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The aim of PCR is to quickly amplify a specific region of a DNA sequence — in
other words to make more copies of it.

Rudimentary explanation of the basis of the method is as follows:

Single strand of DNA (single stranded DNA, ssDNA) constitutes of a backbone
chain and 4 different nitrogen bases (coded as A,T,C,G) that are attached to
the chain in a uniform way. Their arangement is the sequence or information (in
a loose sense) that a strand of DNA holds. The backbone chain has two ends that
are denoted as 5' and 3', unless stated otherwise a DNA sequence is always
expressed looking from the 5' end to the 3' end. For example:

5'—ACTGCTAGCGATCGATCGTAGCGTAGCGTATGCTGATCG—3'

The geometry and complementary electric charges of nitrogen bases allows for
stable eletrostatic attraction between A and T, and C and G, but not between A
and C or T and G. That is, the possible electrostatic bonding pairs are only AT
and CG. This fact, and other not mentioned qualities of DNA geometry allows two
strands of DNA with complementary sequences to allign themselves and form a
double stranded DNA (dsDNA) helical structure that is more stable and has lower
energy — it is a thermodynamically preffered state.

A simple model of two alligned strands of DNA with complementary sequences:

5'—ACTGCTAGCGATCGATCGTAGCGTAGCGTATGCTGATCG—3'

3'—TGACGATCGCTAGCTAGCATCGCATCGCATACGACTAGC—5'

The length of DNA sequences is expressed in nucleotides (nt) or base pairs (bp)
which is numerically equal to the lenght of the sequene expressed with letters
ATCG. The above dsDNA fragment is 39 nt or 39 bp long. Notice that strands are
anti–paralel — their ends are inverted, their sequences go in opposite
directions.

(1) The 1st step of PCR is denaturation: solution of your template DNA is
heated up to 98 °C, which raises the energy to the point where the
electrostatic attraction between nitrogen bases is not strong enough to
withstand the vibration of molecules, and the two strands separate.

(2) The 2nd step of PCR is annealing: the temperature is lowered to 58—68 °C.
Long strands of DNA in solution are disorganized and will not be able to fully
reform the helical structure on thier whole lenght. Two short (18—25 nt) ssDNA
called primers, that are complementary to the regions flanking the sequence of
interest in the template, form a short dsDNA segment with the template. The
lenght of 18—25 nt allows for greater mobility due to small size, but enough
sequence specifity to bind only with a single place in the template. A simple
representation of the end result:

5'—ACTGC—3'

3'—TGACGATCGCTAGCTAGCATCGCATCGCATACGACTAGC—5'

(the primer is shorter for easier representation, and there is only one strand
of the template shown, because non–monospace font makes it impossible to align
the other one properly, but the process for the other one is identical)

(3) The 3rd step of PCR is elongation: the temperature is raised to 72 °C,
which is optimal value for polymerase activity. Polymerase in an enzyme that
catalyses the synthesises of a new DNA strand. The specific kind used in PCR
synthesises does so by attaching appropriate building blocks to the 3' end of a
DNA strand using the complementary strand as a template, like this:

5'—ACTGC—3' —>

3'—TGACGATCGCTAGCTAGCATCGCATCGCATACGACTAGC—5'

...

5'—ACTGCTAGCGATCGATCGTAGCGTAGCGTATGCTGATCG—3'

3'—TGACGATCGCTAGCTAGCATCGCATCGCATACGACTAGC—5'

The same process takes place on both DNA strands of the template molecule — a
single PCR cycle resulted in double the amount of copies of a desired sequence.
The proces is repeated (usually about 30 times) to exponentially increase the
number of copies up to $n_0\times 2^c$ copies, where $n_0$ is the starting
number of copies and $c$ is the number of cycles.

—additional notes—

a) annealing temperature is fitted to the primers used, which is based on their
lenght and sequence (usually calculated by some variation of the Nearest
Neigbour method);

b) first PCRs were carried out using non-thermostable polymerases, that became
denaturated and lost their enzymatic activity after each denaturation, and had
to be manually added before each elongation. Modern PCRs use thermostable
polymerases that are able to withstand high temperatures and sustain their
enzymatic activity;

The aim of PCR is to quickly amplify a specific region of a DNA sequence — in other words to make more copies of it.

Rudimentary explanation of the basis of the method is as follows:

Single strand of DNA (single stranded DNA, ssDNA) constitutes of a backbone chain and 4 different nitrogen bases (coded as A,T,C,G) that are attached to the chain in a uniform way. Their arangement is the sequence or information (in a loose sense) that a strand of DNA holds. The backbone chain has two ends that are denoted as 5' and 3', unless stated otherwise a DNA sequence is always expressed looking from the 5' end to the 3' end. For example:

5'—ACTGCTAGCGATCGATCGTAGCGTAGCGTATGCTGATCG—3'

The geometry and complementary electric charges of nitrogen bases allows for stable eletrostatic attraction between A and T, and C and G, but not between A and C or T and G. That is, the possible electrostatic bonding pairs are only AT and CG. This fact, and other not mentioned qualities of DNA geometry allows two strands of DNA with complementary sequences to allign themselves and form a double stranded DNA (dsDNA) helical structure that is more stable and has lower energy — it is a thermodynamically preffered state.

A simple model of two alligned strands of DNA with complementary sequences:

5'—ACTGCTAGCGATCGATCGTAGCGTAGCGTATGCTGATCG—3'

3'—TGACGATCGCTAGCTAGCATCGCATCGCATACGACTAGC—5'

The length of DNA sequences is expressed in nucleotides (nt) or base pairs (bp) which is numerically equal to the lenght of the sequene expressed with letters ATCG. The above dsDNA fragment is 39 nt or 39 bp long. Notice that strands are anti–paralel — their ends are inverted, their sequences go in opposite directions.

(1) The 1st step of PCR is denaturation: solution of your template DNA is heated up to 98 °C, which raises the energy to the point where the electrostatic attraction between nitrogen bases is not strong enough to withstand the vibration of molecules, and the two strands separate.

(2) The 2nd step of PCR is annealing: the temperature is lowered to 58—68 °C. Long strands of DNA in solution are disorganized and will not be able to fully reform the helical structure on thier whole lenght. Two short (18—25 nt) ssDNA called primers, that are complementary to the regions flanking the sequence of interest in the template, form a short dsDNA segment with the template. The lenght of 18—25 nt allows for greater mobility due to small size, but enough sequence specifity to bind only with a single place in the template. A simple representation of the end result:

5'—ACTGC—3'

3'—TGACGATCGCTAGCTAGCATCGCATCGCATACGACTAGC—5'

(the primer is shorter for easier representation, and there is only one strand of the template shown, because non–monospace font makes it impossible to align the other one properly, but the process for the other one is identical)

(3) The 3rd step of PCR is elongation: the temperature is raised to 72 °C, which is optimal value for polymerase activity. Polymerase in an enzyme that catalyses the synthesises of a new DNA strand. The specific kind used in PCR synthesises does so by attaching appropriate building blocks to the 3' end of a DNA strand using the complementary strand as a template, like this:

5'—ACTGC—3' —>

3'—TGACGATCGCTAGCTAGCATCGCATCGCATACGACTAGC—5'

...

5'—ACTGCTAGCGATCGATCGTAGCGTAGCGTATGCTGATCG—3'

3'—TGACGATCGCTAGCTAGCATCGCATCGCATACGACTAGC—5'

The same process takes place on both DNA strands of the template molecule — a single PCR cycle resulted in double the amount of copies of a desired sequence. The proces is repeated (usually about 30 times) to exponentially increase the number of copies up to $n_0\times 2^c$ copies, where $n_0$ is the starting number of copies and $c$ is the number of cycles.

—additional notes—

a) annealing temperature is fitted to the primers used, which is based on their lenght and sequence (usually calculated by some variation of the Nearest Neigbour method);

b) first PCRs were carried out using non-thermostable polymerases, that became denaturated and lost their enzymatic activity after each denaturation, and had to be manually added before each elongation. Modern PCRs use thermostable polymerases that are able to withstand high temperatures and sustain their enzymatic activity;