Michaelis constant equation

This equation predicts that the initial rate will be proportional to the initial enzyme concentration if the initial substrate concentration is held constant If the initial enzyme concentration is held constant the initial rate will be proportional to the substrate concentration at low substrate concentrations, and substantially independent of substrate concentration at high substrate levels. The maximum reaction rate is equal to k3Eo, and this product is often assigned the symbol The group ( 2 + 3)/ is often assigned the symbol K and is known as the Michaelis constant. Equation (7.3.28) can be written in terms of these parameters as... 

This has become known as the Michaelis-Menten equation, with rmax representing the maximum or limiting rate and Km being called the Michaelis constant. Equation 9.7 has been frequently expressed as ... 

Km for an enzymatic reaction are of significant interest in the study of cellular chemistry. From equation 13.19 we see that Vmax provides a means for determining the rate constant 2- For enzymes that follow the mechanism shown in reaction 13.15, 2 is equivalent to the enzyme s turnover number, kcat- The turnover number is the maximum number of substrate molecules converted to product by a single active site on the enzyme, per unit time. Thus, the turnover number provides a direct indication of the catalytic efficiency of an enzyme s active site. The Michaelis constant, Km, is significant because it provides an estimate of the substrate s intracellular concentration. 

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 1-108 can be considered as the Michaelis-Menten equation, where is the Michaelis constant and represented as... 

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. 

A noncompetitive inhibitor is one that binds to both E and E S. If both dissociation constants are the same, the Michaelis-Menten equation is... 

This form is worthwhile to note, in that many catalytic processes utilize dual substrates. The equation contains an apparent Michaelis constant, given by... 

In summary, the simple Michaelis-Menten form of Equation (12.1) is usually sufficient for first-order reactions. It has two adjustable constants. Equation (12.4) is available for special cases where the reaction rate has an interior maximum or an inflection point. It has three adjustable constants after setting either 2 = 0 (inhibition) or k = 0 (activation). These forms are consistent with two adsorptions of the reactant species. They each require three constants. The general form of Equation (12.4) has four constants, which is a little excessive for a... 

Coe and Bessell and coworkers studied the metabolic fates of 2-deoxy-2-fluoro-D-glucose (2DFG) and related compounds by using yeast hexokinase (as a model for mammalian hexokinase), and determined the kinetic constants K and V ) of the Michaelis-Menten equation D-glucose 0.17 (K in mAf)> 1 00 (relative value, D-glucose taken as 1) 2DG 0.59 0.11, 0.85 2DFG 0.19 0.03, 0.50 2-deoxy-2-fluoro-D-mannose (2DFM) 0.41 0.05, 0.85 2-deoxy-2,2-difluoro-D-nraZ>//Jo-hexose... 

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. 

In comparison with the case of a gas phase molecule that reacts in a monomole-cular reaction on a solid catalyst, the reciprocal of the Michaelis constant takes the place of the equilibrium constant of adsorption in the Langmuir-Hinshelwood equations. 

Because the rates of sugar binding to and dissociation from the transporter are very rapid compared to the rates of transporter re-orientation, the Michaelis constants for transport by the simple asymmetric carrier model are given by the following equations,... 

Using these equations, Lowe and Walmsley [48] have calculated the dissociation constants for sugar binding at the extracellular surface of the membrane (K s = b a in Fig. 2) and at the cytoplasmic surface (K. = elf = bid) x [dgich]) from the estimated rate constants for carrier re-orientation and the measured Michaelis constants. The dissociation constant for binding at the extracellular surface of the membrane, calculated in this way, is approximately lOmM and is largely unaffec-... 

One of the earliest approximations studied is to assume that the solute concentration is small or rapidly becomes small in comparison to the affinity constant for uptake. This then allows the nonlinear Michaelis-Menten equation to be approximated by ... 

Like Ks, the kinetic term Ku (which is commonly referred to as the Michaelis constant) has units of molarity. Considering Equation (2.12), if we were to fix the substrate concentration term to be equivalent to KM, the equation would reduce to... 

The first-order transfer and exit rate constants can be replaced by nonlinear terms dependent on the amount or concentration of drug in a particular compartment. For instance, saturable metabolism of drug in compartment 1 (the central compartment) would result in the Michaelis-Menten equation... 

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... 

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. 

The Km and Vj1iax of the Michaelis-Menten equation are actually made up of sums and products of little k s. You only have to look in most biochemistry texts to see a description of the derivation of the Michaelis-Menten equation in terms of little k s. The little k s are like quarks and leptons—you ve heard the names, but you re not quite sure what they are and even less sure about how they work. There s a section later (actually last) in the book if you haven t heard or can t remember about rate constants. 

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). 

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... 

For a constant-volume BR, integration of the Michaelis-Menten equation leads to a form that can also be linearized. Thus, from equation 10.2-9,... 

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