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Inferential Statistics: Michaelis-Menten equation - Essay Example

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The data below has been adopted from Atkinson, Jackson and Morton and was used before in statistical estimations of errors of Vmax and Km. In the data set, the substrate concentration has been approximated in an inversely proportional way with almost similar data points above Km and below it. In an experiment in the literature, the analysis of the above data was carried out using statistical package FORTRAN for the double reciprocal Michael-Menten kinetics. This R program employed calculated generalized least squares. This least-squire procedure searched for new estimates of KM and Vmax with the Sum of Square Residual reducing. Only the relative size of SSRes was used but not its magnitude. This R program calculated for given values of Vmax and Km the square of the differences of the observed V values and the calculated. The Lineweaver method is a standard linear regression double reciprocal plot with the inverse of V (1/V) on the Y-axis and the inverse of [S] (1/[S]) on the X-axis. Therefore; = 0.798 + 1.708 (Raymond and Tania, 2006)Whereby; Regression (r) = 0.979 Probability (p) = 0.06%Therefore; 1/Vmax = 1.71+/- The approximated inverse error (Z=1/X) can be calculated using the formulae below;SE (Z) = X-1 . On ignoring the covariance terms, the inverse error for a division (z = X/Y) can be obtained through the formula below;SE (Z) = (Sprott, 2001)Using the above formulae of inversion error, the; Km SE (Standard Error) = 0.441 0.0906 and Vmax SE= 0.585 0.104....
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Sample Enzymatic data which was used in analyzing the Michaelis-Menten Kinetics parameters Km and Vmax. Velocity V Substrate Concentration [S] 0.148 0.138 0.171 0.220 0.234 0.291 0.234 0.560 This is the appropriate position of Km 0.390 0.766 0.493 1.460 Adopted from (Atkinson, Jackson and Morton, 1961) In an experiment in the literature by Raymond and Tania (2006), the analysis of the above data was carried out using statistical package FORTRAN for the double reciprocal Michael-Menten kinetics. This R program employed calculated generalized least squares. This least-squire procedure searched for new estimates of KM and Vmax with the Sum of Square Residual (SSRes) reducing. Only the relative size of SSRes was used but not its magnitude. This R program calculated for given values of Vmax and Km the square of the differences of the observed V values and the calculated. This was then followed by the calculation of the SSRes. Formulae employed by the program; SSRes  (Atkinson, Jackson, Morton, 1961) The Lineweaver-Burk method in the determination of the Michaelis-Menten parameters; Km and Vmax The Lineweaver method is a standard linear regression double reciprocal plot with the inverse of V (1/V) on the Y-axis and the inverse of [S] (1/[S]) on the X-axis. Therefore;  = 0.798 + 1.708 (Raymond and Tania, 2006) Whereby; Regression (r) = 0.979 Probability (p) = 0.06% Therefore; 1/Vmax = 1.71+/- 0.303 (SE of mean) and Km/Vmax = 0.758+/- 0.0782 (SE of mean). The approximated inverse error (Z=1/X) can be calculated using the formulae below; SE (Z) = X-1 . On ignoring the covariance terms, the inverse error for a division (z = X/Y) can be obtained through the formula below; SE (Z) =  (Sprott, 2001) Using the above formulae of inversion
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Summary

This paper example will compare the estimation of Km and Vmax using simple Michealis-Menten simple kinetics double reciprocal statistic equation and Eadie-Hofstee kinetics semi-reciprocal equation which is an improvement of the Michealis-Menten estimation…
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