Michaelis Menten constant estimation

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. 

The snbstrate satnration curve (substrate concentrations versns initial velocities) is hyperbolic and its asymptote gives an estimate of the maximum velocity while the substrate concentration at the half-maximnm velocity provides the Michaelis-Menten constant. Historically these kinetic parameters can be obtained readily from the linearly transformed Michaelis-Menten eqnations (Table 11.4). However, these parameters are now routinely evalnated by the statistical and computer analyses (Wilkinson, 1961 Cleland, 1967 Comish-Bowden, 1995). 

Figure 15.7 Lineweaver-Burke plot to estimate the fundamental pharmacokinetic parameters of a drug that exhibits nonlinear kinetics. Km, Michaelis-Menten constant V ax, maximum velocity.

Michaelis-Menten constant (Km) corresponds to the enzyme affinity subjected to biocatalysts, temperature, pH, and ionic strength of the biosensors. The higher value of Km implies the lower affinity, describing a slower process of substrate-enzyme binding. The Km is estimated in many different models however, Lineweaver-Burk (double reciprocal) plot is commonly applied in research studies. Considering these performance quantifications,... 

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 ) ... 

In general, enzyme activity is demonstrated by fluorescence microscopy as follows. A substrate is offered to the enzyme, which is allowed to act on the substrate to obtain a reaction product which is localized at the site of enzyme activity and is either fluorescent or easily rendered so. The technique is usually used for qualitative purposes only, to demonstrate the location of enzyme activity, but quantification of enzymatic activity and estimation of Michaelis-Menten constants (KJ are possible. It is usually... 

In ester synthesis and exchange reactions, as well as in hydrolysis re tions induced by PEG-lipase in hydrophobic media, the existence of a trace amount of water in the reaction system was most important in terms of the reactions proceeding. Matsushima et al. [67] carried out a kinetics study of PEG-lipase in transparent benzene solution to estimate the value of water, one of the substrates of lipase in the ester hydrolytic reaction. Indoxyl acetate was hydrolyzed by PEG-lipase to form acetic acid and 3-hydroxyindole, which was photometrically determined. A double-reciprocal plot of the velocity of the indoxyl acetate hydrolysis against water concentration at a given concentration of indoxyl acetate indicated that the hydrolysis took place as a double-displacement reaction (ping-pong reaction). The apparent Michaelis-Menten constant of water and the maximum velocity were calculated to be = 7 X 10 M and Vmax = 4700 xmol/min/mg of protein, respectively. 

The important kinetic constants, V and Ku, can be graphically determined as shown in Figure E5.1. Equation E5.2 and Figure E5.1 have all of the disadvantages of nonlinear kinetic analysis. Kmax can be estimated only because of the asymptotic nature of the line. The value of Ku, the substrate concentration that results in a reaction velocity of Vj /2, depends on Kmax, so both are in error. By taking the reciprocal of both sides of the Michaelis-Menten equation, however, it is converted into the Lineweaver-Burk relationship (Equation E5.3). 

Dowd, J.E. and Riggs, D.S. (1965) A comparison of estimates of Michaelis—Menten kinetic constants from various linear transformations. /. Biol. Chem., 240, 863. 

Pharmacokinetic studies are in general less variable than pharmacodynamic studies. This is so since simpler dynamics are associated with pharmacokinetic processes. According to van Rossum and de Bie [234], the phase space of a pharmacokinetic system is dominated by a point attractor since the drug leaves the body, i.e., the plasma drug concentration tends to zero. Even when the system is as simple as that, tools from dynamic systems theory are still useful. When a system has only one variable a plot referred to as a phase plane can be used to study its behavior. The phase plane is constructed by plotting the variable against its derivative. The most classical, quoted even in textbooks, phase plane is the c (f) vs. c (t) plot of the ubiquitous Michaelis-Menten kinetics. In the pharmaceutical literature the phase plane plot has been used by Dokoumetzidis and Macheras [235] for the discernment of absorption kinetics, Figure 6.21. The same type of plot has been used for the estimation of the elimination rate constant [236]. 

This equation should look familiar, because it is functionally identical to the Michaelis-Menten equation of enzyme kinetics. This equation also should make clear the experimental design to be used in determining KD and Bmax using saturation isotherms. We have as the independent variable [E] and as dependent variable B. A successful experiment should permit the estimation of the two biologically meaningful constants KD and 5max. 

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