Lineweaver–Burk plot

${\displaystyle [S]}$: substrate concentration. The independent axis of a Lineweaver-Burk plot is the reciprocal of substrate concentration, ${\displaystyle {\frac {1}{[S]}}}$.[2]

${\displaystyle V}$ or ${\displaystyle V_{0}}$: initial velocity of an enzyme-inhibited reaction. The dependent axis of the Lineweaver-Burk plot is the reciprocal of velocity, ${\displaystyle {\frac {1}{V_{0}}}}$.[5]

${\displaystyle V_{max}}$: maximum velocity of the reaction. The y-intercept of the Lineweaver-Burk plot is the reciprocal of maximum velocity, ${\displaystyle {\frac {1}{V_{max}}}}$.[2]

${\displaystyle K_{M}}$: the Michaelis constant, a measure of enzyme affinity. A lower ${\displaystyle K_{M}}$ means a higher affinity. Graphically, the x-intercept of the line is ${\displaystyle -{\frac {1}{K_{M}}}}$[5]

K_cat: turnover number, or reactions per unit time. The lower the K_cat the slower the reaction. K_cat=V_max/[Enzyme]. Graphically this can be evaluated by looking at V_max.[2]

Catalytic Efficiency = K_cat/K_M. A fast catalyst and high affinity results in best catalytic efficiency.[5]

${\displaystyle \alpha =1+{\frac {[I]}{K_{I}}}}$ where ${\displaystyle [I]}$ is the concentration of inhibition and ${\displaystyle K_{I}}$ is the inhibitor constant. Alpha determines the degree that binding of an inhibitor effects enzyme kinetics of a substrate, it always has a positive value.[5]

The plot provides a very useful graphical method for analysis of the Michaelis–Menten equation, as it is difficult to determine precisely the V_max of an enzyme-catalysed reaction:

${\displaystyle V={\frac {V_{\max }[S]}{K_{m}+[S]}}}$

Taking the reciprocal gives us:

${\displaystyle {1 \over V}={{K_{m}+[S]} \over V_{\max }[S]}={K_{m} \over V_{\max }}{1 \over [S]}+{1 \over V_{\max }}}$

The Lineweaver–Burk plot puts 1/[S] on the x-axis and 1/V on the y-axis.[6]

_{Enzyme Inhibition displayed using Lineweaver-Burk (double reciprocal plots)}

When used for determining the type of enzyme inhibition, the Lineweaver–Burk plot can distinguish competitive, pure non-competitive and uncompetitive inhibitors. The various modes of inhibition can be compared to the uninhibited reaction.

While the Lineweaver-Burk is useful for determining important variables in enzyme kinetics, it is prone to error. The y-axis of the plot takes the reciprocal of the rate of reaction, meaning small errors in measurement are more noticeable.[8] Additionally, the values derived from low [S] (and hence the more error prone values) are on the far right of the plot and have a larger impact on the slope of the line, and thus in particular on the value of K_M.

• Michaelis–Menten kinetics
• Eadie–Hofstee diagram
• Hanes–Woolf plot

• NIH guide, enzyme assay development and analysis