Statistical considerations in the estimation of enzyme kinetic parameters by the direct linear plot andother methods.
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ABSTRACT:
SUBMITTER: Cornish-Bowden A
PROVIDER: S-EPMC1166336 | biostudies-other | 1974 Jun
REPOSITORIES: biostudies-other
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Project description:The theoretical basis for the direct linear plot [Eisenthal & Cornish-Bowden (1974) Biochem. J. 139, 715-720], a non-parametric statistical method for the analysis of data-fitting the Michaelis-Menten equation, was reinvestigated in order to accommodate additional experimental designs and to provide estimates of precision more directly comparable with those obtained by parametric statistical methods. Methods are given for calculating upper and lower confidence limits for the estimated parameters, for accommodating replicate measurements and for comparing the results of two separate experiments. Factors that influence the proper design of experiments are discussed.
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Project description:A new plot is described for analysing the results of kinetic experiments in which the Michaelis-Menten equation is obeyed. Observations are plotted as lines in parameter space, instead of points in observation space. With appropriate modifications the plot is applicable to most problems of interest to the enzyme kineticist. It has the following advantages over traditional methods of plotting kinetic results: it is very simple to construct, because it is composed entirely of straight lines and requires no calculation or mathematical tables; the kinetic constants are read off the plot directly, again without calculation; it may be used during the course of an experiment to judge the success of the experiment, and to modify the experimental design; it provides clear and accurate information about the quality of the observations, and identifies aberrant observations; it provides a clear indication of the precision of the kinetic constants; constructed with care, it provides unbiased estimates of the kinetic constants, the same as those provided by a computer program; it may be used to simulate results for illustrative purposes very rapidly and simply.
| S-EPMC1166335 | biostudies-other
Project description: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.
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Project description:A new method is described for estimating initial velocities of enzyme-catalysed reactions. It is simple to apply either graphically or numerically, and is particularly appropriate for experiments in which the initial straight part of the progress curve is very short or non-existent. It requires no more knowledge than is readily available about the details of the system, such as the extent of reaction at equilibrium, the rate of enzyme inactivation, the nature of product inhibition etc., unlike some other methods of analysing progress curves, which are often invalidated by small errors in the defining assumptions.
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Project description:BackgroundFluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the development of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.ResultsWe use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo.ConclusionThe major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods.
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Project description:MOTIVATION:Kinetic models contain unknown parameters that are estimated by optimizing the fit to experimental data. This task can be computationally challenging due to the presence of local optima and ill-conditioning. While a variety of optimization methods have been suggested to surmount these issues, it is difficult to choose the best one for a given problem a priori. A systematic comparison of parameter estimation methods for problems with tens to hundreds of optimization variables is currently missing, and smaller studies provided contradictory findings. RESULTS:We use a collection of benchmarks to evaluate the performance of two families of optimization methods: (i) multi-starts of deterministic local searches and (ii) stochastic global optimization metaheuristics; the latter may be combined with deterministic local searches, leading to hybrid methods. A fair comparison is ensured through a collaborative evaluation and a consideration of multiple performance metrics. We discuss possible evaluation criteria to assess the trade-off between computational efficiency and robustness. Our results show that, thanks to recent advances in the calculation of parametric sensitivities, a multi-start of gradient-based local methods is often a successful strategy, but a better performance can be obtained with a hybrid metaheuristic. The best performer combines a global scatter search metaheuristic with an interior point local method, provided with gradients estimated with adjoint-based sensitivities. We provide an implementation of this method to render it available to the scientific community. AVAILABILITY AND IMPLEMENTATION:The code to reproduce the results is provided as Supplementary Material and is available at Zenodo https://doi.org/10.5281/zenodo.1304034. SUPPLEMENTARY INFORMATION:Supplementary data are available at Bioinformatics online.
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Project description:[This corrects the article on p. 39 in vol. 26.].
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Project description:The enzyme fumarase catalyzes the reversible hydration of fumarate to malate. The reaction catalyzed by fumarase is critical for cellular energetics as a part of the tricarboxylic acid cycle, which produces reducing equivalents to drive oxidative ATP synthesis. A catalytic mechanism for the fumarase reaction that can account for the kinetic behavior of the enzyme observed in both isotope exchange studies and initial velocity studies has not yet been identified. In the present study, we develop an 11-state kinetic model of the enzyme based on the current consensus on its catalytic mechanism and design a series of experiments to estimate the model parameters and identify the major flux routes through the mechanism. The 11-state mechanism accounts for competitive binding of inhibitors and activation by different anions, including phosphate and fumarate. The model is identified from experimental time courses of the hydration of fumarate to malate obtained over a wide range of buffer and substrate concentrations. Further, the 11-state model is found to effectively reduce to a five-state model by lumping certain successive steps together to yield a mathematically less complex representation that is able to match the data. Analysis suggests the primary reaction route of the catalytic mechanism, with fumarate binding to the free unprotonated enzyme and a proton addition prior to malate release in the fumarate hydration reaction. In the reverse direction (malate dehydration), malate binds the protonated form of the enzyme, and a proton is generated before fumarate is released from the active site.
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Project description:We report the application of recently developed microscopic models to estimate the apparent kinetic and thermodynamic parameters in a single molecule force spectroscopy study of the carbonic anhydrase enzyme and a complementary sulfonamide inhibitor. The most probable rupture force for the enzyme-inhibitor interaction shows a nonlinear dependency on the log-loading rate. Estimates for the kinetic and thermodynamic parameters were obtained by fitting the nonlinear dependency to linear cubic potential and cusp potential models and compared to the standard Bell-Evans model. The reliability of the estimated parameters was verified by modeling the experimental rupture force distributions by the theoretically predicted distributions at rupture. We also report that linkers that are attached to the enzyme and inhibitor show appreciable effects on the apparent kinetic and thermodynamic parameters.
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Project description:Stability and biological activity of proteins is highly dependent on their physicochemical environment. The development of realistic models of biological systems necessitates quantitative information on the response to changes of external conditions like pH, salinity and concentrations of substrates and allosteric modulators. Changes in just a few variable parameters rapidly lead to large numbers of experimental conditions, which go beyond the experimental capacity of most research groups. We implemented a computer-aided experimenting framework ("robot lab assistant") that allows us to parameterize abstract, human-readable descriptions of micro-plate based experiments with variable parameters and execute them on a conventional 8 channel liquid handling robot fitted with a sensitive plate reader. A set of newly developed R-packages translates the instructions into machine commands, executes them, collects the data and processes it without user-interaction. By combining script-driven experimental planning, execution and data-analysis, our system can react to experimental outcomes autonomously, allowing outcome-based iterative experimental strategies. The framework was applied in a response-surface model based iterative optimization of buffer conditions and investigation of substrate, allosteric effector, pH and salt dependent activity profiles of pyruvate kinase (PYK). A diprotic model of enzyme kinetics was used to model the combined effects of changing pH and substrate concentrations. The 8 parameters of the model could be estimated from a single two-hour experiment using nonlinear least-squares regression. The model with the estimated parameters successfully predicted pH and PEP dependence of initial reaction rates, while the PEP concentration dependent shift of optimal pH could only be reproduced with a set of manually tweaked parameters. Differences between model-predictions and experimental observations at low pH suggest additional protonation-sites at the enzyme or substrates critical for enzymatic activity. The developed framework is a powerful tool to investigate enzyme reaction specifics and explore biological system behaviour in a wide range of experimental conditions.
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