Biology · Introductory biology · Concept
Enzyme kinetics: Michaelis–Menten and inhibition
Enzyme kinetics measures how fast an enzyme turns substrate into product. In the Michaelis–Menten model the initial rate v rises with the substrate concentration [S] and levels off at a maximum rate Vmax, when nearly every enzyme molecule is busy; Km is the substrate concentration that gives half of Vmax. Inhibitors change these two numbers in telltale ways: a competitive inhibitor raises the apparent Km, and a noncompetitive inhibitor lowers Vmax.
Measure initial rates
Mix a fixed amount of enzyme with a series of substrate concentrations and measure each initial rate v: the speed of product formation before substrate runs down or product builds up. Plotting v against [S] shows how the enzyme responds to substrate.
The Michaelis–Menten equation
At low [S] the rate rises almost in proportion to [S]. At high [S] it levels off at Vmax, because nearly all the active sites are occupied. When [S] = Km, the rate is exactly half of Vmax.
What Km and Vmax tell you
Vmax is proportional to the amount of enzyme: twice the enzyme, twice Vmax. Km describes the enzyme and substrate under the stated conditions: a lower Km means the enzyme reaches half speed at a lower substrate concentration. Km is often read as affinity, but in general it is not the dissociation constant of the enzyme–substrate complex.
Competitive and noncompetitive inhibitors
A competitive inhibitor binds the active site and competes with the substrate, so enough substrate outcompetes it: Vmax stays the same and the apparent Km rises. A pure noncompetitive inhibitor binds elsewhere, to the free enzyme and the enzyme–substrate complex alike, and takes enzyme out of action at every substrate level: Vmax falls and Km stays the same.
| Inhibitor | Apparent Km | Apparent Vmax |
|---|---|---|
| Competitive | Rises | Unchanged |
| Noncompetitive (pure) | Unchanged | Falls |
| Uncompetitive | Falls | Falls |
Fit the curve instead of reading the last point
Rates approach Vmax without reaching it, so the largest measured rate underestimates Vmax. Fitting the Michaelis–Menten curve to all the points by least squares estimates both parameters at once. The older double-reciprocal (Lineweaver–Burk) plot of 1/v against 1/[S] straightens the curve but magnifies the errors in the slowest rates.
The double-reciprocal form
Taking reciprocals gives 1/v = (Km/Vmax)(1/[S]) + 1/Vmax, a line with slope Km/Vmax and intercept 1/Vmax. It shows inhibition patterns clearly, but a fit on the original scale gives better estimates.
Common mistakes
- Reading Km as the substrate concentration that gives Vmax: Km gives half of Vmax, and Vmax is only approached.
- Taking the largest measured rate as Vmax while the curve is still rising.
- Expecting a competitive inhibitor to lower Vmax: enough substrate outcompetes it.
- Treating a good curve fit as proof of an inhibition mechanism: different models can fit the same limited data.
Key terms
- Enzyme
- A biological catalyst, usually a protein, that speeds up a reaction without being used up and without changing the equilibrium. Temperature, pH and its 3D shape affect how well it works.
- Enzyme substrate
- The molecule an enzyme acts on. Substrate concentration and the amount of enzyme are separate things when reading a reaction-rate curve.
- Active site
- The pocket on an enzyme where the substrate binds and the reaction happens. Molecules binding elsewhere can also change its shape and activity.
- Michaelis–Menten model
- v = Vmax[S]/(Km + [S]): the reaction rate rises with substrate concentration and then levels off at Vmax, once the enzyme is saturated.
- Michaelis constant
- Km, the substrate concentration at which the reaction rate is half of Vmax. A low Km means the enzyme works near full speed even at low substrate concentrations.
- Maximum enzyme rate
- The top reaction rate an enzyme reaches when it is saturated with substrate. It rises with the amount of enzyme present.
- Competitive inhibition
- An inhibitor that competes with the substrate for the active site. It raises the apparent Km, but enough substrate still reaches the same Vmax.
- Noncompetitive inhibition
- An inhibitor that binds elsewhere on the enzyme, whether or not substrate is bound. It lowers Vmax without changing Km, and extra substrate can’t overcome it.
Work through an example
An enzyme assay gives initial rates of 4.1, 6.5, 10.2, 13.1, 16.2 and 17.6 µmol/min at 1, 2, 4, 8, 16 and 32 mM substrate. Estimate Vmax and Km, and predict the rate at 10 mM.
Find Km and Vmax from enzyme rate data →Sources and scope
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