5. In an enzyme-catalysed reaction, if [S] = 10 KM the velocity of the reaction is about:
a. 0.9 Vmax
b. 0.7 Vmax
c. 0.5 Vmax
d. 0.1 Vmax
Introduction to Enzyme Catalysed Reaction Velocity
Enzyme catalysed reaction velocity depends on substrate concentration [S] relative to KM in Michaelis-Menten kinetics, crucial for CSIR NET Life Sciences preparation. When [S] = 10 KM, the enzyme approaches full saturation, yielding near-maximum speed—ideal for exam questions on enzyme kinetics.
Michaelis-Menten Equation Basics
The Michaelis-Menten equation describes reaction velocity \( v = \frac{V_{\max} [S]}{K_M + [S]} \), where \( V_{\max} \) is maximum velocity at saturating substrate, \( K_M \) is the substrate concentration yielding half \( V_{\max} \), and [S] is substrate concentration. Substituting [S] = 10 \( K_M \) gives \( v = \frac{V_{\max} \cdot 10K_M}{K_M + 10K_M} = \frac{10V_{\max}}{11} \approx 0.909V_{\max} \). This confirms high substrate saturation drives velocity near maximum.
Why [S] = 10 KM Gives 0.9 Vmax
At [S] >> KM, velocity nears Vmax; specifically, [S] = 10 KM saturates ~91% of active sites, so \( v \approx 0.9V_{\max} \). This contrasts with [S] = KM (0.5 Vmax) or low [S] (linear rise), highlighting hyperbolic kinetics essential for CSIR NET.
Detailed Option Analysis
| Option | Velocity | Analysis | Status |
|---|---|---|---|
| a. 0.9 Vmax | ~91% Vmax | Correct, as \( \frac{10}{11} \approx 0.91 \) (often rounded to 0.9), matching calculations for [S] = 10 KM. | ✅ Correct |
| b. 0.7 Vmax | 70% Vmax | Incorrect; occurs around [S] ≈ 2.33 KM (\( v/V_{\max} = 0.7 \)), far below 10 KM saturation. | ❌ Incorrect |
| c. 0.5 Vmax | 50% Vmax | Incorrect; defines KM exactly where [S] = KM (\( v = 0.5V_{\max} \)). | ❌ Incorrect |
| d. 0.1 Vmax | 10% Vmax | Incorrect; typical for low [S] ≈ 0.11 KM, showing first-order kinetics. | ❌ Incorrect |
Substrate Saturation Table
| [S]/KM Ratio | Velocity (% Vmax) | Kinetics Type |
|---|---|---|
| 0.1 | ~9% | First-order |
| 1 | 50% | Half-max |
| 10 | ~91% | Zero-order |
| ∞ | 100% | Saturated |
Master this table for CSIR NET enzyme kinetics success.
