Question

A double stranded DNA molecule of total 5000 base pairs long, has a melting temperature of 85 °C. What will be the % AT base pairs in this sample? (up to one decimal place).

Answer 1

Correct Answer: 61.6

The relationship between the melting temperature ($\text{Tm}$) of a long double-stranded $\text{DNA}$ molecule and its $\text{G-C}$ content is given by the empirical formula (often assumed at a standard ionic strength):

$$\text{Tm} = 69.3 + 0.41 \times (\% \text{GC})$$

Where:

$\text{Tm}$ is the melting temperature in degrees Celsius ($^\circ \text{C}$).

$\% \text{GC}$ is the percentage of Guanine-Cytosine base pairs (by count).

We are given $\text{Tm} = 85^\circ \text{C}$. The total length ($5000 \text{ bp}$) is large enough that the length correction term is negligible.

$\text{1. Calculate \%GC}$

Substitute the given $\text{Tm}$ into the formula:

$$85 = 69.3 + 0.41 \times (\% \text{GC})$$

$$85 - 69.3 = 0.41 \times (\% \text{GC})$$

$$15.7 = 0.41 \times (\% \text{GC})$$

$$\% \text{GC} = \frac{15.7}{0.41} \approx 38.2927\%$$

$\text{2. Calculate \%AT}$

Since the only base pairs are $\text{A-T}$ and $\text{G-C}$:

$$\% \text{AT} = 100\% - \% \text{GC}$$

$$\% \text{AT} = 100 - 38.2927$$

$$\% \text{AT} \approx 61.7073\%$$

$\text{3. Rounding}$

Rounding the result to one decimal place:

$$\% \text{AT} = 61.7\%$$

$$\text{The } \% \text{ AT base pairs in this sample is } \mathbf{61.7}$$