Lineweaver-Burk plots: reading Km, Vmax and inhibition
A Lineweaver-Burk plot straightens the curved enzyme graph so that Vmax (the maximum rate) and Km (the substrate concentration giving half of Vmax) can be read off.
Remember
The slope (how steeply the line rises) is Km/Vmax, the y-intercept (where the line crosses the vertical axis) is 1/Vmax and the x-intercept (where it crosses the horizontal axis) is -1/Km, so you read Vmax from the y-intercept and Km from the x-intercept.
Memory aid
a competitor cannot lower the ceiling
Think of Vmax as a ceiling: a competitive inhibitor cannot lower it, because a high enough substrate concentration wins the contest, so Vmax and the y-intercept stay put.
A graph of reaction velocity (the rate) against substrate concentration is a curve, which makes Vmax and Km hard to read accurately. A Lineweaver-Burk plot, also called a double-reciprocal plot, turns that curve into a straight line by plotting 1/velocity on the vertical axis against 1/substrate concentration on the horizontal axis. A reciprocal is simply 1 divided by the value.
The straight line has a slope and two intercepts, and each has a meaning. The y-intercept is 1/Vmax, so a low intercept means a high Vmax, a fast maximal rate. The x-intercept is -1/Km, so a more negative value means a lower Km and a higher affinity (how tightly the enzyme binds its substrate). The slope is Km/Vmax, so a steeper line means a larger Km or a smaller Vmax, and the slope alone does not tell you which of the two has changed.
You can also use the plot to compare an enzyme with and without an inhibitor. A competitive inhibitor looks like the substrate and binds to the active site, so Km rises, but enough extra substrate can overcome it and Vmax is unchanged. The lines with and without it meet on the y-axis, with a steeper slope and an x-intercept nearer zero.
In pure non-competitive inhibition Vmax is lower and Km is unchanged. The inhibitor binds at an allosteric site (a site other than the active site) and changes the enzyme's three-dimensional shape, so the substrate still binds with the same affinity. The x-intercept stays fixed, the y-intercept rises and the slope steepens. In uncompetitive inhibition both Vmax and Km fall, which gives parallel lines.
Key facts
- Slope
- equals Km/Vmax, so it combines affinity and maximal rate in one value.
- y-intercept
- equals 1/Vmax, so Vmax is the reciprocal of the y-intercept and a low intercept means a high Vmax.
- x-intercept
- is -1/Km, so a more negative value means a lower Km and a higher affinity for the substrate.
- Competitive inhibitor
- gives lines that meet on the y-axis, with a steeper slope and an x-intercept closer to zero, because Km rises and Vmax is unchanged.
- Pure non-competitive inhibitor
- the x-intercept is fixed and the y-intercept rises, because Vmax falls and Km is unchanged.
- Uncompetitive inhibitor
- lowers both Vmax and Km, which gives a parallel shift of the line.
Exam traps
- The reciprocal of Vmax is not the slope, because 1/Vmax is where the line crosses the vertical axis, the y-intercept, while the slope describes how steeply the line rises.
- Vmax/Km is not the slope, because that turns the ratio upside down: the slope is Km/Vmax and Vmax/Km is the reciprocal of the slope.
- A plateau, the level part where a curve flattens out at high substrate concentration, belongs to the ordinary Michaelis-Menten graph (the curve of reaction velocity against substrate concentration), because a Lineweaver-Burk plot is a straight line and has no plateau.
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