Enzymes Michaelis-Menten equation

Figure 11.1 A plot of the reaction rate as a function of the substrate concentration for an enzyme catalyzed reaction. Vmax is the maximal velocity. The Michaelis constant. Km, is the substrate concentration at half Vmax- The rate v is related to the substrate concentration, [S], by the Michaelis-Menten equation ...

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

Equation (3-150) is the Michaelis-Menten equation, Vm is the maximum velocity (for the enzyme concentration ,), and is the Michaelis constant. 

The Michaelis-Menten equation is, like Eq. (3-146), a rectangular hyperbola, and it can be cast into three linear plotting forms. The double-reciprocal form, Eq. (3-152), is called the Lineweaver-Burk plot in enzyme kinetics. ... 

If the kinetics of the reaction disobey the Michaelis-Menten equation, the violation is revealed by a departure from linearity in these straight-line graphs. We shall see in the next chapter that such deviations from linearity are characteristic of the kinetics of regulatory enzymes known as allosteric enzymes. Such regulatory enzymes are very important in the overall control of metabolic pathways. 

If the three-parameter Michaelis-Menten equation is divided by C i, it becomes the same as the three-parameter Langmuir-I linshelwood equation where 1/Cm = Ka. Both these rate equations can become quite complex when more than one species is competing with the reactant(s) for the enzyme or active sites on the solid catalyst. 

Enzyme kinetics. Data for reactions that follow the Michaelis-Menten equation are sometimes analyzed by a plot of v,/tA]o versus l/[A]o. This treatment is known as an Eadie-Hofstee plot. Following the style of Fig. 4-7b, sketch this function and label its features. 

The Michaelis constant is the substrate concentration at which is half the maximal velocity (V 3 /2) attainable at a particular concentration of enzyme. thus has the dimensions of substrate concentration. The dependence of initial reaction velocity on [S] and may be illustrated by evaluating the Michaelis-Menten equation under three conditions. 

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

Most often the binding of inhibitors to enzymes is measured by their effects on the velocity of the enzyme catalyzed reaction. In the absence of inhibitor, the velocity is defined by the Michaelis-Menten equation (Chapter 2) ... 

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... 

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. 

Table 18.2 lists 30 of the molecules used in this study that are known to be substrates for active transport or active efflux. The mechanistic ACAT model was modified to accommodate saturable uptake and saturable efflux using standard Michaelis-Menten equations. It was assumed that enzymes responsible for active uptake of drug molecules from the lumen and active efflux from the enterocytes to the lumen were homogeneously dispersed within each luminal compartment and each corresponding enterocyte compartment, respectively. Equation (5) is the overall mass balance for drug in the enterocyte compartment lining the intestinal wall. 

Each enzyme has a working name, a specific name in relation to the enzyme action and a code of four numbers the first indicates the type of catalysed reaction the second and third, the sub- and sub-subclass of reaction and the fourth indentifies the enzyme [18]. In all relevant studies, it is necessary to state the source of the enzyme, the physical state of drying (lyophilized or air-dried), the purity and the catalytic activity. The main parameter, from an analytical viewpoint is the catalytic activity which is expressed in the enzyme Unit (U) or in katal. One U corresponds to the amount of enzyme that catalyzes the conversion of one micromole of substrate per minute whereas one katal (SI unit) is the amount of enzyme that converts 1 mole of substrate per second. The activity of the enzyme toward a specific reaction is evaluated by the rate of the catalytic reaction using the Michaelis-Menten equation V0 = Vmax[S]/([S] + kM) where V0 is the initial rate of the reaction, defined as the activity Vmax is the maximum rate, [S] the concentration of substrate and KM the Michaelis constant which give the relative enzyme-substrate affinity. 

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 ... 

Mathematically, the Michaelis-Menten equation is the equation of a rectangular hyperbola. Sometimes you ll here reference to hyperbolic kinetics, this means it follows the Michaelis-Menten equation. A number of other names also imply that a particular enzyme obeys the Michaelis-Menten equation Michaelis-Menten behavior, saturation kinetics, and hyperbolic kinetics. 

If [S] = Km, the Michaelis-Menten equation says that the velocity will be one-half of Vmax. (Try substituting [S] for Km in the Michaelis-Menten equation, and you too can see this directly.) It s really the relationship between Km and [S] that determines where you are along the hyperbola. Like most of the rest of biochemistry, Km is backward. The larger the Km, the weaker the interaction between the enzyme and the substrate. Km is also a collection of rate constants. It may not be equal to the true dissociation constant of the ES complex (i.e., the equilibrium constant for ES E + S). 

The Km is a landmark to help you find your way around a rectangular hyperbola and your way around enzyme behavior. When [S] < Km (this means [S] + Km = Km), the Michaelis-Menten equation says that the velocity will be given by v = CVnvdepends linearly on [S], Doubling [S] doubles the rate. 

This relation is the broadly known Michaelis-Menten equation. The effect of substrate concentration ni on the rate predicted by this equation follows a characteristic pattern. Where substrate concentration is considerably smaller than the half saturation constant (ni <reactive intermediate EA depends on the availability of the substrate A. In this case, (mA + K A ) and reaction rate r+ given by 17.18 is proportional to mA. For the opposite case, (mA K ), little free enzyme E is available to complex with A. Now, (mA + mA and reaction... 

Figure 2.12 Graphical representation of the Michaelis-Menten equation for nonallosteric enzymes.

If a drug is a substrate of an enzyme, it will also be a competitive inhibitor of that enzyme, but it may be a competitive inhibitor without being a substrate. This is because the rate of product formation is determined by k3 of the Michaelis-Menten equation while the rate of ES substrate dissociation and degree of enzyme inhibition is determined by the ratio of A/a i as discussed above. If A 3 is very small it will not be experimentally measurable however, the enzyme will still be bound and occupied as determined by ki/k. ... 

The scaled elasticities of a reversible Michaelis Menten equation with respect to its substrate and product thus consist of two additive contributions The first addend depends only on the kinetic propertiesand is confined to an absolute value smaller than unity. The second addend depends on the displacement from equilibrium only and may take an arbitrary value larger than zero. Consequently, for reactions close to thermodynamic equilibrium F Keq, the scaled elasticities become almost independent of the kinetic propertiesof the enzyme [96], In this case, predictions about network behavior can be entirely based on thermodynamic properties, which are not organism specific and often available, in conjunction with measurements of metabolite concentrations (see Section IV) to determine the displacement from equilibrium. Detailed knowledge of Michaelis Menten constants is not necessary. Along these lines, a more stringent framework to utilize constraints on the scaled elasticities (and variants thereof) as a determinant of network behavior is discussed in Section VIII.E. 

It has been found experimentally that in most cases v is directly proportional to the concentration of enzyme [.E0] and that v generally follows saturation kinetics with respect to the concentration of substrate [limiting value called Vmax. This is expressed quantitatively in the Michaelis-Menten equation originally proposed by Michaelis and Menten. Km can be seen as an apparent dissociation constant for the enzyme-substrate complex ES. The maximal velocity Vmax = kcat E0. ... 

The expression for the effectiveness factor q in the case of zero-order kinetics, described by the Michaelis-Menten equation (Eq. 8) at high substrate concentration, can also be analytically solved. Two solutions were combined by Kobayashi et al. to give an approximate empirical expression for the effectiveness factor q [9]. A more detailed discussion on the effects of internal and external mass transfer resistance on the enzyme kinetics of a Michaelis-Menten type can be found elsewhere [10,11]. 

To achieve maximum velocity, a substrate concentration which is at least ten times greater than the Km value for the enzyme should be used. Although maximum velocity is only theoretically achieved at an infinite substrate concentration, it is possible using the Michaelis-Menten equation to calculate the percentage of maximum velocity given by any concentration of substrate. For a substrate concentration of ten times greater than the Km value the velocity (v) achieved will be ... 

The only rate-limiting factor in a coupled assay should be the concentration of the initial and linking products and all other reagents should be in excess. The role of the auxiliary and indicator enzymes is essentially that of a substrate assay system and under optimum assay conditions the rate of the indicator reaction should be equal to the rate of formation of the initial product. The indicator reaction must be capable of matching the different test reaction rates and its velocity can be defined by the Michaelis-Menten equation in the usual way ... 

Enzyme kinetics Michaelis constant, symbol iCm maximum velocity of an enzyme catalysed reaction, Vm DC inhibitor constant, symbol X Michaelis-Menten equation and graph in the absence and the presence of inhibitors. Lineweaver-Burke and Eadie-Hofstee plots. 

Michaelis-Menten equation predicts the rate of a biological reaction according to the concentration of substrate and the specific enzyme characteristics ... 

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