Michaelis–Menten Inhibition
Distinguish inhibition mechanisms through their changes to apparent Km and Vmax.
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Michaelis–Menten Inhibition: Apparent Km and Vmax
Different types of enzyme inhibition affect the apparent Michaelis–Menten parameters, Km and Vmax, in distinct ways. By studying the initial-rate law v = S / (α + α'S) for normalized baseline parameters (Vmax = Km = Ki = 1), we can understand how competitive, uncompetitive, and pure noncompetitive inhibitors alter the saturation curve.
Worked example: Competitive inhibition
In competitive inhibition, the inhibitor binds to the same active site as the substrate. This increases the apparent Km without affecting the Vmax. Let's calculate the initial velocity for a competitive inhibitor at S = 1 and I = 1.
- For competitive inhibition, α = 1 + I = 1 + 1 = 2, and α' = 1.
- Apparent Vmax = 1 / α' = 1 / 1 = 1.0.
- Apparent Km = α / α' = 2 / 1 = 2.0.
- Initial velocity v = S / (α + α'S) = 1 / (2 + 1 * 1) = 1/3 ≈ 0.3333333333333333.
- Reciprocal velocity 1/v = 3.0.
| Mechanism | Apparent Vmax | Apparent Km | Velocity (S=1) |
|---|---|---|---|
| Competitive | 1.0 | 2.0 | 0.3333 |
| Noncompetitive | 0.5 | 1.0 | 0.25 |
| Uncompetitive | 0.5 | 0.5 | 0.3333 |
Explore the saturation curves
Open Michaelis–Menten Inhibition. The interactive model lets you change the Mechanism, Substrate, and Inhibitor concentrations.
- Set the Mechanism to "Competitive", Substrate to 1, and Inhibitor to 1. Observe that Apparent Vmax remains 1.0, while Apparent Km increases to 2.0.
- Change the Mechanism to "Noncompetitive". Notice that both Apparent Vmax and Apparent Km are affected. Apparent Vmax drops to 0.5, and Apparent Km remains 1.0.
- Change the Mechanism to "Uncompetitive". In this case, both Apparent Vmax and Apparent Km decrease to 0.5.
- Vary the Inhibitor concentration to see how the saturation curve shifts depending on the chosen mechanism. At I = 0, all mechanisms reduce to the standard Michaelis-Menten kinetics.
Assumptions and limitations
This model assumes the ordinary initial-rate Michaelis–Menten regime, where the enzyme concentration is much lower than the substrate concentration, and the system is at a quasi-steady state. It uses normalized parameters (baseline Vmax=1, Km=1, Ki=1) to focus on the relative changes caused by inhibitors. Furthermore, we distinguish substrate affinity shorthand from a general binding-equilibrium claim. At Substrate = 0, the initial velocity is 0, and the reciprocal velocity is "Unavailable" since division by zero is undefined.
References
For a detailed discussion on enzyme kinetics and inhibition mechanisms, refer to the following text:
- Biochemistry. 5th edition. Section 8.5: Enzymes Can Be Inhibited by Specific Molecules. This source explains how different inhibitors alter Vmax and Km.
Experience it interactively
Adjust parameters, observe in real time, and build deep intuition with Riano’s interactive Michaelis–Menten Inhibition module.
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