Biotechnology: Principles and Processes Set-5

Q1. In an ideal PCR (100% efficiency per cycle) starting with $N_0=50$ template molecules and performing $n=18$ cycles, the number of target molecules is given by $N=N_0\times 2^n$. What is the expected number of target DNA molecules after 18 cycles?

Q2. A transformation used $10\ \text{ng}$ of plasmid DNA. After recovery the transformation mix was diluted $1:100$ and $100\ \mu\text{L}$ of this dilution was plated, yielding 150 colonies. Calculate the transformation efficiency in CFU per microgram of DNA. (Use $1\ \mu\text{g}=1000\ \text{ng}$ and show answer as CFU/$\mu$g.)

Q3. To construct a genomic library from a bacterium with genome size $4.0\ \text{Mbp}$ using average insert size $4\ \text{kb}$, what minimum number of independent clones $N$ is required to have at least $99\%$ probability that any given sequence is present? Use $P=1-(1-f)^N$ with $f=\dfrac{\text{insert size}}{\text{genome size}}$ and choose the closest value.

Q4. Assertion (A): In Sanger chain‑termination sequencing, increasing the ratio $r=\dfrac{[\text{ddNTP}]}{[\text{dNTP}]}$ for a particular base (e.g., ddATP:dATP) increases the fraction of fragments terminating at that base and shifts the fragment‑size distribution for that base toward shorter lengths.
Reason (R): A larger $r$ raises the probability that at each incorporation step a terminating ddNTP is incorporated instead of a normal dNTP, so chain termination events become more frequent and occur earlier.

Q5. You start a mixed‑template PCR with 1 copy of a GC‑rich template and 99 copies of an AT‑rich template. Per‑cycle fold‑amplification are $E_{GC}=1.6$ and $E_{AT}=1.95$ respectively (so $N=N_0\times E^n$). After $n=20$ cycles, approximately what percentage of the total amplified molecules will be derived from the GC‑rich template? (Choose the closest value.)

Q6. A plasmid vector has a copy number of 50 per E. coli cell. A culture reaches a cell density of $1\times 10^{9}\ \text{cells mL}^{-1}$. Assuming each plasmid carries a single copy of the target gene, estimate the number of target gene copies per mL.

Q7. In a transformation experiment $50\ \text{ng}$ of plasmid DNA was used. After recovery the final transformed suspension volume was $1.2\ \text{mL}$. From this suspension a $1:20$ dilution was made and $100\ \mu\text{L}$ of that dilution were plated, yielding $240$ colonies. Calculate the transformation efficiency in transformants per microgram of DNA (CFU $\mu$g$^{-1}$).

Q8. In a batch fermentation producing a growth‑associated product, the Luedeking–Piret model applies: $\displaystyle \frac{dP}{dt}=\alpha\mu X+\beta X$. For a culture with constant specific growth rate $\mu=0.4\ \text{h}^{-1}$, $\alpha=0.05$, $\beta=0.01\ \text{h}^{-1}$ and initial biomass $X_0=0.1\ \text{g L}^{-1}$, compute the product concentration $P$ after $5\ \text{h}$ assuming $P(0)=0$ and $X(t)=X_0 e^{\mu t}$.

Q9. In a recombinant expression system the per‑cell protein synthesis rate is proportional to plasmid copy number $c$ (per‑cell rate $=r c$). The specific growth rate depends on copy number as $\mu(c)=0.6-0.06c\ \text{h}^{-1}$. Starting with initial biomass $X_0$ and assuming $rX_0=1$ (arbitrary units), total protein accumulated by time $T$ is $P(c)=rX_0\,c\dfrac{e^{\mu(c)T}-1}{\mu(c)}$. For $T=5\ \text{h}$, which integer copy number $c$ between 1 and 8 maximizes $P(c)$?

Q10. Assertion (A): Treatment of a linearized plasmid vector with calf intestinal alkaline phosphatase (CIP) before ligation completely prevents formation of colonies from religated empty vector. Reason (R): Alkaline phosphatase removes $5'$‑phosphate groups required by DNA ligase to form phosphodiester bonds.

Q11. A PCR reaction begins with $100$ molecules of template DNA. If the reaction proceeds with perfect efficiency (each cycle doubles the DNA), how many molecules will be present after $8$ cycles? Use $N = N_0 \times 2^n$.

Q12. A researcher transforms competent E. coli with $50\ \text{ng}$ of a plasmid. After recovery in $1\ \text{mL}$, $100\ \mu\text{L}$ of the culture is plated and yields $500$ colonies. What is the transformation efficiency in colony-forming units per microgram ($\text{cfu}/\mu\text{g}$) of input DNA? (Use $\displaystyle \text{TE}=\frac{\text{total CFU recovered}}{\text{DNA (µg)}}$.)

Q13. A circular plasmid of length $9\ \text{kb}$ is digested with HindIII and EcoRI. HindIII alone yields fragments of $2\ \text{kb}$ and $7\ \text{kb}$. EcoRI alone yields $3\ \text{kb}$ and $6\ \text{kb}$. A double digest (HindIII + EcoRI) yields fragments of $1\ \text{kb}$, $2\ \text{kb}$ and $6\ \text{kb}$. What is the shortest linear distance along the plasmid between a HindIII site and the nearest EcoRI site?

Q14. Assertion (A): For expressing a eukaryotic protein in E. coli, researchers usually clone the complementary DNA (cDNA) synthesized from mRNA rather than genomic DNA.
Reason (R): cDNA molecules inherently contain bacterial promoter sequences required for transcription in E. coli.

Q15. An E. coli cell has one circular chromosome of length $4.6\ \text{Mb}$ and carries a high-copy plasmid of length $5\ \text{kb}$ at copy number $100$ per cell. Assuming DNA mass ∝ nucleotide length, what percentage of the total intracellular DNA (chromosome + plasmid) is contributed by plasmid DNA? (Nearest percent.)