Question

If a researcher starts with three double stranded DNA molecules, how many such molecules will be produced after 10 PCR cycles? Explain briefly.

Hint:

This calculation assumes $100%$ amplification efficiency, where every template molecule is fully copied in every cycle. In practice, actual yields may be slightly lower due to enzyme degradation, primer depletion, or product inhibition in later cycles.

Answer 1

Step 1: Mathematical Formula for PCR Amplification
The amplification of DNA in PCR is an exponential process. The final number of double-stranded DNA molecules ($N$) produced after $n$ cycles is calculated using the formula:
$$N = N_0 \times 2^n$$ where:
- $N_0$ is the initial number of template DNA molecules.
- $n$ is the number of PCR cycles.


Step 2: Substitution and Calculation
From the problem, we are given:
- Initial DNA molecules ($N_0$) = $3$
- Number of cycles ($n$) = $10$
Substituting these values into our formula:
$$N = 3 \times 2^{10}$$ We know that:
$$2^{10} = 1024$$ Therefore:
$$N = 3 \times 1024 = 3072 \text{ double-stranded DNA molecules}$$

Step 3: Brief Explanation
In each PCR cycle, every double-stranded DNA molecule is denatured into two single-stranded templates. Taq polymerase copies each template, doubling the total population of target DNA molecules. Over 10 cycles, this doubling occurs 10 times, resulting in a $2^{10}$-fold ($1024$-fold) increase. Starting with 3 molecules, we get:
$$3 \times 1024 = 3072 \text{ molecules}$$ Final Answer: After 10 PCR cycles, 3072 double-stranded DNA molecules will be produced. This is calculated using the exponential formula $N = N_0 \times 2^n = 3 \times 2^{10} = 3 \times 1024 = 3072$.