Strings and Genomes - Infobiotics: Information in Biotic Systems - page 63

2.5.1 XPCR

The role of the overlap concatenation in PCR amplification suggested to us an inter-
esting form of PCR where, rather than just one target string, we put two target DNA
double strings of types

< αϕγ > < γψβ >

in a test tube.
Let us analyze what happens if a PCR is performed, starting from such a pool,
extended with primers

and

¯

α , β :

¯

< αϕγ >,< γψβ >, α , β

In this case, after denaturation the following strings will be present in the pool:

αϕγ
λ

λ
( αϕγ )

γψβ
λ

λ
( γψβ )

¯

, , , , α , β .

c c

If the temperatures at which hybridize with their mirror strings are 'close

enough', then the following hybridizations can occur, where the first string, in the
pool given above, overlaps with the fourth one, while the strings in second and third
positions hybridize with the primers (other hybridizations are possible, but it is easy
to realize that they are not “productive” in terms of amplification, because they can
only delay the effect of these “canonical” hybridizations, see Fig. 2.40):

α , β ,and γ

αϕγ
( γψβ )

α
( αϕγ )

γψβ
β

, ,

c .

c c

At this point polymerase can extend strings:

αϕγ
( γψβ )

α
( αϕγ )

( γψβ
β

ext (

c ) ,

ext (

c ) ,

ext )

c

that become:

< αϕγψβ >,< αϕγ >,< γψβ >

in such a way that the blunt string < αϕγψβ > is produced, which results from the

overlap concatenation of with two more strings equal to the

initial target strings. We call this special kind of PCR cross pairing PCR or XPCR
for short; its combinatorial schema implements an operation, which theoretically
can be seen as a special kind of Tom Head's null context splicing rule , given in the
seminal paper [37] where a Formal Language Theory perspective of DNA strings
was introduced (see also [47, 43]). In conclusion, if

< αϕγ > and < γψβ >

Type ( P )= {< αϕγ >, < γψβ >}

then

Type ( PCR ( P , α , β )) ≈{< αϕγψβ >}.

Types of strands different from are present in a minor quantity,

moreover, recombinations different from those considered above are possible (for

< αϕγψβ >