Q.41 Consider a continuous culture provided with a sterile feed
containing 10 mM glucose. The steady-state cell density and substrate
concentration at three different dilution rates are given in the table below.
| Dilution rate (h−1) | Cell density (g L−1) | Substrate concentration (mM) |
|---|---|---|
| 0.05 | 0.248 | 0.067 |
| 0.5 | 0.208 | 1.667 |
| 5 | 0 | 10 |
The maximum specific growth rate
μm (in h−1), will be ______.
Maximum Specific Growth Rate (μm) in Continuous Culture from Chemostat Data
In microbial kinetics, a continuous culture (chemostat) maintains cells at steady state by continuously supplying fresh medium and removing culture at a fixed dilution rate.
One of the most important kinetic parameters is the maximum specific growth rate (μm).
Given Data
A continuous culture is supplied with a sterile feed containing 10 mM glucose.
| Dilution rate (h-1) | Cell density (g L-1) | Substrate concentration (mM) |
|---|---|---|
| 0.05 | 0.248 | 0.067 |
| 0.5 | 0.208 | 1.667 |
| 5 | 0 | 10 |
Chemostat Principle
At steady state in a continuous culture:
μ = D
Where μ is the specific growth rate and D is the dilution rate.
Cells can survive only when:
D ≤ μm
If D exceeds μm, cells are washed out and biomass becomes zero.
Step-by-Step Analysis
D = 0.05 h-1
- Cell density is non-zero
- Substrate is almost completely consumed
- Growth is sustainable
D = 0.5 h-1
- Cell density is still present
- Residual substrate increases
- Growth is still sustainable
D = 5 h-1
- Cell density becomes zero
- Substrate concentration equals feed concentration
- Complete washout occurs
Determination of μm
Cells survive up to a dilution rate of 0.5 h-1 but are washed out at
5 h-1.
Therefore, the maximum specific growth rate is:
μm = 0.5 h-1
Final Answer
μm = 0.5 h-1
Key Takeaways
- At steady state, μ equals the dilution rate
- Washout occurs when D exceeds μm
- μm is identified by the highest D with non-zero biomass
