Question 75:
The substrate concentration at which an enzyme-catalyzed reaction proceeds at one-half of its velocity is called:
The substrate concentration at which an enzyme-catalyzed reaction proceeds at one-half of its maximum velocity (½ Vmax) is called Km, the Michaelis constant.
Correct Answer
(B) Km
Michaelis-Menten Kinetics Core
Km defines enzyme-substrate affinity in the equation:
v = (Vmax × [S]) / (Km + [S])
When v = ½ Vmax, then [S] = Km. Lower Km = higher affinity (enzyme works at low substrate levels).
Option Analysis
| Option | Definition | Correct/Incorrect |
|---|---|---|
| (A) Kcat | Turnover number (s⁻¹); catalytic speed | ❌ Wrong |
| (B) Km | [S] at ½ Vmax; substrate affinity | ✅ Correct |
| (C) V₀ | Initial velocity at specific [S] | ❌ Wrong |
| (D) Vmax | Maximum velocity when saturated | ❌ Wrong |
Detailed Breakdown:
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(A) Kcat: Molecules converted per active site per second. Catalase: 4×10⁷ s⁻¹. Measures speed, not [S]. [prior catalase Q]
-
(B) Correct: By definition, Km = [S] where v = ½ Vmax. Hexokinase Km ≈ 0.1 mM; glucose optimal.
-
(C) V₀: Reaction rate at any given time/[S]. Depends on conditions.
-
(D) Vmax: Plateau velocity when all enzyme saturated. Independent of [S].
Biological Significance
| Enzyme | Km (mM) | Affinity | Example |
|---|---|---|---|
| Hexokinase | 0.1 | High | Low glucose |
| Glucokinase | 10 | Low | Post-meal glucose |
| Catalase | 1.1 | Moderate | H₂O₂ detox |
GATE tip: “Half Vmax” = Km (90% questions). Visualize hyperbolic curve!
The substrate concentration at which an enzyme-catalyzed reaction proceeds at one-half of its maximum velocity defines Km (Michaelis constant), cornerstone of enzyme kinetics for GATE Life Sciences.
Michaelis-Menten Equation
v = Vmax × [S]
Km + [S]
When v = ½ Vmax:
½ Vmax = Vmax × [S] / (Km + [S])
Km = [S] ✓
Km vs Other Parameters
| Parameter | Measures | Units | Curve Position |
|---|---|---|---|
| Km | [S] at ½ Vmax | mM, µM | X-axis |
| Kcat | Catalytic turnover | s⁻¹ | Slope |
| V₀ | Initial rate | µmol/min | Any point |
| Vmax | Saturation rate | µmol/min | Plateau |
Km affinity rule: Low Km = high affinity (hexokinase 0.1 mM); High Km = low affinity (glucokinase 10 mM).
Classic Enzyme Examples
Hexokinase: Km = 0.1 mM → Muscle (constant glucose)
Glucokinase: Km = 10 mM → Liver (post-meal spikes)
Liver senses glucose surges; muscle maintains steady levels. Perfect physiological adaptation!
GATE Exam Pattern Recognition
Question templates:
-
“Substrate concentration giving ½ Vmax?” → Km
-
“Low Km means?” → High affinity
-
“Vmax independent of?” → Substrate concentration
Trick options: Kcat (speed), V₀ (initial), Vmax (max)—all velocity measures, not concentrations.
Graphical Interpretation
Hyperbolic curve: V vs [S]
- X-intercept ≈ Km (½ height)
- Plateau = Vmax
- Slope at origin = Vmax/Km (efficiency)
Master substrate concentration half maximum velocity enzyme = Km for guaranteed biochemistry scores!
