Knowledge-based instantiation of full atomic detail into coarse-grain RNA 3D structural models.

Abstract

The recent development of methods for modeling RNA 3D structures using coarse-grain approaches creates a need to bridge low- and high-resolution modeling methods. Although they contain topological information, coarse-grain models lack atomic detail, which limits their utility for some applications.
We have developed a method for adding full atomic detail to coarse-grain models of RNA 3D structures. Our method [Coarse to Atomic (C2A)] uses geometries observed in known RNA crystal structures. Our method rebuilds full atomic detail from ideal coarse-grain backbones taken from crystal structures to within 1.87-3.31 A RMSD of the full atomic crystal structure. When starting from coarse-grain models generated by the modeling tool NAST, our method builds full atomic structures that are within 1.00 A RMSD of the starting structure. The resulting full atomic structures can be used as starting points for higher resolution modeling, thus bridging high- and low-resolution approaches to modeling RNA 3D structure.
Code for the C2A method, as well as the examples discussed in this article, are freely available at www.simtk.org/home/c2a.
russ.altman@stanford.edu

Full text

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BIOINFORMATICS ORIGINAL PAPER
Vol. 25 no. 24 2009, pages 3259–3266
doi:10.1093/bioinformatics/btp576
Structural bioinformatics
Knowledge-based instantiation of full atomic detail into
coarse-grain RNA 3D structural models
Magdalena A. Jonikas1, Randall J. Radmer1and Russ B. Altman1,2,∗
1Department of Bioengineering and2Department of Genetics, Stanford University, Stanford, CA 94305, USA
Received on April 23, 2009; revised on September 28, 2009; accepted on October 1, 2009
Advance Access publication October 7, 2009
Associate Editor: Ivo Hofacker
ABSTRACT
Motivation: The recent development of methods for modeling RNA
3D structures using coarse-grain approaches creates a need to
bridge low- and high-resolution modeling methods. Although they
contain topological information, coarse-grain models lack atomic
detail, which limits their utility for some applications.
Results: We have developed a method for adding full atomic detail
to coarse-grain models of RNA 3D structures. Our method [Coarse
to Atomic (C2A)] uses geometries observed in known RNA crystal
structures. Our method rebuilds full atomic detail from ideal coarse-
grain backbones taken from crystal structures to within 1.87–3.31Å
RMSD of the full atomic crystal structure. When starting from coarse-
grain models generated by the modeling tool NAST, our method
builds full atomic structures that are within 1.00Å RMSD of the
starting structure. The resulting full atomic structures can be used
as starting points for higher resolution modeling, thus bridging high-
and low-resolution approaches to modeling RNA 3D structure.
Availability:
CodefortheC2A
examples discussed inthis article,
www.simtk.org/home/c2a.
Contact: russ.altman@stanford.edu
method,
are
as well
available
asthe
at freely
1
Large RNA molecules perform diverse functions within cells and
have complex 3D structures. For example, the 3D structures of
RNA enzymes (ribozymes) allow them to catalyze RNA cleavage
(Guerrier-Takadaetal.,1983;Krugeretal.,1982;Starketal.,1978).
Other structured functional RNA molecules include riboswitches
(Nahvi et al., 2002) and ribosomal RNA(Ban et al., 2000; Yusupov
etal.,2001).Althoughknowingthe3Dstructuresofthesemolecules
is critical in understanding their functions, the protein databank
contains few high-resolution RNA crystal structures. For these
reasons, computational modeling of RNA 3D structures is an
important goal.
Both manual and automated methods for building full atomic
RNA structures have had success but continue to be challenged
by significant limitations. Manual approaches have successfully
modeled a number of molecules, including several group I introns
(Lehnert et al., 1996; Michel and Westhof, 1990) and the yeast
INTRODUCTION
∗To whom correspondence should be addressed.
phenylalanine tRNA(Levitt, 1969), but require expert knowledge of
RNAstructure. Semi-automated methods, such as MANIP(Massire
and Westhof, 1998) and ERNA-3D (Tanaka et al., 1998) use a
fragment-based approach to build full atomic 3D RNA models.
However, these methods are limited by the need for significant user
interaction as well as expert knowledge.
Several automated tools model RNA structure in 3D. The
MC-Fold/MC-Sym pipeline uses constraint satisfaction algorithms
tobuildfullatomicmodelsofstructures(Majoretal.,1993;Parisien
and Major, 2008). FARNA (Das and Baker, 2007) is an automated
fragment-based tool that has been used to model molecules as
large as 158nt when combined with multiplexed hydroxyl radical
cleavage analysis (MOHCA; Das et al., 2008).
Coarse-grain approaches to modeling RNA 3D structures are
fully-automated, can model very large structures (>160nt) and can
be used in multiscale approaches for modeling large systems. These
methods include YAMMP (Malhotra et al., 1994), YUP (Tan et al.,
2006), DMD (Ding et al., 2008), RNA2D3D (Martinez et al., 2008)
and NAST (Jonikas et al., 2009).Although coarse-grain topological
models of RNA molecules provide significantly more structural
information than secondary structure alone, full atomic models
are preferable for studying structure function relationships, and
are a prerequisite for most energy-based dynamics and refinement
methods.
As a result, several of these methods include tool-specific
protocols for adding atomic resolution to their coarse-grain models.
For example, DMD and its related web-based tool iFoldRNA
(Sharma et al., 2008) use a coarse-grained approach to generate
predictions for structures <50nt in size, which are then refined
to atomic resolution by an unpublished reconstruction protocol.
RNA2D3Dstartswithanucleotide-resolutionfirstapproximationof
themolecule3Dstructurebasedonsecondarystructureinformation,
and adds atomic resolution early in its protocol, using nucleotide
geometries observed in crystal structures. Neither of these tools can
be used on independently generated coarse-grain structures.
In some cases, users of these tools develop their own application-
specific approach to adding atomic detail. A recently reported
all-atomic model of Pariacoto virus included coarse-grained
modeling of RNA followed by addition of atomic detail (Devkota
et al., 2009). The authors extended a crystal structure that
contained 35% of the RNAstructure by initially modeling the RNA
with YAMMP, which uses a coarse-grained one-point-per-residue
representation centered on phosphate atoms. To add full atomic
© The Author(s) 2009. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/
by-nc/2.5/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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M.A.Jonikas et al.
detail to the coarse-grain structure, the authors used a fragment-
basedapproachtomatchexistingfullatomicstructuresinthePDBto
both base-paired and non-base-paired regions. The authors searched
for compatible pieces to generate plausible structures, which they
minimized and annealed. Such multiscale approaches are becoming
increasingly promising, but are limited by the need for each research
group to develop their own protocols for adding atomic detail to
coarse-grain models.
Several methods in both RNA and protein structure prediction
use knowledge-based fragment approaches, most notably FARNA
and Rosetta (Simons et al., 1997), these methods search for similar
fragments at the sequence level to inform the structure prediction.
Our approach to instantiating full atomic detail is inspired by these
methods and based on the observation that fragments in RNA
molecules that are similar at the coarse-grain level are often also
similar at the full atomic level. Therefore, if a ribosomal RNA
fragment is similar to a model fragment at the coarse-grain level, the
full atomic detail from the ribosomal crystal structure may contain
useful geometric information about how full atomic detail should be
instantiated in the coarse-grain model.
None of the methods for adding full atomic detail to coarse-grain
structures mentioned above are (i) generalized for many types of
independently generated coarse-grain structures, (ii) validated on
a range of structures sizes and (iii) publicly available. We present
a fully automated fragment- and knowledge-based method, called
Coarse to Atomic (C2A) for instantiating full atomic detail into
coarse-grain structures of RNA molecules. We evaluate the full
atomic structures generated by our method, and make the method
freely available (along with a manual). Our method can use any
atom-based coarse-grain structure template as input, and provides
a full atomic, GROMACS energy-minimized structure as output.
We use geometric information from RNA crystal structures to
reconstruct full atomic detail. We have tested our method on both
ideal coarse-grain structures for molecules ranging in size from 70
to 244 residues, as well as on coarse-grain one-point-per-residue
models of tRNA generated by NAST. In addition to improving
the usefulness of coarse-grain modeling methods, this tool has the
potential to bridge the computationally expensive but precise full
atomic modeling approach and the fast but detail-poor coarse-grain
modeling approach.
2
In brief, C2A searches within a reference full atomic structure for
coarse-grain matches to fragments of a target molecule, and combines the
full atomic versions of the matches to generate a full atomic structure. We
then perform a minimization step to reduce any collisions and gaps. We need
the following three inputs to perform this method:
METHODS
• A coarse-grain template for the target molecule (e.g. a structure with
one point per residues representing the C3?or P atom) (Fig. 1A).
• A fragment definition for the target molecule (e.g. the secondary
structure) (Fig. 1B).
• A reference full atomic RNA 3D structure database (e.g. ribosomal
RNA structures) (Fig. 1C).
Based on this input, we generate a full atomic structure by following these
steps:
(i) Usethefragmentdefinitiontobreakthetargetmoleculeintostructural
subsets (e.g. helices, loops and junctions) (Fig. 1D).
(ii) Findcoarse-grainmatchesforeachfragmentinareferencefullatomic
RNA structure (Fig. 1E).
(iii) Combine matches to generate a full atomic structure free of major
atomic collisions (Fig. 1F).
(iv) Minimize the structure to eliminate any chemically unrealistic gaps
or collisions (Fig. 1G).
2.1
For our method, we define substructures of the target molecule, which we
call fragments.Although we use the secondary structure of a target molecule
to define these fragments in this article, other fragment definitions that use
both single- and double-stranded regions can be easily implemented as well.
Thefragmentdefinitionisprovidedbytheuser,andC2Aparsesthedefinition
to determine the substructures. We use the secondary structure to define two
types of fragments within the target molecule: single and double stranded.
Helices are double-stranded base-pairing regions and may include bulges of
any length. Regions between helices are single stranded and overlap by one
residue in the primary sequence with adjacent helices. Fragments may not
contain fewer than four residues, and more than one residue of overlap is
allowed in cases where there would otherwise be fewer than four residues
in a fragment. The result is a ensemble of structural coarse-grain subsets,
either double or single stranded, of the target molecule (we show examples
in Fig. 1D).
Defining structure fragments
2.2
We search within the reference full atomic database of structures for
coarse-grain matches to the fragments we have defined (Fig. 1E). We then
use the full atomic detail of the matches to build complete full atomic
structures. In this article, we use the Thermus thermophilus 16S ribosomal
RNA solved at 3.00Å resolution (PDB ID 1N32 chain A) as the primary
database of full atomic structure. This database does not contain any
structures upon which we tested the method. In our search for coarse-grain
matches, we only consider the level of coarse-graining that is represented
in the template structure. Thus, for NAST structures, we use template
structures where each nucleotide is represented by the C3?atom position.
When searching for matches, we will only consider the C3?positions of
each residue within the reference database. However, our method allows
other coarse-graining schemes such as residues represented with the position
of the P atom or by more than one atom. Since using P atoms is a more
common coarse-grained representation, we have provided an example that
uses a P-centered coarse-grain scheme in the examples directory of the
download associated with this article. For single-stranded fragments such
as loops, junctions and ends, we determine the length of the fragment (in
number of residues) and the distance between the defining points of the
first and last residues in the template structure (in Angstroms). We search
through the reference database for continuous runs of residues of the same
length as the fragment. Of these, we keep the ones that have distances
between the first and last residue defining atoms (in our case C3?) within
a certain user-specified error (typically 10%) of the distance observed in the
template fragment. This results in an ensemble of matches within the full
atomic structure to the coarse-grain template fragment. We then calculate
the coarse-grain RMSD (Root Mean Square Deviation) of each potential
match to the coarse-grain template fragment and rank the matches. We keep
the 10 best matches by RMSD for each fragment as part of the working set
for assembling a full atomic structure. For double-stranded fragments such
as helices, we first find all the possible matches for each single-stranded
element individually. From each possible combination of matches, we keep
those that are within a certain error (we use 10%) of the distances observed
in the template fragment between the 5?and 3?ends of each fragment. As
with the single-stranded fragments, we calculate the coarse-grain RMSD to
Searching for fragment matches
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Instantiating full atomic detail into coarse-grain RNA structures
Fig. 1. C2Amethod overview. The C2Amethod uses three pieces of information as input: (A) a coarse-grain template for the target molecule; (B) a fragment
definition for the target molecule, such as the secondary structure; and (C) a reference database of full atomic RNA structures. (D) In Step 1, the coarse-grain
template is divided into structural subsets based on the fragment definition, here we show as an example a double- and a single-stranded fragment. (E) Step 2
searches for coarse-grain matches to each fragment in the reference structure and extracts the full atomic detail of each match, we show here the full atomic
detail for two matches found in ribosomal RNA for each of the two example fragments. (F) Step 3 searches for combinations of matches free of major
collisions, we show here how matches for the two example fragments align to the coarse-grain template. (G) Finally, Step 4 minimizes the resulting full
atomic structure to remove unrealistic gaps and collisions.
the coarse-grain template fragment, rank the matches and keep the 10 best
for the working set.
2.3
Since we do not consider the residue sequence in our search for matches,
many of the matches will have incorrect base atoms. To remedy this, we
replace the incorrect nucleoside base atoms with the correct ones while
maintaining the orientation of the base plane. We keep the sugar group
and phosphate group atoms in the same positions, and replace the base
atoms with the correct geometry. We use three atoms to define the plane and
orientationoftheoriginalbase(N9,N1andC5forAdenineandGuanine,and
N1, N3 and C5 for Cytosine and Uracil). We insert the correct base atoms
into the appropriate plane and orientation, resulting in coordinates for the
correct residue. This results in fragment matches with the correct nucleotide
Processing fragment matches
sequencewhilemaintainingthegeometryofthematchfoundinthereference
structure.
2.4
We use a Metropolis Monte Carlo approach to assemble a full atomic
structure using the coarse-grain template and a working set of best matches
for each fragment. We start by randomly selecting one match for each
fragment from the working set and aligning the matches to the coarse-
grain template. Since we defined single-stranded fragments to overlap by
one residue with double-stranded fragments, each of these junctions will
have two sets of coordinates for that residue. In these cases, we use only the
coordinates from the double-stranded fragment. In each step, we search for
pairs of atoms within the full atomic structure that are closer than a cutoff
distance(user-specified,1.0Åhere)andcheckthefragmentscontainingthese
pairs for collisions. If we observe any collisions, we randomly select one of
Assembling full atomic structures
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M.A.Jonikas et al.
thecollidingfragmentstobereplacedwithanotherrandomlyselectedmatch.
WeacceptthereplacementwiththeprobabilityshowninEquation(1),where
Noldis the number of collisions in the old state and Nnewis the number of
collisions in the new state.
if
Nnew<Nold
then
P=1.0
else
P=0.5×exp
?
−Nnew−Nold
Nold
?
(1)
We continue this attempt for a user-specified number of steps, or until we
find a combination of matches with no collisions, whichever occurs first.
If no such combination is found within a user-defined number of steps and
attempts, the output will be the full atomic structure with least number of
collisions observed over the course of this search. In this article, we make
five attempts of 500 steps each to generate a full atomic structure free of
major collisions.
2.5
The structures resulting from our assembly protocol are likely to contain
both gaps (unrealistically long covalent bonds) and collisions (unrealistically
short distances between any atoms), and which may prevent the structures
from being used in full atomic studies. In particular, the regions at junctions
between fragments may contain significant gaps between atoms that should
be bonded because the coordinates for those atoms came from different
matches. To remedy these two structural issues, we minimize the full atomic
structures with GROMACS using steepest descent minimization.We include
the scripts we used for running GROMACS, including parameter files, on
our project’s web site.
Minimizing full atomic structures
2.6
We evaluated the effect of minimization on junction bonds by calculating
the lengths of covalent bonds between fragments both before and after
minimization. We compared these values with those of non-junction bonds.
We also calculated the lengths of these bonds observed in the relevant crystal
structures.
We submitted our minimized structures to the MolProbity tool, which
calculates a Clashscore and assigns a percentile to the structure (Davis et al.,
2007; Lovell et al., 2003). We also submitted our structures to the RCSB
ADIT structure validation tool which outputs a full report on the structure
including RMSD values for covalent bonds and angles relative to standard
values for nucleotides (Clowney et al., 1996; Gelbin et al., 1996). We made
thefullreportsavailableonourprojectwebsiteunderthedocumentssection.
For all minimized full atomic structures, we calculated the RMSD value
relative to the known crystal structure. We also calculated RMSD values
for helical (double-stranded) and non-helical (single-stranded) fragments
separately. We also applied the recently developed metric of interaction
network fidelity (INF) to all of our structures, which considers base–base-
stacking and base–base-pairing interactions (Parisien et al., 2009). We
calculated the INF for pairings alone, as well as pairings and stackings
combined, which is a much stricter measure. INF values range from 0.00
(worst) to 1.00 (best).
Evaluating full atomic structures
2.7 Validation using ideal backbones from crystal
structures
To validate our approach, we applied it to seven crystal structures of RNA
molecules ranging in size from 70 to 244 residues:
• Yeast ai5g group II intron (‘Ai5gamma’, PDB ID 1KXK) 70 residues
(Zhang and Doudna, 2002).
• Yeast phenylalanine tRNA (‘tRNA’, PDB ID 6TNA) 76 residues
(Sussman et al., 1978).
• Aminoacyl-tRNA synthetase ribozyme (‘flexizyme’, PDB ID 3CUL)
92 residues (Xiao et al., 2008).
• P4-P6 RNA ribozyme domain (‘P4-P6’, PDB ID 1GID) 158 residues
(Cate et al., 1996).
• Azoarcus group I intron (‘Azoarcus’, PDB ID 1ZZN) 195 residues
(Stahley and Strobel, 2005).
• Twort ribozyme (‘Twort’, PDB ID 1Y0Q) 244 residues (Golden et al.,
2005).
We stripped each crystal structure of atomic detail, leaving only the
position of the C3?atom for each residue. We defined fragments using the
known secondary structure of each molecule and the rules described above.
Thedatabasedidnotcontainanyofthesestructures.Wesearchedformatches
to each fragment and created a working set by keeping the 10 best matches
by RMSD at the coarse-grain level. We searched for 10 combinations of
matchesfreeofmajorcollisionsandminimizedthefullatomicstructures.For
the two structures we modeled that were missing the residues (the Twort and
Azoarcusribozymes),weusedthecompletecoarse-grainstructuresgenerated
using the NAST tool by Jonikas et al. as the template input.
2.8 Building full atomic models of NAST tRNA
topologies
We applied the C2Amethod to the problem of building full atomic structures
based on coarse-grain models built by the tool NAST. For each of the three
topologies generated by NAST, we used five models as template starting
structures and generated 10 full atomic structures which we then minimized.
3RESULTS
3.1Recovering full atomic detail from ideal
coarse-grain templates
The full atomic RMSD values of full atomic models built from
coarse-grain crystal structure templates ranged from 1.87 to 3.31Å,
we give the average values in Table 1. The average RMSD for the
60 full atomic structures we generated from ideal backbones was
2.75 ± 0.37Å. We report INF scores for all structures in Table 2.
Wecalculatedjunctionbond-distancesbeforeandafterminimization
and report the values in Table 3. We report MolProbity Clashschore
and percentiles, as well as RMSD values for covalent bonds and
angles as evaluated by the RCSBADIT tool in Table 4. We compare
Table 1. RMSD of minimized full atomic structures
Molecule
ID
Overall
RMSD (Å)
Helical
fragments
RMSD (Å)
Non-helical
fragments
RMSD (Å)
Validation structures (10 models)
1KXK
6TNA
3CUL
1GID
1ZZN
1Y0Q
2.13 ± 0.21
2.81 ± 0.11
3.06 ± 0.18
3.16 ± 0.08
2.79 ± 0.16
2.76 ± 0.07
1.36 ± 0.44
1.10 ± 0.09
1.77 ± 0.82
2.03 ± 1.22
2.10 ± 0.74
1.92 ± 0.68
2.41 ± 1.39
3.02 ± 1.27
2.48 ± 1.90
2.75 ± 1.45
2.56 ± 1.42
2.50 ± 1.54
NAST tRNA models (50 models)
Model A
Model B
Model C
8.39 ± 0.27
13.30 ± 0.31
15.99 ± 0.76
2.65 ± 0.71
3.08 ± 1.28
3.06 ± 1.13
4.13 ± 1.91
3.82 ± 1.51
4.19 ± 1.95
We report both overall RMSD values and separate values for helical and non-helical
fragments.
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Instantiating full atomic detail into coarse-grain RNA structures
Table 2. Averages and ranges for INF for base pairs alone and base pairs
with stacking
Molecule ID INF on pairings and stacking INF on pairings alone
Average Range Average Range
1KXK
6TNA
3CUL
1GID
1ZZN
1Y0Q
0.51±0.10
0.69±0.01
0.67±0.02
0.61±0.03
0.58±0.02
0.61±0.01
0.46±0.04
0.41±0.05
0.41±0.04
0.44−0.78
0.66−0.71
0.64−0.70
0.56−0.64
0.55−0.60
0.58−0.63
0.38−0.55
0.31−0.51
0.34−0.49
0.83±0.03
0.69±0.04
0.65±0.04
0.51±0.03
0.67±0.02
0.54 ± 0.02
0.35±0.07
0.27±0.09
0.26±0.08
0.77−0.89
0.59−0.73
0.57−0.69
0.46−0.55
0.64−0.70
0.52−0.57
0.18−0.51
0.07−0.46
0.11−0.45
6TNA-A
6TNA-B
6TNA-C
INF scores range from 0.0 (worst) to 1.0 (best).
Table 3. Covalent bond lengths before and after minimization for junctions
and non-junctions
Molecule ID Non-junction bonds (Å) Junction bonds (Å)
RangeAverageRange Average
1KXK
Crystal
Pre-min
Post-min
1.58−1.61
1.59−1.63
1.54−1.65
1.60±1.60
1.61±1.61
1.59±1.59
1.59−1.63
1.12−6.24
1.56−1.75
1.60±0.01
3.29±1.22
1.64±0.04
6TNA
Crystal
Pre-min
Post-min
1.54−1.64
1.59−1.62
1.53−1.65
1.60±1.60
1.60±1.60
1.59±1.59
1.58−1.62
1.01−6.49
1.51−1.78
1.60±0.01
2.49±1.21
1.62±0.05
3CUL
Crystal
Pre-min
Post-min
1.48−1.62
1.59−1.62
1.55−1.65
1.60±1.60
1.61±1.61
1.59±1.59
1.59−1.62
1.14−8.26
1.56−1.86
1.61±0.01
4.07±1.69
1.67±0.07
1GID
Crystal
Pre-min
Post-min
1.57−1.64
1.59−1.64
1.49−1.70
1.60±1.60
1.61±1.61
1.59±1.59
1.58−1.62
1.04−12.72
1.50−2.90
1.60±0.01
3.82±2.50
1.67±0.13
1ZZN
Crystal
Pre-min
Post-min
1.57−1.63
1.59−1.63
1.42−2.09
1.61±1.61
1.60±1.60
1.59±1.59
1.57−1.64
1.00−13.36
1.44−2.47
1.61±0.01
3.64±1.67
1.67±0.11
1Y0Q
Crystal
Pre-min
Post-min
1.58−1.65
1.59−1.63
1.46−1.87
1.60±1.60
1.61±1.61
1.59±1.59
1.57−1.64
0.55−10.96
1.48−2.13
1.60±0.01
3.53±1.88
1.66±0.07
We report ranges as well as average values. We also report the bond lengths in the
relevant crystal structures for the same bonds.
thesevaluesforourmodelstothosecalculatedontherelevantcrystal
structures. We show a sample full atomic tRNAmolecule built from
the ideal backbone template in Figure 2B and show the full atomic
crystal structure for comparison (Fig. 2A). The full atomic models
we generated for the Azoarcus and Twort molecules contain full
atomic detail for the loop regions that are missing in the crystal
structure. We have posted these structures and all code necessary to
reproduce these examples on our project web site.
3.2Building full atomic models from coarse-grain
NAST models of tRNA
We show sample full atomic models built from the three NAST
topology predictions of tRNA in Figure 2C–E. The full atomic
structures that we generated had full atomic RMSD values within
1Å of the coarse-grain RMSD of their templates. We report RMSD
values to the tRNA crystal structure in Table 1 along with separate
values for helical versus non-helical fragments. We also report INF
scoresforpairingsalone,aswellaspairingsandstackingsinTable2.
We report MolProbity Clashscores and RCBS ADIT RMSD values
for covalent bonds and angles in Table 5. The fragment combination
search step succeeded in 50, 24 and 20 of the 50 attempts for each
model A, B, and C, respectively. For model B, two of the five
templates succeeded in 10 of the 10 combination search attempts,
one succeeded in 4 of the 10 attempts, and two succeeded in 0 of
the 10 attempts. For model C, two templates succeeded in 10 of the
10 attempts and three succeeded in 0 of the 10 attempts.
3.3
We used a 2.2GHz CPU to run the C2A method. We analyzed
the CPU load for the two parts of C2A code: creating a working
library of fragment matches (which only needs to be performed
once per template structure) and combining fragments into full
atomic structures (which we performed 10 times for each template
structures).
There are two contributing factors to the time needed to generate
the working library of fragment matches: the number and types of
fragments, and the size of the reference full atomic database. It
took 95s to load the reference database [Thermus thermophilus 16S
ribosomal RNA solved at 3.00 Å resolution (PDB ID 1N32 chain
A)]. It took between 3s and 20s to find matches for single-stranded
fragments and between 40s and 440s to find matches for double-
stranded fragments. In total, the first part of C2A took 1226, 1550,
1034, 1297, 1836, 2741 and 3847s to find matches to all fragments
for the Ai5gamma, tRNA, flexizyme, SPR19, P4-P6, Azoarcus and
Twort molecules, respectively.
When using ideal backbones as the input for the C2A method,
finding combinations of matches free of major collisions took an
average of 47±30s, with the maximum being 117s. For NAST
tRNA models A, B and C, finding matches took average times of
1970, 1956 and 2206s, respectively.
Thecodeandexampleswehavemadeavailablearepythonscripts
that have been tested on both unix and Mac OSX platforms.
Computational resources
4
We have presented a method for instantiating full atomic detail in
coarse-grain RNA structure backbones using geometry knowledge
from a reference database of one or more full atomic RNA crystal
structures, in this case the Thermus thermophilus 16S ribosome. We
assume that if a fragment matches well to pieces of known RNA
structure at the coarse-grain level, then the full atomic geometry of
the match is a good predictor of the fragment’s full atomic detail.
In this article, we used only data from one ribosomal RNA as a
DISCUSSION
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M.A.Jonikas et al.
Table 4. Evaluation of minimized full atomic structures with MolProbity and the RCSB ADIT tool
Molecule ID MolProbityRCSB ADIT
Clashscore (goal=0)Percentile (N =1784)Covalent bonds Covalent angles
Crystal
structure
Best
model
Average (10
models)
Crystal
structure
Best
model
Average (10
models)
RMSD (Å)RMSD (degrees)
CrystalModels CrystalModels
1KXK
6TNA
3CUL
1GID
1ZZN
1Y0Q
14.03
26.46
7.67
35.78
32.67
40.47
3.33
4.92
6.11
13.31
15.29
15.9
8.54±5.54
9.11±4.54
8.56±2.30
23.21±14.67
29.46±9.82
40.82±17.72
54
19
83
10
13
8
97
94
90
57
48
46
78.30±22.53
76.60±19.10
79.10±10.81
35.80±18.36
21.11±16.00
13.60±15.03
0.006
0.079
0.007
0.009
0.008
0.007
0.017
0.017
0.020
0.031
0.032
0.036
0.9
3.4
1.0
0.9
1.1
1.0
2.8
2.7
3.2
3.4
3.6
3.8
We give MolProbity Clashscores and percentiles for validation structures. Clashscore is the number of serious steric overlaps (>0.4Å) per 1000 atoms. ADIT reports the RMSD
values for covalent bonds and angles calculated relative to standard values for nucleotide units.
Fig. 2. Images of C2Afull atomic modeling results. We show both a full atomic stick and a cartoon representation for each of the following tRNAstructures:
the full atomic crystal structure (PDB ID 6TNA) (A), a full atomic model generated by C2A using the ideal backbone from the crystal structure (B), a full
atomic model based on the NAST tRNA model A (C), model B (D), and model C (E).
reference structure, through which we search for matches to coarse-
grain templates. We did not include any geometric data from our
template structures in the reference full atomic structure.
To validate our method, we applied it to ideal backbones taken
from the crystal structures of seven RNA molecules. For each
structure, we kept only the C3?position of each residue, creating
ideal backbone structures with one point per residue and recovered
the full atomic detail at an average resolution <3.0Å. We were
also able to generate full atomic structures of two large RNA
moleculesthatweremissingresiduesinthecrystalstructuresolution
(the Azoarcus and Twort ribozymes) by using the NAST generated
complete coarse-grain templates. We were able to minimize the full
atomic structures with GROMACS, and remove significant clashes
and gaps. The resulting minimized full-atomic structures compare
well with the known crystal structures in terms of clashes and gaps.
Users with expertise in structure minimization and refinement can
use these structures as starting points for further studies.
For the two ribozymes that are missing loops in the crystal
structure (Azoracus and Twort), we used the coarse-grain loops
modeled by NAST as part of the input template and modeled full
atomic detail for the entire molecule, resulting in complete full
atomic structures. These two examples show that the combination
of NAST and C2A can be used to complete crystal structures that
are missing pieces of the molecule. However, the quality of the
modeling of the missing pieces depends entirely on the modeling
choices by the user when building the coarse-grain template. In our
case, we used the geometry of existing loops to build coarse-grain
models of the missing loops.
We then applied our method to fill in atomic resolution in NAST
coarse-grain models of the tRNA molecule. For each of the three
coarse-grain topology models generated by NAST, we used five
representative structures and applied our method to generate full
atomic versions of the models. As an aside, we noticed that the
amount of time necessary to find a combination of fragments
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Instantiating full atomic detail into coarse-grain RNA structures
Table 5. MolProbity Clashscores for full atomic tRNA models built from NAST coarse-grained models
Molecule ID MolProbityRCSB ADIT
Clashscore (goal=0)Percentile (N =1784, 0–9999Å )Covalent bonds Covalent angles
Best modelAverage Best modelAverageRMSD (Å) RMSD (degrees)
Model A: all structures1.236.93±5.0399 84.32±16.670.022 3.2
Structures A-0
Structures A-1
Structures A-2
Structures A-3
Structures A-4
3.08
1.23
5.54
1.23
1.23
7.14±3.36
9.29±8.38
8.80±2.51
6.52±4.34
2.89±1.56
98
99
92
99
99
84.2±14.54
78.1±24.59
77.4±11.89
84.6±16.32
97.3±2.50
0.021
0.024
0.022
0.022
0.020
3.2
3.4
3.3
3.2
3.1
Model B: all structures7.3837.77±26.96 8525.16±24.340.041 4.0
Structures B-0
Structures B-1
Structures B-2
Structures B-3
Structures B-4
7.38
13.54
24.00
14.77
14.77
13.29±4.18
40.41±23.72
62.83±34.44
37.17±17.14
35.39±22.44
85
56
23
50
50
57.7±18.66
18.78±20.09
8.2 ± 10.53
17.4±17.88
23.1±20.36
0.022
0.039
0.050
0.046
0.044
3.3
4.0
4.5
3.9
4.0
Model C: all structures 3.08 19.04±13.78 9848.42±28.220.029 3.6
Structures C-0
Structures C-1
Structures C-2
Structures C-3
Structures C-4
9.23
15.38
3.08
6.15
5.54
18.34±9.96
22.65±4.36
12.19±7.56
11.57±4.39
30.46±23.76
75
48
98
90
92
46.4±24.17
27.8±10.41
64.5±29.39
65.8±19.44
37.6±34.25
0.033
0.023
0.025
0.026
0.035
3.7
3.5
3.4
3.6
3.8
For each of three groups of coarse-grained models (A–C), we selected five models as templates for building 10 full atomic structures. We list statistics for each of the three groups,
as well as for each coarse-grain template we used.
free of major collisions is an indicator of the quality of the
topology. Additionally, all five of the templates used for model A
successfully generated full atomic structures, while only three and
two templates for models B and C, respectively, were able to do
so. We were able to minimize the full atomic structures we built
using GROMACS which corrected any gaps or collisions. Until
this last minimization step, the method is entirely geometric and
does not consider any chemical opportunities such as hydrogen
bonds. Through this example, we show that coarse-grain topology
models generated from limited structural information (in this case,
only primary, secondary and limited tertiary structure data) can be
used as starting points for building full atomic structures. These full
atomicstructurescanbeusedasstartingpointsforfurtherrefinement
using physics-based approaches, or more detailed knowledge-based
approaches.
The full atomic structures we generated for tRNA, both from
the crystal structure template and the NAST model template, did
not recover any tertiary contact base pairings with adequate detail.
Recovering these interactions is an important goal of model RNA
3D structure and remains a significant challenge. Our need to
avoid serious clashes during the assembly step selects against the
close interactions needed to recover these non-helical base pairings.
However, once a full-atomic structure is built from a coarse-
grain template, knowledge of tertiary interactions and finer-grained
dynamicstoolscanbeusedtorecovertheseinteractions.Preliminary
results of using the RNAbuilder tool (S.C.Flores et al., submitted for
publication) to constrain known tertiary contacts in our full atomic
models show improved INF scores. RNAbuilder uses a full atomic
model as a rigid template onto which it threads another full atomic
moleculewhichattemptstosatisfyboththegeometryofthetemplate
and the specified tertiary contacts. This method maintains most of
the original geometry which additionally constrains tertiary contacts
that were not previously present.
The C2A method for instantiating full atomic detail into coarse-
grain models is limited by the quality of the template structure
and information in the reference full atomic structure. Although the
process of instantiating atomic detail does not decrease the quality
ofthemodel,itdoesnotimproveiteither.Ourmethodisalsolimited
by the geometric information contained in the chosen reference
database. C2Acannot predict entirely new fragment geometries, and
assumesthatknownstructuresarereasonablesourcesfordataforthe
structures we are attempting to predict. Although we used only one
ribosomalRNAstructure,usersofC2Acanincludedifferentormore
crystal structures as reference full atomic structural information.
FullatomicstructuresgeneratedbyC2Ainheritthelimitationsand
problems associated with their coarse-grain templates.Additionally,
thereisnoguaranteeofconvergenceonacombinationoffullatomic
fragments free of major collisions. However, we noticed a trend
that a lack of convergence tended to correlate with a coarse-grain
template model of poor quality.
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M.A.Jonikas et al.
Our code works with any atom-based coarse-graining scheme.
The results we presented in the article are for coarse-grain template
structures with a one-point-per-residues representation centered on
the C3?atom. We have also tested our code on P, P-C3?and P-C2-
C3?coarse-grain representations (not presented in this article). We
observe that the more points representing a residue, the better the
resulting full atomic structures.
The method we have proposed connects the coarse-grain and full
atomic approaches for modeling RNA 3D structures. Coarse-grain
approaches are generally faster and able to handle large molecules
but lack in accuracy and detail. Full atomic approaches are limited
computationally, but provide accurate and detailed results. Being
able to move back and forth between these two approaches has not
beenpossiblebecausenopublished,validatedandpubliclyavailable
method existed for building full atomic detail into coarse-grain
models. Our method will allow models generated by coarse-grain
methods to be refined using full atomic tools. Using full atomic
models in coarse-grain methods simply requires removal of full
atomic detail to the desired coarse-grain level.
We make all code and examples from this article, along
with instructions, available for free on our project web
site: www.simtk.org/home/c2a under the Documents link.
Detailed instructions for running C2A are including in the
NAST/C2A manual which is available at the same address.
ACKNOWLEDGEMENTS
WethankAlainLaederach,DanielHerschlag,RhijuDasandSamuel
Flores for helpful discussions. We are grateful to Christopher Bruns
for developing the GROMACS interface Zephyr (available free at
https://simtk.org/home/zephyr). We also thank Marc Parisien for
providing us with code to calculate the INF scores of our structures.
Funding: NIH Roadmap for Medical Research (grant U54
GM072970); National Institutes of Health (grant P01-GM66275).
National Library of MedicineTraining (grant LM-07033 to M.A.J.).
NIH BiotechnologyTraining (grant 5T32GM008412-15 to M.A.J.).
Conflict of Interest: none declared.
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