Woolfe equation

Hanes-Woolf equation The Hanes-Woolf equation is a rearranged form of the Michaelis-Menten equation. 

The Woolfe equation has been used to estimate the shelf life of a product from data obtained at the same temperature/conditions as those expected for the final product.764 The time at which drug content diverges from its specifications is estimated by extrapolating the time course of degradation at a specific temperature/condition. When the time course of drug content (C) is represented by... 

The Hanes-Woolf equation can be easily derived from (6.83) leading to... 

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

Also referred to as the Hanes-Hultin plot and the Hanes-Woolf (or, Woolf-Hanes) plot, the method is based on a transformation of the Michaelis-Menten equation i.e., the expression for the Uni Uni mechanism) [A]/v = (i a/ max) + ([A]/Umax) whcrc U ax IS the maximum forward velocity and is the Michaelis constant for A. In the Hanes plot, the slope of the line is numerically equal to Umax, the vertical intercept is equivalent to, ... 

In addition to being easier to fit than the hyperbolic Michaelis-Menten equation, Lineweaver-Burk graphs clearly show differences between types of enzyme inhibitors. This will be discussed in Section 4.5. However, Lineweaver-Burk equations have their own distinct issues. Nonlinear data, possibly indicating cooperative multiunit enzymes or allosteric effects, often seem nearly linear when graphed according to a Lineweaver-Burk equation. Said another way, the Lineweaver-Burk equation forces nonlinear data into a linear relationship. Variations of the Lineweaver-Burk equation that are not double reciprocal relationships include the Eadie-Hofstee equation7 (V vs. V7[S]) (Equation 4.14) and the Hanes-Woolf equation8 ([S]/V vs. [S]) (Equation 4.15). Both are... 

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. 

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 ... 

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,)... 

To find the rale law parameters and K,. we first apply the differential formulas in Chapter 5 to columns 1 and 2 of Table E7-5.1 to find r,. Because C, K, initially, it is best to regress the data using the Hanes-Woolf form of the Monod equation... 

Another way of converting the Michaelis-Menten equation in the form of eq. (6.17) to give the equation of a straight line is the method of Hanes-Woolf... 

In a similar fashion as for other types of inhibition the Hanes-Woolf and the Eadie -Hofstee equations for uncompetitive inhibition could be used respectively for analysis if this type of inhibition is present... 

Hughes, E. D. Ingold, C. K. Maw, G. A. Woolf, L. I. /. Chem. Soc. 1948, 2077. The product distributions in equation 10.38 reflect only the elimination products. More than 30% substitution product was also obtained. 

---