Cornish-Bowden plots

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. 

Plotting [S]/r as a function ofinhibitor concentration leads to Cornish-Bowden plots. The slope of this plot is K / and is thus independent of the inhibitor concentra-... 

Cornish-Bowden, A. and Eisenthal, R. (1978). Estimation of Michaelis constant and maximum velocity from the direct linear plot. Biochim Biophys Acta 523, 268-272. 

Cornish-Bowden A, Koshland DE. 1975. Diagnostic uses of the Hill (logit and Nernst) plots. J Mol Biol 95 201. 

This modification is a direct linear graph that results from plotting each pair of experimental values ofi>0 and [S]. Figure E5.3 is an example of the Eisenthal and Cornish-Bowden analysis. Ku and V values are read directly from the graph. 

Eisenthal and Cornish-Bowden (direct linear) plot for an enzyme-catalyzed reaction. 

Enzymologists will recognize the complete equivalence of the Kitz-Wilson and Lineweaver-Burk plots. This equivalence extends to the practical statistical problems characteristic of the Lineweaver-Burk plot. [These have been discussed by Segel (19) and Cornish-Bowden (20).]... 

Eisenthal and Cornish-Bowden (21) and Cornish-Bowden (20) have described a rather different type of enzyme kinetics plot that should be useful in analyzing affinity-labeling kinetics. The equation that forms the basis of the direct linear plot (21) is obtained from Equation 11 by rearrangement of terms to give Equation 12... 

Note that Vmax and Km may be estimated from data on steady state flux and substrate concentration based on a number of different ways of plotting J and [S], Cornish-Bowden illustrates that the Lineweaver-Burk plot (or double-reciprocal plot) is not recommended when one would like to minimize the effect of experimental error on parameter estimates. For a detailed discussion see Section 2.6 of [35]. 

Cornish-Bowden, A., Eisenthal, R. (1974) Statistical Considerations in the Estimation of Enzyme Kinetic Parameters by the Direct Linear Plot and other Methods, Biochem.J. 139, 721-730. 

Unlike competitive inhibitors, noncompetitive inhibitors affect Umax (interception on the y-axis is different at different inhibitor concentrations) but not (all concentrations of inhibitor give lines with the same interception on the x-axis). A replot of these data either as the slope versus [I] (Fig. 9a) or l/Umax.app versus [I] (Fig. 9b) provides the K value. Dixon (5) and Cornish-Bowden (6) plots also can be constructed. 

Much of the chemistry of albumin can be understood from detailed observations of the 2,3,5-triiodobenzoic acid (TIB) complexes with albumin. The crystalline complex of TIB with HSA and ESA has been determined with resolution sufficient to position the molecule within the binding pocket unambiguously and to identify the chemistry of interaction (Fig. 15, see color insert). This ligand has a moderate and equal affinity for IIA and IIIA in both HSA and ESA. Association constants were estimated by Scatchard analysis (Scatchard, 1949) using direct linear plots (Eisenthal and Cornish-Bowden, 1974) to be 2.2 x 10 M and 8.3 X lO" M for HSA and ESA, respectively. 

Cornish—Bowden—Eisenthal Method.9 This method is distinct from the previous three linear regression methods, in that each pair of (v, [S]) values is used to construct a separate line on a plot in which VW and Km form the y and x axes, respectively. Beginning with another version of the Michaelis-Menten equation, in which Vmax is the y value and Km is the x value as shown in Eq. 2.23,... 

Another method to obtain estimates for Km and is the rearrangement of the Michaelis-Menten equation to a linear form. The estimation for the initial velocities, Vo, from progress curves is not a particularly reliable method. A better way to estimate Vn is by the integrated Michaelis-Menten equation (Cornish-Bowden, 1975). Nevertheless, the graphical methods are popular among enzymolo-gists. The three most common linear transformations of the Michaelis-Menten equation are the Lineweaver-Burk plot of 1/Vo vs. 1/[S] (sometimes called the double-reciprocal plot), the Eadie-Hofstee plot, i.e. v vs. vo/[S], and the Hanes plot, i.e., [SJ/vo vs. [S] (Fig. 9.3). 

Despite their appealing simplicity, these methods have serious limitations. The Lineweaver-Burk and Hanes plots are unreliable, e.g., the variation of the variance almost certainly results in an incorrect weighting, whereas in the Eadie-Hofstee plot Vo is present in both variables. The direct linear plot of Eisenthal and Cornish-Bowden (1974), for which the Michaelis-Menten equation is rearranged to relate to A , i.e., = Vo -f- Vo A ,/[S] is very simple but... 

Notes It is recommended that statistical and computer analysis of kinetic data should be carried out to evaluate kinetic parameters (Cleland, 1967 Cornish-Bowden, 1995), however these linear plots may still retain their diagnostic values. The linear plots indicate the compliance to die Michaelis-Menten kinetics whereas nonlinear plots imply multiple substrate addition, substrate inhibition or homotropic allosterism. 

A somewhat different method, also based on initial rate measurements, is the one proposed by Eisenthal and Cornish-Bowden (1974). The method is based on tracing straight lines joining the data points (0, —Si) and (vi,0) in a v versus s plot. Such lines intersect at a point whose coordinates are V and K, as can be easily demonstrated. Advantages of such method have been highlighted (Henderson 1978). 

Dixon M, Webb EC (1979) Enzymes, 3rd edn. Academic Press, New York, 1116 pp Eisenthal R, Cornish-Bowden A (1974) The direct linear plot. A new graphical procedure for estimating enzyme kinetic parameters. Biochem J 139(3) 715-720 Ertan H, Kazan D, Erarslan (1997) Cross-hnked stabilization of Escherichia coli penicilhn G acy-lase against pH by dextran-dialdedhyde polymers. Biotechnol Tech 11 225-229 Ferreira JS, Straathof AJJ, Franco TT et al. (2004) Activity and stability of immobilized penicillin acylase at low pH values. J Mol Catal B Enzym 27 29-35 Guranda DT, Volovik TS, Svedas VK (2004) pH stability of penicillin acylase from Escherichia coli. Biochemistry (Moscow) 69(12) 1700-1705... 

Cornish-Bowden, A. (1975). The use of the direct linear plot for determining initial velocities. The Biochemical Journal, vol. 149, no.2, (August 1975), pp. 305-312, ISSN 0264-6021... 

Figure 4.27. Parameter estimation without model identification of saturation-type kinetics (enzyme and Monod kinetics) using the direct linear plot (Eisenthal and Cornish-Bowden, 1974) of r versus s or versus (a) according to Equ. 4.46. The right-side graph (b) shows the conventional plot of saturation-type kinetics, for better comprehensiveness. (Reprinted by permission from Biochem. Journal vol. 139, p. 715, copyright (c) 1974. The Biochemical Society, London.)...

A most satisfactory treatment of kinetic data is the direct linear plot of Eisenthal and Cornish Bowden (1974). Axes are drawn with -S on the abscissa and V on the ordinate, but instead of making the usual hyperbolic plot of S/v (see Enzyme kinetics), corresponding points (each reading of -S and its related v value) are joined by straight lines. The point of intersection of this family of lines gives the values of V and K . Mathematically, this plot corresponds to a rearrangement of the general equation = v + vK ,/... 

Linear transformations of the equation v=V S/Km + S. Error bars are also shown. 1. Lineweaver-Burk, or double reciprocal plot 2. Eadie-Hofstee plot 3. Hanes-Wilkinson plot 4. Eisenthal-Cornish Bowden, or direct linear plot 5. The Scatchard plot which is used for determination of ligand binding constants. 

Purified cottonseed NAPE synthase enzyme exhibited non-Michaelis-Menten biphasic kinetics with respect to the free fatty acid substrates, palmitic and linoleic acids. Kinetic parameters for the two saturable sites were calculated from various transformations e.g., double-reciprocal and Hill plots Cornish-Bowden, 1995) of initial velocity/ substrate concentration data and are summarized in TABLE 1. Preliminary experiments with several group-specific modifiers indicated that NAPE synthase was progressively inactivated by increasing concentrations of 5,5 -dithiobis(2-nitrobenzoic acid) (DTNB), diisopropyl fluorophosphate (DFP), phenylmethylsulfonylfluoride (PMSF), diethylpyrocarbonate (DEPC) (TABLE 2). These results suggest that NAPE synthase may form a thioester- or ester-intermediate through a cysteine or serine residue, respectively, and a histidine residue may participate in catalysis as well. 

Eisenthal, R., and Cornish-Bowden, A., 1974, The direct linear plot. A new graphical procedure for estimating enzyme kinetic parameters, Biochem. J. 139 715-20. 

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