PCR doubling logic: Starting from one duplex DNA molecule, how many double-stranded DNA products exist after 4 full amplification cycles?

Introduction / Context:PCR amplifies a target DNA region exponentially. Understanding the doubling principle per cycle is fundamental for estimating product yields and planning reactions.

Given Data / Assumptions:

• Starting template: 1 double-stranded DNA (dsDNA) molecule.
• Each cycle ideally doubles the number of dsDNA molecules (perfect efficiency).
• We are asked for the count after 4 cycles.

Concept / Approach:Exponential amplification rule: after n cycles, the theoretical number of dsDNA molecules is 2^n times the starting number, assuming 100% efficiency and no limiting reagents. Thus, after 4 cycles from 1 dsDNA, total dsDNA = 2^4 = 16.

Step-by-Step Solution:Let N0 = 1 dsDNA.After cycle 1: N1 = 2 * N0 = 2.After cycle 2: N2 = 2 * N1 = 4.After cycle 3: N3 = 8; after cycle 4: N4 = 16.

Verification / Alternative check:General formula: Nn = N0 * 2^n For N0 = 1 and n = 4, N4 = 16. Counting single strands is unnecessary since PCR analysis tracks dsDNA amplicons.

Why Other Options Are Wrong:

• 16 single strands / 18 single strands: The question asks for double-stranded products; single-strand counts are irrelevant.
• 18 double-stranded: Does not follow doubling logic.
• 8 double-stranded: Corresponds to 3 cycles, not 4.

Common Pitfalls:Mixing up dsDNA counts with single-strand numbers or forgetting to include the original template in totals.

Final Answer:16 double-stranded DNA molecules.