Michaelis-Menten kinetics experimental determination

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

Various aspects of the kinetic behavior of the tyrosinase biosensor were investigated, including parameters affecting the enzyme activity and the rate of oxygen consumption. The Michaelis-Menten constant was determined for tyrosinase using several substrates and different experimental conditions. Performance parameters of the biosensor in the... 

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. 

Once ku has been experimentally determined (see section 3.5.2), the curve of reactor operation (X vs t) can be obtained for a certain enzyme concentration (meat)-Eq. 5.69 also allows reactor design (determination of reactor volume), since meat is simply the ratio of enzyme load to reaction volume (Mcat/VR). Simulation of batch bioreactor operation under different scenarios of enzyme inactivation is presented in Fig. 5.16 for simple Michaelis-Menten kinetics (a = 14-K/Si b = -1 c = 0) with Si/K =10. Enzyme load in the reactor was calculated to obtain 90% conversion after 10 h of reaction under no inactivation. The strong impact of enzyme inactivation on bioreactor performance can be easily appreciated. 

In such a mechanism, Michaelis-Menten kinetics are observed only if the initial equilibrium constant is greater than that for the rate-determining process, conditions which are observed experimentally in ca. 4M-H2SO4. 

Michaelis kinetics (Michaelis-Menten kinetics) A simple and useful model of the kinetics of enzyme-catalyzed reactions. It assumes the formation of a specific enzyme-substrate complex. Many enzymes obey Michaelis kinetics and a plot of reaction velocity (V) against substrate concentration [S] gives a characteristic curve showing that the rate increases quickly at first and then levels off to a maximum value. When substrate concentration is low, the rate of reaction is almost proportional to substrate concentration. When substrate concentration is high, the rate is at a maximum, V iax) independent of substrate concentration. The Michaelis constant is the concentration of substrate at half the maximum rate and can be determined experimentally by measuring reaction rate at varying substrate concentrations. Different types of inhibition can also be distinguished in this way. Allosteric enzymes do not obey Michaelis kinetics. 

Before adequate computer hardware and software were widely available, fitting experimental kinetic data to a curve to determine Km and Vmax was a significant challenge. Lineweaver and Burk rearranged the Michaelis-Menten equation to form a new linear relationship, the Lineweaver-Burk equation (Equation 4.13).6... 

This equation should look familiar, because it is functionally identical to the Michaelis-Menten equation of enzyme kinetics. This equation also should make clear the experimental design to be used in determining KD and Bmax using saturation isotherms. We have as the independent variable [E] and as dependent variable B. A successful experiment should permit the estimation of the two biologically meaningful constants KD and 5max. 

Table 3 lists the kinetic rate expressions for each of the hydrolysis and fermentation reaction rates shown in Fig. 5 and in the mass balance equations of Tables 1 and 2. Each of the reaction rates were found to fit the data through trial and error, starting with the simplest model. For the hydrolysis reaction rates (rs,arch and / maltose), the simplest form was the Michaelis-Menten model without inhibition. For all other reaction rates which described fermentation kinetics, the simplest form was the Monod model without inhibition. More descriptive models were found in the literature and tested one by one until the set of kinetic rate equations with the best fit to the experimental data were determined. This was completed with the hydrolysis datasets first, then the complete SSF datasets. 

Eqn. 1 has the form of the Michaelis-Menten equation, well-known to students of enzyme kinetics. The various ways in which these equations and the similar forms that we will come across later in this chapter can be manipulated so as to yield values of F,2 given experimental determination of 0 2 at various values of... 

The Michaelis-Menten equation developed in 1913 ushered in the era of enzyme kinetics and mechanism (chapter 2). Experimentally, its application involves graphing rates (velocities) of reaction (v) against trial concentrations of substrate ([S]). A "saturation" curve is usually observed in which there is a leveling off of v, so as to approach the maximum rate (V a ) as [S] reaches saturation concentration. In practice, it is difficult to accurately determine the onset of saturation and this led to considerable uncertainty in the values of Vmax as well as the enzyme-substrate binding constants (K in chapter 2). 

The kinetic parameters in Equations 4.21 and 4.22 can be determined from experimental data using nonlinear regression techniques. Nevertheless, these equations can be simplified by considering the excess concentration of one of the substrates. For example, at high values of [52], the reaction rate can be simplified to a Michaelis-Menten equation form. 

In this case the Michaelis-Menten equation reflects a first-order reaction in which the rate of substrate breakdown depends on substrate concentration. In using a kinetic method for the determination of substrate concentration (cf. 2.6.1.3), the experimental conditions must be selected such that Equation 2.46 is valid. 

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