Michaelis-Menten equation applicability

Although the Michaelis-Menten equation is applicable to a wide variety of enzyme catalyzed reactions, it is not appropriate for reversible reactions and multiple-substrate reactions. However, the generalized steady-state analysis remains applicable. Consider the case of reversible decomposition of the enzyme-substrate complex into a product molecule and enzyme with mechanistic equations. 

Km and Umax have different meanings for different enzymes. The limiting rate of an enzyme-catalyzed reaction at saturation is described by the constant kcat, the turnover number. The ratio kcat/Km provides a good measure of catalytic efficiency. The Michaelis-Menten equation is also applicable to bisubstrate reactions, which occur by ternary-complex or Ping-Pong (double-displacement) pathways. 

An equation of the form of Eq. (2.32) was given by Langmuir (Carberry, 1976) for the treatment of data from the adsorption of gas on a solid surface. If the Michaelis-Menten equation is applicable, the Langmuir plot will result in a straight line, and the slope will be equal to l/rmax. The intercept will be KM/rmax, as shown in Figure 2.5. 

This is an important question that has been addressed by many enzyme kineticists over the years. For the correct application of the Briggs-Haldane steady-state analysis, in a closed system, [S]0 must be >[E](), where the > sign implies a factor of at least 1,000. M. F. Chaplin in 1981 noted that the expression v0= V max[S]c/(Km + [S]0 + [E]0) yields, for example, only a 1 percent error in the estimate of v() for [S]0 = 10 x [E]0 and [S]0 = 0.1 Km the expression thus applies under much less stringent conditions than does the simple Michaelis-Menten equation. In open systems [S]0 can approximate [E]0 and a steady state of enzyme-substrate complexes can pertain computer simulation of both types of system is the best way to gain insight into the conditions necessary for a steady state of the complex. 

The Michaelis-Menten equation is also applicable if E is present in large excess, in which case the concentration [E] appears in the equation instead of [S]. 

Magnetic moment, 153, 155, 160 Magnetic quantum number, 153 Magnetization, 160 Magnetogyric ratio, 153, 160 Main reaction, 237 Marcus equation, 227, 238, 314 Marcus plot, slope of, 227, 354 Marcus theory, applicability of, 358 reactivity-selectivity principle and, 375 Mass, reduced, 189, 294 Mass action law, 11, 60, 125, 428 Mass balance relationships, 19, 21, 34, 60, 64, 67, 89, 103, 140, 147 Maximum velocity, enzyme-catalyzed, 103 Mean, harmonic, 370 Mechanism classification of. 8 definition of, 3 study of, 6, 115 Medium effects, 385, 418, 420 physical theories of, 405 Meisenheimer eomplex, 129 Menschutkin reaction, 404, 407, 422 Mesomerism, 323 Method of residuals, 73 Michaelis constant, 103 Michaelis—Menten equation, 103 Microscopic reversibility, 125... 

Interestingly, a fully appropriate model was developed at the same time as the Langmuir model using a similar basic approach. This is the Michaelis-Menten equation which has proved to be so useful in the interpretation of enzyme kinetics and, thereby, understanding the mechanisms of enzyme reactions. Another advantage in using this model is the fact that a graphical presentation of the data is commonly used to obtain the reaction kinetic parameters. Some basic concepts and applications will be presented here but a more complete discussion can be found in a number of texts. ... 

Spreadsheet Summary The second exercise in Chapter 13 of Applications of Microsoft Excel in Analytical Chemistry involves enzyme catalysis. A linear transformation is made so that the Michaelis constant, K, and the maximum velocity, can be determined from a least-squares procedure. The nonlinear regression method is used with Excel s Solver to find these parameters by fitting them into the nonlinear Michaelis-Menten equation. 

A model for enzyme kinetics that has found wide applicability was proposed by Michaelis and Menten in 1913 and later modified by Briggs and Haldane. The Michaelis-Menten equation relates the initial rate of an enzyme-catalyzed reaction to the substrate concentration and to a ratio of rate constants. This equation is a rate equation,... 

If the Michaelis-Menten equation is applicable, the Langmuir plot of Cs/r versus Q will result in a straight line with slope l/r and intercept Similarly, the Lineweaver-Burk plot of 1/r... 

The Michaelis-Menten equation (8.8) and the irreversible Uni Uni kinetic scheme (Scheme 8.1) are only really applicable to an irreversible biocatalytic process involving a single substrate interacting with a biocatalyst that comprises a single catalytic site. Hence with reference to the biocatalyst examples given in Section 8.1, Equation (8.8), the Uni Uni kinetic scheme is only really directly applicable to the steady state kinetic analysis of TIM biocatalysis (Figure 8.1, Table 8.1). Furthermore, even this statement is only valid with the proviso that all biocatalytic initial rate values are determined in the absence of product. Similarly, the Uni Uni kinetic schemes for competitive, uncompetitive and non-competitive inhibition are only really applicable directly for the steady state kinetic analysis for the inhibition of TIM (Table 8.1). Therefore, why are Equation (8.8) and the irreversible Uni Uni kinetic scheme apparently used so widely for the steady state analysis of many different biocatalytic processes A main reason for this is that Equation (8.8) is simple to use and measured k t and Km parameters can be easily interpreted. There is only a necessity to adapt catalysis conditions such that... 

Allosteric enzymes exhibit different behaviors compared to nonallosteric enzymes, and the Michaelis-Menten equations are not applicable. 

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). 

Please note, these approximations are all dealing with the simple reaction sequence from Scheme 4.2. The application of e.g. the King-Altman method for multistep reactions will lead to the Michaelis-Menten equation in its typical form but with much more complex values for and Vkf The typical curve resulting from applying eqn (4.1) with = 4at = 1 is shown in Figure 4.1 adapted from ref. 26. 

A plot of 1/rate versus 1/[S], the inverse of the substrate concentration, gives a straight line with slope K/ k2[Eo ) and y-intercept 1/V. Equation 20.68 is called the Michaelis-Menten equation, and a plot of 1/rate versus 1/[S] is called a Lineweaver-Burk plot. An example of such a plot is shown in Figure 20.18. This is one common application of the steady-state approximation to enzyme kinetics. 

Such an effect can be useful in the case of enzymatic substrate determinations (cf. 2.6.1.3). When inhibitor activity is absent, i. e. [I] = 0, Equation 2.72 is transformed into the Michaelis-Menten equation (Equation 2.41). The Line-weaver-Burk plot (Fig. 2.30a) shows that the intercept 1 /V with the ordinate is the same in the presence and in the absence of the inhibitor, i. e. the value of V is not affected although the slopes of the lines differ. This shows that the inhibitor can be fully dislodged by the substrate from the active site of the enzyme when the substrate is present in high concentration. In other words, inhibition can be overcome at high substrate concentrations (see application in Fig. 2.49). The inhibitor constant, Ki, can be calculated from the corresponding intercepts with the abscissa in Fig. 2.30a by calculating the value of from the abscissa intercept when [I] = 0. 

Covering key topics such as the critical point of a van der Waals gas, the Michaelis-Menten equation, and the entropy of mixing, this classroom-tested text highlights applications across the range of chemistry, forensic science, pre-medical science and chemical engineering. In a presentation of fundamental topics held together by clearly established mathematical models, the book supplies a quantitative discussion of the merged science of physical chemistry. 

The following section deals with kinetic equations for the simple Michaelis-Menten kinetics with more than two intermediates subsequently, their application for the interpretation of hydrogenations in practical examples is discussed. 

Figure 5. Application of Michaelis— Menten—Lineweaver—Burk s equation (PVPA 0.1 g, H20 10 cm3 85°C, 3 hr, P c indicates the degree of polymerization of poly-MMA)...

Furthermore, it can be shown that, in the limiting cases of first-order kinetics [Equation (11.35) also holds for this case] and zero-order kinetics, the equal and optimal sizes are exactly the same. As shown, the optimal holding times can be calculated very simply by means of Equation (11.40) and the sum of these can thus be used as a good approximation for the total holding time of equal-sized CSTRs. This makes Equation (11.31) an even more valuable tool for design equations. The restrictions are imposed by the assumption that the biocatalytic activity is constant in the reactors. Especially in the case of soluble enzymes, for which ordinary Michaelis-Menten kinetics in particular apply, special measures have to be taken. Continuous supply of relatively stable enzyme to the first tank in the series is a possibility, though in general expensive. A more attractive alternative is the application of a series of membrane reactors. 

The Hill equation is used to estimate Km for allosteric enzymes. Equations based on classic Michaelis-Menten kinetics are not applicable. 

Due to the formation of an intermediate complex, this type of reaction mechanism was described as being analogous to Michaelis-Menten kinetics [39]. A common error made when examining the behaviour of systems of this type is to use the Koutecky-Levich equation to analyse the rotation speed-dependence of the current. This is incorrect because the Koutecky-Levich analysis is only applicable to surface reactions obeying strictly first-order kinetics. Applying the Koutecky-Levich analysis to situations where the surface kinetics are non-linear, as in this case, leads to erroneous values for the rate constants. Below, we present the correct treatment for this problem based on an extension of a model originally developed by Albery et al. [42]... 

In the previous chapter it was shown that the simple chemostat produces competitive exclusion. It could be argued that the result was due to the two-dimensional nature of the limiting problem (and the applicability of the Poincare-Bendixson theorem) or that this was a result of the particular type of dynamics produced by the Michaelis-Menten hypothesis on the functional response. This last point was the focus of some controversy at one time, inducing the proposal of alternative responses. In this chapter it will be shown that neither additional populations nor the replacement of the Michaelis-Menten hypothesis by a monotone (or even nonmonotone) uptake function is sufficient to produce coexistence of the competitors in a chemostat. This illustrates the robustness of the results of Chapter 1. It will also be shown that the introduction of differing death rates (replacing the parameter D by D, in the equations) does not change the competitive exclusion result. 

The term should be used for enzymes that display Michaelis-Menten kinetics. Thus, it is not used with allosteric enzymes. Technically, competitive and noncompetitive inhibition are also terms that are restricted to Michaelis-Menten enzymes, although the concepts are applicable to any enzyme. An inhibitor that binds to an allosteric enzyme at the same site as the substrate is similar to a classical competitive inhibitor. One that binds at a different site is similar to a noncompetitive inhibitor, but the equations and the graphs characteristic of competitive and noncompetitive inhibition don t work the same way with an allosteric enzyme. 

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