MIcro Channeled Cell for Synthesis monitoring) is a microfluidic chip for such purposes, which is used to rapidly activate reactions by mixing the reactant solutions in the chip inserted into the typical NMR tube. Although it allows monitoring of chemical reactions of small compounds, its simple mixing system dependent on diffusion in the microchannel was not suitable for macromolecules such as proteins with low diffusion rates. Here we developed a new microfluidic chip based on MICCS by incorporating a mixer of split-and-recombination type within the microchannel. We applied it to monitoring of the protein-folding reaction in a stopped-flow mode. A solution of denaturant-unfolded RNase A was injected from a syringe pump into the microchip set inside the NMR magnet and mixed with a buffer for dilution to reach the folding condition. Immediately after dilution, the reaction was initiated and detected by a series of NMR measurements that were synchronized with activation and inactivation of the pump. The process was repeated for accumulation of the data. By analyzing the change of the spectra by factor analysis, a kinetic constant of 0.57 min-1 was obtained.

NMR-Based Assay for the Ex Vivo Determination of Soluble CD73 Activity in Serum

Extracellular adenosine, produced through the activity of ecto-5'-nucleotidase CD73, elicits potent immunosuppressive effects, and its upregulation in tumor cells as well as in stromal and immune cell subsets within the tumor microenvironment is hypothesized to represent an important resistance mechanism to current cancer immunotherapies. Soluble CD73 (sCD73) enzymatic activity measured in patient serum or plasma at a baseline is reported to have prognostic as well as predictive relevance, with higher sCD73 activity associating with poor overall and progression-free survival in melanoma patients undergoing anti-PD1 monoclonal antibody treatment. Here, we report a novel NMR-based method that measures the ex-vivo kinetics of sCD73 activity with high specificity and reproducibility and is suitable for future high-throughput implementation. Unlike the existing assays, this method has the advantage of directly and simultaneously measuring the concentration of both the CD73 substrate and product with minimal sample manipulation or special reagents. We establish the utility of the assay for measuring the activity of sCD73 in human serum and show a strong linear correlation between sCD73 protein levels and enzyme activity. Together with our finding that sCD73 appears to be the predominant activity for the generation of adenosine in human blood, our results demonstrate a link between activity and protein levels that will inform future clinical application.

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.

Systems NMR: single-sample quantification of RNA, proteins and metabolites for biomolecular network analysis

Cellular behavior is controlled by the interplay of diverse biomolecules. Most experimental methods, however, can monitor only a single molecule class or reaction type at a time. We developed an in vitro Nuclear Magnetic Resonance spectroscopy (NMR) approach, which permitted dynamic quantification of an entire “heterotypic” network – simultaneously monitoring three distinct molecule classes (metabolites, proteins, RNA) and all elementary reaction types (bimolecular interactions, catalysis, unimolecular changes). Focusing on an 8-reaction co-transcriptional RNA folding network, in a single sample we recorded over 35 time-points with over 170 observables each, and accurately determined 5 core reaction constants in multiplex. This reconstruction revealed unexpected cross-talk between the different reactions. We further observed dynamic phase-separation in a system of five distinct RNA binding domains in the course of the RNA transcription reaction. Our Systems NMR approach provides a deeper understanding of biological network dynamics by combining the dynamic resolution of biochemical assays and the multiplexing ability of “omics”.

Workflow for Data Analysis in Experimental and Computational Systems Biology: Using Python as ‘Glue’

Bottom-up systems biology entails the construction of kinetic models of cellular pathways by collecting kinetic information on the pathway components (e.g., enzymes) and collating this into a kinetic model, based for example on ordinary differential equations. This requires integration and data transfer between a variety of tools, ranging from data acquisition in kinetics experiments, to fitting and parameter estimation, to model construction, evaluation and validation. Here, we present a workflow that uses the Python programming language, specifically the modules from the SciPy stack, to facilitate this task. Starting from raw kinetics data, acquired either from spectrophotometric assays with microtitre plates or from Nuclear Magnetic Resonance (NMR) spectroscopy time-courses, we demonstrate the fitting and construction of a kinetic model using scientific Python tools. The analysis takes place in a Jupyter notebook, which keeps all information related to a particular experiment together in one place and thus serves as an e-labbook, enhancing reproducibility and traceability. The Python programming language serves as an ideal foundation for this framework because it is powerful yet relatively easy to learn for the non-programmer, has a large library of scientific routines and active user community, is open-source and extensible, and many computational systems biology software tools are written in Python or have a Python Application Programming Interface (API). Our workflow thus enables investigators to focus on the scientific problem at hand rather than worrying about data integration between disparate platforms.

The best models of metabolism

Biochemical systems are among of the oldest application areas of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring a model and for formulating reactions has been constantly growing, and yet, it is still unclear whether or to what degree some models are better than others and how the modeler is to choose among them. In fact, the variety of options has become overwhelming and difficult to maneuver for novices and experts alike. This review outlines the metabolic model design process and discusses the numerous choices for modeling frameworks and mathematical representations. It tries to be inclusive, even though it cannot be complete, and introduces the various modeling options in a manner that is as unbiased as that is feasible. However, the review does end with personal recommendations for the choices of default models. WIREs Syst Biol Med 2017, 9:e1391. doi: 10.1002/wsbm.1391 For further resources related to this article, please visit the WIREs website.

Kinetic modelling: an integrated approach to analyze enzyme activity assays

BACKGROUND

In general, enzyme activity is estimated from spectrophotometric data, by taking the slope of the linear part of the progress curve describing the rate of change in the substrate or product monitored. As long as the substrate concentrations are sufficiently high to saturate the enzyme and, the velocity of the catalyzed reaction is directly proportional to the enzyme concentration. Under these premises, this velocity can be taken as a measure of the amount of active enzyme present. Estimation of the enzyme activity through linear regression of the data should only be applied when linearity is true, which is often not the case or has not been checked.

RESULTS

In this paper, we propose a more elaborate method, based on a kinetic modelling approach, to estimate the in vitro specific enzyme activity from spectrophotometric assay data. As a case study, kinetic models were developed to estimate the activity of the enzymes pyruvate decarboxylase and alcohol dehydrogenase extracted from 'Jonagold' apple (Malus x domestica Borkh. cv. 'Jonagold'). The models are based on Michaelis-Menten and first order kinetics, which describe the reaction mechanism catalyzed by the enzymes.

CONCLUSIONS

In contrast to the linear regression approach, the models can be used to estimate the enzyme activity regardless of whether linearity is achieved since they integrally take into account the complete progress curve. The use of kinetic models to estimate the enzyme activity can be applied to all other enzymes as long as the underlying reaction mechanism is known. The kinetic models can also be used as a tool to optimize the enzyme assays by systematically studying the effect of the various design parameters.

Advances in NMR Methods To Map Allosteric Sites: From Models to Translation

The last five years have witnessed major developments in the understanding of the allosteric phenomenon, broadly defined as coupling between remote molecular sites. Such advances have been driven not only by new theoretical models and pharmacological applications of allostery, but also by progress in the experimental approaches designed to map allosteric sites and transitions. Among these techniques, NMR spectroscopy has played a major role given its unique near-atomic resolution and sensitivity to the dynamics that underlie allosteric couplings. Here, we highlight recent progress in the NMR methods tailored to investigate allostery with the goal of offering an overview of which NMR approaches are best suited for which allosterically relevant questions. The picture of the allosteric "NMR toolbox" is provided starting from one of the simplest models of allostery (i.e., the four-state thermodynamic cycle) and continuing to more complex multistate mechanisms. We also review how such an "NMR toolbox" has assisted the elucidation of the allosteric molecular basis for disease-related mutations and the discovery of novel leads for allosteric drugs. From this overview, it is clear that NMR plays a central role not only in experimentally validating transformative theories of allostery, but also in tapping the full translational potential of allosteric systems.

Real-time NMR monitoring of biological activities in complex physiological environments

Biological reactions occur in a highly organized spatiotemporal context and with kinetics that are modulated by multiple environmental factors. To integrate these variables in our experimental investigations of 'native' biological activities, we require quantitative tools for time-resolved in situ analyses in physiologically relevant settings. Here, we outline the use of high-resolution NMR spectroscopy to directly observe biological reactions in complex environments and in real-time. Specifically, we discuss how real-time NMR (RT-NMR) methods have delineated insights into metabolic processes, post-translational protein modifications, activities of cellular GTPases and their regulators, as well as of protein folding events.