Simultaneous estimation ofV max, Km, and the rate of endogenous substrate production (R) from substrate depletion data

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Abstract
The nonlinear and 3 linearized forms of the integrated Michaelis-Menten equation were evaluated for their ability to provide reliable estimates of uptake kinetic parameters, when the initial substrate concentration (S0) is not error-free. Of the 3 linearized forms, the one where t/(S0−S) is regressed against ln(S0/S)/(S0−S) gave estimates ofV max and Km closest to the true population means of these parameters. Further, this linearization was the least sensitive of the 3 to errors (±1%) in S0. Our results illustrate the danger of relying on r2 values for choosing among the 3 linearized forms of the integrated Michaelis-Menten equation. Nonlinear regression analysis of progress curve data, when S0 is not free of error, was superior to even the best of the 3 linearized forms. The integrated Michaelis-Menten equation should not be used to estimateV max and Km when substrate production occurs concomitant with consumption of added substrate. We propose the use of a new equation for estimation of these parameters along with a parameter describing endogenous substrate production (R) for kinetic studies done with samples from natural habitats, in which the substrate of interest is an intermediate. The application of this new equation was illustrated for both simulated data and previously obtained H2 depletion data. The only means by whichV max, Km, and R may be evaluated from progress curve data using this new equation is via nonlinear regression, since a linearized form of this equation could not be derived. Mathematical components of computer programs written for fitting data to either of the above nonlinear models using nonlinear least squares analysis are presented.