Michaelis integrated

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... 

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. 

The integrated form of the simple Michaelis-Menten kinetics (Eq. (8)), is most suitable to analyze the time-dependent progressive substrate conversion or the corresponding product formation. 

The order of reaction is not always integral and sometimes the rate cannot be expressed in a simple form. For example, some enzyme-catalysed reactions obey Michaelis—Menten kinetics and the rate is given by... 

The following sections describe the reactor performance of the three main types of reactors in the presence of mass transfer effects integrated with Michaelis-Menten kinetics. 

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

In the section entitled Special Forms we introduced Michaelis-Menten kinetics rather abruptly as an example of integration by quadrature. The substrate, as it is often called in biochemical circles, in the reaction A —> B disappears at a rate... 

D. Srivastava and D. A. Micha. Complex path integration for extended molecular systems. Computer Phys. Comm., 63 331, 1991. 

Integrated Michaelis-Menten Equation in Ideal Reactors... 

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. 

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

Barrowman, J., and Michaelis, S. (2009). ZMPSTE24, an integral membrane zinc metal-loprotease with a connection to progeroid disorders. Biol Chem 390 761-773. 

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