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Hidden details of competitive inhibition: What do Lineweaver–Burk plots tell us?
In biochemistry, a Lineweaver–Burk plot (or double reciprocal plot) is a graphical representation of the Michaelis–Menten equation for enzyme kinetics, first described by Hans Lineweaver and Dean Burk in 1934. Although this plot has historically been widely used to assess enzyme kinetic parameters, it suffers from a distorted error structure in its data and is not an optimal tool for determining enzyme kinetic parameters. Currently, methods using nonlinear regression are more accurate and have become more accessible with the popularization of desktop computers.
Definition of Lineweaver–Burk Diagram
The Lineweaver–Burk plot is derived from a transformation of the Michaelis–Menten equation. This equation expresses the relationship between the enzyme rate v and the substrate concentration a, involving two parameters: V (limiting rate) and Km (Michaelis constant). By taking the reciprocal of both sides of this equation, the result forms a straight line. The vertical intercept of this line is 1/V, the horizontal intercept is -1/Km, and the slope is Km/V.
Applications
When used to determine the type of enzyme inhibition, the Lineweaver–Burk plot can distinguish between competitive, purely noncompetitive, and noncompetitive inhibitors. Different modes of inhibition can be contrasted with uninhibited responses.
Competitive inhibition will not affect the apparent value of V, but will increase the apparent value of Km and reduce substrate affinity.
Competitive inhibition
The characteristic of competitive inhibition is that the inhibitor competes with the substrate for the binding site of the enzyme. Therefore, in this case, the apparent value of V will not be affected, but the Km will increase, which means that the affinity between the enzyme and the substrate will decrease. As can be seen in the figure, the value of the intercept for the inhibited enzyme is greater than that for the uninhibited enzyme.
Pure noncompetitive inhibition
In pure noncompetitive inhibition, the apparent value of V will decrease, while Km will not be affected. In the Lineweaver–Burk plot, this is reflected as an increase in the vertical intercept, but a constant horizontal intercept, indicating that substrate affinity is not affected.
Mixed Inhibition
Pure noncompetitive inhibition is actually very rare, while mixed inhibition is much more common. Under mixed inhibition, the apparent value of V will decrease, while the value of Km will generally increase, indicating that the affinity of the substrate will generally decrease. Many scholars agree with Cleland in this regard, recognizing the influence of mixed inhibition.
Noncompetitive inhibition
In the case of noncompetitive inhibition, the apparent value of V will decrease, while the value of Km will not change. This is reflected in the figure as an increase in the vertical intercept but an unchanged slope. The substrate affinity will increase instead, and the apparent value of Km will decrease.
Shortcomings
Lineweaver–Burk plots are poor at visualizing experimental error. In particular, if the error in the rate v has a uniform standard error, then the error in 1/v will be very wide. Lineweaver and Burk were aware of this problem and investigated the error distribution experimentally, ultimately deciding to use appropriate weighting for fitting. However, this aspect is almost universally ignored among those who cite "Lineweaver and Burk's approach".
ConclusionLineweaver–Burk plots provide an effective way to analyze enzyme kinetics in biochemistry, but their limitations cannot be ignored. In the current technological environment, the correct nonlinear regression method shows its superiority. As biochemical research progresses further, will these tools find more precise applications?
