Enzyme Michaelis-Menten constant

When whole cell containing plural enzymes with opposite selectivities and different (Michaelis-Menten constant) values are used, problems of low selectivities occur. If the substrate concentration is decreased, one of the enzymes with low Kra value catalyzes the reaction so that the selectivity can be improved. 

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... 

The question arises as to whether comparisons with protein enzymes are justified. In other words, what can ribozymes really do An important parameter for measuring the efficiency of enzymes is the value of kc-JK. This quotient is derived from the values of two important kinetic parameters kc-Al is a rate constant, also called turnover number, and measures the number of substrate molecules which are converted by one enzyme molecule per unit time (at substrate saturation of the enzyme). Km is the Michaelis-Menten constant it corresponds to the substrate concentration at which the rate of reaction is half its maximum. 

The Michaelis-Menten constant defined by Eq. 11, is the equilibrium constant for the dissociation of he ES complex and is inversely related to the affinity of the enzyme for the substrate, therefore, a low KM value reflects high affinity ... 

Hydrolysis of methyl hydrocinnamate is catalyzed by the enzyme chymotripsin. Data were obtained at 25 C with pH k7.6 and a constant enzyme concentration. These are of initial reaction rate, mol/1iter-sec, and corresponding initial substrate concentrations. Find the Michaelis-Menten constants. 

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 is essential to maintain high maximal velocities of enzymatic activity for the attainment of optimal therapeutic efficacy. As a general rule, only enzymes whose Michaelis-Menten constants lie between 1—100 xM are effective as drugs (16) because most substrates for therapeutically useful enzymes are present in body fluids and cells at siihmillimolar concentrations. 

Calculate (a) the value of Michaelis-Menten constants of the enzyme, Ks, and (b) the dissociation constant of enzyme-inhibitor complex, fCj [Contributed by Professor Gary F. Bennett, The University of Toledo, Toledo, OH]... 

It can be shown that Km equals the concentration of the substrate at which the reaction velocity is one half of its maximum. The Michaelis-Menten constant is an important figure of merit for the enzyme. It is the measure of its activity. Although it describes a kinetic process, it has the physical meaning of dissociation constant, that is, a reciprocal binding constant. It means that the smaller the Km is, the more strongly the substrate binds to the enzyme. 

The concentrations of the enzyme substrate have to be selected with some care. In the GC experiment, it should be well above the Michaelis-Menten constant of the enzyme for this substrate. The presence of the UME with its sheath will also limit the diffusion of the enzyme substrate towards the active regions. This may lead to an underestimation of enzyme activity on the surface or to great distorsion in recorded images. Using electrodes with a small RG is a good idea for GC experiments. This question is explained in Procedure 52 (see in CD accompanying this book). 

The activity of [i-galactosidasc (P-Gal) was studied on a quartz chip using a static micromixer to mix the enzyme and substrate on the ms time scale. Inhibition by phenylethyl-P-D-thio-galactoside was also studied [1048]. In another report, the enzyme P-Gal was assayed on a chip in which P-Gal would convert a substrate, resoruhn-P-D-galactopyranoside (RBG), to resoruhn to be detected fluorescently [1049]. By varying the substrate concentrations and monitoring the amount of resoruhn by LIF, Michaelis-Menten constants could be determined. In addition, the inhibition constants of phenylethyl-P-D-thiogalactoside, lactose, and p-hydroxymercuribenzoic acid to the enzyme P-Gal were determined [1049]. 

The linear response range of the glucose sensors can be estimated from a Michaelis-Menten analysis of the glucose calibration curves. The apparent Michaelis-Menten constant KMapp can be determined from the electrochemical Eadie-Hofstee form of the Michaelis-Menten equation, i = i - KMapp(i/C), where i is the steady-state current, i is the maximum current, and C is the glucose concentration. A plot of i versus i/C (an electrochemical Eadie-Hofstee plot) produces a straight line, and provides both KMapp (-slope) and i (y-intercept). The apparent Michaelis-Menten constant characterizes the enzyme electrode, not the enzyme itself. It provides a measure of the substrate concentration range over which the electrode response is approximately linear. A summary of the KMapp values obtained from this analysis is shown in Table I. 

In Equation (5.17), the ratio of constants (k2 + k3)/kx has been replaced by a single constant, the Michaelis-Menten constant, Km. Km is therefore approximately equal to the dissociation constant of the enzyme-substrate complex (ES). 

Enzyme kinetics Km Michaelis-Menten constant is substrate concentration [S] that produces half maximum enzyme velocity v enzyme velocity, V maximum enzyme velocity... 

Given the following data for rate of an enzyme reaction at different substrate concentrations, determine the Michaelis-Menten constant, Km and the maximum reaction rate ... 

Equation (19.7) assumes that the system is at equilibrium. To make sense of it, think about a few different values for [ligand]. When [ligand] = 0, the fractional occupancy equals zero. When [ligand] is very, very high (i.e., many times the KD), the fractional occupancy approaches 100%. When [ligand] = KD, fractional occupancy is 50% (just as the Michaelis-Menten constant Km describes the concentration of enzyme substrate that gives half-maximal velocity). 

In a study of the highly purified alanine racemase of E. coli, Lambert and Neuhaus determined significant differences in the maximal velocities and the Michaelis-Menten constants of the substrates in the forward (L - dl) and reverse directions (d - dl) [37]. From these data the value calculated for Keq is 1.11 0.15. The time course of the reaction showed that in 10 min with L-alanine as substrate ca. 0.09 jumol of D-alanine were formed. With the same amount of enzyme (750 ng) and in the same time period, ca. 0.05 jamol of L-alanine were formed from D-alanine. Similar results have been reported for the same enzyme from S. faecalis and for proline racemases [37]. Thus, in these cases, there are definite kinetic differences, as expected for the existence of two diastereoisomers formed between enzyme and two substrate enantiomers. 

If we set up the same enzyme assay with a fixed amount of enzyme but vary the substrate concentration we will observe that initial velocity (va) will steadily increase as we increase substrate concentration ([S]) but at very high [S] the va will asymptote towards a maximal value referred to as the Vmax (or maximal velocity). A plot of va versus [S] will yield a hyperbola, that is, v0 will increase until it approaches a maximal value. The initial velocity va is directly proportional to the amount of enzyme—substrate complex (E—S) and accordingly when all the available enzyme (total enzyme or E j) has substrate bound (i.e. E—S = E i -S and the enzyme is completely saturated ) we will observe a maximal initial velocity (Pmax)- The substrate concentration for half-maximal velocity (i.e. the [S] when v0 = Vmax/2) is termed the Km (or the Michaelis—Menten constant). However because va merely asymptotes towards fT ax as we increase [S] it is difficult to accurately determine Vmax or Am by this graphical method. However such accurate determinations can be made based on the Michaelis-Menten equation that describes the relationship between v() and [S],... 

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