Problem 1: Chargaff's Rule Calculation

Given: A double-stranded DNA has 30% adenine (A). Find: % of T, G, C; ratio of $\frac{A+G}{(T+C)}$.

Solution:

• A = T = 30% (Chargaff's rule)
• G + C = 100 − 60 = 40%; G = C = 20%
• $\frac{A+G}{(T+C)}$ = $\frac{30+20}{(30+20)}$ = 50/50 = 1.0 (always 1.0 for dsDNA)

Problem 2: mRNA Length Calculation

Given: A protein has 200 amino acids. Find: Minimum length of mRNA coding sequence.

Solution:

• Codons for amino acids: 200
• Stop codon: +1
• Total codons: 201
• Total nucleotides: 201 × 3 = 603 nucleotides

Problem 3: Semiconservative Replication Count

Given: A bacterium with one circular dsDNA undergoes 4 rounds of replication. Find: Total DNA molecules; molecules with at least one original strand.

Solution:

• Total molecules = 2^4 = 16 molecules
• Molecules with original strand = 2 (one per original strand; two original strands → two molecules)
• Molecules with only new DNA = 16 − 2 = 14

Problem 4: Okazaki Fragment Count

Given: E. coli chromosome: 4.6 × 10^6 bp; Okazaki fragments ~1000 bp each. Find: Number of Okazaki fragments per replication.

Solution:

• Lagging strand = 50% of total DNA = 2.3 × 10^6 bp
• Okazaki fragments = 2.3 × 10^6 / 1000 = 2,300 fragments

Problem 5: Intron/Exon Calculation

Given: Pre-mRNA = 3000 nt; mature mRNA = 1200 nt. Find: % of transcript removed as introns.

Solution:

• Introns removed = 3000 − 1200 = 1800 nt
• % introns = (1800/3000) × 100 = 60%