Lineweaver–Burk plot
In biochemistry, the Lineweaver–Burk plot (or double reciprocal plot) is a graphical representation of the Lineweaver–Burk equation of enzyme kinetics, described by Hans Lineweaver and Dean Burk in 1934.^{1}
Derivation
The plot provides a useful graphical method for analysis of the Michaelis–Menten equation:
Taking the reciprocal gives
where V is the reaction velocity (the reaction rate), K_{m} is the Michaelis–Menten constant, V_{max} is the maximum reaction velocity, and S is the substrate concentration.
Use
The Lineweaver–Burk plot was widely used to determine important terms in enzyme kinetics, such as K_{m} and V_{max}, before the wide availability of powerful computers and nonlinear regression software. The yintercept of such a graph is equivalent to the inverse of V_{max}; the xintercept of the graph represents −1/K_{m}. It also gives a quick, visual impression of the different forms of enzyme inhibition.
The double reciprocal plot distorts the error structure of the data, and it is therefore unreliable for the determination of enzyme kinetic parameters. Although it is still used for representation of kinetic data,^{2} nonlinear regression or alternative linear forms of the Michaelis–Menten equation such as the HanesWoolf plot or Eadie–Hofstee plot are generally used for the calculation of parameters.^{3}
When used for determining the type of enzyme inhibition, the Lineweaver–Burk plot can distinguish competitive, noncompetitive and uncompetitive inhibitors. Competitive inhibitors have the same yintercept as uninhibited enzyme (since V_{max} is unaffected by competitive inhibitors the inverse of V_{max} also doesn't change) but there are different slopes and xintercepts between the two data sets. Noncompetitive inhibition produces plots with the same xintercept as uninhibited enzyme (K_{m} is unaffected) but different slopes and yintercepts. Uncompetitive inhibition causes different intercepts on both the y and xaxes .
Problems with the method
The Lineweaver–Burk plot is classically used in older texts, but is prone to error, as the yaxis takes the reciprocal of the rate of reaction – in turn increasing any small errors in measurement. Also, most points on the plot are found far to the right of the yaxis (due to limiting solubility not allowing for large values of [S] and hence no small values for 1/[S]), calling for a large extrapolation back to obtain x and yintercepts.^{4}
See also
References
 ^ Lineweaver, H and Burk, D. (1934). "The Determination of Enzyme Dissociation Constants". Journal of the American Chemical Society 56 (3): 658–666. doi:10.1021/ja01318a036.
 ^ Hayakawa, K.; Guo, L.; Terentyeva, E.A.; Li, X.K.; Kimura, H.; Hirano, M.; Yoshikawa, K.; Nagamine, T. et al. (2006). "Determination of specific activities and kinetic constants of biotinidase and lipoamidase in LEW rat and Lactobacillus casei (Shirota)". J Chromatogr B Analyt Technol Biomed Life Sci 844 (2): 240–50. doi:10.1016/j.jchromb.2006.07.006. PMID 16876490.
 ^ Greco, W. R. and Hakala, M. T., (1979). "Evaluation of methods for estimating the dissociation constant of tight binding enzyme inhibitors," (PDF). J. Biol. Chem. 254 (23): 12104–12109. PMID 500698.
 ^ Dowd, John E., and Douglas S. Riggs. "A comparison of estimates of MichaelisMenten kinetic constants from various linear transformations." J. biol. Chem 240.2 (1965): 863869.
External links
 NIH guide, enzyme assay development and analysis

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