Integrated Michaelis-Menten Equation

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

Integrated Michaelis-Menten Equation in Ideal Reactors... 

Integrated Michaelis-Menten Equation for Substrate and Product Inhibition... 

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). 

In the same manner that the target constants and Vkt are calculable from just one concentration-time diagram by differentiating the values obtained as outlined above, it is also feasible to utilize the integrated Michaelis-Menten equation with the time-dependent values directly. Eqn (4.8) and its detailed integration from eqn (4.1) can be found in the literature... 

In order to develop an optimized system, each of these parameters must be considered. The first of these, conversion of analyte, can be considerred simply by using the integrated Michaelis-Menten equation. 

Goudar C.T., Sonnad J.R. Duggleby R.G. (1999). Parameter estimation using a direct solution of the integrated Michaelis-Menten equation, Biochim. Biopht/s. Acta, 1429, 377-383. 

Russell R.W. Drane J.W. (1992). Improved rearrangement of the integrated Michaelis-Menten equation for calculating in vivo kinetics of transport and metabolism. / Dairy Set, 75, 3455-3464. 

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

With the Michaelis-Menten equation, there is no integrated solution for the concentration, but only for the time... 

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. 

The integrated rate equation corresponding to the Michaelis-Menten equation... 

The simplest case of a reactor is a cuvette, such as that in a photometer. From the Michaelis-Menten equation and the equation for the batch reactor [Eqs. (5.11) and (5.12)], respectively, as well as the definition for the degree of conversion % for the simple reaction S —> P, x = 1 - [S]/[S0] = [P]/[S0], the integrated equation (5.15) for an enzyme reaction following a Michaelis-Menten law in a batch reactor is obtained. 

A completely different system for the determination of kinetic parameters is based on the evaluation of substrate concentration through time. In fact, by integration of the Michaelis-Menten equation ... 

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... 

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 ... 

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