Biochemistry
Enzyme kinetics: Km, Vmax and Michaelis-Menten
Two constants describe most of what you need to know about how an enzyme behaves — and students routinely mix up what they mean.
The Michaelis-Menten equation
v = (Vmax × [S]) / (Km + [S])
Where v is reaction velocity and [S] is substrate concentration.
What the two constants mean
- Vmax — the maximum rate, reached when every enzyme active site is saturated with substrate. Adding more substrate beyond this point does nothing.
- Km — the substrate concentration at which the reaction runs at half Vmax. It is an inverse measure of affinity: a low Km means high affinity, because little substrate is needed to reach half-maximal rate.
The most common mistake
Km is not a rate and not a measure of enzyme speed. It has units of concentration. Low Km = high affinity is the relationship to memorize, and the inversion trips up more students than any other part of this topic.
Reading the curves
The Michaelis-Menten plot (v against [S]) is a hyperbola: steep at low substrate concentration, flattening toward a plateau at Vmax. Because that plateau is approached asymptotically, reading Vmax accurately off it is difficult.
The Lineweaver-Burk plot solves this by plotting 1/v against 1/[S], producing a straight line:
- y-intercept = 1/Vmax
- x-intercept = −1/Km
- slope = Km/Vmax
How inhibitors change the plot
| Inhibitor | Km | Vmax | Lineweaver-Burk |
|---|---|---|---|
| Competitive | Increases | Unchanged | Same y-intercept, steeper slope |
| Non-competitive | Unchanged | Decreases | Same x-intercept, higher y-intercept |
A quick way to identify the type from a plot: if the lines meet on the y-axis it is competitive; if they meet on the x-axis it is non-competitive.
Frequently asked questions
What does Km tell you about an enzyme?
Km is the substrate concentration at which the reaction proceeds at half of Vmax. It is an inverse measure of affinity: a low Km means high affinity, because little substrate is needed to reach half-maximal velocity.
What is Vmax?
Vmax is the maximum reaction velocity, reached when all enzyme active sites are saturated with substrate. Beyond that point, adding more substrate does not increase the rate.
Why use a Lineweaver-Burk plot?
Plotting 1/v against 1/[S] linearises the hyperbolic Michaelis-Menten curve, making Vmax and Km much easier to read accurately from the intercepts than from the asymptotic plateau.
Keep reading: Enzymes explained · Levels of protein structure · Glycolysis explained