Lineweaver–Burk plot
In biochemistry, the Lineweaver–Burk plot (or double reciprocal plot) is a graphical representation of the Michaelis–Menten equation of enzyme kinetics, described by Hans Lineweaver and Dean Burk in 1934.
[1] The double reciprocal plot distorts the error structure of the data, and is therefore not the most accurate tool for the determination of enzyme kinetic parameters.
Properly weighted non-linear regression methods are significantly more accurate and have become generally accessible with the universal availability of desktop computers.
The Lineweaver–Burk plot derives from a transformation of the Michaelis–Menten equation, in which the rate
Taking reciprocals of both sides of this equation it becomes as follows: Thus plotting
generates a straight line with ordinate intercept
When used for determining the type of enzyme inhibition, the Lineweaver–Burk plot can distinguish between competitive, pure non-competitive and uncompetitive inhibitors.
The various modes of inhibition can be compared to the uninhibited reaction.
Therefore competitive inhibitors have the same intercept on the ordinate as uninhibited enzymes.
Competitive inhibition increases the apparent value of
Graphically this can be seen as the inhibited enzyme having a larger intercept on the abscissa.
, as pure noncompetitive inhibition does not effect substrate affinity.
is changed—usually increased, meaning that the affinity usually decreases with mixed inhibition.
Cleland recognized that pure noncompetitive inhibition was very rare in practice, occurring mainly with effects of protons and some metal ions, and he redefined noncompetitive to mean mixed.
This can be seen on the Lineweaver–Burk plot as an increased intercept on the ordinate with no change in slope.
Substrate affinity increases with uncompetitive inhibition, or lowers the apparent value of
Graphically uncompetitive inhibition can be identified in the plot parallel lines for the different concentrations of inhibitor..
The Lineweaver–Burk plot does a poor job of visualizing experimental error.
vary over a very wide range, as can be seen from the following example: Lineweaver and Burk were aware of this problem, and after investigating the error distribution experimentally,[5] finding a uniform standard deviation in
, they consulted the eminent statistician W. Edwards Deming.
This aspect of their paper has been almost universally ignored by people who refer to the "method of Lineweaver and Burk.
"[citation needed] The values measured at low
lead to points on the far right of the plot and have a large effect on the slope of the line, and thus in particular on the value of
