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In this fraction notation the following concatenation verses are implicitly assumed:
α
rev
( β )
that is, the Oxydryl terminal of the inferior string is located on the opposite side
with respect to that of the superior string. Sometimes, fraction notation is a way to
make explicit the verse of single strings. In fact, we put (superior notation):
α
λ = α
and (inferior notation):
λ
α = α =
rev
( α ) .
For notation completeness it is assumed that:
λ
λ = λ .
We write:
α ][ β
if
α
and
β
hybridize (with an exact pairing on some internal portions) and
α ][ β
when they do not hybridize. Pairing is a crucial operation of double strings forma-
tion, where the phenomena of bilinearity , complementarity ,and antiparallelism are
jointly involved. It is a partial operation that is defined on two strings only when they
hybridize. The set of single or double DNA strings will be denoted by
Γ / Γ .By
the symmetry of the pairing relation, double strings satisfy the following equation:
α
rev
β
rev
( β ) =
( α ) .
This is an important aspect of double strings, that formalizes the mobility of DNA
strands in a fluid environment (superior and inferior positions are relative concepts).
On the other hand, any
α
hybridizes exactly with ¯
α
by definition of exact pairing,
hence the double string:
α
rev
¯
(
α )
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