Michaelis parameters determination from initial rate

In our previous work [63], we studied the hydrolysis kinetics of lipase from Mucor javanicus in a modified Lewis cell (Fig. 4). Initial hydrolysis reaction rates (uri) were measured in the presence of lipase in the aqueous phase (borate buffer). Initial substrate (trilinolein) concentration (TLj) in the organic phase (octane) was between 0.05 and 8 mM. The presence of the interface with octane enhances hydrolysis [37]. Lineweaver-Burk plots of the kinetics curve (1/Uj.] = f( /TL)) gave straight lines, demonstrating that the hydrolysis reaction shows the expected kinetic behavior (Michaelis-Menten). Excess substrate results in reaction inhibition. Apparent parameters of the Michaelis equation were determined from the curve l/urj = f /TL) and substrate inhibition was determined from the curve 1/Uj.] =f(TL) ... 

Experimental determination of kinetic parameters for inhibition mechanisms follows the same pattern as in simple Michaelis-Menten kinetics (section 3.2.2). Linearization methods are particularly useful to determine the mechanism of inhibition as a previous step to the quantification of the kinetic parameters. Experimental design consists now in a matrix in which initial rate data are gathered at different substrate and inhibitor concentrations (s and i respectively) as depicted in Table 3.3. Inhibitor is here considered in general terms as any substance exerting enzyme inhibition, be it a product of reaction, as previously considered, or catalytically inert. Of course inhibition by products and/or substrate is more technologically relevant, since catalytically inert inhibitors can be simply kept out from the reaction medium. 

However, the above equations will only give reasonable values for the parameters in the unlikely case when the reaction is both essentially irreversible and not subject to product inhibition. Much more complex equations with many more parameters have to be used fora fit of the whole time course of the reaction to a realistic mechanism. There are hazards, too, in the determination of true initial rates. It is necessary to check that the change in substrate concentration during the period of initial rate measurement is sufficiently small so that the observed rate is the correct one for each specified value of Cs(0). After a preliminary estimate for and one can readily calculate whether these parameters would cause a significant deviation from true linearity of initial rates, that is adherence to the steady state condition because of the difference in substrate concentration at the beginning and end of the measurement. This must not be left to the appearance of the initial slope. It is also important, for the correct evaluation of the Michaelis parameters, to heed the advice of Dowd Riggs (1965) that the range of Cg(0) must straddle both sides of by a factor of 10. 

Methane oxidation kinetics was assessed as follows. In these experiments, cells were inoculated into medium containing different initial amounts of copper sulfate and grown to an optical density at 600 nm of 0.5-0.7. Aliquots were then placed in closed vials at different initial dissolved methane concentrations. These aliquots were incubated under optimal conditions, and head-space samples were taken at four different time points (1-4 h) for determination of methane concentrations by gas chromatography. From these data, initial methane consumption rates determined for different methane concentrations were used to obtain the Michaelis-Menten parameters Ks (half-saturation constant) and Vmax (rate at substrate saturation). Under these conditions sMMO was not expressed, as described previously (9). 

Studies of enzyme kinetics involve measurements of initial velocity v of the reaction as a function of substrate concentration [S]. Values of the kinetic constants are determined by fitting the initial velocity and concentration data to the appropriate rate equations by the least-squares method. The maximal velocity and Michaelis constant are obtained from experimental data, usually from different methods of plotting the kinetic parameters, the most common of which is to plot llv versus... 

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