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

Monod Growth Kinetics: Effect of Increased KS on Bacterial Specific Growth Rate

Introduction

The growth of microorganisms depends largely on the availability of nutrients in their surrounding environment. One of the most widely used mathematical models to describe microbial growth under substrate-limited conditions is the Monod equation, proposed by Jacques Monod in 1949. This equation relates the specific growth rate of microorganisms to the concentration of the limiting nutrient present in the medium.

The Monod equation introduces an important parameter called the substrate-specific constant (KS), also known as the half-saturation constant. KS represents the substrate concentration at which the microbial growth rate becomes half of the maximum specific growth rate (μ_max). A lower KS indicates a higher affinity of the microorganism for the substrate, whereas a higher KS indicates a lower substrate affinity. Consequently, mutations that increase KS reduce the organism’s ability to efficiently utilize nutrients at low substrate concentrations, even if μ_max remains unchanged.

Correct Answer

Correct Answer: 5.5 (approximately)

Detailed Explanation

The relationship between substrate concentration and microbial growth is described by the Monod equation:

μ = μ_max × S / (KS + S)

where:

• μ = Specific growth rate
• μ_max = Maximum specific growth rate
• S = Substrate concentration
• KS = Half-saturation constant

Since μ_max remains unchanged, only the value of KS changes.

Step 1: Convert the Substrate Concentration

Given ammonium concentration:

0.5 mM = 500 μM

Step 2: Calculate the Original Growth Rate

Original KS = 50 μM

μ_original = μ_max × 500 / (50 + 500)

= μ_max × 500 / 550

= 0.909 μ_max

Step 3: Calculate the Mutant Growth Rate

Mutant KS = 5000 μM

μ_mutant = μ_max × 500 / (5000 + 500)

= μ_max × 500 / 5500

= 0.0909 μ_max

Step 4: Determine the Decrease Factor

The decrease factor is obtained by dividing the original growth rate by the mutant growth rate.

Decrease Factor = μ_original / μ_mutant

= 0.909 / 0.0909

= 10

Therefore, the mutation decreases the specific growth rate by a factor of 10.

Step-by-Step Calculation Summary

Formula Used

Biological Interpretation

The substrate-specific constant (KS) reflects the affinity of a microorganism for its nutrient. A lower KS means that the organism can efficiently utilize nutrients even when substrate concentrations are low. Conversely, a large increase in KS indicates a significant reduction in substrate affinity. In this problem, increasing KS from 50 μM to 5000 μM causes the bacterium to grow much more slowly at the same ammonium concentration because the transport system or nutrient uptake mechanism has become much less efficient.

Although the mutation does not alter the maximum possible growth rate (μ_max), the organism can no longer approach μ_max under the given nutrient concentration. This demonstrates why KS is considered a measure of nutrient affinity rather than maximum growth capacity.

Importance of the Monod Equation

Final Answer

Given:

KS changes from 50 μM to 5000 μM

Substrate concentration = 0.5 mM = 500 μM

Original growth rate = 0.909 μ_max

Mutant growth rate = 0.0909 μ_max

Decrease Factor = 10

Correct Answer: 10