Parameter Estimation in Different Enzyme Reactions

Nelatury, Sudarshan R.; Nelatury, Charles F.; Vagula, Mary C.

doi:10.4236/aer.2014.21002

Cited by 7 publications

(6 citation statements)

References 12 publications

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“…The algorithms used include the Levenberg-Marquardt method, the Gauss-Newton method, the steepestdescent method, and simplex minimization. Numerous software packages, such as Excel, MATLAB, and GraphPrism, nowadays include readily available routines and scripts to perform nonlinear least-squares fitting [11,12].…”

Section: Journal Of Chemistrymentioning

confidence: 99%

Robust Nonlinear Regression in Enzyme Kinetic Parameters Estimation

Marasović

Miloš

2017

Journal of Chemistry

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Accurate estimation of essential enzyme kinetic parameters, such as Km and Vmax, is very important in modern biology. To this date, linearization of kinetic equations is still widely established practice for determining these parameters in chemical and enzyme catalysis. Although simplicity of linear optimization is alluring, these methods have certain pitfalls due to which they more often then not result in misleading estimation of enzyme parameters. In order to obtain more accurate predictions of parameter values, the use of nonlinear least-squares fitting techniques is recommended. However, when there are outliers present in the data, these techniques become unreliable. This paper proposes the use of a robust nonlinear regression estimator based on modified Tukey’s biweight function that can provide more resilient results in the presence of outliers and/or influential observations. Real and synthetic kinetic data have been used to test our approach. Monte Carlo simulations are performed to illustrate the efficacy and the robustness of the biweight estimator in comparison with the standard linearization methods and the ordinary least-squares nonlinear regression. We then apply this method to experimental data for the tyrosinase enzyme (EC 1.14.18.1) extracted from Solanum tuberosum, Agaricus bisporus, and Pleurotus ostreatus. The results on both artificial and experimental data clearly show that the proposed robust estimator can be successfully employed to determine accurate values of Km and Vmax.

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Section: Journal Of Chemistrymentioning

confidence: 99%

Robust Nonlinear Regression in Enzyme Kinetic Parameters Estimation

Marasović

Miloš

2017

Journal of Chemistry

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“…The motivation behind the desire to seek alternative ways of producing reliable Michaelian parameters by means of a robust nonlinear regression estimator based on a modified Tukey’s biweight function is the belief that outliers can lead to misleading values for the parameters of the nonlinear regression [8]. Similar beliefs and experiences have also prompted the suggestion for and use of software (MATLAB and any other software) for estimating enzyme kinetic parameters via the Wilkinson nonlinear regression technique [8, 9].…”

Section: Introductionmentioning

confidence: 99%

Alternative equations and “pseudo-statistical” approaches that enhance the precision of initial rates for the determination of kinetic parameters

Udema¹

2023

Preprint

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A burning concern among researchers studying enzyme kinetics has been ways of improving the accuracy of initial rates (v) with much greater precision. The goal of this study was to establish a formal (mathematical) way of achieving more accurate v values in enzyme assay. By adopting Bernfeld method of assay, the v values generated and other values in the literature were explored with two main objectives:1) to derive equations for a correctional calculation of initial rates and for the calculation of Michaelis-Menten (MM) parameters and 2) to evaluate the derived equations. The results of study showed that the maximum velocity (Vmax) and the MM constant (KM) obtained from a robust nonlinear regression (RNR) using v values in the literature were respectively between 21 and 26-fold and 6.56 to 61.2-fold greater than values generated from other method such as double reciprocal plot (drp), reciprocal variant of direct linear plot (RVDLP), and new method (z-model) derived based on MM equation; the Vmax and KM values (for alpha-amylase) calculated based on the RVDLP using the uncorrected v values were respectively 1.26- and 1.264-fold greater than the values using corrected v values; based on the z method, the Vmax and KM values using the uncorrected v values were 179.8- and 9.35-fold greater than the values using their corrected counterparts. In conclusion, the erroneous initial rates can be corrected using new equations before fitting RNR, RVDLP, drp, and any other equation to the corrected v values for the determination of MM parameters.

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“…For nonlinear regression, we used NONMEM, the estimation method of which is based on maximum likelihood estimation (MLE) and STP whereas other software packages usually used in enzyme kinetics, such as Excel and GraphPrism, perform fitting based on least square estimation (LSE) and original scaled and untransformed parameters. [11,12] The latter require a good initial guess of parameters and there is no guarantee of convergence to the global minimum. [13,14] The former is generally insensitive to initial values and reaches the global minimum in our experience.…”

Section: Discussionmentioning

confidence: 99%

Comparison of various estimation methods for the parameters of Michaelis-Menten equation based on in vitro elimination kinetic simulation data

Cho

Lim

2018

Transl Clin Pharmacol

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The Michaelis-Menten equation is one of the best-known models describing the enzyme kinetics of in vitro drug elimination experiments, and takes a form of equation relating reaction rate (V) to the substrate concentration ([S]) via the maximum reaction rate (V max ) and the Michaelis constant (K m ). The current study was conducted to compare the accuracy and precision of the parameter estimates in the Michaelis-Menten equation from various estimation methods using simulated data. One thousand replicates of simulated [S] over serial time data were generated using the results of a previous study, incorporating additive or combined error models as a source of random variables in the Monte-Carlo simulation using R. From each replicate of simulated data, V max and K m were estimated by five different methods, including traditional linearization methods and nonlinear ones without linearization using NONMEM. The relative accuracy and precision of the estimated parameters were compared by the median values and their 90% confidence intervals. Overall, V max and K m estimation by nonlinear methods (NM) provided the most accurate and precise results from the tested 5 estimation methods. The superiority of parameter estimation by NM was even more evident in the simulated data incorporating the combined error model. The current simulation study suggests that NMs using a program such as NONMEM provide more reliable and accurate parameter estimates of the Michaelis-Menten equation than traditional linearization methods in in vitro drug elimination kinetic experiments.

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Parameter Estimation in Different Enzyme Reactions

Cited by 7 publications

References 12 publications

Robust Nonlinear Regression in Enzyme Kinetic Parameters Estimation

Robust Nonlinear Regression in Enzyme Kinetic Parameters Estimation

Alternative equations and “pseudo-statistical” approaches that enhance the precision of initial rates for the determination of kinetic parameters

Comparison of various estimation methods for the parameters of Michaelis-Menten equation based on in vitro elimination kinetic simulation data

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