Q.54 In a bacterium, a mutation resulted in an increase of KS (substrate-specific constant) for ammonium
from 50 μM to 5000 μM without affecting μ max . The specific growth rate (μ) of the mutant growing
on 0.5 mM ammonium in the medium decreases by a factor of ________.

Introduction to KS Mutation Impact

In bacterial growth kinetics, a mutation raising the KS (substrate-specific constant) for ammonium from 50 μM to 5000 μM reduces affinity without altering μ_max, slashing specific growth rate (μ) on 0.5 mM ammonium by a factor of 10 per Monod equation.

This CSIR NET-style problem tests Monod model application in microbial physiology.

Understanding KS reveals why mutants struggle at low substrate levels.

Monod Kinetics Basics

Bacterial growth follows the Monod equation: μ = μ_max × [S] / (K_S + [S]), where μ is the specific growth rate, μ_max is unchanged, [S] is substrate concentration, and K_S is the substrate-specific constant (half-saturation constant).

A higher K_S reduces substrate affinity, lowering μ at fixed [S] since the denominator increases.

Here, ammonium [S] = 0.5 mM = 500 μM, original K_S = 50 μM, mutant K_S = 5000 μM.

Original Strain Calculation

For wild-type: μ / μ_max = 500 / (50 + 500) = 500 / 550 ≈ 0.909.

Thus, μ_original ≈ 0.909 μ_max.

Growth occurs near maximum since [S] >> original K_S.

Mutant Strain Calculation

For mutant: μ / μ_max = 500 / (5000 + 500) = 500 / 5500 ≈ 0.091.

Thus, μ_mutant ≈ 0.091 μ_max.

Growth slows as [S] << mutant K_S, resembling substrate limitation.

Decrease Factor

The ratio μ_original / μ_mutant = 0.909 / 0.091 = 10.

μ decreases by a factor of 10 exactly, since 550 / 55 = 10 and 5550 / 550 = 10.

No options provided, but answer fills numerical blank as 10.

Monod Equation Explained

The Monod equation μ = μ_max × [S] / (K_S + [S]) mirrors Michaelis-Menten kinetics for growth-limited substrates like ammonium.

K_S signifies [S] yielding half μ_max; low K_S means high affinity.

At [S] = 500 μM, original strain nears μ_max (90.9%), mutant hits 9.1%.

Step-by-Step Solution

Original: μ = μ_max × 500/550 = 0.909 μ_max.

Mutant: μ = μ_max × 500/5500 = 0.091 μ_max.

Factor: 0.909/0.091 = 10, exact due to 100-fold K_S rise vs. fixed [S].

Biological Implications

• Higher K_S mutants grow poorly at typical ammonium levels (e.g., 63-170 μM in chemostats), favoring wild-types in nature.
• Impacts bioremediation, wastewater treatment where ammonia-oxidizers compete.
• For CSIR NET, master via practice: compute μ ratios directly from parameters.