Michaelis-Menten equation integrated form

Before the Michaelis-Menten equation can be integrated, it is necessary to introduce into it some relationship that exists between the reactant concentrations. Therefore, let us write Uo as -dA/dt, and substitute it into the Michaelis-Menten equation to form ... 

Linearized Form of the Integrated Michaelis-Menten Equation... 

For a constant-volume BR, integration of the Michaelis-Menten equation leads to a form that can also be linearized. Thus, from equation 10.2-9,... 

A major limitation of the linearized forms of the Michaelis-Menten equation is that none provides accurate estimates of both Km and Vmax. Furthermore, it is impossible to obtain meaningful error estimates for the parameters, since linear regression is not strictly appropriate. With the advent of more sophisticated computer tools, there is an increasing trend toward using the integrated rate equation and nonlinear regression analysis to estimate Km and While this type of analysis is more complex than the linear approaches, it has several benefits. First, accurate nonbiased estimates of Km and Vmax can be obtained. Second, nonlinear regression may allow the errors (or confidence intervals) of the parameter estimates to be determined. 

In principle, the differential form (Eq. (1)), as well as the integrated form (Eq. (8)), can be used. The differential form of the Michaelis-Menten equation is applied in many cases, since differential values (e.g., flow meter or heat flow data) are often available by contrast, time-dependent substrate or product concentrations (or proportional quantities) can easily be differentiated numerically. 

Another method to obtain estimates for Km and is the rearrangement of the Michaelis-Menten equation to a linear form. The estimation for the initial velocities, Vo, from progress curves is not a particularly reliable method. A better way to estimate Vn is by the integrated Michaelis-Menten equation (Cornish-Bowden, 1975). Nevertheless, the graphical methods are popular among enzymolo-gists. The three most common linear transformations of the Michaelis-Menten equation are the Lineweaver-Burk plot of 1/Vo vs. 1/[S] (sometimes called the double-reciprocal plot), the Eadie-Hofstee plot, i.e. v vs. vo/[S], and the Hanes plot, i.e., [SJ/vo vs. [S] (Fig. 9.3). 

Gerber N, Wagner J (1972). Explanation of dose-dependent decline of diphenylhydantoin plasma levels by fitting to the integrated form of the Michaelis-Menten equation. Res Commun Chem Pathol Pharmacol 3 455. 

To test whether the logistic kinetic equation (82), which is a natural generalization of the Michaelis-Menten equation, may provide a workable analytical solution in an elementary form, we first integrate it tmder the form... 

Note that the data points in Fig. 8B are converging to r/uo (9 s on ordinate) and to i/A(, C0.033 on abscissa), as the time tends to zero. Thus, the main advantage of the integrated forms of the Michaelis-Menten equation is the possibihty to obtain an accurate estimate of the initial rate of reaction, Vo-In cases when it is not convenient to use the integrated rate equation, it is still possible to use progress curve data advantageously instead of fitting the data to the tme equation, they can be fitted to an equation of the form... 

The approach was initially used to describe the inhibition of P-galactosidase by imidazole using a global kinetic data fitting aj>proach (Walsh et al., 2010). The open structure of the expression when comp>ared to integral forms of the Michaelis-Menten equation found in the literature allowed for the insertion of modifier terms in the same way outlined in the previous section (Walsh et al., 2010 Equation 36). 

Integral forms of the Michaelis Menten equation have been proposed for use in time course analysis for many years, with more complex mathematical models appearing with time (Russell Drane, 1992 Goudar et al., 1999). Integral forms of the Michaelis Menten equation however have been found to be limited in their usefulness for time course models... 

LINEARIZED FORM OF THE INTEGRATED MICHAELIS-MENTEN (MM) EQUATION... 

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