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OVERVIEW

    The purpose of RNA_2D3D is to
facilitate the generation, viewing
and comparing of 3D models of RNA.
The initial design specifications for
RNA_2D3D were arrived at in
collaboration with Drs. Danielle
Konings, Jacob Maizel Jr. and Bruce Shapiro.
Implementation of these and subsequent
specifications upto and including this
version is the sole
responsibility of the author,
Hugo M. Martinez.

GENERATION

    The method used for generating
3D models is based on the following five observations.
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(1) The atomic coordinates of a nucleotide
can be generated by knowing only those
of three of its atoms that serve as a
reference triad.
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(2) A hairpin or branching loop
can be generated by knowing the
coordinates of its reference triads relative
to the reference triad of its 5' bounding
nucleotide.
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(3) Any stem (double-stranded
helix) can be generated from the reference
triad of any one of its nucleotides by using
helical coordinates.
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(4) Secondary structure information can be
used to generate
a planar template which roughly
approximates what the 3D version would
look like if the double-stranded helices
(stems)  were unwound,
tertiary bonds broken, and then the
backbone, defined as connecting the
successive C1' atoms of the primary 
sequence, were laid out flat.
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(5) This planar
template contains the absolute atomic coordinates
of every nucleotide
and thus provides the information for
determining relative coordinates
for the reference triads of nucleotides in
loops and of stem generating nucleotides.
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(6) The secondary structure of an RNA molecule
is hierarchical in form. Accordingly, once one
of the stems of the planar template has been
converted to its 3D form, the coordinates of
its 5' loop-bounding nucleotide can be used
to determine the 3D coordinates of its loop
nucleotides so that the loop continues to
remain attached to the stem in the same manner
as it was in the planar template.  In addition,
since the 5' nucleotide of any stem in the loop
is considered to be a member of the loop, this
nucleotide can be used to generate the 3D form
of its stem.  The conversion of the planar
template to the "wound" 3D form can thus
be recursively obtained starting from the
5' end of the topmost stem.

    Referring to observation (4), the specifics are
that the planar 3D template is generated from a conventional
2D backbone drawing (scaled to molecular dimensions)
of the secondary structure by a special
3D embedding procedure.  This procedure
amounts to the
incorporation of atomic models of the
nucleotides such that (1) the base portion
of a nucleotide is nearly perpendicular
to the backbone plane and the backbone line, and
(2) nucleotides which form a basepair are
properly positioned with respect to each
other.  (An actual viewing of the planar
template for a specific RNA can be obtained
by clicking on the "3D-Template" item available
on the menubar of the 2D viewing window.)

    The result of carrying out the recursive procedure
described in observation (5) is
taken  to be a first order approximation
to the actual 3D form of the molecule.
Relative to a specific template, it
can be improved in two ways.  The first is 
by means of standard molecular modelling refinement
procedures.  These are provided by an interactive
interface to TINKER.  The kinds of refinement
provided in this interface are described in the
help topic titled REFINEMENT.  The second is
by means of interactively editing the approximation.
A segment (a contiguous set of nucleotides) or a
group of segments or a group of stems can
be translated and rotated as a rigid body.
Described, respectively, in
the help topics SEGMENT POSITIONING, SEGMENT-GROUP POSITIONING
and STEM-GROUP POSITIONING, this kind of interactive
editing serves the purpose of eliminating nucleotide
clashes as sometimes occur in the first order
approximation, and for the repositioning of stems
prior to enforcing tertiary interactions to eliminate
potential clashes during the enforcement.  Another
rigid-body form of editing relates to pseudoknot stacking
in which one of the pseudoknot stems can be moved relative
to the other in order to modify the extent of their
mutual stacking.  This is described in the help topic
PSEUDOKNOT STACKING.

   Improving the first order approximation can also be
obtained by editing the 2D drawing from which the template
is generated.  Noting that a template 
specifies how the stems are interconnected and, upon
conversion to the unwound form, how these stems are
disposed relative to each other, there is provided
the feature of being able to edit the 2D drawing to
obtain various
forms of stem stacking and compacting.  These
features are briefly described below in the section
titled STRUCTURE EDITING AT 2D LEVEL and in more detail
in the corresponding help topics STEM STACKING  and
COMPACTING.

    Modeling experience has shown that it is generally
difficult to generate structures which precisely match
those obtained by x-ray methodology.  This is because 
we lack the actual folding algorithm of RNA (if such exists)
that would enable one to pick out kinetically or
energetically preferred 3D conformations.
The degree to which successful matches can be obtained is
therefore very much dependent upon the kinds of constraints
that are imposed in doing subsequent refinement of the
first order approximations.  Accordingly, there is included
constraint editing features in the form of interactively
specifying arbitrary hydrogen bonding and arbitrary
backbone dihedral angles.  These are described, respectively,
in the help topics HYDROGEN BONDING and BACKBONE DIHEDRALS.

    Our method of generating 3D models of
RNA is applicable to any size of RNA and is designed to
handle arbitrary branching complexity and pseudoknot content.
A PDB file of the 3D model is availabe as input to other
molecular modelling programs. 

MODEL COMPARISON and VIEWING

   To facilitate the comparing and viewing of 
models, whether generated or obtained
from an external source, there is provided
the feature of two independent model arrays.
One is designated Model A and the other
Model B.  The models comprising each array
are unlimited in number and are mutually
independent.  Typically, a model array
will consist of models corresponding
to the same primary sequence but different
base pairing schemes.

   There are two model viewing windows
which can be used in a number of combinations.
If used simultaneously, each occupies
half the total viewing area.  Used
individually, the total viewing area
will be occupied by the one chosen.
Typically, it is convenient to
simultaneously view the 2D and 3D
structures of the same model, in which
case both windows are used.  But either
structure can be viewed in the single
window mode.  Further, one of the windows
can be assigned to a member of the
Model A array and the other to a member
of the Model B array in order to
simultaneously view their 2D or 3D
structures.  And for detailed comparison
purposes, one window can be used for
superimposing the 3D structures of
a Model A member and a Model B member.

    Although of general utility, this last feature has
primarily been incorporated for comparing 3D versions
of the same molecule.  In particular, it is for
the convenient comparison of a model produced by
the winding method with subsequent refinements.

    The comparing of two 3D models is done by
either a global or local alignment.  In the global
one, the centers of mass are superimposed and then
one model rotated so that its backbone fits the other 
as close as possible in the least square sense.
For the local alignment mode, a backbone segment is
selected from each model and the models are
first superimposed relative to the centers of mass
of the selected segments.  Then one model is rotated
about its segment's center of mass until its segment
fits the other as close as possibe in the least square
sense.  The global method assumes that the two
molecules have the same number of nucleotides.  This
is not required for the local method. 

STRUCTURE EDITING AT 2D LEVEL

   A number of editing features are
provided to facilitate consideration of
structure alternatives which relate
to base pairing, stem stacking and 
region stacking.  Thus, base pairs
may individually be deleted or added
in ordered to loosen or tighten a
structure.  The same applies to
stem stacking for altering the
bounding constraints on a branching
loop, and to region stacking for 
altering the bounding constraints
on an inner loop.  Also available is
the feature of compacting
which, relative to specified stem
and region stacking, extends stems
to achieve a maximally 
tight structure which can subsequently
be modified with the individual base
pairing editing feature. 
Details on
these editing features are described
in the topics STEM/REGION STACKING 
and COMPACTION.

LEVELS

    For concentrating on parts of an RNA molecule,
advantage is taken of its hierachical structure
which consists of stems branching into other stems
or terminating in hairpin loops.
The topmost level is called MOLECULE and comprises
the entire molecule.  The
next is BRANCH, whereby an individual branch
may be selected and then operated on independently
of the rest of the molecule.  The third and final
level is that of SUBSET.  Defining a segment
as a contiguous sequence of nucleotides, the 
SUBSET level is used to concentrate on a single
or group of seqments. Both the BRANCH and SUBSET
level may be entered prior to the preliminary 
refinement step which follows the production of
the initial 3D model (see 'GENERATION' above).
Preliminary refinement may then be independently done on the
selected portion, - branch or subset.  In any case,
a PDB file may be generated of the selected portion
to serve as input to other programs.

MULTIPLE STRUCTURES

    It is sometimes required to generate and compare
3D structures for different 2D structures having the
same primary structure. The input file to the program allows
for the specification of multiple secondary structures
for the same primary structure. These are automatically
recognized by the program and generates the drawings for
the 2D structures and generates
an initial 3D structure for each. Stored in either
the model A or B array, as specified by the user, they are made
available for their sequential display.  Detailed comparison
of any two is achieved by copying one of them into the other
model array and then using the model comparison feature
by which the two structures are viewed and manimpulated in
the same window. Simultaneous viewing and manipulation of
two structures is therefore conveniently implemented with
two model arrays.  For more than two structures, as might
be required for building RNA n-mers that result from the
monomers interacting via base-pairing, there is provided
a model C array. How it is
used for the building of tectosquares and patterns
of the type advocated by Chworos et al. "Building Programmable
Jigsaw Puzzles with RNA", Science 306, 2068-207 (2004), is
described in the help topic 'rna_tecto_structures'.


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