                    RNA TECTO STRUCTURES

    An  RNA  tecto  structure can be defined as a set of RNA
monomers which are linked together by means of base pairing.
Referring  to the publication "Building Programmable Puzzles
with RNA" by Chworos  et  al,  (Science  2006,  v306,p2068),
there  is described a monomer, termed a tectoRNA, which con-
ists of two stem-loop  regions  joined  by  a  short  single
strand.  Its  overall  conformation  is one in which the two
stem-loop regions have a right-angle  relative  orientation.
If one monomer has a hairpin loop complementary to a hairpin
loop of another, then the two monomers can be joined  via  a
base-pairing  interaction  of  their complementary loops and
thereby share a coaxially stacked pair of  stems.  Theoreti-
cally,  a  ’tectosquare’  would  therefore  result  from the
cyclic joining of  four  tectoRNAs.  In  addition,  if  each
monomer  were provided with a helical 5’ or 3’ tail, comple-
mentation of tails would also theoretically provide for  the
joining  of  tectosquares  and hence of forming ’tectosquare
patterns’.  The experimental results presented in the refer-
enced  article  strongly  suggest  all  this to be true, but
since coordinates were not provided with any of the  experi-
mental structures, it was difficult to assess their fidelity
with regard to the proposed geometry. For instance, to  form
a true tectosquare there is required cyclization of the four
monomers.  If we label them as A, B, C and D, there would be
no special constraints hindering formation of the complex A-
B-C-D.  But to get the cyclic structure A-B-C-D-A, in  which
the two As signify the same monomer, requires that the A and
D monomers of the complex A-B-C-D  have  relative  positions
favorable  to  their  complementary interaction.  It is this
concern that prompted our effort to model  these  particular
RNA  tectostructures,  and  hence  to  develop computational
tools generally applicable to the design of  tectostructures
based  on  RNA  monomer complementation. The current design,
though specifically aimed at generating  proposed  tectoRNAs
and  testing  the  closure property of proposed tectosquares
and tectosquare patterns based on them, can be used for oth-
er  tecto RNA structures so long as they can be generated in
the squential manner used for tecto squares and patterns  as
described below.

DEFINING A TECTO STRUCTURE

  This  is  by  means of file that contains the names of the
monomers to be used and how these monomers are to be  inter-
connected.   The  file  is called a TPL (Tecto Pairing List)
file, an example of which is the following one  that  speci-
fies a tectosquare.

        MONO    1   LT17.A3s   1  1:68-2:22     1:86-7:92
        MONO    2   LT17.B1s   1  2:68-3:22     0:0-0:0
        MONO    3   LT17.C8s   1  3:68-4:22     0:0-0:0
        MONO    4   LT17.D6s   1 *4:68-1:22     0:0-0:0

Any  line of the file in which the first non-white string is
not the word MONO is regarded as  a  remark.   So  the  MONO
lines  have  the actual data in a free-type format. The word
MONO (short for monomer) is like the  ATOM  word  of  a  PDB
file, but here signifies a molecule.  The second column enu-
merates the monomers, the third column  names  the  monomers
relative  to a database (to be described), the fourth column
is the group to which the monomer belongs (here  tectosquare
#1),  and  the fifth and sixth columns specify the key base-
pairs to construct to implement  the  required  interconnec-
tion.   Referring to the entry "1:68-2:22" in column five of
the first line, it says that nucleotide number 68 of monomer
1 is to pair with nucleotide 22 of monomer 2.  All of column
five relates to intra-group pairing, while  column  six  re-
lates  to  inter-group  pairing which, in this example, uses
monomers 1 and 7.  Because monomer 7 does not exist  in  the
file,  the specified pairing will be ignored. Blank pairings
are formally denoted as the word "0:0-0:0".  Use of the  as-
terisk  in  the  connection word "*4:68-1:22" tells the con-
structing program to ignore this particulr  pairing  connec-
tion  because it would lead to a never ending cycle of pair-
ings.  This is because formation of the pairings is  carried
out  sequentially,  a requirement that is best understood by
the algorithm that is used to form a specific pairing.

    To describe this algorithm, consider again  the  connec-
tion  word  "1:68-2:22".  The coordinates of both monomers 1
and 2 are known, and it  is  required  to  change  those  of
monomer  2  so  that its nucleotide 22 forms a basepair with
nucleotide 68 of monomer 1. Because the corresponding  kiss-
ing  loops  already possess a putative kissing conformation,
formation of any one of the kissing basepairs will automati-
cally insure that all of them will be formed. Hence the need
to only be concerned with constructing one  of  the  kissing
basepairs.   Thus, knowing the coordinates of nucleotide 68,
there is first calculated the coorinates  of  nucleotide  22
required of it to base pair with nucleotide 68.  This calcu-
lation is derived from a database  of  RNA  basepairs.   And
having  previoiusly determined coordinates of all of monomer
2 relative to those of its nucleotide 22,  the  new  coordi-
nates  of  nucleotide  22 serve to caculate the new ones for
all  of  monomer  2.  The  kissing  connection  between  two
monomers is thus simply described in terms of a single base-
pair.

    Our second example of a TPL  file  is  that  of  a  tec-
tosquare pattern consisting of four tectosquares.

        MONO    1   LT17.A3s   1  1:68-2:22     1:87-7:92
        MONO    2   LT17.B1s   1  2:68-3:22     0:0-0:0
        MONO    3   LT17.C8s   1  3:68-4:22     0:0-0:0
        MONO    4   LT17.D6s   1 *4:68-1:22     0:0-0:0
        MONO    5   LT18.A8ps  2  5:68-6:22     0:0-0:0
        MONO    6   LT18.B5ps  2  6:68-7:22     6:92-12:87
        MONO    7   LT18.C3ps  2  7:68-8:22     0:0-0:0
        MONO    8   LT18.D7ps  2 *8:68-5:22     0:0-0:0
        MONO    9   LT19.A4s   3  9:68-10:22    0:0-0:0
        MONO    10  LT19.B7s   3  10:68-11:22   0:0-0:0
        MONO    11  LT19.C2s   3  11:68-12:22   11:92-13:87
        MONO    12  LT19.D5s   3 *12:68-9:22    0:0-0:0
        MONO    13  LT20.A2ps  4  13:68-14:22   0:0-0:0
        MONO    14  LT20.B6ps  4  14:68-15:22   0:0-0:0
        MONO    15  LT20.C4ps  4  15:68-16:22   0:0-0:0
        MONO    16  LT20.D1ps  4 *16:68-13:22  *16:92-2:87

Via  the  sixth  column the inter-group connections now come
into play.  The order of pairing is  first  to  sequentially
perform all the intra-goup pairing and then sequentially all
the inter-group ones.

    These  two  TPL  files  are  in  the  sample   directory
"TPLfiles" listed as LT17 and LT17-LT20 and accessed via the
command "File->(Tecto Pairing Lists)->Sample".  They  can be
displayed using the DISPLAY button or input to the construc-
tion program using the APPLY button to generate 3D models of
the corresponding tecto structures.

GENERATING AND EDITING A 3D TECTO STRUCTURE

   Try  the  first  one,  LT17,  which encodes a single tec-
tosquare.  Immediately evident is that the resulting  struc-
ture  is far from being closed.  Redesign of the monomers is
therefore in order.  For this purpose there  is  provided  a
tool  for automatically changing the length of either of the
two stems of of all four monomers. It is  invoked  with  the
command  Utils->(Edit  Stem  Length),  whereupon the current
window is replaced by two.  The left one displays  the  sec-
ondary  structure  of  the first monomer and the second is a
redisplay of the 3D tecto structure.   You  are  invited  to
pick one of the two stems whose length is to be changed. The
INCREASE and DECREASE buttons are thereby activated. The in-
cremental change of stem length is that corresponding to in-
creasing or decreasing the number of basepairs by one and is
implemented,  respectively, by inserting or removing a base-
pair immediately before the topmost one. An A-U basepair  is
used as the inserted basepair. The incremental length change
amounts to a rotation of the kissing loop by about forty de-
grees,  and thus a significant relative reorientation of the
coaxially stacked stems. A few trials quickly  reveals  that
increasing  the  length  by  one unit gives the best result,
that is, the unpaired kissing loops are brought  closer  to-
gether than by any other change.

   Now  try  working  with  the putative tectosquare pattern
LT17-LT20.  Again, it is immedately evident  that  not  only
are  the  composing  four squares are each far from closure,
the pattern is also far from closure. We  can  take  are  of
closure  within  tectosquares  using the stem length editing
tool.  Its invocation  automatically  applies  to  all  four
squares.  To adjust the relative orientation of coupled tec-
tosquares, we now use the 3’_tail_kissing_tool for  changing
the  number  of basepairs alloted for tail kissing under the
constraint that the terminal 3’ nucleotide is always paired.
The  result  is  that  tail  overlap changes while maintaing
coaxial interaction. This gives a change in relative  orien-
tation of the participating tectosquares.  As in the case of
intra-square closure intra-pattern closure is  best  favored
by  an  increase  of  one  unit,  that is, the two tails are
pulled apart by a distance equivalent to  the  loss  of  one
basepair.

   The  editing  tools used in these examples facilitate de-
termining optimal values for two key design parameters whose
resolution is very coarse. It is therefore not expected that
the optimal values insure complete closure of the model. In-
stead, they should be interpreted as the design values which
best enhance spontaneous closure under  experimental  condi-
tions.

SAVING AND RESTORING A GENERATED TECTO STRUCTURE

   Saving the current generated tecto structure, modified or
not, is done with the command ’Utils->(Save the  Tecto  Mod-
el)’.  You will be asked to provide a name for it, whereupon
it is saved in the "User 3DM->TECTO" directory by that name.
Restoring  it  for viewing or further modification is by se-
lection from the stored list generated with the  command

CONSTRUCTING THE TECTO RNA MONOMER DATA BASE

    We now consider the problem of constructing the  initial
3D models of the four monomers starting from their secondary
structure which is assumed to exist as a BPL file. Normally,
the  one-word name used for the sequence in the BPL file has
no special meaning.  But we now require that the name of the
tectosquare to which the monomer is to belong be incorporat-
ed as the one and only prefix. This file is  prepared  sepa-
rately  from  the  program  by the user and entered into the
database directory presentation these files have  been  con-
structed  and placed in the ’sample BPL’ directory.  It con-
tains the ’.bpl’ files for the four tectosquares LT17, lT18,
LT19  and LT20. For the tectosquare LT17 these are labled as
LT17.A3s.bpl,  LT.B1s.bpl,  LT17.C8s.bpl  and  LT17.D6s.bpl.
They  were derived from the online supplementary material of
the above reference.

    Clicking the first of these into the model A channel re-
sults  in  a  display  of the secondary structure and of the
corresponding initial 3D structure. We  perform  two  opera-
tions  on  the  initial 3D structure.  The first is to shape
each of the haipin loops into a kissing conformation.   This
amounts to approriately extending the helicity of a support-
ing stem into its loop. Using the  on  the  pair  C(24)  and
G(22)  to  shape  the first loop, and then on the pair C(70)
and G(63) to shape the second loop.  This particular  choice
of where the extended helicity begins and stops includes the
kissing segment and also insures that kissing will result in
the coaxial stacking of the participating stems.

    The  second  operation  is to provide the single strand,
A(44)-A(45), which connects the two stems, with the  confor-
mation  recommended  in the noted reference. It is available
as  the  item  ’File->(Sample   PDB->MSI(BIOSYM)   format)->
A_TURN.pdb’,and we use the ’subset replacement’ tool for the
substitution.  Use of this tool requires that a Model A sub-
set  replaces a Model B subset.  We therefore first copy the
current  Model  A  into  Model  B  and  then  retrieve   the
A_TURN.pdb  structure as Model A.  Next, we identify and se-
lect from each model the subset to be substituted.  For  in-
stance, by viewing model B we put it into the ’subset’ level
with the menu item command subset of interest. This  results
in  model  B being at the subset level of specific interest.
We do the same with model A and then invoke the command  the
’2D A 2D B’ view with the subsets involved highlighted for a
quick check that the subsets  have  been  correctly  chosen.
Each  must  consist of a single segment and they must be the
same with respect to composition and nucleotide  order.  For
model  A, which is the donor model, the subset is G(2)-U(7);
for model B it is the subset G(42)-U(47).  Click on the menu
item  ’Do  Replacement’.  This results in model B having the
new subset.

    That we have chosen subset lengths of 6 instead of  just
2  is  prompted by the requirement that changing the coordi-
nates of a subset necessarily entails changing  the  coordi-
nates  of  the  5’ and 3’ complements of the subset and that
these changes need to be calculated.  We  therefore  enlarge
the  subset so that it’s 5’ and 3’ complements move as rigid
bodies that include the respective subset ends. The 5’  sub-
set  end can then serve as a reference nucleotide for the 5’
complement as can the 3’ end for the  3’  complement.  Thus,
before  the substitution is made there is calculated coordi-
nates for the 5’ complement relative to the 5’  subset  end,
and  the  same  is done for the 3’ complement relative to 3’
subset end. When the substitution is made, the  new  coordi-
nates  for the 5’ and 3’ ends are then used to calculate the
new coordinates for the respective complements.

    It will be noticed that there are two A  nucleotides  in
each of the hairpin loops whose positioning would need to be
ajusted were we interested in that kind of detail. This  can
easily be taken care of by performing a local energy refine-
ment.  But since their unrefined status does not affect  the
the  coaxial  stacking of the corresponing kissing loops, we
bypass this chore and accept the  current  3D  structure  as
suitable  for  participating  in a tectosquare. We therefore
would  normally  save  it  with  the   command   Utils->(3DM
Utils)->(Save as 3DM file).

CONTEMPLATED NEW FEATURES (generality and ease of use)

    The  current  Tecto  software was developed primarily to
address the design problem of enhancing spontaneous  closure
in  tectosquares  and  tectosquare patterns. The kind of TPL
file used was therefore of the simplest  type.   It  is  not
aimed  at handling arbitray types of tecto structures as can
be achieved by not having to specify the ordering  in  which
the  pairing  is done and by not having to specify key base-
pairs.  Only an arbitray list of the monomers used and iden-
tifying  markers  for  locating the start and end of kissing
segments of a monomer need be given.   The  general  pairing
program  would then determne the connection topology and the
connection pathway for  implementing  the  monomer  pairing.
What  can  also  be  automated is the 3D construction of the
monomers.  The kissing segments can be automatically  shaped
and subsets can automatically be replaced with ones of known
conformation. Also to be considered is the inclusion of  the
many  rendering  features that are normally used for A and B
models. Further, there is the need to significantly  improve
upon the closure enhancement provided by the stem-length and
tail-pairing tools in order to obtain  conformations  better
suited  to  energy minimization and dynamics calculations. A
promising approach under development is to  manipulate  con-
formation  parameters, such as rotating a monomer stem about
its helical axis. A premliminary version of a tool for  per-
forming this and other conformation manipulations is invoked
with the command ’Utils->(Edit Segment Position)’.  Its  use
is described in the following example.

    Consider the sample LT17 tectosquare. Having first opti-
mally enhanced closure with the stem-length and tail-pairing
editing  tools,  we  now edit its first monomer (model C) by
changing the position of one of its segments considered as a
rigid  body. As in the stem-length and tail-pairing editing,
any  changes  will  automatically  be  applied  to  all  the
monomers  of the tectosquare while preserving the base-pair-
ing that defines their  interconnection.  Pick  the  segment
consisting  of nucs 1-45, the axis of roation as ’S:MP-COM’,
and style as ’closed’. Then incrementally rotate the segment
to -10 degrees. A significant closure enhancement is thereby
achieved and provides  a  reasonable  conformation  starting
point  for  performing  modeling  ala energy refinement. The
same conformation editing can be applied to the sample tecto
pattern  L17-L20. Here, a subsequent editing of tail-pairing
further enhances closure, and thus suggests that editing  of
tail-pairing should be done after fully enhanced tectosquare
closure.


                          THE END





