Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
The contour length of a B-DNA molecule that encodes a bacterial protein of
33 kDa is ______ nm.
Consider the average molecular weight of an amino acid as 110 Da and helix
rise per base pair for B-DNA as 0.34 nm.
(Round off to the nearest integer)
Official Answer Key:
300 to 310
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2025 Q.31)**
**1. Governing Concept & Definition**:
- **Topic**: Molecular Biology & Structural Properties of B-DNA
- **Key Parameters**:
- Average molecular weight of an amino acid $\approx 110\text{ Da}$
- Number of nucleotides per amino acid codon = $3\text{ bp}$
- B-DNA axial rise per base pair ($h$) = $0.34\text{ nm}$ ($3.4\text{ Å}$)
**2. Detailed Step-by-Step Calculation**:
- **Step 1: Calculate number of amino acids in the 33 kDa protein**:
$\text{Molecular weight} = 33\text{ kDa} = 33000\text{ Da}$
$\text{Number of amino acid residues} = \frac{33000}{110} = 300\text{ residues}$
- **Step 2: Calculate number of base pairs in the encoding DNA**:
$\text{Number of base pairs} = 300 \times 3 = 900\text{ bp}$
- **Step 3: Calculate contour length of the B-DNA duplex**:
$\text{Contour length} = \text{number of base pairs} \times \text{rise per bp} = 900 \times 0.34\text{ nm} = 306\text{ nm}$
**3. Final Answer**:
- **Calculated Value**: **306 nm**
- **Official GATE Accepted Range**: **300 to 310**
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