Biotechnology: Principles and Processes Set-2

Q1. In an ideal PCR (100% amplification efficiency), starting from a single double‑stranded DNA molecule, the number of double‑stranded DNA molecules after 20 cycles will be:

Q2. During a transformation experiment, $0.02\ \mu\text{g}$ of plasmid DNA was mixed with competent E. coli and after recovery the final volume was $1.0\ \text{mL}$. If $200\ \mu\text{L}$ of this suspension was plated and $400$ colonies were counted, the transformation efficiency (transformants per $\mu\text{g}$ DNA), calculated as

is approximately:

Q3. A PCR primer has sequence 5′‑ATGCGTACGTTAGC‑3′. Using the approximation

and the rule of thumb $T_a \approx T_m - 5^\circ\mathrm{C}$ for annealing temperature, the best approximate annealing temperature $T_a$ to use is:

Q4. Assertion (A): Using a mixture of Taq DNA polymerase and Pfu DNA polymerase in PCR typically gives higher amplification yield and reduced error rate compared to using Taq alone.
Reason (R): Pfu possesses a 3′→5′ exonuclease (proofreading) activity, whereas Taq lacks proofreading activity.

Q5. A researcher trying to clone a protein that is toxic to E. coli into a T7 promoter–based expression vector (e.g., pET) and transform BL21(DE3) observes very few colonies; those recovered often lack the insert or contain mutations. Which modification will most effectively improve recovery of correct clones without changing the gene sequence?

Q6. In a PCR experiment with ideal amplification (each cycle doubles the number of target molecules), starting with $N_0=500$ template molecules the number after $n=10$ cycles is given by $N=N_0\times 2^n$. What is the expected number of target molecules?

Q7. In a bacterial transformation experiment $10\ \text{ng}$ of plasmid DNA were used. After recovery, $100\ \mu\text{L}$ of a $1\!:\!1000$ dilution of the transformation mixture was plated and produced 50 colonies. Using the transformation efficiency formula $TE=\dfrac{N\times DF\times(1/V_{\text{plated}})}{M}$ where $N$ = colonies counted, $DF$ = dilution factor, $V_{\text{plated}}$ in mL and $M$ is DNA mass in µg, calculate $TE$ (transformants per µg).

Q8. A circular plasmid of size $5400\ \text{bp}$ was analyzed by restriction digestion. Results: (i) BamHI single digest produced two fragments of $2000\ \text{bp}$ and $3400\ \text{bp}$. (ii) EcoRI single digest produced a single linear band of $5400\ \text{bp}$. (iii) BamHI + EcoRI double digest produced three fragments of $2000\ \text{bp}$, $2400\ \text{bp}$ and $1000\ \text{bp}$. Which statement best describes the arrangement of restriction sites?

Q9. During a batch fermentation biomass follows $X(t)=X_0 e^{\mu t}$ with $X_0=0.5\ \mathrm{g\,L^{-1}}$ and $\mu=0.693\ \mathrm{h^{-1}}$. Product formation follows Luedeking–Piret kinetics $r_P=\alpha\dfrac{dX}{dt}+\beta X$ with $\alpha=0.5\ \mathrm{g\ product/g\ biomass}$ and $\beta=0.2\ \mathrm{h^{-1}}$. If $P(0)=0$, what is $P(2\ \mathrm{h})$? (Use $\int_0^t X(t)\,dt=\dfrac{X_0}{\mu}\big(e^{\mu t}-1\big)$.)

Q10. In qPCR, fold-difference in starting template between two samples can be approximated by $Fold=E^{\Delta Ct}$ where $E$ is the amplification factor per cycle (e.g., $E=2$ for 100% efficiency) and $\Delta Ct=Ct_{\text{later}}-Ct_{\text{earlier}}$. Sample A has $Ct=18$ and Sample B has $Ct=21$. If assay efficiency is $90\%$ (i.e., $E=1.9$), by what factor is the initial template in Sample A greater than in Sample B?