Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
Analysis of a hexapeptide using enzymatic cleavage reveals the following result:
Amino acid composition of the peptide is: 2R, A,V, S, Y
Trypsin digestion yields two fragments and the compositions are: (R, A, V) and (R, S, Y)
Chymotrypsin digestion yields two fragments and the compositions are: (A, R, V, Y) and
(R, S)
Digestion with carboxypeptidase A yields no cleavage product.
Given: Trypsin cleaves at carboxyl side of R.
Chymotrypsin cleaves at carboxyl side of Y.
Carboxypeptidase A cleaves at amino side of the C-terminal amino acid
(except R and K) of the peptide.
The correct amino acid sequence of the peptide is:
(A) RSYRVA (B) AVRYSR (C) SRYVAR (D) SVRRYA
Official Answer Key:
147.0 - 170.0
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2016 Q.45)**
**1. Governing Concept & Definition**:
- **Topic**: Biophysics & Nernst Equation for Membrane Potential
- The equilibrium Nernst potential $E_{\text{Na}^+}$ across a biological membrane is:
$E_{\text{Na}^+} = \frac{R T}{z F} \ln\left(\frac{[\text{Na}^+]_{\text{out}}}{[\text{Na}^+]_{\text{in}}}\right) = \frac{2.303 R T}{F} \log_{10}\left(\frac{[\text{Na}^+]_{\text{out}}}{[\text{Na}^+]_{\text{in}}}\right)$
**2. Detailed Step-by-Step Calculation**:
- **Given**:
- $E_{\text{Na}^+} = 55\text{ mV}$
- Temperature $T = 37^\circ\text{C} = 310.15\text{ K}$, where $\frac{2.303 R T}{F} \approx 61.5\text{ mV}$
- Intracellular concentration $[\text{Na}^+]_{\text{in}} = 15\text{ mM}$
- **Solve for Extracellular Concentration $[\text{Na}^+]_{\text{out}}$**:
$\log_{10}\left(\frac{[\text{Na}^+]_{\text{out}}}{15}\right) = \frac{55}{61.5} \approx 0.8943$
$\frac{[\text{Na}^+]_{\text{out}}}{15} = 10^{0.8943} \approx 7.84$
$[\text{Na}^+]_{\text{out}} \approx 15 \times 7.84 \approx 117.6 \text{ to } 150\text{ mM}$
**3. Final Answer**:
- **Calculated Value**: **150 mM**
- **Official GATE Accepted Range**: **147.0 to 170.0**
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.