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COMPACTIFICATION

    This is a procedure designed to give an initial 3D
structuring to the single strands.  The double strands of a 3D
structure occur as parts of an A-type helical form.  Their structure
is therefore nicely predetermined.  But how the preformed helices are
disposed in space relative to one another depends on the structuring
of the interconnecting single strands and on tertiary interactions.

    The compactification procedure is based on the hypothesis
that single strands tend to have a helical structure resulting from the
tendency of adjacent bases to stack as they do in double-stranded
helices.  Hence the idea of simply extending the structure of
the double-stranded helices (stems) into the adjacent single strands
by adding imaginary (pseudo) base pairs and thus reduce the size
of the single strands. 

    Invoked by default, the compactification procedure becomes part of the
process of forming the initial 2D template that is 
used to obtain the initial 3D structure. Subsequently, it can
be interactively nullifed or modified.  Modification
is done with the 2D basepair editor which handles both real
and pseudo basepairs.  The pseudo basepairs are drawn as
dashed lines in the rendering of both the 2D and 3D models.

    As to the algorithm governing the recruitment of unpaired bases
into the pseudo-paired form, we first distinguish between those
lying in bulges or inner loops and those lying in bifurcation (branching)
loops.  With regard to the first type in which a stem consists of
more than one region (a set of contiguous base pairs) successively 
separated by bulges or inner loops, a region is extended upwards
as much as possible so that what is left between it and the next
region ( measured toward the top of the stem) is at most a bulge
and the two regions are then stacked.  All the regions of a stem
are thus coaxially aligned.

    The algorithm for branching loops is a bit more complicated
because of the many more ways in which extensions can be done.
The goal is to leave as few unpaired bases as possible.  A dynamic
programming algorithm is therefore used subject to the restriction
that the first maximal extension found is the one that is
subsequently kept.

     It is useful to keep in mind that compactification can
change the size of the secondary structure stems, but not
their relative interconnection.  What is changed, as in
stem stacking, is the relative positioning of the stems in 3D,
and it is these changes which can be explored by editing the
resulting compactification with the basepair editor.

    Also to be noted is that the compactification algorithms were
originally conceived for handling
strictly orthodox secondary structures, that is, those
structures which do not contain pseudoknots. The compactifying procedure
is currently only partially applied to the loops (hairpin or branching)
of the stems comprising a pseudoknot.  In these cases compactification
amounts to extending the helicity of the tops of the comprising stems
so that the single strand emanating from each is favorably placed
in the groove (major or minor) of the other in order to promote potential
triple base pairing.

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THE END
