Woolf plots

The Hanes-Woolf plot is another rearrangement of the Michaelis-Menten equation that yields a straight line ... 

First draw both Lineweaver-Burk plots and Hanes-Woolf plots for the following a Monod-Wyman-Changeux allosteric K enzyme system, showing separate curves for the kinetic response in (1) the absence of any effectors (2) the presence of allosteric activator A and (3) the presence of allosteric inhibitor I. Then draw a similar set of curves for a Monod-Wyman-Changeux allosteric Uenzyme system. 

Substrate and product inhibitions analyses involved considerations of competitive, uncompetitive, non-competitive and mixed inhibition models. The kinetic studies of the enantiomeric hydrolysis reaction in the membrane reactor included inhibition effects by substrate (ibuprofen ester) and product (2-ethoxyethanol) while varying substrate concentration (5-50 mmol-I ). The initial reaction rate obtained from experimental data was used in the primary (Hanes-Woolf plot) and secondary plots (1/Vmax versus inhibitor concentration), which gave estimates of substrate inhibition (K[s) and product inhibition constants (A jp). The inhibitor constant (K[s or K[v) is a measure of enzyme-inhibitor affinity. It is the dissociation constant of the enzyme-inhibitor complex. 

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... 

On the other hand, the macrolides showed unusual enzymatic reactivity. Lipase PF-catalyzed polymerization of the macrolides proceeded much faster than that of 8-CL. The lipase-catalyzed polymerizability of lactones was quantitatively evaluated by Michaelis-Menten kinetics. For all monomers, linearity was observed in the Hanes-Woolf plot, indicating that the polymerization followed Michaehs-Menten kinetics. The V, (iaotone) and K,ax(iaotone)/ m(iaotone) values increased with the ring size of lactone, whereas the A (iactone) values scarcely changed. These data imply that the enzymatic polymerizability increased as a function of the ring size, and the large enzymatic polymerizability is governed mainly by the reachon rate hut not to the binding abilities, i.e., the reaction process of... 

The specific activity of the activated wild-type tyrosinase towards L-tyrosine monooxygenation, as determined by the HPLC method, was 1.69 katal/ kg of protein. A Km of 0.82 mM and a cat of 23.6 s 1 for L-tyrosine mono-oxygenation were calculated from Hanes-Woolf plots. 

Construct a Hanes-Woolf plot and show how Km and Fmax are obtained from it. 

Two other possible transformations of saturation binding data mentioned earlier are the Hofstee (B versus B/F) and Woolf Plots (F/B versus / ). As with the Scatchard equation, these equations can be derived from algebraic manipulations of the equations listed above. 

Another linear representation of the Michaelis-Menten equation is the Hanes-Woolf plot (Equation 17.14). 

Competitive inhibitors do not change the value of Vmax> which is reached when sufficiently high concentrations of the substrate are present so as to completely displace the inhibitor. However, the affinity of the substrate for the enzyme appears to be decreased in the presence of a competitive inhibitor. This happens because the free enzyme E is not only in equilibrium with the enzyme-substrate complex E. S, but also with the enzyme-inhibitor complex E. L Competitive inhibitors increase the apparent of the substrate by a factor of (1 + The evaluation of the kinetics is again greatly facilitated by the conversion of Equation 17.15 into a linear form using Line-weaver-Burk, Eadie-Hofstee, or Hanes-Woolf plots, as shown in Fig. 17.7. 

Figure 17.7. (a)Lineweaver-Burk, (b) Eadie-Hofstee, and (c) Hanes-Woolf plots exhibiting competitive inhibition patterns. The dashed line indicates the reaction in the absence of inhibitor, whereas the solid lines represent enzymatic reactions in the presence of increasing concentrations cf inhibitor. 

The Lineweaver-Burk reciprocal plot is not the only linear transformation of the basic velocity (or ligand binding) equation. Indeed, under some circumstances one of the other linear plots described below may be more suitable or may yield more reliable estimates of the kinetic constants. For example, the Hanes-Woolf plot of [S]/u versus [S] may be more convenient... 

The Lineweaver-Burk equation may be rearranged to yield the linear equation for the Hanes-Woolf plot ... 

Figure 4-33 Hanes-Woolf Plot [S]/u versus [S] (a) Competitive inhibition, (i) Noncompetitive inhibition, (c)... 

In addition to the Lineweaver-Burk plot, one can al.so use a Hanes-Woolf plot or an Eadie-Hofsiee plot. Here S s Cu , and Equation (7-26,)... 

Figure 6.6. FTanes-Woolf plot for Michaelis-Menten kinetics.

Figure 6.5-2. The Woolf plot was constructed according to the relationship ...

Fig. 10.2. Hanes-Woolf plot of phosphomonoesterase activity of Fontinalis antipyretica from Cranecleugh Burn, UK showing two rates of reaction at low (0-100 pM) and high (100-1000 jjlM) substrate concentrations (where the Y axis [S/V is substrate concentration (jjlM) divided by the velocity of the reaction (pmol para-nitrophenol (pNP) per g dry weight/h)). Units of are pmol pNP/g dry weight/h. Reproduced from Turner et al. (2001).

Because of the limitation of double-reciprocal plots described above, other linear plotting forms have been devised. One of these, the Eadie plot, graphs V versus V/[S]. Another, the Elanes-Woolf plot, ([S]/V versus [S]) is perhaps the most useful in minimizing the difficulties of the double-reciprocal plot. 

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