Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
Which one of the following represents non-growth associated product
formation kinetics in a bioprocess system? X and P denote viable cell and
product concentrations, respectively.
Options:
(A) Concentration
Time
(B) X
Concentration
Time
X
Concentration
Time
(D) =----=
Concentration
Time
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2021 Q.36)**
**1. Governing Concept**:
- **Topic**: Bioprocess Kinetics & Luedeking-Piret Model
- Product formation kinetics in fermentation are described by the **Luedeking-Piret equation**:
$q_p = \frac{1}{X}\frac{dP}{dt} = \alpha \mu + \beta$
where $\alpha$ is growth-associated product formation coefficient and $\beta$ is non-growth-associated product formation coefficient.
- For **purely non-growth-associated products** ($\alpha = 0, \beta > 0$, e.g., secondary metabolites like antibiotics):
- Product synthesis occurs primarily during the **stationary phase** after cell growth has ceased ($dX/dt \approx 0$).
- Viable cell concentration $X$ plateaus, while product concentration $P$ increases linearly during stationary phase. Curve (C) illustrates this distinct plateau in $X$ coupled with linear production of $P$.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Represents growth-associated kinetics (simultaneous growth and product accumulation).
- **Option (B) is INCORRECT**: Distorted cell-product profile.
- **Option (C) is CORRECT**: Depicts cell mass reaching stationary phase while product concentration $P$ rises independently.
- **Option (D) is INCORRECT**: Erroneous curves.
**3. Final Answer**:
- **Correct Choice**: **C**
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