Michaelis-Menten model nonlinear regression

Determine the kinetics parameters Km and Vmax, assuming that the standard Michaelis-Menten model applies to this system, (a) by nonlinear regression, and (b) by linear regression of the Lineweaver-Burk form. 

Kinetic parameters were determined by following the reduction of the nicotinamide coenzymes at 340 nm as described by Dean and Dvorak (7). Rates were calculated using a molar extinction coefficient for NAD(P)H of 6200 M f cm" and protein concentrations were determined at 280 nm using a molar extinction coefficient of 30,420 M cm f Nonlinear least squares Gauss-Newton regressions were used to determine the fit of the data to the Michaelis-Menten model. 

The Michaelis-Menten model was fitted to the experimental data using standard nonlinear regression techniques to obtain estimates of and K (Fig. 4.1). Best-fit values of and K of corresponding standard errors of the estimates plus the number of values used in the calculation of the standard error, and of the goodness-of-fit statistic are reported in Table 4.3. These results suggest that succinate is a competitive inhibitor of fumarase. This prediction is based on the observed apparent increase in Ks in the absence of changes in Vmax (see Table 4.1). At this point, however, the experimenter cannot state with any certainty whether the observed apparent increase in Ks is a tme effect of the inhibitor or merely an act of chance. A proper statistical analysis has to be carried out. For the comparison of two values, a two-tailed t-test is appropriate. When more than two values are compared, a one-way analysis of variance (ANOVA),... 

Another approach for the determination of the kinetic parameters is to use the SAS NLIN (NonLINear regression) procedure (SAS, 1985) which produces weighted least-squares estimates of the parameters of nonlinear models. The advantages of this technique are that (1) it does not require linearization of the Michaelis-Menten equation, (2) it can be used for complicated multiparameter models, and (3) the estimated parameter values are reliable because it produces weighted least-squares estimates. 

Biphasic kinetics should preferably be analyzed using such a computational approach. The above mathematic model can be revised to comprise two independent hyperbolic components y = axj(b + v) + cxj d + x). Here a and b are, respectively, Vmax and for one kinetic component, and c and d are those for the other, respectively. After the raw data (5 and V), used for the construction of the Michaelis-Menten plot shown in Fig. 13.3, were processed using SigmaPlot, following the procedure as described, the results for the nonlinear regression analyses were generated, they are summarized in Table 13.5. Of the... 

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