Lineweaver–Burk Plot

• Since, V_max is achieved at infinite substrate concentration, it is impossible to estimate V_max and hence K_m from a hyperbolic plot.
• Because of this difficulty, the Michaelis–Menten equation was transformed into an equation for a straight line by Lineweaver and Burk.
• 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.
• This plot is a derivation of the Michaelis–Menten equation and is represented as:

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.

• It gives a straight line, with the intercept on the y-axis equal to 1/V_max, and the intercept on the x-axis equal to K_m/V_max. The slope of the line is equal to K_m/V_max.
• V_max and K_m can be determined experimentally by measuring V₀ at different substrate concentrations. Then a double reciprocal or Lineweaver–Burk plot of 1/V₀ against 1/[S] is made.

• Reversible enzyme inhibitors can be classified as either competitive or noncompetitive, and can be distinguished via a Lineweaver–Burk plot.
• It is a useful way of determining how an inhibitor binds to an enzyme.
• Competitive inhibition can be recognized by using a Lineweaver–Burk plot if V₀ is measured at different substrate concentrations in the presence of a fixed concentration of inhibitor.
• A competitive inhibitor increases the slope of the line on the Lineweaver–Burk plot, and alters the intercept on the x-axis (since Km is increased), but leaves the intercept on the y- axis unchanged (since V_max remains constant).
• Noncompetitive inhibition can also be recognized on a Lineweaver–Burk plot since it increases the slope of the experimental line, and alters the intercept on the y-axis (since V_max is decreased), but leaves the intercept on the x-axis unchanged (since Km remains constant).

Uses of Lineweaver–Burk Plot

1. Used to determine important terms in enzyme kinetics, such as K_mand V_max, before the wide availability of powerful computers and non-linear regression software.
2. Gives a quick, visual impression of the different forms of enzyme inhibition.

References

1. David Hames and Nigel Hooper (2005). Biochemistry. Third ed. Taylor & Francis Group: New York.
2. Smith, C. M., Marks, A. D., Lieberman, M. A., Marks, D. B., & Marks, D. B. (2005). Marks’ basic medical biochemistry: A clinical approach. Philadelphia: Lippincott Williams & Wilkins.
3. https://en.wikipedia.org/wiki/Lineweaver%E2%80%93Burk_plot