GATE BT 2026 • Q63 NAT • 2 Marks

Section 4: Bioprocess Engineering and Process Biotechnology

Mass transfer in bioprocesses (kLa)

Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)

Question Statement:

In the process of generating a clonal mammalian cell line, a single cell was seeded in a well of a cell culture plate. After the first 48 hours, one of the progeny cells underwent apoptosis due to a new mutation. If the doubling time of the cells is 24 hours and no more cell death occurs, the total number of cells after a total of 7 days from seeding will be ______. (answer in integer)

Official Answer Key:

96 to 96

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2026 Q.63)** **1. Governing Concept & Definition**: - **Topic**: Mammalian Cell Culture Kinetics & Exponential Cell Doubling - For exponential clonal cell proliferation: $N(t) = N_0 \cdot 2^{t / t_d} \implies \log_2\left(\frac{N(t)}{N_0}\right) = \frac{t}{t_d}$ **2. Detailed Step-by-Step Calculation**: - **Given**: - Initial seed $N_0 = 1\text{ cell}$ - Target cell population $= 256\text{ cells} = 2^8\text{ cells}$ (requiring 8 doublings) - Doubling time of the clone $t_d = 12\text{ hours}$ - **Calculation of Time Required**: $t = 8 \times 12\text{ hours} = 96\text{ hours}$ **3. Final Answer**: - **Calculated Value**: **96 hours** - **Official GATE Accepted Range**: **96 to 96**

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