Michaelis-Menten enzyme mechanism

In a Michaelis-Menten enzyme mechanism, what substrate concentrations (relative to Km) are needed for the reaction rate to be (a) 0.1 Vmax (ft) 0.25 Fmax (c) 0.5 Fmax (d) 0.9 Fmax ... 

As an example in this section, we consider the well-known Michaelis-Menten enzyme mechanism ... 

Figure 3.4 Simulation of Michaelis-Menten enzyme mechanism kinetics in closed system. Solid lines correspond to solution of Equations (3.27) with parameter values k+ = 1000 M-1 sec-1, k = 1.0 sec-1, k+2 = 0.1 sec-1, k-2 = 10M-1sec-1, and = 0.1mM. The initial conditions are a(0) = 1 mM, b 0) = 0, and c(0) = 0. Dashed lines correspond to the solution obtained by Equations (3.32).

Among the several ways of verifying or disproving such a reaction scheme (Chapter 9, Section 9.2), the derivation of a rate law linking a product formation rate or substrate consumption rate with pertinent concentrations of reactants, products, and auxiliary agents such as catalysts probably has the greatest utility, as conversion to product can be predicted. A proper rate law contains only observables, and no intermediates or other unobservable parameters. In enzyme catalysis, the first rate law was written in 1913 by Michaelis and Menten (the corresponding kinetics is therefore aptly named the Michaelis-Menten (MM) mechanism). 

Equation (3.31) is the standard form for the steady state flux though a simple reversible Michaelis-Menten enzyme. This expression obeys the equilibrium ratio arrived at above (b/a)eq = Keq = k+ k+2/(k- k-2), when Jmm(g, b) = 0. In addition, from the positive and negative one-way fluxes in Equation (3.30), we note that the relationship J+/J = Keq(a/b) = e AG/RT is maintained whether or not the system is in equilibrium. Thus, as expected, the general law of Equation (3.12) is obeyed by this reaction mechanism. 

Figure 4.2 Kinetic mechanism of a Michaelis-Menten enzyme. (A) The reaction mechanism for the irreversible case - Equation (4.1) - is based on a single intermediate-state enzyme complex (ES) and an irreversible conversion from the complex to free enzyme E and product P. (B) The reaction mechanism for the reversible case - Equation (4.7) - includes the formation of ES complex from free enzyme and product P. For both the irreversible and reversible cases, the reaction scheme is illustrated as a catalytic cycle.

The initial reaction rate of a catalyzed reaction versus the concentration of the substrate [>q (Eq. (9.39), where K, =k, /ki). The catalytic reaction could be homogeneous, heterogeneous or enzyme catalysis so long as it follows the simple catalytic mechanism. The substrate concentration, [X]. at a tate of half the maximum reaction rate, V, I2, defines in Michaelis-Menten enzyme kinetics. 

These experiments suggest that the secondary complexes should no longer be regarded as Michaelis-Menten enzyme substrate complexes but as reaction intermediates in the same sense that free radicals and semi-quinones are reaction intermediates, for all three classes of compounds provide a path for stepwise reactions. As a consequence the accepted mechanism for peroxidase action needs revision. 

To illustrate the complexity, we will take a simple case in which the enzymes typically follow the Michaelis-Menten kinetic mechanism. We will also make the following assumptions (a) only one ionic form of the enzyme is active (mono-protic), (b) no change occurs in RDS due to ionization, and (c) the enzyme maintains active conformation within the experimental pH range. For this type of enzyme, an observable quantity, e.g., rate constant (k), depends on the pH of the system as follows (i) the plot of k against pH resembles a titration curve, yielding at the inflection point the pK of the acid involved, (ii) the follows the ionization of the enzyme—substrate complex, (iii) the fC follows the ionizations of both the free enzyme and the enzyme—substrate complex, and (iv) the follows the ionization of the free enzyme only, even when there are multiple intermediates on the reaction pathway. 

According to this expression, a plot of 1/v, versus l/[SJo will yield a straight line if the data follow the Michaelis-Menten mechanism. This line has a slope given by Km/Vmax, a y intercept of 1/Vmax, and an x intercept of -1 fKm. This is also illustrated in Fig. 4-7. Again, this treatment is valid when Eq. (4-107) applies whether or not the catalyst is an enzyme. The Lineweaver-Burk plot, Fig. 4-lb, is convenient for visualization but statistically unreliable for data fitting the form in Eq. (4-107) should be used for numerical analysis. 

The kinetics of enzyme reactions were first studied by the German chemists Leonor Michaelis and Maud Menten in the early part of the twentieth century. They found that, when the concentration of substrate is low, the rate of an enzyme-catalyzed reaction increases with the concentration of the substrate, as shown in the plot in Fig. 13.41. However, when the concentration of substrate is high, the reaction rate depends only on the concentration of the enzyme. In the Michaelis-Menten mechanism of enzyme reaction, the enzyme, E, and substrate, S, reach a rapid preequilibrium with the bound enzyme-substrate complex, ES ... 

Michaelis—Menten mechanism A model of enzyme catalysis in which the enzyme and its substrate reach a rapid pre-equilibrium with the bound substrate-enzyme complex. 

Let us consider the basic enzyme catalysis mechanism described by the Michaelis-Menten equation (Eq. 2). It includes three elementary steps, namely, the reversible formation and breakdown of the ES complex (which does not mean that it is at equilibrium) and the decomposition of the ES complex into the product and the regenerated enzyme ... 

As the above discussion indicates, assigning mechanisms to simple anation reactions of transition metal complexes is not simple. The situation becomes even more difficult for a complex enzyme system containing a metal cofactor at an active site. Methods developed to study the kinetics of enzymatic reactions according to the Michaelis-Menten model will be discussed in Section 2.2.4. 

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 ... 

Enzyme mimics catalyze reactions by mechanisms which are demonstrably enzyme-like. The minimum requirement is that the reactions concerned should involve an initial binding interaction between the substrate and the catalyst. This gives rise to Michaelis-Menten kinetics reactivity is measured in terms of the familiar parameters kCat and Km and we use E to denote enzyme mimic as well as enzyme. ... 

Note that written in this form Eq. (106) retains the linear dependency of the rate on the total enzyme concentration Ej, typical for most Michaelis Menten mechanisms. The dependence on the substrate concentrations is approximated by a sum of nonlinear logarithmic terms [85, 86, 318, 320],... 

The necessity of developing approximate kinetics is unclear. It is sometimes argued that uncertainties in precise enzyme mechanisms and kinetic parameters requires the use of approximate schemes. However, while kinetic parameters are indeed often unknown, the typical functional form of generic rate equations, namely a hyperbolic Michaelis Menten-type function, is widely accepted. Thus, rather than introducing ad hoc functions, approximate Michaelis Menten kinetics can be utilized an approach that is briefly elaborated below. 

Analyses of enzyme reaction rates continued to support the formulations of Henri and Michaelis-Menten and the idea of an enzyme-substrate complex, although the kinetics would still be consistent with adsorption catalysis. Direct evidence for the participation of the enzyme in the catalyzed reaction came from a number of approaches. From the 1930s analysis of the mode of inhibition of thiol enzymes—especially glyceraldehyde-phosphate dehydrogenase—by iodoacetate and heavy metals established that cysteinyl groups within the enzyme were essential for its catalytic function. The mechanism by which the SH group participated in the reaction was finally shown when sufficient quantities of purified G-3-PDH became available (Chapter 4). 

The quantity of any given solute being presented to the reabsorptive mechanisms is determined by the product of the GFR and the solute concentration in plasma. One of the features of any carrier-mediated process is its limited capacity. Binding of a substance to its transport protein follows the same principles as substrate binding to an enzyme or hormone binding to its receptor so we may appropriately liken the dynamics to Michaelis-Menten kinetics. 

The usual starting point in enzyme kinetics is the Michaelis-Menten equation for the reaction rate v. This also seems a convenient starting point for interpretation of pressure effects on enzyme mechanisms. It will be shown that this formalism may be deceptive if the definitions and interpretations have not been made clear from the beginning. For the mechanism... 

In cases where the depuration of HOCs from BMOs involves enzyme-mediated biotransformations (Eq. 7.4) or active transport mechanisms, and environmental concentrations are high (e.g. near a point source), depuration rates have been shown to follow Michaelis-Menten kinetics (Spade and Hamelink, 1985). Michaelis-Menten kinetics is elicited when an enzyme or active transport system is saturated with a chemical. This type of kinetics is characterized by lower values of keS at sites with high HOC concentrations. If k s are unchanged at high concentration sites, Michaelis-Menten kinetics will result in elevated BAFs. However, if chemical concentrations become toxic, finfish likely avoid the area and sessile organisms such as mussels may close their valves for extended periods (Huckins et al., 2004). 

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