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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 conists 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. Theoretically, 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, complementation of tails would also theoretically provide 
for the joining of tectosquares and hence of forming 'tectosquare patterns'.  The experimental results presented in the referenced article strongly suggest
all this to be true, but since coordinates were not provided with any of
the experimental 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 other 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 interconnected.  The file is
called a TPL (Tecto Pairing List) file, an example of which is the
following one that specifies a tectosquare.
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	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

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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
enumerates 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 basepairs to construct to implement the required
interconnection.  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 relates 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 asterisk in the connection word "*4:68-1:22"
tells the constructing program to ignore this particulr pairing connection
because it would lead to a never ending cycle of pairings.  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 connection 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 kissing loops already
possess a putative kissing conformation, formation of any one of the kissing
basepairs will automatically 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 calculation 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 coordinates 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 basepair.

    Our second example of a TPL file is that of a tectosquare pattern
consisting of four tectosquares.

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	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

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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 construction 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 tectosquare.  Immediately
evident is that the resulting structure 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
secondary 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 incremental change of stem length is that corresponding
to increasing or decreasing the number of basepairs by one and is implemented,
respectively, by inserting or removing a basepair 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 degrees,
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 together 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 tectosquares,
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 orientation
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 determining 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. Instead, they should be interpreted as the design values which
best enhance spontaneous closure under experimental conditions. 

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 Model)'. 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
selection from the stored list generated with the  command
'File->(User 3DM)->TECTO'.

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 incorporated
as the one and only prefix. This file is prepared separately
from the program by the user and entered into the database directory
'./RNA_2D3D/BPLfiles' with the menu item 'File->User BPL'. As an aid to this
presentation these files have been constructed and placed in the 'sample BPL'
directory.
It contains 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 results in a display of the secondary
structure and of the corresponding initial 3D structure. We perform two
operations 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 supporting stem into its loop. Using the 
'3D A: Edit->(Extend Single Strand Helicity 0)' menu item, we first click
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 conformation 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 subset 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 select from
each model the subset to be substituted. For instance, by viewing model B
we put it into the 'subset' level with the menu item command
'2B->level->subset' which then prompts us to identify and select the
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
'Utils->3D Utils->(Replace a B subset with an A subset)'.  This results in
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 coordinates of a subset necessarily
entails changing the coordinates 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' subset 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
coordinates 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 coordinates 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 refinement.  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 basepairs.  Only an arbitray list of
the monomers used and identifying 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 conformation parameters, such as
rotating a monomer stem about its helical axis. A premliminary version of a
tool for performing 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 optimally 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-pairing 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.


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