Erratum: Comparison of various estimation methods for the parameters of Michaelis-Menten equation based on in vitro elimination kinetic simulation data.
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ABSTRACT:
SUBMITTER: Cho YS
PROVIDER: S-EPMC6989230 | biostudies-literature | 2018 Sep
REPOSITORIES: biostudies-literature
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Erratum: Comparison of various estimation methods for the parameters of Michaelis-Menten equation based on <i>in vitro</i> elimination kinetic simulation data.
Cho Yong-Soon YS Lim Hyeong-Seok HS
Translational and clinical pharmacology 20180914 3
[This corrects the article on p. 39 in vol. 26.]. ...[more]
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Project description:Biochemical transformation kinetics is based on the formation of enzyme-substrate complexes. We developed a robust scheme based on unit productions of enzymes and reactants in cyclic events to comply with mass action law to form enzyme-substrate complexes. The developed formalism supports a successful application of Michaelis-Menten kinetics in all biochemical transformations of single parameters. It is an essential tool to overcome some challenging healthcare and environmental issues. In developing the formalism, we defined the substrate [S]= [Product]3/4 and rate of reaction based on rate and time perspectives. It allowed us to develop two quadratic equations. The first, represents a body entity that gave a useful relationship of enzyme E?=?2S0.33, and the second nutrients/feed, each giving [Enzymes] and [Enzyme-substrate complexes], simulating rate of reaction, [substrate], and their differentials. By combining [Enzymes] and [Enzyme-substrate complexes] values, this quadratic equation derives a Michaelis-Menten hyperbolic function. Interestingly, we can derive the proportionate rate of reaction and [Enzymes] values of the quadratics resulting in another Michaelis-Menten hyperbolic. What is clear from these results is that between these two hyperbolic functions, in-competitive inhibitions exist, indicating metabolic activities and growth in terms of energy levels. We validated these biochemical transformations with examples applicable to day to day life.
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Project description:Nonlinear ordinary differential equations (ODEs) are common in pharmacokinetic-pharmacodynamic systems. Although their exact solutions cannot generally be determined via algebraic methods, their rapid and accurate solutions are desirable. Thus, numerical methods have a critical role. Inductive Linearization was proposed as a method to solve systems of nonlinear ODEs. It is an iterative approach that converts a nonlinear ODE into a linear time-varying (LTV) ODE, for which a range of standard integration techniques can then be used to solve (e.g., eigenvalue decomposition [EVD]). This study explores the properties of Inductive Linearization when coupled with EVD for integration of the LTV ODE and illustrates how the efficiency of the method can be improved. Improvements were based on three approaches, (1) incorporation of a convergence criterion for the iterative linearization process (for simulation and estimation), (2) creating more efficient step sizes for EVD (for simulation and estimation), and (3) updating the initial conditions of the Inductive Linearization (for estimation). The performance of these improvements were evaluated using single subject stochastic simulation-estimation with an application to a simple pharmacokinetic model with Michaelis-Menten elimination. The reference comparison was a standard non-stiff Runge-Kutta method with variable step size (ode45, MATLAB). Each of the approaches improved the speed of the Inductive Linearization technique without diminishing accuracy which, in this simple case, was faster than ode45 with comparable accuracy in the parameter estimates. The methods described here can easily be implemented in standard software programme such as R or MATLAB. Further work is needed to explore this technique for estimation in a population approach setting.
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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:The aim was to elucidate how steps in drug translocation by a solute carrier transporter impact Michaelis-Menten parameters Km, Ki, and Vmax. The first objective was to derive a model for carrier-mediated substrate translocation and perform sensitivity analysis with regard to the impact of individual microrate constants on Km, Ki, and Vmax. The second objective was to compare underpinning microrate constants between compounds translocated by the same transporter. Equations for Km, Ki, and Vmax were derived from a six-state model involving unidirectional transporter flipping and reconfiguration. This unidirectional model is applicable to co-transporter type solute carriers, like the apical sodium-dependent bile acid transporter (ASBT) and the proton-coupled peptide cotransporter (PEPT1). Sensitivity analysis identified the microrate constants that impacted Km, Ki, and Vmax. Compound comparison using the six-state model employed regression to identify microrate constant values that can explain observed Km and Vmax values. Results yielded some expected findings, as well as some unanticipated effects of microrate constants on Km, Ki, and Vmax. Km and Ki were found to be equal for inhibitors that are also substrates. Additionally, microrate constant values for certain steps in transporter functioning influenced Km and Vmax to be low or high.
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Project description:Aldo-keto reductases (AKRs) are responsible for the detoxification of harmful aldehydes. Due to the large number of isotypes, the physiological relevance of AKRs cannot be obtained using mRNA or protein quantification, but only through the use of enzymatic assays to demonstrate functionality. Here, we present a fast and simple protocol to determine the important Michaelis-Menten kinetics of AKRs, which includes various aldehyde substrates of interest such as 4-hydroxynonenal, methylglyoxal, and malondialdehyde. For complete details on the use and execution of this protocol, please refer to Morgenstern et al. (2017) and Schumacher et al. (2018).
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Project description:Nearly 100 years ago Michaelis and Menten published their now classic paper [Michaelis, L., and Menten, M. L. (1913) Die Kinetik der Invertinwirkung. Biochem. Z. 49, 333-369] in which they showed that the rate of an enzyme-catalyzed reaction is proportional to the concentration of the enzyme-substrate complex predicted by the Michaelis-Menten equation. Because the original text was written in German yet is often quoted by English-speaking authors, we undertook a complete translation of the 1913 publication, which we provide as Supporting Information . Here we introduce the translation, describe the historical context of the work, and show a new analysis of the original data. In doing so, we uncovered several surprises that reveal an interesting glimpse into the early history of enzymology. In particular, our reanalysis of Michaelis and Menten's data using modern computational methods revealed an unanticipated rigor and precision in the original publication and uncovered a sophisticated, comprehensive analysis that has been overlooked in the century since their work was published. Michaelis and Menten not only analyzed initial velocity measurements but also fit their full time course data to the integrated form of the rate equations, including product inhibition, and derived a single global constant to represent all of their data. That constant was not the Michaelis constant, but rather V(max)/K(m), the specificity constant times the enzyme concentration (k(cat)/K(m) × E(0)).
| S-EPMC3381512 | biostudies-literature
Project description:BackgroundStandard pediatric growth curves cannot be used to impute missing height or weight measurements in individual children. The Michaelis-Menten equation, used for characterizing substrate-enzyme saturation curves, has been shown to model growth in many organisms including nonhuman vertebrates. We investigated whether this equation could be used to interpolate missing growth data in children in the first three years of life and compared this interpolation to several common interpolation methods and pediatric growth models.MethodsWe developed a modified Michaelis-Menten equation and compared expected to actual growth, first in a local birth cohort (N = 97) then in a large, outpatient, pediatric sample (N = 14,695).ResultsThe modified Michaelis-Menten equation showed excellent fit for both infant weight (median RMSE: boys: 0.22 kg [IQR:0.19; 90% < 0.43]; girls: 0.20 kg [IQR:0.17; 90% < 0.39]) and height (median RMSE: boys: 0.93 cm [IQR:0.53; 90% < 1.0]; girls: 0.91 cm [IQR:0.50;90% < 1.0]). Growth data were modeled accurately with as few as four values from routine well-baby visits in year 1 and seven values in years 1-3; birth weight or length was essential for best fit. Interpolation with this equation had comparable (for weight) or lower (for height) mean RMSE compared to the best performing alternative models.ConclusionsA modified Michaelis-Menten equation accurately describes growth in healthy babies aged 0-36 months, allowing interpolation of missing weight and height values in individual longitudinal measurement series. The growth pattern in healthy babies in resource-rich environments mirrors an enzymatic saturation curve.
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Project description:The Michaelis-Menten equation was fitted to simulated data containing different sorts of error by using the three linear transformations, and the methods of S. R. Cohen [Anal. Biochem. (1968) 22, 549-552], R. Eisenthal & A. Cornish-Bowden [Biochem. J. (1974) 139, 715-120], F. de M. Merino [Biochem. J. 143, 93-95] and G. N. Wilkinson [Biochem. J. (1961) 808 324-332). The best methods were those of Eisenthal & Cornish-Bowden (1974) and Wilkinson (1961).
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Project description:Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.
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