The bootstrap analysis in a comparison of estimates of Michaelis-Menten kinetic constants from various methods

• Main Author: Pasaribu, U. S.
• Published: Swansea University 1993
• Subjects: 510
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.638420

The bootstrap is a resampling nonparametric technique which can be applied to many statistics problems. This thesis uses bootstrap analysis to compare methods of estimating Michaelis-Menten kinetic constants: namely the plot of 1/<i>V</i> against 1/<i>S</i> (Lineweaver-Burk), the plot of <i>S/V</i> against <i>S</i> (Hanes), the plot of <i>V</i> against <i>V/S</i> (Eadie-Hofstee), each using regression, the plot of <i>V</i> against <i>V/S</i> using principal components and iterative least squares (ILS). These are applied to simulated data with Normally distributed errors but with various assumptions about the variance. We also consider the effect on the bootstrap distributions of introducing an outlier to the data. Recommendations are made for obtaining good estimates of V<SUB>max</SUB> and K<SUB>m</SUB>. Two methods, the ILS and Hanes plot are generally good. The commonly-used Lineweaver-Burk plot is always bad: it should never be used. In the presence of an outlier, the superiority of the ILS method over the others is confirmed. However, ILS is not really robust when a high outlier is present at larger substrate concentrations. Iteratively reweighted least squares (IRLS), a robust modification of the ILS method, is proposed in this case. The asumption of Normally distributed velocities is unlikely to be maintained in the laboratory, but departures from Normality are unlikely to be serious, as long as there are no outliers. However, the assumptions that the variance is constant or that the standard deviation is proportional to the mean are not satisfactory. In laboratory experiments we found it reasonable to assume the variance of <i>V</i> is proportional to its mean. Furthermore, there is variablity between results on different day/concentration batches, probably due to variation in the amounts of enzyme or substrate, temperature, distilled water etc. These should be allowed for in assessing the accuracy of the estimates.