Michaelis Menten rate equation kinetics

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. ... 

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. 

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... 

Most problems associated with approximate kinetics are avoided when Michaelis Menten-type rate equations are utilized. Though this choice sacrifices the possibility of analytical treatment, reversible Michaelis Menten-type equations are straightforwardly consistent with fundamental thermodynamic constraints, have intuitively interpretable parameters, are computationally no more demanding than logarithmic functions, and are well known to give an excellent account of biochemical kinetics. Consequently, Michaelis Menten-type kinetics are an obvious choice to translate large-scale metabolic networks into (approximate) dynamic models. It should also be emphasized that simplified Michaelis Menten kinetics are common in biochemical practice almost all rate equations discussed in Section III.C are simplified instances of more complicated rate functions. 

The generalized parameters are invariant with respect to different functional forms of the rate equation. All results hold for a large class of biochemical rate functions [84], For example, the Michaelis Menten rate function used in Eq. (133) is not the only possible choice. A number of alternative rate equations are summarized in Table VI. Although in each case the specific kinetic parameters may differ, each rate equation is able to generate a specified partial derivative and is thereby consistent with results obtained from an analysis of the corresponding Jacobian. Note that, obviously, not each rate equation is capable to generate each possible Jacobian. However, vice versa, for each possible Jacobian there exists a class of rate equations that is consistent with the Jacobian. 

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 ... 

The deviation of the reaction rate 31, from the rectangular hyperbola which would be shown by a true Michaelis-Menten reaction law, is best illustrated by considering the data as represented by an Eadie-Hofstee plot. The original equation for the Michaelis-Menten or Monod kinetics ... 

Using a similar approach to that used in the derivation of the Michaelis-Menten model, the kinetic equations of the peroxidase-catalyzed removal of an aromatic substrate were derived from the reaction pathways illustrated in Fig. 2 [92]. The rate of change of the aromatic compound concentration can be written as... 

Often the key entity one is interested in obtaining in modeling enzyme kinetics is the analytical expression for the turnover flux in quasi-steady state. Equations (4.12) and (4.38) are examples. These expressions are sometimes called Michaelis-Menten rate laws. Such expressions can be used in simulation of cellular biochemical systems, as is the subject of Chapters 5, 6, and 7 of this book. However, one must keep in mind that, as we have seen, these rates represent approximations that result from simplifications of the kinetic mechanisms. We typically use the approximate Michaelis-Menten-type flux expressions rather than the full system of equations in simulations for several reasons. First, often the quasi-steady rate constants (such as Ks and K in Equation (4.38)) are available from experimental data while the mass-action rate constants (k+i, k-i, etc.) are not. In fact, it is possible for different enzymes with different detailed mechanisms to yield the same Michaelis-Menten rate expression, as we shall see below. Second, in metabolic reaction networks (for example), reactions operate near steady state in vivo. Kinetic transitions from one in vivo steady state to another may not involve the sort of extreme shifts in enzyme binding that have been illustrated in Figure 4.7. Therefore the quasi-steady approximation (or equivalently the approximation of rapid enzyme turnover) tends to be reasonable for the simulation of in vivo systems. 

The Michaelis-Menten Formalism did not anticipate the type of enzyme-enzyme organization described above. One of its fundamental assumptions has been that complexes do not occur between different forms of an enzyme or between different enzymes (Segal, 1959 Webb, 1963 Cleland, 1970 Segel, 1975 Wong, 1975). From the derivation of the classical Michaelis-Menten rate law, it can be seen that such complexes must be excluded or they will destroy the linear structure of the kinetic equations. 

This rate equation is called Michaelis-Menten double substrate kinetics . It is a formal multiplication of two Michaelis-Menten models for both substrates A and B. This model can be used to describe rate kinetics of two substrate reactions in the absence of the product(s). The kinetic measurements have to be performed by varying the concentration of one substrate keeping the concentration of the second substrate at a constant value well above the Km value. The model cannot be used if back reactions occur and an equilibrium has to be described by an appropriate Haldane equation. 

If the concentrations of the products P and Q in the models summarized in Table 7-1 are set to zero, the resulting rate equations will be identical to Eq. (44) in all cases with the exception of the ping-pong mechanism. This means that the Michaelis-Menten double substrate kinetics is valid under the above circumstances. 

Most enzymes catalyse reactions and follow Michaelis-Menten kinetics. The rate can be described on the basis of the concentration of the substrate and the enzymes. For a single enzyme and single substrate, the rate equation is ... 

The above rate equation is in agreement with that reported by Madhav and Ching [3]. Tliis rapid equilibrium treatment is a simple approach that allows the transformations of all complexes in terms of [E, [5], Kls and Kjp, which only deal with equilibrium expressions for the binding of the substrate to the enzyme. In the absence of inhibition, the enzyme kinetics are reduced to the simplest Michaelis-Menten model, as shown in Figure 5.21. The rate equation for the Michaelis-Menten model is given in ordinary textbooks and is as follows 11... 

The parameters of the Monod cell growth model are needed i.e. the maximum specific growth rate and the Michaelis-Menten constant are required for a suitable rate equation. Based on the data presented in Tables 10.1 and 10.2, obtain kinetic parameters for... 

Kinetic data fitting the rate equation for catalytic reactions that follow the Michaelis-Menten equation, v = k A]/(x + [A]), with[A]0 = 1.00 X 10 J M, k = 1.00 x 10 6 s 1, and k = 2.00 X 10-J molL1. The left panel displays the concentration-time profile on the right is the time lag approach. 

A classical non-linear model of chemical kinetics is defined by the Michaelis-Menten equation for rate-limited reactions, which has already been mentioned in Section 39.1.1 ... 

The reaction rate for this enzyme kinetics example is expressed by the Michaelis-Menten equation and with product inhibition. 

In our previous work [63], we studied the hydrolysis kinetics of lipase from Mucor javanicus in a modified Lewis cell (Fig. 4). Initial hydrolysis reaction rates (uri) were measured in the presence of lipase in the aqueous phase (borate buffer). Initial substrate (trilinolein) concentration (TLj) in the organic phase (octane) was between 0.05 and 8 mM. The presence of the interface with octane enhances hydrolysis [37]. Lineweaver-Burk plots of the kinetics curve (1/Uj.] = f( /TL)) gave straight lines, demonstrating that the hydrolysis reaction shows the expected kinetic behavior (Michaelis-Menten). Excess substrate results in reaction inhibition. Apparent parameters of the Michaelis equation were determined from the curve l/urj = f /TL) and substrate inhibition was determined from the curve 1/Uj.] =f(TL) ... 

Let us consider the determination of two parameters, the maximum reaction rate (rITOIX) and the saturation constant (Km) in an enzyme-catalyzed reaction following Michaelis-Menten kinetics. The Michaelis-Menten kinetic rate equation relates the reaction rate (r) to the substrate concentrations (S) by... 

A kinetic model describing the HRP-catalyzed oxidation of PCP by H202 should account for the effects of the concentrations of HRP, PCP, and H202 on the reaction rate. To derive such an equation, a reaction mechanism involving saturation kinetics is proposed. Based on the reaction scheme described in Section 17.3.1, which implies that the catalytic cycle is irreversible, the three distinct reactions steps (Equations 17.2 to 17.4) are modified to include the formation of Michaelis-Menten complexes ... 

This equation is fundamental to all aspects of the kinetics of enzyme action. The Michaelis-Menten constant, KM, is defined as the concentration of the substrate at which a given enzyme yields one-half of its maximum velocity. is the maximum velocity, which is the rate approached at infinitely high substrate concentration. The Michaelis-Menten equation is the rate equation for a one-substrate enzyme-catalyzed reaction. It provides the quantitative calculation of enzyme characteristics and the analysis for a specific substrate under defined conditions of pH and temperature. KM is a direct measure of the strength of the binding between the enzyme and the substrate. For example, chymotrypsin has a Ku value of 108 mM when glycyltyrosinylglycine is used as its substrate, while the Km value is 2.5 mM when N-20 benzoyltyrosineamide is used as a substrate... 

Microbial Biotransformation. Microbial population growth and substrate utilization can be described via Monod s (35) analogy with Michaelis-Menten enzyme kinetics (36). The growth of a microbial population in an unlimiting environment is described by dN/dt = u N, where u is called the "specific growth rate and N is microbial biomass or population size. The Monod equation modifies this by recognizing that consumption of resources in a finite environment must at some point curtail the rate of increase (dN/dt) of the population ... 

The kinetics of the general enzyme-catalyzed reaction (equation 10.1-1) may be simple or complex, depending upon the enzyme and substrate concentrations, the presence/absence of inhibitors and/or cofactors, and upon temperature, shear, ionic strength, and pH. The simplest form of the rate law for enzyme reactions was proposed by Henri (1902), and a mechanism was proposed by Michaelis and Menten (1913), which was later extended by Briggs and Haldane (1925). The mechanism is usually referred to as the Michaelis-Menten mechanism or model. It is a two-step mechanism, the first step being a rapid, reversible formation of an enzyme-substrate complex, ES, followed by a slow, rate-determining decomposition step to form the product and reproduce the enzyme ... 

Substrate-limited growth in terms of reduced availability of both the electron donor and the electron acceptor is common in wastewater of sewer systems. Based on the concept of Michaelis-Menten s kinetics for enzymatic processes, Monod (1949) formulated, in operational terms, the relationship between the actual and the maximal specific growth rate constants and the concentration of a limiting substrate [cf. Equation (2.14)] ... 

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