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A competitive inhibitor raises apparent Michaelis constant while Vmax remains unchanged in the ideal model.
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Formula
v and Vmax same rate unit · substrate and inhibitor concentrations, Km and Ki same concentration unit · α dimensionless
| Symbol | Meaning | Unit |
|---|---|---|
| Initial rate with substrate and inhibitor | concentration/time | |
| Vmax | Maximum rate at unchanged enzyme amount | concentration/time |
| Substrate concentration | concentration | |
| Michaelis constant without inhibitor | concentration | |
| Inhibition factor 1+[I]/Ki | dimensionless | |
| [I], Ki | Inhibitor concentration and dissociation constant | concentration |
v=\frac{V_{max}[S]}{\alpha K_m+[S]},\quad \alpha=1+\frac{[I]}{K_i}The model assumes inhibitor and substrate compete for free enzyme and that the ES complex remains productive. Then Km,app=αKm, while Vmax is theoretically unchanged. Real enzymes may show mixed inhibition, slow binding, cooperativity or substrate inhibition. Initial rates and controlled conditions are needed for estimation.
Initial-rate Michaelis–Menten model for reversible competition at free enzyme; mixed or time-dependent inhibition needs other models.
Inhibitor occupancy reduces free enzyme; more substrate can compete in the ideal model.
Solve for a quantity
Apparent Km rises in proportion to α.
Km=2 mM, α=3. What apparent Km follows?
Km,app=3·2=6 mM; Vmax is unchanged.
Modeling every inhibition as competitive.
Check mechanism and the pattern in Km and Vmax.
Formula cluster
Increasing substrate can overcome ideal competitive inhibition, not every inhibitor.
Let Km=2 mM, [I]=3 mM and Ki=3 mM. Then α=2 and Km,app=4 mM. At [S]=4 mM, v/Vmax=4/(4+4)=0.50. Check: half-maximal rate occurs at Km,app.
Comparing idealized enzyme rates with and without a competitive inhibitor
Here is how to work through a typical Competitive enzyme inhibition (v = Vmax[S]/(αKm+[S])) task step by step:
Task
Km=2 mM, α=3. What apparent Km follows?
Solution path
Km,app=3·2=6 mM; Vmax is unchanged.
In the ideal model, inhibitor binds free enzyme and competes with substrate for that form. At the same substrate concentration, less free enzyme is available to form ES; more substrate is needed to reach half-maximal rate. This appears as increased Km,app=αKm. The intrinsic substrate-binding constant need not change; it is an apparent kinetic value in the inhibitor’s presence. Parameters apply to initial rates and the assumed pure inhibition mechanism. Apparent changes in Km or Vmax require checking mixed inhibition and assay artifacts. High substrate does not generally reverse other inhibitor types.
At very high substrate concentration, substrate largely outcompetes the reversible competitive inhibitor at the active site. The enzyme can then reach the same theoretical maximum rate, although rates at lower substrate levels decline. This applies to pure competitive inhibition in the Michaelis–Menten model. An observed Vmax change can indicate a mixed mechanism, enzyme inactivation or an insufficient concentration range. Parameters apply to initial rates and the assumed pure inhibition mechanism. Apparent changes in Km or Vmax require checking mixed inhibition and assay artifacts. High substrate does not generally reverse other inhibitor types.
Ki is an equilibrium dissociation constant for inhibitor binding in the model. A lower Ki indicates tighter binding under comparable conditions. α=1+[I]/Ki describes how inhibitor concentration raises apparent Km. Ki is not a universal potency number across assays: pH, temperature, enzyme state, substrate and mechanism matter. Comparisons require consistent units and experimental conditions. Parameters apply to initial rates and the assumed pure inhibition mechanism. Apparent changes in Km or Vmax require checking mixed inhibition and assay artifacts. High substrate does not generally reverse other inhibitor types.
Reproduce the example calculation: Let Km=2 mM, [I]=3 mM and Ki=3 mM. Competitive enzyme inhibition uses v = Vmax[S]/(αKm+[S]). In plain terms, a competitive inhibitor raises apparent Michaelis constant while Vmax remains unchanged in the ideal model. Unit check: v and Vmax same rate unit · substrate and inhibitor concentrations, Km and Ki same concentration unit · α dimensionless. Initial-rate Michaelis–Menten model for reversible competition at free enzyme; mixed or time-dependent inhibition needs other models. Values are comparable only when their definitions, denominators and periods match. Record these details next to the result so the reference group is clear. If the direction is implausible, check data preparation and the calculation basis before discussing biological causes.
A key limit of Competitive enzyme inhibition is this: Initial-rate Michaelis–Menten model for reversible competition at free enzyme; mixed or time-dependent inhibition needs other models. Do not use the metric without its reference; it is useful for Comparing idealized enzyme rates with and without a competitive inhibitor. A competitive inhibitor raises apparent Michaelis constant while Vmax remains unchanged in the ideal model. When comparing populations or experiments, check whether definitions, denominators and observation periods match. If the assumption is implausible, the result shows only what the simplified model calculates from its inputs; it is not a reliable estimate for the target population. State this limitation in the report, and do not infer a causal effect from the formula alone.
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Which formula describes Competitive enzyme inhibition?
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