Enzymes Michaelis constant

These considerations can be explained from a theoretical point of view as follows considering the response in the transient time and at the steady state. The concentration of the substrate and product at the transducer depends on the enzyme Michaelis constant K, the activity of the enzymatic layer, the thickness of the layer, and the diffusion coefficients of the substrate and of the product. The product concentration at the external surface of the electrode is assumed to be zero because the diffusion of the species occurs in the active layer. The temperature, K , and coefficient of diffusion and Dp (diffusion... 

The response of an enzyme sensor in the steady state depends largely on the ratio of the substrate concentration [5] to the enzyme Michaelis constant K. When [S K is large, the reaction rate reaches a maximal value V,, which is proportional to the number of active sites of the immobilized enzyme. The reaction rate is independent of the substrate concentration, and the product concentration at the contact with the electrode is the same for all high substrate concentration. The quantify of enzyme in the layer determines the linear zone in the response to the substrate concentration. This zone corresponds to first-order kinetics with respect to substrate concentration, whereas the region with a plateau has zeroth-order kinetic. When the substrate concentration is very high([5] K ), the biosensor is no longer capable of determining the substrate but may determine inhibitors which affect the minimal rate of the enzymatic reaction... 

Both threonine aldolases were demonstrated to be pyridoxal phosphate-dependent and to be sulfhydryl enzymes. Michaelis constants were calculated to have the values of 69 X 10 M for L-threonine and 4.25 X 10 M for L-allothreonine. 

The response of an enzyme sensor in the steady state depends largely on the ratio of the substrate concentration [S] to the enzyme Michaelis constant K , (Figure 4.3). When [S]/K is large, the reaction rate reaches a maximal value V . which is proportional to the number of active sites of the immobilized enzyme. The reaction rate is then... 

The detectable product concentration [P]e is proportional to the concentration of the substrate [S]o, provided that the latter is small compared with the enzyme Michaelis constant. This confirms the results of the digital simulation in log-log coordinates, and from Equation (8) we obtain ... 

Michaelis constant An experimentally determined parameter inversely indicative of the affinity of an enzyme for its substrate. For a constant enzyme concentration, the Michaelis constant is that substrate concentration at which the rate of reaction is half its maximum rate. In general, the Michaelis constant is equivalent to the dissociation constant of the enzyme-substrate complex. 

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 ...

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 constant has the units of a dissociation constant however, the dissociation constant of the enzyme—substrate complex is k dk, which is not equal to Km unless k 2-... 

The Michaelis constant (fCM) is an index of the stability of an enzyme-substrate complex. Does a high Michaelis constant indicate a stable or an unstable enzyme-substrate complex Explain your reasoning. 

If, as it is usually done, the interaction of enzyme with glycal is studied in the presence of substrate S having Michaelis constant K , the observed rate constant k pp, for the approach to the steady-state inhibition has to be corrected for the competition of substrate for the free enzyme, in order to calculate the rate constants kp , kp, and k yj, from the experimental data. 

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. 

Stated another way, the smaller the tendency of the enzyme and its substrate to dissociate, the greater the affinity of the enzyme for its substrate. While the Michaelis constant often approximates the dissociation constant fCj, this is by no means always the case. For a typical enzyme-catalyzed reaction,... 

Maximal speed (Vmax) and supposed Michaelis constant (K ) of pectin hydrolysis reaction (catalyzed by the studied pectinesterase) were determined in Zinewedwer — Berk coordinated, They were determined in the range of substrate concentration values that was below optimum one V = 14.7 10 M min K = 5.56 10 M. The value of dissociated constant (KJ of the triple enzyme—substrate complex was determined from the experimental data at high substrate concentration. It was the following Kj= 0.22 M. Bunting and Murphy method was used for determination. 

Important inherent characteristics of an enzyme that should be considered are the substrate affinity, characterized by the Michaelis constant the rate of turnover fecat> providing the catalytic efficiency fecat/ M. and the catalytic potential. Several attempts to compare enzyme catalysis with that of platinum have been published. Direct comparisons are difficult, because enzyme electrodes must be operated in aqueous electrolyte containing dissolved substrate, whereas precious metal electrodes aie often supplied with a humidified gaseous stream of fuel or oxidant, and produce water as steam. It is not straightforward to compare tme optimal turnover rates per active site, as it is often unclear how many active sites are being engaged in a film of enzyme on an electrode. 

E I is a kinetic chimera Kj and kt are the constants characterizing the inactivation process kt is the first-order rate constant for inactivation at infinite inhibitor concentration and K, is the counterpart of the Michaelis constant. The k,/K, ratio is an index of the inhibitory potency. The parameters K, and k, are determined by analyzing the data obtained by using the incubation method or the progress curve method. In the incubation method, the pseudo-first-order constants /cobs are determined from the slopes of the semilogarithmic plots of remaining enzyme activity... 

The kinetic data below were reported for an enzyme catalyzed reaction of the type E + S ES E + P. Since the data pertain to initial reaction rates, the reverse reaction may be neglected. Use a graphical method to determine the Michaelis constant and Fmax for this system at the enzyme concentration employed. 

The turnover number of an enzyme is defined as the maximum number of moles of substrate reacted per mole of enzyme (or molecules per molecule) per minute under optimum conditions (i.e., saturating substrate concentration, optimum pH, etc). If 2 mg/cm3 of a pure enzyme (50,000 molecular weight, Michaelis constant Km = 0.03 mole/m3) catalyzes a reaction at a rate of 2.5 jumoles/nUksec when the substrate concentration is 5 x 10 3 moles/m3, determine the turnover number corresponding to this definition and the actual number of moles of substrate reacting per minute per mole of enzyme. 

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. 

These values are then plotted against 1/C . The slope of this linear secondary plot provides k, while the intercept gives the value of I /k 2 + 1/ 2 2- It follows that the two rate constants k 2 and k22 may not be derived separately from this type of experiment. The same is, of course, true for the two Michaelis constants. One has to know the value of one of them independently, or at least know that one is much larger than the other. Dealing with redox enzymes, the variations of the intercept in a series of cosubstrates of increasing reducing power may be used to solve the problem. Indeed, if for the most reducing cosubstrates, the intercept becomes independent of the cosubstrate, one is entitled to conclude that it represents the value of l/k t2. The procedure is illustrated with an experimental example in the next section. 

The inhibition can be interpreted as an increase of the Michaelis constant KM. In the case of uncompetitive inhibition (Fig. 9B), the binding of the substrate to the enzyme is not affected. However, the [ES] complex becomes inactive upon binding of the inhibitor Using Kj —> oo, the corresponding rate equation is... 

In contrast to the condition specificity of the Vm values, the binding constants of metabolite to enzymes, the Michaelis constants Km, are not dependent on enzyme concentration but rather result from the structure and amino acid... 

The dissociation constant of the complicated equilibrium involving the enzyme-substrate complex is known as the Michaelis constant, Km, and involves the rate constants for each of the four reactions involving the ES complex kn I kl... 

The value for the maximum velocity is related to the amount of enzyme used but the Michaelis constant is peculiar to the enzyme and is a measure of the activity of the enzyme. Enzymes with large values for Km show a reluctance to dissociate from the substrate and hence are often less active than enzymes with low Km values. The substrate concentration required for a particular enzyme assay is related to and when developing an assay, the value for Km should be determined. 

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