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STEM and REGION STACKING

    To describe the concept of stem stacking it is useful to
first define some terminology. Thus,
by a 'base-pair region' or simply 'region' is meant a set of contiguous
base pairs configured as a double helix, and by a 'stem'
is meant a sequence of base-pair regions whose members are
separated by single strands in the form of 'inner loops' or
bulges.  Four numbers, b5,t5, b3 and t3 serve to delimit the
extent of a stem.  The numbers b5 and t5 stand for the bottom
5' and top 5' base numbers of the stem, while b3 and t3 are the
corresponding 3' base numbers.  Relative to the 5' end of the
parent RNA sequence these numbers bear the relation
b5<t5<t3<b3.  Between the base positions t5 and t3, which delimit
the top of the stem, there may or may not be any base pairs.
In the absence of base pairs the corresponding single strand is
said to form a "hairpin loop" and the stem then constitutes the
supporting part of the hairpin.  When there are base pairs
between positions t5 and t3, the stem is said to branch or
bifurcate into other stems which in turn may or may not branch.
What would otherwise be called a hairpin is now called a
"branching" or "bifurcation" loop.  A stem in the branching loop
of a stem X is said to constitute a primary member of stem X's
branching loop if it is not a member of any other branching loop. 
The secondary structure of an RNA molecule may thus be viewed
as that of a tree, the root of which is an imaginary stem of 
length zero whose loop is the entire sequence.

    With this kind of structuring and nomenclature in mind, the
concept of stem-stacking is now easily described.  First of all,
stem-stacking is simply a means of forming a larger double
stranded helix out of two stems by joining them together in
a coaxial manner. 
This means that an end basepair of one
of the stems is stacked with an end basepair of the other
stem. This may occur in any of four ways, depending on which
ends are stacked.  Top-bottom stacking occurs when a branching stem
stacks with either the first or last primary member of its branching
loop.  Bottom-bottom stacking occurs when successive primary members of
a branching loop are stacked.  Top-top stacking occurs relative
to pseudoknots.  (Recall that two stems can form a pseudknot 
when  a strand of each is part of the hairpin or branching loop
of the other stem in such a manner that one stem can be regarded
as a coaxial extension of the other by stacking their tops together).
It should also be noted that pseudoknots can bottom stack with
each other or with stems that are not one of the two members of
a pseudoknot, thus extending the variety of bottom stacking which
can occur.

    The concept of region-stacking is also straightforward.
It applies to a pair of successive regions from the same stem,
and is a means of increasing stacking interaction of successive
basepairs.

    It will be appreciated that stacking or not stacking can
markedly affect the 3D structure of an RNA molecule.  But because
there is no definitve experimental evidence of when the stacking
of two stems or regions is to be favored or disfavored, we leave it to the
user to invoke his or her criteria in an interactive manner subject
to certain constraints relative to pseudoknots which reflect a
policy adopted in generating the 2D-template of a structure
which contains pseudoknots.  This policy is described in the
help topic PSEUDOKNOTS and rules out interactive 2D editing of the stacking of
two stems when either is one of the two stems forming a pseudoknot.
However, the degree of stacking of two such stems can be edited
at the 3D level as described in the help topic PSEUDOKNOT STACKING/EDITING.
Top-bottom and bottom-bottom stacking is otherwise unrestricted
and is invoked by simply pointing to the two stems to be so stacked.
A user-stacked stem pair can be unstacked.

    The stacking of a stem pair may sometimes result in an 
overlapping of the stacked pair with other stems of the structure. Such a violation
can someimes be relieved by deleting one or more of the
pseudo basepairs introduced by the compactification procedure.
The deletion is done with the built-in basepair editor.  Also
available is a means of rotating the stacked pair about a designated
axis formed by a line joining two bases.

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