Michaelis-Menten analysis

When the concentration of substrate is varied over wide Umits while the concentration of the enzyme is held constant, the reaction rate increases until a certain concentration of substrate is reached. This large concentration of substrate is sufficient to complex with all of the enzyme so any further increase in concentration of the substrate does not lead to the 

The total enzyme concentration, [E](, is equal to the sum of the concentration of free enzyme, [E], and that which is bound in the enzyme-substrate complex, [ES], 

Performing the multiphcation of the left-hand side of this equation gives 

Since the rate of product formation, which can be represented as R, is fe2[ES], after multiplying both sides by 2, we can write 

This equation is known as the Michaelis—Menten equation, and the constant (k-i + k2)jki is called the Michaelis constant, K.  

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The modified electrode, in turn, enhances Mb to catalyze the reduction of H2O2. Addition of H202 increases in the cathodic peak intensity for the modified electrode. This electrochemical response is specific for the Mb silver NP modified electrode because no signals are observed for either the bare electrode or an electrode with only a silver NP film. A Michaelis-Menten analysis demonstrates that the modified electrode shows higher affinity for H202 than other gold-cytochrome c and gold-horseradish peroxidase modified electrodes. The apparent enhanced catalytic activity... 

Bentz J, Tran TT, Polli JW, et al. The steady-state Michaelis-Menten analysis of P-glycoprotein mediated transport through a confluent cell monolayer cannot predict the correct Michaelis constant Km. Pharm Res 2005 22(10) 1667-1677. 

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. 

Briggs and Haldane in 1925 examined the earlier Michaelis-Menten analysis and made an important development. Instead of assuming that the first stage of the reaction was at equilibrium, they merely assumed, for all intents and purposes, that the concentration of the enzyme-substrate complex scarcely changed with time i.e., it was in a steady state. Written mathematically, this amounts to... 

The elimination rate for zero-order processes may also be treated as a maximal rate of reaction (Fmax) and thus this type of data may be subject to ordinary Michaelis-Menten analysis (see further, below). Note that first-order elimination curves are so common that drug disappearance curves are routinely analyzed as semi-logarithmic plots (which linearizes the curve). The literature is sometimes ambiguous in its use of the term linear data , authors may or may not assume that the semi-logarithmic transformation is to be taken as read. 

Michaelis-Menten analysis suggests that the molecular mechanism of substrate enan-tioselectivity can occur in the binding step (different affinities, K, in the catalytic step (different reactivities, V ax) or in both. There... 

Kinetic templates accelerate reaction of bound substrates, which makes it tempting to quantify template effects in terms of rate enhancement . In this section, we will show how this can be misleading because such rate enhancements are concentration dependent. We will elucidate the parameters which determine the rate enhancement achieved with a kinetic template, by analyzing the thermodynamic and kinetic behavior of simple theoretical models, and applying these models to published template systems. Our theoretical models are similar to the Michaelis-Menten analysis of enzyme catalyzed reactions [51], except that we assume there is no catalytic turnover. First, we consider linear templates, then cyclization templates. In general, the rate of reaction varies as the reaction proceeds whenever we refer to rates in the following discussion, we mean initial rates. 

Upon UV irradiation of the trans-capped CD, the overall rate of hydrolysis of p-nitrophenyl acetate was accelerated five times, owing to the higher binding ability of the photoproduced cis form. The Michaelis-Menten analysis of the reaction kinetics showed that both the maximum rate and the values for the cis isomer are smaller than those for the trans isomer. This indicates that the substrate is included in the cis pocket more deeply than in the trans, but is in an unfavorable geometry [353]. The same... 

The inhibition of carbonic anhydrase by anions has long been recognized. The inhibitory effect of Cl was noted by early investi-gators(19). A later study of anion inhibition by stopped-flow techniques was compromised by the presence of 80mM Cl in buffers used (20). The inhibition of the hydrase activity of the Cobalt(II) substituted enzyme has been investigated over the full pH range(21). Anionic inhibition of esterase activity has been studied by initial rate techniques(11-13) and by complexometric titration(22). None of the work thus far published has included full scale Michaelis-Menten analysis of the inhibition of the native Zinc(II) enzyme towards its natural substrate over an extended pH range. 

The linear respcmse range of the sensors can be estimated from a Michaelis-Menten analysis of the glucose calibration gra in Figures 4 and 5. The apparent Michaelis-Menten constant Km PP can be determined from the electrochemical Eadie-Hofstee form of the Michaelis-Menten equation (30 ) ... 

FIGURE 14A Michaelis-Menten analysis of the data from Figure 14.3 to determine the and of the hyaluronidase. Reprinted with permission from Drenski MF, Reed WF. Simultaneous multiple sample hght scattering for characterization of polymer solutions. J Appl Polym Sci 2004 92 2724—2732. 

Fig. 4.10 Michaelis-Menten analysis of WT KSl and KS1(N206A). Lineweaver-Burk plots for BaeJ KSl WT and N206A are shown. Kinetic parameters were calculated from the plot using the equations shown, and errors were determined using a a confidence intervcd...

The Michaelis-Menten analysis yielded a Km value of 1.8 iiiM 0.4 for WT KSl. In comparison, the Km value for KS1(N206A) was 3.7 iiiM 1.3, suggesting a decreased affinity towards SNAC 27 upon removal of the active site Asn residue. Additionally, the kcat/Km value was reduced by a factor of 2, implying that the catalytic efficiency of KS1(N206A) has also been reduced by removal of the Asn residue. It is noteworthy that this reduction in kcat/Km is largely due to the difference in Km values, as kcat values for WT and mutant are extremely similar (Table 4.2). 

Applying the irreversible inhibition analysis to both KS domains yielded a Ki valne of 2.0 mM 0.2 for WT KSl and 4.2 mM 1.2 for KS1(N206A), again snggesting a decreased affinity towards SNAC 27 upon removal of the active site Asn residne. Fnrthermore, the rate constant for the formation of the acyl-KS thioester (kmact) is extremely similar for both WT and mutant, which is to be expected. Comparison of the ki act/Ki values reveals a decrease in efficiency of a factor 2, similar to the Michaelis-Menten analysis. It is worth noting, that fitting the data shown in Fig. 4.11 to a hnear model (which assumes a single-step, as opposed to the formation of a [KS SNAC] complex) yields a decrease in the kmact/ Ki values of -1.7. 

With the IT-Lambert dependence (1.26) of the kinetic solution of the reaction (1.4), we arrive at the mathematical disadvantages of the traditional Michaelis-Menten analysis. For example, it can return multiple values for the same argument or result in an infinitely iterated exponential function (Hayes, 2005). 

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