Michaelis Menten rate equation equations

The Effect of Various Types of Inhibitors on the Michaelis-Menten Rate Equation and on Apparent K, and Apparent F ,ax ... 

Develop a suitable rate expression using the Michaelis-Menten rate equation and the quasi-steady-state approximations for the intermediate complexes formed. 

The Michaelis-Menten rate equation for enzyme reactions is typically written as the rate of formation of product (Eq. 19a). This equation implies that 1/Rate (where rate is the rate of formation of product) depends linearly on the inverse of the substrate concentration [S]. This relation allows KM to be determined. Derive this equation and sketch 1/Rate against 1/[S]. Label the axes, the y-intercept, and the slope with their corresponding functions. 

P4.04.32. MICHAELIS-MENTEN RATE EQUATION For a reaction with rate equation,... 

To obtain an expression for the Michaelis Menten rate equation, the dissociation of the product from the complex needs to be evaluated. Using a... 

Figure 7. The Michaelis Menten rate equation as a function of substrate concentration S (in arbitrary units). Parameters are Km 1 and Vm 1. A A linear plot. B A semilogarithmic plot. At a concentration S Km, the rate attains half its maximal value Vm.

For power-law functions the (scaled) elasticities do not depend on the substrate concentration, that is, unlike Michaelis Menten rate equations, power-law functions will not saturate for increasing substrate concentration. 

Figure 27. Interpretation of the saturation parameter. Shown is a Michaelis Menten rate equation (solid line) and the corresponding saturation parameter d (dashed line). For small substrate concentration S Km the reaction acts in the linear regime. For increasing concentrations the saturation parameter d ... 

This ratio is of fundamental importance in the relationship between enzyme kinetics and catalysis. In the analysis of the Michaelis-Menten rate law (equation 5.8), the ratio cat/Km is an apparent second-order rate constant and, at low substrate concentrations, only a small fraction of the total enzyme is bound to the substrate and the rate of reaction is proportional to the free enzyme concentration ... 

Originally published in 1913 as a rate law for enzymatic sugar inversion [19], the Michaelis-Menten rate equation is also used frequently for describing homogeneously catalyzed reactions. It describes a two-step cycle (Eqs. (2.34) and (2.35)) the catalyst (the enzyme, E) first reacts reversibly with the substrate S, forming an enzyme-substrate complex ES (a catalytic intermediate). Subsequently, ES decomposes, giving the enzyme E and the product P. This second step is irreversible. 

The epoxidation of alkenes by sodium hypochlorite in the presence of manganese porphyrins under phase-transfer conditions has been thoroughly studied. Kinetic studies of this reaction revealed a Michaelis-Menten rate equation. As in Scheme 12, the active oxidant is thought to be a high-valent manganese( V)-oxo-porphyrin complex which reversibly interacts with the alkene to form a metal oxo-alkene intermediate which decomposes in the rate determining step to the epoxide and the reduced Mn porphyrin. Shape selective epoxidation is achieved when the sterically hindered complex Mn(TMP)Cl is used as the catalyst in the hypochlorite oxidation. ... 

Assuming a Michaelis-Menten rate equation, substrate mass transport through region 1 is governed by ... 

Under sufficient conditions, an enzyme mechanism exhibits a multidimensional inflection point around which a set of linear flow-force equations may be valid over an extended range outside of equilibrium. Enzyme catalyzed reactions obey approximately the Michaelis-Menten rate equation, which can show a high degree of linearity in the chemical affinity for certain values of substrate concentrations. 

As far as the mass transfer is concerned, the enzyme reaction process can be modelled in terms of the film theory combined with the description of a surface reaction. In other words, it is assumed that substrate mass transfer resistance is concentrated in a thin film adjacent to the membrane surface where enzyme molecules have been entrapped. The substrate diffuses through the film and reacts on the membrane surface. Equation [1.1] can also be used in this case with the assumption of the Michaelis-Menten rate equation in which R ax is defined as the amount of substrate that reacts per unit support volume and unit time ... 

The Michaelis-Menten rate equation shows the relationship between v (rate of reaction), (maximal rate when enzyme is saturated with substrate), and S (substrate concentration) v = V S/(A + S). When S the reaction is first order, and v = (V /AJ5.WhenA S, the reaction is zero order, and v = V = constant. V and are enzyme kinetic parameters. The Michaelis-Menten equation is often valid for other cases, where the derivation of the kinetic parameters from the rate constants is more complicated. 

Assuming that the hyperbolic Michaelis-Menten rate equation holds. Equation 7.9 becomes... 

Solution. The Michaelis-Menten rate equation is as follows ... 

Many reactions catalyzed by enzymes obey kinetics described by the Michaelis-Menten rate equation however, this adherence does not guarantee that a simple mechanism occurs, such as that represented by steps 9.1 and 9.2 to give the overall reaction 9.3. More complicated reaction sequences can result in exactly the same kinetic behavior. For example, there is considerable evidence that the following mechanism describes a number of enzyme... 

Derive the rate expression for an enzyme-catalyzed unimolecular (single substrate) reaction, such as that shown in steps 9.1 and 9.2, assuming that the decomposition of the reactive intermediate to give the product is reversible, rather than irreversible as indicated in step 9.2. Can the initial rate in the forward direction and the initial rate in the reverse direction be expressed in the form of a Michaelis-Menten rate equation If so, how If not, why ... 

The origin of Langmuir-Hinshelwood/Michaelis-Menten rate equations will be explored in Chapter 5. In the meanwhile, we will use this form of rate equation in Chapter 4, when we tackle some problems in sizing and analysis of ideal reactors. The next chapter is devoted to defining an ideal reactor and to providing the tools that are required for their sizing and analysis. 

Hinshelwood or Michaelis-Menten Rate Equation Against Experimental Data... 

We could construct residual plots for variables other than the fructose concentration. For example, it is common to plot the residuals against the measured values of the dependent variable, in this case the rate of fructose disappearance. We shall construct and discuss such a plot shortly, when we test a Michaelis-Menten rate equation against the data. 

Second Hypothesis Michaelis-Menten Rate Equation... 

Figtue 6-9e is one form of residual plot for the Michaelis-Menten rate equation. The values of the residuals generally are much smaller than they were for the first-order rate equation. Moreover, the scatter about the zero line is rather random. An equal munber of points fall above and below this line. 

Figure 6-9d Test of Michaelis-Menten rate equation for fructose isomerization at 70 °C using xylose isomerase derived from T. neapolitana.

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