Molecular Basis of Inheritance Set-1

Q1. In an ideal PCR reaction (100% efficiency per cycle) starting from a single double-stranded DNA molecule, the number of molecules after $n$ cycles is $N=2^n$. How many double-stranded DNA molecules are expected after $30$ cycles?

Q2. During DNA replication the base misincorporation probability is $10^{-4}$ per base. Proofreading by DNA polymerase corrects $99\%$ of misincorporations and post-replicative mismatch repair corrects $99\%$ of the remaining mismatches. What is the approximate final error rate per base after both corrections?

Q3. A eukaryotic coding gene has three exons of lengths $150\ \text{bp}$, $300\ \text{bp}$ and $90\ \text{bp}$ respectively; the coding frame starts at the first base of exon 1 and ends at the last base of exon 3. If an alternative splicing event skips the middle exon (300 bp), which of the following is the most likely consequence for the translated protein?

Q4. Statement I: A mutation that changes the anticodon sequence of a charged tRNA (while leaving its acceptor stem intact) can lead to the original amino acid being incorporated at codons corresponding to the new anticodon, producing missense substitutions.
Statement II: Aminoacyl-tRNA synthetases recognise multiple identity elements on tRNAs (including the acceptor stem and specific bases in the anticodon loop); therefore altering only the anticodon often does not change which amino acid the tRNA is charged with.
Which of the following is correct?

Q5. A haploid eukaryotic genome of size $L=3.0\times10^{9}$ bases must be replicated within an S-phase of duration $T_s=8$ hours. Replication is bidirectional from each origin and each replication fork moves at speed $v=50\ \text{nt s}^{-1}$. Assuming each origin fires once and forks move continuously until meeting, the minimum number of origins required is given approximately by $\left\lceil\frac{L}{2vT_s}\right\rceil$. What is the minimum number of origins (round up to nearest whole number)?

Q6. A circular bacterial chromosome of size $4.6\times10^{6}\ \text{bp}$ initiates replication bidirectionally from a single origin. If each replication fork synthesizes DNA at $1000\ \text{nt s}^{-1}$, approximately how long will it take to complete one round of replication (ignore initiation/termination delays)?

Q7. A haploid eukaryotic genome of size $3\times10^{9}\ \text{bp}$ must be completely replicated within an $8\ \text{h}$ S phase. If each replication fork moves at $50\ \text{nt s}^{-1}$ and replication is bidirectional from each origin, estimate the minimum number of origins required per haploid genome to finish replication within S phase.

Q8. Sanger sequencing of a PCR-amplified exon from a heterozygous individual yields an electropherogram with clean single peaks up to nucleotide position $150$, but from position $151$ onward the peaks become overlapping and out-of-phase with roughly equal intensities across channels. Which mutation most plausibly explains this pattern?

Q9. A gene has exon 1 of length $120\ \text{bp}$, an intron of length $41\ \text{bp}$, and exon 2 of length $180\ \text{bp}$. A point mutation changes the canonical 5' splice donor (GT) to AT, abolishing recognition of this intron; the intron is retained in the mature mRNA. What is the most likely consequence for the encoded protein?

Q10. DNA polymerase misincorporates bases at a rate of $10^{-6}$ per nucleotide. Proofreading exonuclease activity reduces errors by $100$-fold and mismatch repair reduces the remaining errors by a further $1000$-fold. For a bacterial genome of $4.6\times10^{6}\ \text{bp}$, estimate the probability that a single round of replication introduces at least one permanent base substitution. (Use Poisson approximation.)