Inhibition Kinetics Graphical Plots

As with estimation of enzyme kinetic parameters, the most accurate method for determining inhibition kinetic parameters is through nonlinear regression fitting of the data set. However, it may be beneficial to plot the data graphically 

Two of the most common plots for determining inhibition constants and the type of inhibition are those as described by Dixon (1953) and Comish-Bowden (1974). The two methods are actually very complementary and can serve as a double check on determinations of the type of inhibition. In addition, they each make up for the inability of the other method to estimate the inhibition constant in all types of inhibition. 

FIGURE 4.10 Diagnostic plots to determine the type of inhibition occurring in a kinetic reaction. Left side, panels (a), (b), and (c) are Dixon plots representative of competitive, mixed, and uncompetitive inhibition, respectively. Right side, panels (d), (e), and (f) are Cornish-Bowden plots representative of competitive, mixed, and uncompetitive inhibition, respectively. 

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The inhibition analyses were examined differently for free lipase in a batch and immobilised lipase in membrane reactor system. Figure 5.14 shows the kinetics plot for substrate inhibition of the free lipase in the batch system, where [5] is the concentration of (S)-ibuprofen ester in isooctane, and v0 is the initial reaction rate for (S)-ester conversion. The data for immobilised lipase are shown in Figure 5.15 that is, the kinetics plot for substrate inhibition for immobilised lipase in the EMR system. The Hanes-Woolf plots in both systems show similar trends for substrate inhibition. The graphical presentation of rate curves for immobilised lipase shows higher values compared with free enzymes. The value for the... 

This same [e] experimental protocol leads to a graphical overlay plot that yields valuable kinetic information if the two experiments described in Table 50.1 are plotted together as reaction rate vs. [2], the two curves will fall on top of one another ( overlay ) over the range of [2] common to both only if the rate is not significantly influenced by changes in the overall catalyst concentration within the cycle, including catalyst activation, deactivation or product inhibition. Overlay in same excess plots, therefore, may be used to confirm catalyst robustness or identify problems such as catalyst deactivation or product inhibition. 

If a noncompetitive or an uncompetitive inhibitor were present with the substrate at constant ratio, then graphical analysis would suggest that the phenomenon of substrate inhibition is present. If an investigator analyzed the apparent substrate inhibition via a Marmasse plot, wrong estimates of both the K a and K s values would be reported and the investigator would be mislead with respect to the kinetic mechanism. If partial inhibitors or alternative substrates are present in constant ratio, depending on the relative sizes of the Ymax and values,... 

Based on the result from the IC50 determination, determination of additional kinetic parameters such as Ki and the inhibition mode are useful (variation of the substrate concentration e.g. Km/4 1 Km with time). Transformation of the Michaelis-Menten equation are used both for calculation the Ki value as well as for graphical depiction of the type of inhibition (e.g. direct plot ([rate]/[substrate], Dixon plot [l/rate]/[inhibitor], Linewaver-Burk plot [l/rate]/[l/substrate] or Eadie-Hofstee plot [rate]/[rate/substrate]). 

The kinetic tests of these elastomers were conducted in the same adiabatic reactor as described above. The main goal of evaluation of this group of elastomers was to determine the effect of the content of plasticizer on inhibition of the lateral Intercohesion forces between the interspaces of the crystalline aggregates. The kinetic data were obtained experimentally, calculated by a regression method using a computer and graphically from the plots as above. The data obtained are presented in Figure 7. 

Graphical representation of Eq. 3.46 for all mechanisms is in Fig. 3.5. Lineweaver-Burke plots are quite useful for determining kinetic mechanisms. Competitive inhibition will be represented by straight lines with a common intercept in the Y-axis,... 

A useful graphical method for the estimation of kinetic parameters in substrate inhibition was described by Marmasse (1963). However, with substrate inhibition plots, even after a successful graphical analysis is completed, one should always fit the data to the appropriate equation with a computer program in order to estimate the kinetic constants. 

Figure 2.23 graphically depicts a plot of I/vq versus l/[Aoj. The values V and Km are obtained from the intercepts of the ordinate (1/V) and of the abscissa (—1 /Km), respectively. If the data do not fit a straight line, then the system deviates from the required steady-state kinetics e. g., there is inhibition by excess substrate or the system is influenced by allosteric effects (cf. 2.5.1.3 allosteric enzymes do not obey Michaelis-Menten kinetics). 

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