Michaelis-Menten model applicability

The kinetics of biochemical processes may be simple or complex, depending on the number of variables having a significant influence. One of the simplest approach but with wide applications is the Michaelis-Menten model. The enzymatic reaction takes place by a two-step mechanism ... 

The Michaelis-Menten model has greatly assisted the development of enzyme chemistry. Its virtues are simplicity and broad applicability. However, the Michaelis-Menten model cannot account for the kinetic properties of many enzymes. An important group of enzymes that do not obey Michaelis-Menten kinetics comprises the allosteric enzymes. These enzymes consist of multiple subunits and multiple active sites. 

The Michaelis-Menten model has greatly assisted the development of en-zymology. Its virtues are simplicity and broad applicability. However, the... 

Perhaps the most elementary consideration that should be satisfied is that the measured rates of enzyme reactions under aU conditions represent initial velocities (vq). The indication that initial rates or linear rates were measured are other ways to convey that this standard of experimentation has been met. One of the original stipulations of the general applicability of the Michaelis-Menten model (as well as many others) is that d[So /dt 0 during the time period over which the rate of product formation is measured. Thus, the measured reaction rate is representative of that taking place initially at the [So] selected. This condition is especially important at low [Sol values, where reaction rates are nearly first order with respect to [Sol- In practice, up to 5 to 10% depletion of [Sol can be tolerated over the time frame used to assay [P] for the purpose of determining reaction rates, because error caused by normal experimental... 

To make an appropriate assessment of the pattern of inhibition, one need only compare the pattern of reaction velocity versus [S] observed relative to the pattern predicted from an application of the hyperbolic kinetics model. This requires making an estimate of V ax and from the data available. Transforming the original data to a Lineweaver-Burke plot (despite the aforementioned limitations) indicates that only four data points (at low [S]) can be used to estimate Vmax and Km (as 3.58 units and 0.48 mM, respectively. Fig. 14.10). The predicted (uninhibited) behavior of the enzyme activity can now be calculated by applying the rectangular hyperbola [Eq. (14.5)] (yielding the upper curve in Fig. 14.11), and it becomes clear that inhibition was obvious at [S] <1 mM. The degree of inhibition is expressed appropriately as the difference between observed and predicted activity at any [S] value, if one makes interpretations within the context of the Michaelis-Menten model. 

In order to predict the effect of a mixture of chemicals with the same target receptor, but with different nonlinear dose-effect relationships, either physiological or mathematical modeling can be applied. For interactions between chemicals and a target receptor or enzyme, the Michaelis-Menten kinetics (first order kinetics but with saturation) are often applicable. This kind of action can then be considered a special case of similar combined action (dose addition). 

Tewis DL, Holm HW, Hodson RE. 1984. Application of single and multiphasic Michaelis-Menten kinetics to predictive modeling for aquatic ecosystems. Env Tox Chem 3 563-574. 

With deeper understanding of the rate laws applicable to these hydrolases, now we need to deduce the parameters that combine to give corresponding khl0 values for Michaelis-Menten cases (Eq. 17-80). We may now see that the mathematical form we used earlier to describe the biodegradation of benzo[f]quinoline (Eq. 17-82) could apply in certain cases. Further we can rationalize the expressions used by others to model the hydrolysis of other pollutants when rates are normalized to cell numbers (e.g., Paris et al., 1981, for the butoxyethylester of 2,4-dichlorophenoxy acetic acid) or they are found to fall between zero and first order in substrate concentration (Wanner et al., 1989, for disulfoton and thiometon). 

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]... 

The effects of macromolecules other than surfactants on the rates of organic reactions have been investigated extensively (Morawetz, 1965). In many cases, substrate specificity, bifunctional catalysis, competitive inhibition, and saturation (Michaelis-Menten) kinetics have been observed, and therefore these systems also serve as models for enzyme-catalyzed reactions and, in these and other respects, resemble micellar systems. Indeed, in some macromolecular systems micelle formation is very probable or is known to occur, and in others mixed micellar systems are likely. Recent books and reviews should be consulted for a more detailed description of macromolecular systems and for their applicability as models for enzymatic catalysis and other complex interactions (Morawetz, 1965 Bruice and Benkovic, 1966 Davydova et al., 1968 Winsor, 1968 Jencks, 1969 Overberger and Salamone, 1969). 

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. ... 

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,... 

Early applications of the transform-both-sides approach generally were done to transform a nonlinear problem into a linear one. One of the most common examples is found in enzyme kinetics. Given the Michae-lis-Menten model of enzyme kinetics... 

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 first application of the QSSA is usually attributed to Bodenstein (Bodenstein 1913 Bodenstein and Lutkemeyer 1924), but Chapman and Underhill (1913) and Semenov (1939, 1943) were also early users of the technique. Further pioneers of the application of the QSSA are Michaelis and Menten (1913) and Briggs and Haldane (1925). The history of the application of the QSSA can be divided into three periods (Turanyi et al. 1993b). In the early period (1913-1960), accurate experimental data for various applications were obtained and compared with solutions of simple kinetic systems of differential equations that were formulated to model the experimental behaviour. Due to the limited availability of computer power during this time, the kinetic DDEs had to be solved analytically and using the QSSA helped to convert the systems into an analytically solvable form. 

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