Q.63 Consider a simple uni-substrate enzyme that follows Michaelis-Menten kinetics. When the
enzyme catalyzed reaction was carried out in the presence of 10 nM concentration of an
inhibitor, there was no change in the maximal velocity. However, the slope of the
Lineweaver-Burk plot increased 3-fold. The dissociation constant for the enzyme-inhibitor
complex (in nM) is _________
Lineweaver-Burk Plot Slope 3-Fold Increase with Unchanged Vmax – Dissociation Constant Revealed
A Michaelis-Menten enzyme shows a tripling of Lineweaver-Burk slope at 10 nM inhibitor while retaining the same Vmax, confirming competitive inhibition and revealing Ki = 5 nM.
Core Enzyme Kinetics Recap
The Lineweaver-Burk equation is the double-reciprocal form of Michaelis-Menten:
1/v = (Km/Vmax)(1/[S]) + 1/Vmax
Slope = Km/Vmax
Y-intercept = 1/Vmax
Unchanged Vmax keeps the y-intercept constant, eliminating non-competitive or uncompetitive inhibition types.
Competitive Inhibition Mechanism
Competitive inhibitors bind the free enzyme, producing EI complex with dissociation constant:
Ki = [E][I]/[EI]
Apparent Km increases according to:
Kmapp = Km(1 + [I]/Ki)
Given:
- [I] = 10 nM
- Slope increases 3×
Thus:
1 + [I]/Ki = 3
1 + 10/Ki = 3 → 10/Ki = 2 → Ki = 5 nM
Why Not Other Inhibitor Types?
Non-competitive inhibition
- Vmax decreases
- Slope rises due to Vmax drop
- Y-intercept changes
- Does not match unchanged Vmax
Uncompetitive inhibition
- Lowers both Km and Vmax
- Parallel Lineweaver-Burk lines
- No slope change
No inhibition
- Slope & intercept identical
- Contradicts 3-fold slope increase
Lineweaver-Burk Diagnostic Table
| Inhibitor Type | Vmax Effect | Slope Change | X-Intercept | Plot Pattern |
|---|---|---|---|---|
| Competitive | Unchanged | Increases | Shifts right | Same y-intercept, steeper slope |
| Non-competitive | Decreases | Increases | Unchanged | Higher y-intercept, steeper |
| Uncompetitive | Decreases | Unchanged | Shifts left | Parallel lines |
Conclusion
This system displays competitive inhibition. A 10 nM inhibitor increasing slope 3-fold corresponds to Ki = 5 nM. Understanding this helps in drug discovery, fermentation engineering, and metabolic regulation.
