                          OVERVIEW

    The purpose of RNA_2D3D is to facilitate the generation,
viewing and comparing of 3D models of RNA.  The initial  de-
sign specifications for RNA_2D3D were arrived at in collabo-
ration with Drs. Danielle  Konings,  Jacob  Maizel  Jr.  and
Bruce Shapiro.  Implementation of these and subsequent spec-
ifications upto and including this version is the  sole  re-
sponsibility of the author, Hugo M. Martinez.

GENERATION

    The method used for generating 3D models is based on the
following five observations.

(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.

(2) A hairpin or branching loop can be generated by  knowing
the coordinates of its reference triads relative to the ref-
erence triad of its 5' bounding nucleotide.

(3) Any stem (double-stranded helix) can be  generated  from
the  reference  triad of any one of its nucleotides by using
helical coordinates.

(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.

(5)  This planar template contains the absolute atomic coor-
dinates of every nucleotide and thus provides  the  informa-
tion  for determining relative coordinates for the reference
triads of nucleotides in loops and of  stem  generating  nu-
cleotides.

(6) The secondary structure of an RNA molecule is hierarchi-
cal in form. Accordingly, once one of the stems of the  pla-
nar  template has been converted to its 3D form, the coordi-
nates of its 5' loop-bounding nucleotide can be used to  de-
termine  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  consid-
ered 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 recur-
sively 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 back-
bone  drawing  (scaled  to molecular dimensions) of the sec-
ondary 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  nu-
cleotide  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 ac-
tual 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  de-
scribed in observation (5) is taken  to be a first order ap-
proximation 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  inter-
face are described in the help topic titled REFINEMENT.  The
second is by means of interactively editing  the  approxima-
tion.   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  in-
teractions  to  eliminate  potential  clashes during the en-
forcement.  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  ob-
tained  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  dif-
ficult  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  pre-
ferred  3D  conformations.   The  degree to which successful
matches can be obtained is therefore very much dependent up-
on the kinds of constraints that are imposed in doing subse-
quent refinement of the first order approximations.  Accord-
ingly,  there is included constraint editing features in the
form of interactively specifying arbitrary hydrogen  bonding
and  arbitrary  backbone  dihedral  angles.   These  are de-
scribed, 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  mod-
elling 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 mutu-
ally independent.  Typically, a model array will consist  of
models  corresponding  to the same primary sequence but dif-
ferent base pairing schemes.

   There are two model viewing windows which can be used  in
a  number of combinations.  If used simultaneously, each oc-
cupies half the total viewing area.  Used individually,  the
total viewing area will be occupied by the one chosen.  Typ-
ically, 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  pri-
marily  been  incorporated  for comparing 3D versions of the
same molecule.  In particular, it is for the convenient com-
parison  of a model produced by the winding method with sub-
sequent refinements.

    The comparing of two 3D models is done by either a glob-
al  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 seg-
ment  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 as-
sumes that the two molecules have the  same  number  of  nu-
cleotides.  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  branch-
ing  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  struc-
ture  which can subsequently be modified with the individual
base pairing editing feature.  Details on these editing fea-
tures  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  indi-
vidual  branch may be selected and then operated on indepen-
dently 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 concen-
trate  on a single or group of seqments. Both the BRANCH and
SUBSET level may be entered prior to the preliminary refine-
ment  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  pri-
mary 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 com-
parison 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  manimpu-
lated in the same window. Simultaneous viewing and manipula-
tion 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  tec-
tosquares  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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