A two-dimensional mutate-and-map strategy for
non-coding RNA structure
Wipapat Kladwang1, Christopher C. VanLang2, Pablo Cordero3 and Rhiju Das1,3,4*
Non-coding RNAs fold into precise base-pairing patterns to carry out critical roles in genetic regulation and protein
synthesis, but determining RNA structure remains difficult. Here, we show that coupling systematic mutagenesis with
high-throughput chemical mapping enables accurate base-pair inference of domains from ribosomal RNA, ribozymes and
riboswitches. For a six-RNA benchmark that has challenged previous chemical/computational methods, this ‘mutate-and-
map’ strategy gives secondary structures that are in agreement with crystallography (helix error rates, 2%), including a
blind test on a double-glycine riboswitch. Through modelling of partially ordered states, the method enables the first test
of an interdomain helix-swap hypothesis for ligand-binding cooperativity in a glycine riboswitch. Finally, the data report on
tertiary contacts within non-coding RNAs, and coupling to the Rosetta/FARFAR algorithm gives nucleotide-resolution
three-dimensional models (helix root-mean-squared deviation, 5.7 Å) of an adenine riboswitch. These results establish a
promising two-dimensional chemical strategy for inferring the secondary and tertiary structures that underlie non-coding
RNA behaviour.
The transcriptomes of living cells and viruses continue to revealnovel classes of non-coding RNA (ncRNA) with critical func-tions in gene regulation, metabolism and pathogenesis1–3. The
functional behaviours of these molecules are intimately tied to
specific base-pairing patterns, and these patterns are challenging
to identify using existing strategies based on phylogenetic analysis4,5,
nuclear magnetic resonance (NMR)6,7, crystallography8–14, molecu-
lar rulers15,16 or functional mutation/rescue experiments17,18.
A more facile approach to the characterization of RNA structure
involves high-throughput chemical mapping at single-nucleotide
resolution. This method is applicable to RNAs as large as the
ribosome as well as entire viruses, both in vitro and in their
cellular milieu19–21. Measurements of the accessibility of every
nucleotide to solution chemical modification can guide or
filter structural hypotheses from computational models22,23.
Nevertheless, approximations in computational models and in
correlating structure to chemical accessibility limit the inherent
accuracy of this approach22–25.
This Article presents a strategy to expand the information
content of chemical mapping by means of a two-dimensional
‘mutate-and-map’ methodology26. Here, sequence mutation acts
as a second dimension in a manner analogous to initial perturbation
steps in multidimensional NMR pulse sequences for structure deter-
mination7 or pump–probe experiments in other spectroscopic
fields27. Based on elegant precedents in group I intron studies28,29,
we reasoned that if one nucleotide involved in a base pair is
mutated, its partner might become more exposed and thus be
readily detectable by chemical mapping. In practice, some
mutations might not lead to the desired ‘release’ of the pairing part-
ners, and some mutations might produce larger perturbations, such
as the unfolding of an entire helix. Nevertheless, if even a subset of
the probed mutations leads to precise release of interacting nucleo-
tides, the base-pairing pattern of the RNA could potentially be read
out from this extensive data set. Indeed, our recent proof-of-concept
studies have demonstrated systematic inference of Watson–Crick
base pairs in a 20-base-pair DNA/RNA duplex26 and a 35-nucleo-
tide RNA hairpin30. However, these artificial systems were designed
to include single long helices and thus may not adequately represent
natural, functional non-coding RNAs with many shorter helices,
extensive non-canonical interactions and multiple solution states.
We therefore sought to apply the mutate-and-map strategy to a
diverse set of non-coding RNAs with available crystal structures
for some states and unknown structures for other states. The bench-
mark, which includes ribozymes, riboswitches and ribosomal RNA
domains (Supplementary Table S1), is challenging; an earlier (one-
dimensional) chemical/computational approach missed and mis-
predicted 20% of the benchmark’s helices24. We can report that
our mutate-and-map strategy achieves 98% accuracy in inferring
Watson–Crick base-pairing patterns and gives useful confidence
estimates through bootstrap analysis. Furthermore, the method
permits the generation and falsification of structural hypotheses
about partially ordered RNA states, as highlighted by new results
on a glycine-sensing riboswitch. We focus predominantly on the
basic but unsolved problem of RNA secondary structure infer-
ence24,25,31 from biochemical data. Extensions of the method and
advances in computational modelling may permit robust tertiary
contact inference and three-dimensional models, and we present
one such case as a proof-of-concept.
Results
Proof-of-concept for an adenine-binding riboswitch. We first
established the information content and accuracy of the strategy
for the 71-nucleotide adenine-sensing add riboswitch from Vibrio
vulnificus, which has been studied extensively6,17,32–35 and solved
in the adenine-bound state using crystallography9. The add
secondary structure is incorrectly modelled by the RNAstructure
algorithm alone, but can be recovered through the inclusion of
standard one-dimensional SHAPE (selective 2′ hydroxyl acylation
with primer extension) data24; this RNA therefore serves as a well-
characterized control. We prepared 71 variants of the RNA,
1Department of Biochemistry, Stanford University, Stanford, California 94305, USA, 2Department of Chemical Engineering, Stanford University, Stanford,
California 94305, USA, 3Program in Biomedical Informatics, Stanford University, Stanford, California 94305, USA, 4Department of Physics, Stanford
University, Stanford, California 94305, USA. *e-mail: rhiju@stanford.edu
ARTICLES
PUBLISHED ONLINE: 30 OCTOBER 2011 | DOI: 10.1038/NCHEM.1176
NATURE CHEMISTRY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturechemistry 1
© 2011 Macmillan Publishers Limited. All rights reserved.

mutating each base to its complement using high-throughput
polymerase chain reaction (PCR) assembly, in vitro transcription
and magnetic bead purification methods in a 96-well format, as
discussed previously30. SHAPE data for all mutants were collected
in a single afternoon. For a detailed view, Fig. 1a compares
electrophoretic traces for the starting sequence and the C18G
variant in the presence of 5 mM adenine. For a global view, the
electropherograms for all constructs are given in Fig. 1b. As in
earlier studies26,30, Z-scores (Fig. 2a, number of standard
deviations from the mean accessibility; see Methods) highlight the
most significant features of the data.
As with simpler model systems, the add mutate-and-map data
demonstrate perturbations near mutation sites (marked at nucleotide
18 in Fig. 1a; distinct diagonal stripes (I) in Fig. 1b). More impor-
tantly, the data show numerous features corresponding to interacting
pairs of sequence-separated nucleotides. For example, mutation
C18G led to increased exposure of nucleotides 74–79, with the stron-
gest effect at G78 (Fig. 1a; marked II in Fig. 1b). This observation
44.555.566.577.58
Electrophoresis time (min)
Fl
uo
re
sc
en
ce
(a
.u
.)
a
Site of mutation C18G Pairing
partner G78
93
C
92
A
91
A
90
A
89
A
88
C
87
A
86
A
85
A
84
A
83
G
82
U
81
G
80
A
79
A
78
G
77
U
76
A
75
U
74
U
73
A
72
G
71
U
70
U
69
C
68
U
67
C
66
A
65
A
64
A
63
U
62
U
61
C
60
C
59
G
58
A
57
G
56
A
55
A
54
C
53
C
52
A
51
U
50
C
49
U
48
U
47
U
46
G
45
A
44
G
43
G
42
G
41
U
40
U
39
U
38
G
37
G
36
U
35
A
34
U
33
A
32
G
31
U
30
A
29
A
28
U
27
C
26
C
25
U
24
A
23
A
22
U
21
A
20
U
19
A
18
C
17
U
16
U
15
C
14
G
13
C
12
A
11
A
10
A
9G8
A7A6A5G4G3G2
A1A0A
–1
G
–2
G
–3
A
–4
A
–5
A
–6
G
–7
G
WT
C13G
G14C
C15G
U16A
U17A
C18G
A19U
U20A
A21U
U22A
A23U
A24U
U25A
C26G
C27G
U28A
A29U
A30U
U31A
G32C
A33U
U34A
A35U
U36A
G37C
G38C
U39A
U40A
U41A
G42C
G43C
G44C
A45U
G46C
U47A
U48A
U49A
C50G
U51A
A52U
C53G
C54G
A55U
A56U
G57C
A58U
G59C
C60G
C61G
U62A
U63A
A64U
A65U
A66U
C67G
U68A
C69G
U70A
U71A
G72C
A73U
U74A
U75A
A76U
U77A
G78C
A79U
A80U
G81C
U82A
G83C
b
D
im
en
si
on
1
: m
ut
at
io
n
Dimension 2: site of 2´-OH acylation
I IIIII IV
VII
VI XIXII
VIII
V
X
IX
Figure 1 | The mutate-and-map method gives an information-rich picture of RNA structure. a, Mutating a nucleotide and mapping chemical accessibility
reveals interactions in the three-dimensional structure of the RNA. The traces are for wild-type (blue) and C18G-mutated (red) variants of the adenine-
binding domain of the add riboswitch. These 2′-OH acylation (SHAPE) data were read out by reverse transcription with fluorescently labelled primers and
capillary electrophoresis; peaks (left to right) correspond to nucleotides from the 5′ to 3′ end of the RNA. Arrows mark exposure of the mutation site (C18)
and of sequence-distant regions brought near this nucleotide by base-pairing (partner G78). b, Entire mutate-and-map data set across 71 single mutations,
plotted in grey scale, revealing numerous elements of riboswitch structure. Dark features highlight: (I) the main diagonal stripe showing localized
perturbations following C18G mutation; (II–IV) punctate features marking base pairs C18–G78, C26–G44 and C54–G72 in three different helices; (V–VII)
more delocalized effects upon helix mutations G14C, G44C and G59C; (VIII) large-scale changes from C69G mutation due to secondary structure
rearrangement; (IX) perturbations consistent with loss of adenine binding in A52U variant; (X) evidence for long-range tertiary contact between L2 and L3
upon mutation of C60 and C61 in L3; (XI) ‘symmetric’ mutations in L2 that affect L3; (XII) evidence for U22–A52 base pair in the adenine binding site.
ARTICLES NATURE CHEMISTRY DOI: 10.1038/NCHEM.1176
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© 2011 Macmillan Publishers Limited. All rights reserved.

strongly supports a C18–G78 base pair in the P1 helix. Such ‘punc-
tate’ single-nucleotide-resolution base-pair features are also visible
for the other helical stems of this RNA (for example, C26–G44 and
C54–G72, marked III and IV in Fig. 1b). Several mutations led to
more delocalized perturbations (V–VII, Fig. 1b; stems marked in
Fig. 2a) due to disruption of multiple consecutive base pairs.
Although not punctate, these features confirm interactions at helix-
level resolution. Some single mutations produce larger-scale
changes, reflecting shifts in the secondary structure (for example,
C69G, VIII in Fig. 1b; see also U25A, G46C) or loss of adenine
binding (for example, A52U, IX in Fig. 1b; see also Supplementary
Figs S1 and S2). Interestingly, within each helix, some mutations
gave strong signals, whereas others led to minimal perturbations
(for example, the 3′ segment of P2 in Fig. 2a)26,30, underscoring the
need to survey all possible mutations.
To assess the predictive power of these data for structure
modelling, we applied the measured Z-scores as energetic bonuses
in the RNAstructure secondary structure prediction algorithm.
We further estimated confidence values for all inferred helices
by bootstrapping the mutate-and-map data and repeating the
secondary structure calculation36. As expected from the visual
analysis above, the crystallographic secondary structure was
robustly recovered (Fig. 2a,b), with ≥99% bootstrap values for
helices P1, P2 and P3. An ‘extra’ two-base-pair helix was also
found, with a weak bootstrap value (58%); these nucleotides are in
fact base-paired in the add riboswitch crystallographic model9,
but one pairing is a non-canonical Watson–Crick/Hoogsteen
pair and part of a base triple. Together with additional mutate-
and-map signals (X–XII, Fig. 1b), these data were sufficient for
determining the global tertiary fold of the RNA, as described in
the following.
A challenging benchmark of base pair inference. To complete
our benchmark of the mutate-and-map strategy, we applied the
method to RNAs for which base-pairing patterns have been
more challenging to recover. The smallest of these, unmodified
tRNAphe from Escherichia coli10, offers a simple illustration of
the information content of the new method (Fig. 3a). The
RNAstructure algorithm mispredicted two of the four helices of
the tRNA ‘cloverleaf’ (the D and anticodon helices; cf. Fig. 3b,c).
Inclusion of one-dimensional SHAPE reactivities corrected these
errors, but introduced an additional error, mispredicting the TcC
helix (Fig. 3d); protection of the loop of this helix by tertiary
contacts renders its modelling uncertain with one-dimensional
data alone. The mutate-and-map SHAPE data for this tRNA
(Fig. 3a) gave clear signals for all four helices. Applying the two-
dimensional mutate-and-map data set to RNAstructure corrected
the inherent inaccuracies of the algorithm and recovered the
entire four-helix secondary structure (.99% bootstrap values;
Fig. 3e). One additional edge base pair was predicted for the
anticodon arm; this and other fine-scale errors are discussed in
the following.
The remaining RNAs in our benchmark exceeded 100 nucleo-
tides in length. As in the tRNAphe case, earlier chemical/computa-
tional methods assigned incorrect secondary structures to these
sequences, but the mutate-and-map strategy led to accurate base-
pairing patterns. The mutate-and-map data for a widely studied
model RNA, the P4–P6 domain of the group I Tetrahymena ribo-
zyme, gave visible features corresponding to all helices in the
RNA14 (Fig. 4a) and led to correct recovery of the secondary struc-
ture (Fig. 4b). One of the helices, P5c, was correctly modelled but
with a weak bootstrap value (48%); this low score is consistent
with conformational fluctuations in P5c identified in previous
biochemical and NMR studies37,38.
As a more stringent test of the mutate-and-map strategy, we
applied the method to the E. coli 5S ribosomal RNA, a notable
problem case for earlier chemical/computational approaches22,39.
In particular, the segments around the non-canonical loop E
motif have been mispredicted in all previous studies, including the
most recent (one-dimensional) SHAPE-directed approach24.
By providing pairwise information on interacting nucleotides
(Fig. 4c), the mutate-and-map method recovered the entire second-
ary structure with high confidence (.90%; Fig. 4d). One extra helix
(blue in Fig. 4d) corresponds to a segment that in fact forms non-
canonical base pairs within the loop E motif.
The ligand-binding domain of the cyclic di-GMP riboswitch
from Vibrio cholerae provided an additional challenge; helix P1 of
this RNA was not found in the original phylogenetic analysis18,
C
G
C
U
U
C
A
U
A
U
A
A
U
C
C
U
A
AU
G
A
U
A
U G G
U
U
U
G
G
G
A G
U
U
U C
U
A
C
C A
A G
A G
C C U
U
A
AACUCUUG
A
U
U
A
U
G
A
A
G
U
G
1 71
20
40
60
80
a b
99%
58%
100%
100%
20 30 40 50 60 70 80
20
30
40
50
60
70
80
Dimension 2: site of 2´-OH acylation
D
im
en
si
on
1
: m
ut
at
io
n
P1
P1
P2
P2
P3
P3
L2/L3
L2/L3
Base triple
Base triple
Adenine
binding
pocket
0.0 2.0
1D SHAPE reactivity
1.0 2.0
P1
P2
P3
2D Z-score
Figure 2 | Mutate-and-map data and secondary structure. a, Strong features of mutate-and-map data isolated by Z-score analysis (number of standard
deviations from mean at each residue). Squares show secondary structure model guided by mutate-and-map data (red, match to crystallographic Watson–
Crick stems; blue, match to non-Watson–Crick stem). b, Secondary structure derived from incorporating Z-scores into the RNAstructure modelling algorithm;
bootstrap confidence estimates given as red percentage values. Additional tertiary contacts inferred from a separate clustering analysis are given in green.
Nucleotides are coloured according to SHAPE reactivity.
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but was instead later revealed by crystallography. Based on measure-
ments in the presence of 10 mM ligand, the mutate-and-map strat-
egy (Fig. 4e) recovered nearly the entire secondary structure (7 of 8
helices), including P1 (Fig. 4f).
Blind prediction for the glycine riboswitch. As a final rigorous test,
we acquired mutate-and-map data for an RNA for which a
crystallographic model was not available at the time of modelling:
the ligand-binding domain of the glycine-binding riboswitch from
Fusobacterium nucleatum40,41. The mutate-and-map data in the
presence of 10 mM glycine gave a secondary structure with nine
helices (Fig. 5a); the model agreed with the nine helices that were
identified by phylogeny. The secondary structure was confirmed
by a crystallographic model released at the time of the submission
of this Article43.
Overall accuracy of secondary structure modelling. Overall, the
mutate-and-map method demonstrated high accuracy in secondary
structure inference for a benchmark of six diverse RNAs including
661 nucleotides in 42 helices (Table 1). As a baseline, an earlier
method, using RNAstructure directed by one-dimensional SHAPE
data, gave a false negative rate and false discovery rate of 17% and
21%, respectively, on this benchmark24. The mutate-and-map
method recovered 41 of 42 helices, giving a sensitivity of 98% and
a false negative rate of 2%, nearly an order of magnitude less than
the previous method. The only missing helix was a two-base-pair
G
C
G
G
A
U
U
U
A
G
C
U
C
A
G
U
U
G
G
G
A
G
A
G C
G
C
C
A
G
A
C
U
G
A A G
A
U
C
U G
G
A
G
G
U
C
C
U
G
U
G U U
C
G
AU
C
C
A
C
A
G
A
A
U
U
C
G
C A C C A
20
40
60
c e
G
C
G
G
A
U
U
U
A
GCUC
AG
U
U
G
G
G A
G A G C
G
C
C
A
G
A
C
U
G
A A
G
A
U
C
U
G
G A
G
G
U
C
C
U
G
U
G U
U
C
G
AU
C
C
A
C
A
G
A
A
U
U
C
G
C A C C A
20
40
60
100%
100%
100%
100%
0.0 2.0
1D SHAPE reactivity
d
G
C
G
G
A
U
U
U
A
GCUC
AGU
U
G
G
G A G A
G C
G
C
C
A
G
A
C
U
G
A A G
A
U
C
U
G
G A G
G
U
C
C
U G U
G
U
U
CG
A
U
C
C
A
C
A
G
A
A
U
U
C
G
C A C C A
20
40
60
99%
99%
55%
100%
10 20 30 40 50 60 70
10
20
30
40
50
60
70
a b
G
C
G
G
A
U
U
U
A
GCUC
AG
U
U
G
G
G A
G A G C
G
C
C
A
G
A
C
U
G
A A G
A
U
C
U
G
G A
G
G
U
C
C
U
G
U
G U
U
C
G
AU
C
C
A
C
A
G
A
A
U
U
C
G
C A C C A
20
40
60
Anticodon
Anticodon
Anticodon
Acceptor
Acceptor
TψC
TψC
D
D
Dimension 2: site of 2´-OH acylation
D
im
en
si
on
1
: m
ut
at
io
n
D
Acceptor
TΨC
1.0 2.0
2D Z-score
1
1 76
1 76
1
Figure 3 | Comparison of chemical/computational modelling approaches on tRNAphe. a, Mutate-and-map Z-score data for tRNAphe from E. coli.
b–e, Secondary structure models of this RNA from crystallography (b), the RNAstructure algorithm without data (c), calculations guided by one-dimensional
SHAPE data (d) and calculations guided by the two-dimensional mutate-and-map data (e). Red squares (a) give Watson–Crick base pairs from the mutate-
and-map model that match the crystallographic secondary structure. Blue squares (a) or lines (b–e) give model Watson–Crick base pairs not present in the
crystallographic secondary structure. Orange lines give crystallographic Watson–Crick base pairs missed in each model. Helix confidence estimates from
bootstrapping one-dimensional (d) or two-dimensional (e) data are given as red percentage values; nucleotides are coloured according to SHAPE reactivity.
ARTICLES NATURE CHEMISTRY DOI: 10.1038/NCHEM.1176
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© 2011 Macmillan Publishers Limited. All rights reserved.

helix in the cyclic diGMP riboswitch (see below). At a finer
resolution, a small number (,6%) of base pairs in mutate-and-map
calculated helices were either missed or added relative to the
crystallographic secondary structures (1 and 11 of 197 base pairs,
respectively; Supplementary Table S2). All these errors were either
G–U or A–U pairs at the edges of otherwise correct helices
(Figs 2– 5 and Table S2). Variation of the assumed coefficient of
the two-dimensional Z-scores in the RNAstructure energy bonus
G
G
A
A
U
U
G
C
G
G
GA
A
A
G
G
G
G
U
C
U
C
C
U A
A
C
C A
C
G
C
A
G
CC
A
A
G
U
C
CU
A
A U
G
G
A
U G
C
A
G
U
U
C
A
120
220
260
100%
92%
88%
91%
76%P4
P5
P6
P6a
b
AA
C
A
G
C
C
G
U
U
C
A
G
U
ACC
A
A
G
U
C
U
C
A
G
G
G
G
AA
A
C
U
U
U
G
A
G
A
U
G
G
C
C
U
U
G
C A A
A
G
G G U
A
U G G U
A A
U
A
A
G
C
U
G
A
C
G
G A
C
A
U
G
G
G
U
C
A
A
C
A
G
A
U
C U
U
C
U
G
U
U
G
A
U
A
140
160
180
200
240100%
48%
100%
100%
100% 100%
P5c
P5a
P5b
P6b
A-rich bulge
L5b tetraloop Tetraloop
receptor
11
0
12
0
13
0
14
0
15
0
16
0
17
0
18
0
19
0
20
0
21
0
22
0
23
0
24
0
25
0
26
0
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
10 20 30 40 50 60 70 80 90 10
0
11
0
12
0
10
20
30
40
50
60
70
80
90
100
110
120
10 20 30 40 50 60 70 80 90 10
0
10
20
30
40
50
60
70
80
90
100
c
a
e
d
U
G
C
C
U
G
G
C
G
G
C
C
G
U
A
G
C
G
C
G
G
U
GG
U
C
C
C
A
C
CU
GA
CCC
C
A
U
G
C
C G A A
C
U C A G A
A
G
U
G A
A
A
C
G
C
C
G
U
A
G
C G
C
C
G A
U
G
G
U A G
U
G
U
G
G
G
G
U
C
U
C
C
C
C
A
U
G
C
G
A
GAGU
AG
G
G
A
A
C
U
G
C
C
A
G
G
C
A U
20
40
60
80
100
100%
100%
100%
94%
99%
96%
47%
100%
Helix I
Loop E
Loop A
Loop C
Loop B
Helix II
Helix III
Helix IV
Helix V
Dimension 2: site of 2´-OH acylation
Dimension 2: site of 2´-OH acylation
Dimension 2: site of 2´-OH acylation
D
im
en
si
on
1
: m
ut
at
io
n
D
im
en
si
on
1
: m
ut
at
io
n
D
im
en
si
on
1
: m
ut
at
io
n
1.0 2.0
2D Z-score
f
A
G
U
C
A
C
G
C
A
C
A G
G
G
CA
A
A
C
C
A
U
U
C
G
A
A A
G
A
G
U
G
G G
A
C
G
C A
A
A
G
C
C U
C
C
G
G C C U A A
A
C
C
A G
A
A
GAC
A
U
G
G
U
AGG
UA
G
C
G
G
G
G
U
UAC
C
G
A
U
G
G
C A A A A U G
1 97
20
40
60
80
100
100%
88%
100%
100%
74%
81%
60%
64%
0.0 2.0
1D SHAPE reactivity
P1
P2
P3
Cyclic di-GMP
binding
1 120
1 97
Figure 4 | Accurate secondary structure models for non-coding RNAs. a–f, Mutate-and-map Z-score data and resulting secondary structure models for the
P4–P6 domain of the Tetrahymena group I ribozyme (a,b), the 5S ribosomal RNA from E. coli (c,d) and the domain that binds cyclic di-guanosine monophosphate
from the V. cholerae VC1722 riboswitch (in the presence of 10mM ligand; e,f). Colouring of squares (a,c,e) and lines and nucleotides (b,d,f) are as in Fig. 3.
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or addition/subtraction of an offset did not improve the recovery at
the level of base pairs or helices (data not shown).
In terms of the false discovery rate, the mutate-and-map method
gave only three extra helices, all of which were the smallest possible
length (2 bp). As discussed above, two of these extra helices in fact
correspond to non-canonical stems observed in crystallographic
models. The remaining false helix gave a weak bootstrap value
(60%) and may correspond to a stem sampled in the ligand-free
conformation of the cyclic diGMP riboswitch (see below). The
overall positive predictive value was 93–98% depending on
whether the non-canonical helices are counted as correct. The
false discovery rate was 2–7%, nearly an order of magnitude less
than the earlier one-dimensional SHAPE-directed method (21%).
Somewhat surprisingly, using both the one-dimensional SHAPE
data and two-dimensional mutate-and-map data gave slightly
worse accuracy than using the two-dimensional data alone (false
negative rate of 7% compared with 2%); this result may reflect
inaccuracies in interpreting absolute SHAPE reactivity, as
opposed to Z-score changes in reactivity induced by mutations.
We conclude that secondary structures derived from the
mutate-and-map method are accurate (2% error rates) for
structured non-coding RNAs.
Testing an ‘inter-domain helix swap’ hypothesis for glycine
riboswitch cooperativity. Beyond recovering known information
about non-coding RNA secondary structure, we sought to
generate or falsify novel hypotheses that would be difficult to
explore using standard structural methods. The three riboswitch
ligand-binding domains for adenine, cyclic di-GMP and glycine
provide interesting test cases because their ligand-free states will
generally be partially ordered and thus difficult to crystallize. First,
application of the mutate-and-map strategy indicated that the
secondary structure of the add riboswitch ligand-binding domain
remains the same in adenine-free and adenine-bound states
10 20 30 40 50 60 70 80 90 10
0
11
0
12
0
13
0
14
0
15
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
10 20 30 40 50 60 70 80 90 10
0
11
0
12
0
13
0
14
0
15
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
b
c
a
Dimension 2: site of 2´-OH acylation
Dimension 2: site of 2´-OH acylation
D
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1
: m
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D
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: m
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G
A
U
A
U
G
A
GG
A
G
A
G
A
U
U
U
C
A
U
U
U
U A
A
U
G
A
A
A
C A
C
C
G
A
A G
A
A
G
U
A A
A
U
C
U
U
U
C
A
G
G
U
A
A
A
A
A
G
G
AC
U
C
A
U
A
U
U G G A C G A A C C
U
C
U
G
G
A
G
A
G
C
U
U
A
U
C
U
A
A G
A
G
A
U
A
A C A
C
C
G
A
A G
G
A
G
C
A
A
A G
C
U
A
A
U
U
U
U
A
G
C
C
U
A
AAC
U
C
U
C
A
G
G
U
A
A
A
A
G
G
A
C
G
G
A
G
1
1581
1 158
20
40
60
80
100
120
140100%
86%
100%
100%
100%
100%
100%
100%
81%
1.0 2.0
2D Z-score
P1
P2
P3
P3a
P3a
P3
P3b
P2
P1
Domain 1
Domain 2
Linker
d
G
A
U
A
U
G
A
GG
A
G
A
G
A
U
U
U
C
A
U
U
U
U A
A
U
G
A
A
A
C A
C
C
G
A
A G
A
A
G
U
A A
A
U
C
U
U
U
C
A
G
G
U
A
A
A
A
A
G
G
AC
U
C
A
U
A
U
U G G A C G A A C C
U
C
U
G
G
A
G
A
G
C
U
U
A
U
C
U
A
A G
A
G
A
U
A
A C A
C
C
G
A
A G
G
A
G
C
A
A
A G
C
U
A
A
U
U
U
U
A
G
C
C
U
A
AAC
U
C
U
C
A
G
G
U
A
A
A
A
G
G
A
C
G
G
A
G
20
40
60
80
100
120
140100%
48%
100%
100%
100%
100%
97%
100%
54%P1
P2
P3
P3a
P3a
P3
P3b
P2
P1
Linker
Glycine
Glycine
Figure 5 | Two states of a glycine-binding riboswitch. a–d, Mutate-and-map Z-score data and resulting secondary structure models for the double-ligand-
binding domain of the F. nucleatum glycine riboswitch with 10 mM glycine (a,b) and without glycine (c,d), indicating no inter-domain helix swap upon glycine
binding. Colouring of squares (a,c) and lines and nucleotides (b,d) are as in Fig. 3.
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(Supplementary Fig. S3), consistent with biophysical data from
other approaches6,35. In contrast, mutate-and-map data indicate
that the cyclic di-GMP riboswitch shifts its secondary structure
near P1 on ligand binding (Supplementary Fig. S4). This shift is
potentially involved in the mechanism of the riboswitch12,13,18 and
may account for the weak phylogenetic signature of the P1 helix.
Among these ‘non-crystallographic’ targets, we were most inter-
ested in the glycine-binding riboswitch, which exhibits cooperative
binding of two glycines to separate domains and is under intense
investigation by several groups40–44. Analogous to the tense/relaxed
equilibrium in the Monod–Wyman–Changeaux model for haemo-
globin45, we considered that cooperativity might stem from an inter-
domain helix swap. In this model, an alternative (‘tense’) secondary
structure involving non-native interactions between the two
domains would be rearranged upon glycine binding. Although
one-dimensional mapping experiments (Fig. 5 and refs 40–42)
show changes in the RNA following glycine binding, these data are
consistent with a range of secondary structures and do not provide
stringent tests of the inter-domain swap model. Furthermore, the
model is not easily testable by crystallography43,44, which, if
successful, is biased towards more structured conformations.
Application of the mutate-and-map strategy (Fig. 5b,d) gave a
strong test of the hypothesis; the data in the absence of glycine
gave the same domain-separated secondary structure as under con-
ditions with glycine bound (Fig. 5a,c). Any changes in secondary
structure for these constructs are thus either at edge base pairs or
are negligible. We note that additional 5′ and 3′ flanking elements
are likely to play critical roles in the modes of genetic regulation
of these RNAs2; these longer segments are now under investigation.
Tertiary structure and cooperative fluctuations. The analysis
described above focused on the first level of RNA structure, the
Watson–Crick base-pairing pattern. Nevertheless, many non-
coding RNAs use tertiary contacts and ordered junctions to
position Watson–Crick helices into intricate three-dimensional
structures. Qualitatively, we found evidence for numerous such
tertiary interactions in the mutate-and-map data of these RNAs.
For example, the add riboswitch is stabilized by tertiary
interactions between the loops L2 (nucleotides 32–38) and L3
(nucleotides 60–66). In the presence of 5 mM adenine, mutations
at G37 and G38 resulted in exposure of their partners C61 and
C60 (X, Fig. 1b), and vice versa (XI, Fig. 1b; L2/L3 pseudoknot
marked in Fig. 1b). Nevertheless, other mutations led to longer
range effects (VIII, IX in Fig. 1b) due to cooperative unfolding of
subdomains of tertiary structure or loss of adenine binding. For
example, mutation of nucleotide A52 (VIII) gave chemical
accessibilities that were different from the adenine-bound wild
type RNA throughout the sequence, but consistent with the
adenine-unbound state (Supplementary Fig. S1).
To extract tertiary base-pairing information, we could not use the
RNAstructure method above, as it focuses on Watson–Crick base
pairs. We therefore implemented filters enforcing strong, punctate
signals and symmetry but not A–U, G–C or G–U pairing (see
ref. 30, Methods and Supplementary Fig. S5). This analysis, inde-
pendent of any computational models of RNA structure, recovered
the majority of Watson–Crick helices in this benchmark. The analy-
sis also recovered three tertiary contacts: the L2/L3 interaction of
the add riboswitch (X and XI in Fig. 1b) and a U22–A52 base
pair in the adenine binding pocket (XII, Fig. 1b); and a
tetraloop/receptor interaction in the P4–P6 RNA (Fig. 4a,b).
These features are accurate, but, in most test cases, their number
is significantly less than the number of helices, precluding effective
three-dimensional modelling. For the one case in which multiple
tertiary contacts could be determined, the add adenine-sensing
Table 1 | Accuracy of RNA secondary structure models.
RNA Length* Number of helices†
Cryst. No data 1D 1D12D 2D
TP FP TP FP TP FP TP FP
Adenine riboswitch‡ 71 3 2 3 3 0 (1) 3 0 (1) 3 0 (1)
tRNAphe 76 4 2 3 3 1 4 0 4 0
P4–P6 RNA 158 11 10 1 9 2 9 2 11 0
5S rRNA 118 7 1 9 6 3 7 0 (1) 7 0 (1)
c-di-GMP riboswitch‡ 80 8 6 2 6 2 7 1 7 1
Glycine riboswitch‡ 158 9 5 3 8 1 9 0 9 0
Total 661 42 26 21 35 9 (10) 39 3 (5) 41 1 (3)
False negative rate§ 38.1% 16.7% 7.1% 2.4%
False discovery rate‖ 44.7% 20.4 (22.2)% 7.1 (11.4)% 2.3 (6.8)%
*Length of RNA in nucleotides. †Cryst, number of helices in crystallographicmodel; TP, true positive helices; FP, false positive helices; 1D, models using one-dimensional SHAPE chemical mapping data; 2D, models
using mutate-and-map data. For FP, a helix was considered incorrect if its base pairs did not match the majority of base pairs in a crystallographic helix. Numbers in parentheses required that the matching
crystallographic base pairs have Watson–Crick geometry. ‡Ligand-binding riboswitches were probed in the presence of small-molecule partners (5 mM adenine, 10mM cyclic di-guanosine-monophosphate
or 10 mM glycine). All experiments were carried out with 10 mM MgCl2, 50 mM Na-HEPES, pH 8.0.
§False negative rate¼ (Cryst–TP)/TP. ‖False discovery rate¼ FP/(FPþ TP). Numbers in parentheses
count matches of model base pairs to non-Watson–Crick crystallographic base pairs as false discoveries.
a b
P1
P3
P2
P2
P1
P3
L2/L3
contact
L2/L3
contact
Contacts in
adenine-
binding
region
Contacts in
adenine-
binding
region
Crystallographic Mutate/map +
FARFAR 3D modelling
Figure 6 | Three-dimensional modelling from mutate-and-map data.
a,b, Models of the (ligand-bound) adenine riboswitch derived from X-ray
crystallography (a) and from the chemical/computational protocol
introduced here (b). De novo modelling (using the Rosetta FARFAR
algorithm) was carried out with secondary structure (P1, P2, P3) and tertiary
contacts (L2/L3 and two contacts in adenine-binding region) inferred from
solution mutate-and-map data. The mutate-and-map model agrees with the
crystallographic model at nucleotide resolution (helix root-mean-squared
deviation (RMSD) of 5.7 Å; overall RMSD of 7.7 Å).
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riboswitch, we carried out three-dimensional modelling using the
FARFAR de novo assembly method. The algorithm gave a structural
ensemble with helix RMSD of 5.7 Å and overall RMSD of 7.7 Å to
the crystallographic model9 (Fig. 6a,b). This resolution is compar-
able to the average distance between nearest nucleotides (5.9 Å)
and significantly better than model accuracy without mutate-and-
map data (helix RMSD 8.9 Å; overall RMSD 16.9 Å) or values
expected by chance (P, 1× 1023 for modelling a 71-nt RNA with
secondary structure information46). These results on a favourable
case suggest that rapid inference of three-dimensional structure for
general RNAs might be achievable with other chemical probes that
discriminate non-canonical interactions (for example, dimethyl
sulfate30,47 for A-minor interactions) or more sophisticated methods
for mining tertiary information or ligand-binding sites from mutate-
and-map data.We note also that features corresponding to cooperative
changes in chemical accessibility, while not reporting on specific
tertiary contacts, can reveal ‘excited’ states in the folding landscapes
of the RNA that may be functional48,49. We are making the infor-
mation-rich data sets acquired for this Article publicly available in
the Stanford RNA Mapping Database (http://rmdb.stanford.edu) to
encourage the development of novel analysis methods to explore
tertiary contact extraction and landscapes.
Discussion
We have demonstrated that a mutate-and-map strategy permits the
high-throughput inference of non-coding RNA base-pairing patterns.
With error rates of 2% and confidence estimates via bootstrapping,
the method determines the secondary structures of riboswitch, riboso-
mal and ribozyme domains for which earlier chemical/computational
approaches gave incorrect models. In addition to recovering known
structures, the mutate-and-map data permit the rapid generation
and falsification of hypotheses for structural rearrangements in three
ligand-binding RNAs in partially ordered ligand-free states, including
a cooperative glycine riboswitch with a poorly understoodmechanism.
Finally, the data yield rapid information on tertiary contacts of
ncRNAs. Although not sufficient to yield crystallographic-quality
structure models, in an adenine-sensing riboswitch, the data permit
the modelling of the three-dimensional helix arrangement of the
RNA at nucleotide resolution (5.7 Å). Further insights will come
from detailed biophysical modelling of secondary and tertiary
structure fluctuations induced by mutations; the public availability
of these information-rich data sets should promote such analyses.
The mutate-and-map method only requires commercially avail-
able reagents, widely accessible capillary electrophoresis sequencers
and freely available software. Further, each data set was acquired and
analysed in a week or less. Therefore, for non-coding RNA domains
up to 300 nucleotides in length, the technology should be appli-
cable as a front-line structural tool. The combined expense of the
mutagenesis and mapping grows as the square of the RNA length.
Thus, characterization of transcripts with thousands of nucleotides
is presently challenging but may be facilitated by next-generation
sequencing strategies50.
Expanding experimental technologies from one to multiple
dimensions has transformed fields ranging from NMR to infrared
spectroscopy. We propose that the mutate-and-map strategy will be
analogously enabling for chemical mapping approaches, permitting
the confident secondary structure determination and tertiary
contact characterization of non-coding RNAs that are difficult or
intractable for previous experimental methods. Applications to full-
length RNA messages in vitro or in extract, to complex ribo-
nucleoprotein systems, and even to full viral RNA genomes appear
feasible and are exciting frontiers for this high-throughput approach.
Methods
Mutate-and-map experimental protocol and data processing. Preparation of DNA
templates, in vitro transcription of RNAs, SHAPE chemical mapping, and capillary
electrophoresis were carried out in a 96-well format, accelerated through the use of
magnetic bead purification steps, as has been described previously26,30,51. Data were
analysed with the HiTRACE52 software package, and Z-scores were computed in
MATLAB. A complete protocol is given in the Supplementary Methods. Code for
analysing mutate-and-map data is being made available as part of HiTRACE.
Z-scores were used for secondary structure inference and sequence-independent
feature analysis by single-linkage clustering, as described in the
Supplementary Methods.
Secondary structure inference. The Fold executable of the RNAstructure package
(v5.3) was used to infer secondary structures. The entire RNA sequences
(Supplementary Table S1), including added flanking sequences, were used for all
calculations. The flag ‘–T 297.15’ set the temperature to match our experimental
conditions (24 8C). The flags ‘–sh’ and ‘–x’ were used to input (one-dimensional)
SHAPE data files and (two-dimensional) base-pair energy bonuses (equal to
21 kcal mol21 times the Z-scores), respectively. In the RNAstructure
implementation, the pseudoenergies were applied to each nucleotide forming an
edge base pair, and doubly applied to each nucleotide forming an internal base
pair23. Additional flags ‘–xs’ and ‘–xo’ permitted scaling and offset of the Z-score
bonuses, but default values of 1.0 kcal mol21 and 0.0 kcal mol21, respectively, were
found to be optimal. For bootstrap analyses, mock SHAPE data replicates were
generated by randomly choosing mutants with replacement36. The analysis is being
made available as a server at http://rmdb.stanford.edu/structureserver. Secondary
structure images were prepared in VARNA53.
Assessment of secondary structure accuracy. A crystallographic helix was
considered correctly recovered if more than 50% of its base pairs were observed in a
helix by the computational model. (In practice, 40 of 41 such helices in models based
on mutate-and-map data retained all crystallographic base pairs.) Helix slips of+1
were not considered correct (that is, the pairing (i,j ) was not allowed to match the
pairings (i,j–1) or (i,jþ 1)).
Three-dimensional modelling with Rosetta. Three-dimensional models were
acquired using the Fragment Assembly of RNA with Full Atom Refinement
(FARFAR) methodology51 in the Rosetta framework. Briefly, ideal A-form helices
were created for each helix greater than two base pairs in length in the modelled
secondary structure. Then, remaining nucleotides were modelled by FARFAR as
separate motifs interconnecting these ideal helices, generating up to 4,000 potential
structures. Finally, these motif conformations were assembled in a Monte Carlo
procedure, optimizing the FARNA low-resolution potential and tertiary
constraint potentials defined by the sequence-independent clustering analysis
of mutate-and-map data. Runs without mutate-and-map data used the
one-dimensional SHAPE-directed secondary structure (which agrees with
crystallography for the add riboswitch) and constraints only for the two-base-pair
non-canonical helix (G47–C54,U48–A53). Explicit command lines and example
files are given in the Supplementary Information. The code, as well as a Python
job-setup script setup_rna_assembly_ jobs.py and documentation, are being
incorporated into Rosetta release 3.4, which is freely available to academic users at
http://www.rosettacommons.org. Before release, the code is available on request
from the authors. The P-value for the add riboswitch was estimated by comparing
the all-atom RMSD (7.7 Å) to the range expected by chance (13.5+1.8 Å), as
described in ref. 46.
Received 18 April 2011; accepted 15 September 2011;
published online 30 October 2011
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Acknowledgements
The authors thank A. Laederach and J. Lucks for comments on the manuscript and the
authors of RNAstructure for making their source code freely available. This work was
supported by the Burroughs-Wellcome Foundation (CASI to R.D.), the National Institutes
of Health (T32 HG000044 to C.C.V.) and a Stanford Graduate Fellowship (to P.C.).
Author contributions
R.D. conceived and designed the experiments. W.K., C.C.V. and R.D. performed the
experiments. C.C.V., P.C. and R.D. analysed the data. R.D. wrote the paper. All authors
discussed the results and commented on the manuscript.
Additional information
The authors declare no competing financial interests. Supplementary information
accompanies this paper at www.nature.com/naturechemistry. Reprints and permission
information is available online at http://www.nature.com/reprints. Correspondence and
requests for materials should be addressed to R.D.
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