Reading a gel and counting copies in PCR

Reading a gel

In gel electrophoresis, the DNA is placed in wells at one end of a gel, and an electric field is applied. The DNA has negative charge on its phosphate groups, so it moves to the positive end. The gel is like a sieve. Small fragments move farther and large fragments move less.

For a range of sizes, the distance that a fragment moves is a straight line against the logarithm of its size. A lane with fragments of known sizes, the ladder, lets you draw this line.

To find an unknown size:

1. Measure the distances of the ladder bands.
2. Fit a straight line of $\log_{10}(\text{size})$ against the distance.
3. Measure the distance of the unknown band, and read its size from the line.

The line that fits the ladder of the picture is $\log_{10}(\text{size}) = 5.00 - 0.0833\,d$, with $d$ in millimetres. The band U1 is at 17.0 mm, so its size is $10^{5.00 - 0.0833 \times 17.0} = 3830$ base pairs. Do not read a size by a straight-line interpolation between the two nearest ladder bands. A linear interpolation gives an answer that is a little too large.

A band that is twice as thick holds about twice as much DNA. Two fragments of the same size lie in one band.

Restriction digests

A restriction enzyme cuts DNA at its own recognition site. If a ring of DNA is cut at $n$ sites, it gives $n$ pieces. If a straight piece is cut at $n$ sites, it gives $n + 1$ pieces. The sizes come from the distances between the cut sites.

Take a ring of 6000 base pairs. The enzyme A cuts at 1000 and 3500, and the enzyme B cuts at 2000 and 4700. Measure positions from the start.

• A alone: $3500 - 1000 = 2500$, and $6000 - 2500 = 3500$.
• B alone: $4700 - 2000 = 2700$, and $6000 - 2700 = 3300$.
• A and B together: the four cuts at 1000, 2000, 3500 and 4700 make pieces of $1000$, $1500$, $1200$ and $2300$ base pairs. The last one runs round the ring from 4700 to 1000: $6000 - 4700 + 1000 = 2300$.

The sizes of every set of pieces add up to the size of the DNA. This is a check.

DNA profiles and chance

In a DNA profile, the chance of a match by accident is the product of the chances for each band, if the bands are independent. If each band is found in 1 person in 10, then 6 bands give $\left(\dfrac{1}{10}\right)^6 = \dfrac{1}{1\,000\,000}$. This is why a profile with many bands is strong evidence.

The polymerase chain reaction (PCR)

The polymerase chain reaction copies a chosen stretch of DNA, the target, many times in a tube. Kary Mullis invented it in 1983. A tube holds the template DNA and two primers. The primers are short pieces of DNA, about 18 to 25 nucleotides long, that match the two ends of the target. The tube also has the four deoxynucleoside triphosphates, a buffer, and a heat-stable DNA polymerase. This is often Taq polymerase from the bacterium Thermus aquaticus, which lives in hot springs. A machine changes the temperature in a cycle.

• Denaturation, about 94 to 95 °C: the two strands separate.
• Annealing, about 50 to 65 °C: the primers pair with the ends of the target.
• Extension, about 72 °C: Taq polymerase extends each primer 5′ to 3′.

In each cycle, every target molecule is copied once. With perfect efficiency, the number of copies doubles. After $n$ cycles, one starting molecule gives $2^n$ copies. With an efficiency $E$, between 0 and 1, it is $(1 + E)^n$.

After 30 cycles, one molecule gives $2^{30} = 1.07 \times 10^9$ copies, and at an efficiency of 0.95 it gives $5.0 \times 10^8$. The first cycles also make pieces that are longer than the target. The pieces with exactly the length of the target appear from cycle 3, and from one starting molecule there are $2^n - 2n$ of them after $n$ cycles. After 30 cycles this is almost the same as $2^{30}$.

You should find that a loss of efficiency lowers the final number of copies very strongly, and that a thousand starting molecules save about 10 cycles.

A rule for the primer

The temperature at which a short primer comes off the template is its melting temperature. A rule of thumb for a short primer is the Wallace rule:

A good annealing temperature is about 5 °C below $T_m$. A G-C pair has three hydrogen bonds, so each one adds more to the melting temperature than an A-T pair.

Practise with new numbers

Common mistakes

• Saying that large fragments run farther. The small ones do.
• Saying that the size falls in a straight line with the distance. It is the logarithm of the size.
• Saying that a ring cut at 2 sites gives 3 pieces. A ring gives as many pieces as cuts, 2. A straight piece gives 3.
• Saying that the number of copies grows by 2 in each cycle. It is multiplied by 2.
• Saying that Taq polymerase is destroyed at 95 °C. It is heat-stable, and this is why it is used.

Remember these

• DNA is negative and runs to the positive end. Small pieces run farthest. The distance is a straight line against $\log_{10}$ of the size.
• A ring with $n$ cuts gives $n$ pieces. A straight piece gives $n + 1$. The pieces add up to the whole.
• PCR: denaturation (about 95 °C), annealing (about 50 to 65 °C), extension (about 72 °C, Taq polymerase). Copies: $(1 + E)^n$, or $2^n$ when perfect.
• Wallace rule: $T_m = 4(\text{G} + \text{C}) + 2(\text{A} + \text{T})$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Why does DNA move to the positive end of a gel?

2. A straight DNA of 8000 base pairs is cut at three sites. How many pieces are there?

3. Why is Taq polymerase used in PCR?

4. How many copies does one molecule give after 12 cycles of perfect doubling?

5. A primer of 20 nucleotides has 12 G and C. What is its melting temperature by the Wallace rule?

References

• Clark M. A. et al. (2018). Biology 2e, OpenStax, chapter 17, section 17.1, Biotechnology.
• Mullis K. B. and Faloona F. A. (1987). Specific synthesis of DNA in vitro via a polymerase-catalyzed chain reaction. Methods in Enzymology, 155, 335 to 350.
• NCERT (2023). Biology, Textbook for Class XII, chapter 5, Molecular Basis of Inheritance, and chapter 9, Biotechnology: Principles and Processes.