![A proole graph for the sequence from Figure 2 up to position 78. Prooling identiied 5 distinct structural modes present in the Boltzmann sample, corresponding to the eve rectangles/selected prooles listed. The table lists the feature locations by (i, j, k) triple and sampled frequencies. For instance, pairings from the purple helix (which is maximal) are the rst feature and occurred in 968 of the structures sampled. The four colored helices from Figure 2 correspond to the proole [3[1][2]][6], where the brackets indicate the nesting relationship. This selected proole appears in the bottom left rectangle. It diiers from the selected proole above by the sixth feature. The proole [3[1][2]] has a speciic frequency of 239, and a general frequency of 430 since the latter includes the structures from the [3[1][2]][6] proole.](https://www.researchgate.net/publication/337314911/figure/fig3/AS:826206442254337@1573994374968/A-proole-graph-for-the-sequence-from-Figure-2-up-to-position-78-Prooling-identiied-5_Q320.jpg)
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Content may be subject to copyright.
Open Access. ©2019 Hee Rhang Yoon et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution
alone 4.0 License.
Comput. Math. Biophys. 2019; 7:48–63
Communication
Hee Rhang Yoon, Aaztli Coria, Alain Laederach, and Christine Heitsch*
Towards an understanding of RNA structural
modalities: a riboswitch case study
https://doi.org/10.1515/cmb-2019-0004
Received July 22, 2019; accepted October 10, 2019
Abstract: A riboswitch is a type of RNA molecule that regulates important biological functions by changing
structure, typically under ligand-binding. We assess the extent that these ligand-bound structural alterna-
tives are present in the Boltzmann sample, a standard RNA secondary structure prediction method, for three
riboswitch test cases. We use the cluster analysis tool RNAStructProling to characterize the dierent modal-
ities present among the suboptimal structures sampled. We compare these modalities to the putative base
pairing models obtained from independent experiments using NMR or uorescence spectroscopy. We nd,
somewhat unexpectedly, that proling the Boltzmann sample captures evidence of ligand-bound conforma-
tions for two of three riboswitches studied. Moreover, this agreement between predicted modalities and ex-
perimental models is consistent with the classication of riboswitches into thermodynamic versus kinetic
regulatory mechanisms. Our results support cluster analysis of Boltzmann samples by RNAStructProling as
a possible basis for de novo identication of thermodynamic riboswitches, while highlighting the challenges
for kinetic ones.
Keywords: RNA secondary structures; Boltzmann distribution; suboptimal sample; multimodality; proling
1Introduction
Unlike Deoxy riboNucleic Acid (DNA), RiboNucleic Acid (RNA) exists in the cell as a single-stranded polymer
molecule [14, 44]. As such, the bases of RNA are able to pair intramolecularly forming complex secondary
structures [8, 18, 24, 39, 45] which are organized by tertiary interactions into the three-dimensional structure.
Since 3D structural determination remains challenging for RNA molecules, computational predictions of RNA
secondary structures from sequence are still an important resource for experimentalists.
Most algorithms used to predict RNA secondary structure are based on the nearest neighbor thermody-
namic model (NNTM) [25, 41]. Originally, the goal was to predict the minimum free energy (MFE) structure,
which remains a popular approach to this day [22, 30]. However, predictions of suboptimal structures [48, 49]
and of base pairing probabilities under the Boltzmann partition function [12, 23, 26] have long been used to
complement MFE predictions. These two approaches are unied by the method of sampling suboptimal sec-
ondary structures from the Boltzmann ensemble [5]. Moreover, these Boltzmann sample predictions often re-
veal that the suboptimal secondary structures are organized into two or more distinct modalities [4, 20, 31, 42].
In recent years, it has become increasingly clear that such distinct structural modalities should not be
treated as an artifact of thermodynamic prediction methods. For instance, the existence of dierent base pair-
ing congurations for the same sequence can be experimentally conrmed using a variety of RNA structural
determination techniques including Nuclear Magnetic Resonance (NMR), single molecule uorescence res-
onance energy transfer (sm-FRET) and chemical structure probing [1, 10, 15, 19, 29, 37]. It remains unclear,
Hee Rhang Yoon: School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332
Aaztli Coria: Department of Biochemistry and Biophysics, University of North Carolina, Chapel Hill, NC, 27599
Alain Laederach: Department of Biology, University of North Carolina, Chapel Hill, NC, 27599
*Corresponding Author: Christine Heitsch: School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332
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Towards an understanding of RNA structural modalities |49
(a) Unimodal Boltzmann sample. (b) Bimodal Boltzmann sample.
Figure 1:
Schematic representations of two Boltzmann samples for a 2-state riboswitch with unbound and ligand-bound struc-
tural modes. The relative probability gradient indicates the sampling ratio with the MFE prediction. Recall that small changes
in free energy result in signicant dierences in probability under the Boltzmann distribution; see Equation 2 on page 51 and
related discussion. On the left, the ligand-bound mode is too thermodynamically unfavorable under the NNTM to appear in the
Boltzmann sample. On the right, however, it would be sampled with sucient frequency to be identied by RNAStructProling
as a structural mode. Although it might seem like all riboswitches should resemble Figure 1a, our results demonstrate that
thermodynamic riboswitches are better described by Figure 1b, although kinetic ones do indeed follow the rst model.
however, to what extent predicted structural modalities are a true biological signal of alternative base pairing
congurations.
Riboswitches are the canonical example of RNA sequences which are known to assume distinct structural
conformations. However, the change in structure is typically mediated by the binding of a small molecule
called a ligand. One might well expect, then, that only the unbound structure should be suciently thermo-
dynamically favorable under the NNTM to appear in a Boltzmann sample prediction. If so, then although the
sequence is known to assume more than one base pairing conguration, the Boltzmann sample (which does
not include the ligand-binding biophysics) is eectively unimodal. This expectation is captured schematically
in Figure 1a. If indeed this is true, the prospect of using Boltzmann sampling to identify new riboswitches and
other multimodal RNA molecules does not look promising.
We investigate the validity of this assumption for three known riboswitches which have proposed base
pairing models grounded in experimental data. Using the RNA suboptimal structure cluster analysis tool
RNAStructProling [31], we nd that there exist riboswitches whose ligand-bound thermodynamics are ac-
cessible to Boltzmann sampling, as represented in Figure 1b.
More precisely, we conrm that the extent to which helices from the proposed models are present in
the predicted modalities aligns with the classication of riboswitches into “thermodynamic” and “kinetic”
regulatory mechanisms [2, 11, 28]. This suggests that new thermodynamic riboswitches might be identi-
able via Boltzmann sampling while also highlighting some challenges to be overcome as the sequence
length/structural complexity of the putative riboswitch increases.
For the simple thermodynamic riboswitch considered in Section 3.1, both proposed models are clearly
identied as structural modalities by proling. In other words, this ligand-bound conformation is suciently
favorable under the NNTM that the Boltzmann sample resembles Figure 1b rather than Figure 1a. Hence, the
modalities reported by proling are a true structural signal.
For the more complex thermodynamic riboswitch considered in Section 3.2, the situation is more compli-
cated. To begin, all helices from the proposed models do appear in the Boltzmann sample. Hence, the assump-
tion captured in Figure 1a again does not hold. In this case, though, the agreement between the modalities
predicted by proling and the proposed base pairing models is not as good as the previous one.
In particular, there is one crucial helix from the ligand-bound structure which, although present in the
sample, has low frequency/estimated probability. While this could be interpreted as evidence for Figure 1a,
that would be incorrect since one of the unbound structure models also includes this “missing” helix. In
other words, factors such as folding kinetics [7] not included in the NNTM are likely a consideration here,
but not ones directly related to the ligand-binding. As discussed in Section 3.2, this means that — subject to
the accuracy of the NNTM approximation to folding biophysics — proling identies the structural signal in
the Boltzmann sample with both high precision and high recall. Hence, while not perfect, this approach of
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50 |Hee Rhang Yoon et al.
proling Boltzmann samples to identify putative structural modes may yield useful insights into potential
new thermodynamic riboswitches.
The situation for the kinetic riboswitch considered in Section 3.3 is markedly dierent. The helices from
the unbound structure do indeed dominate the Boltzmann sample as expected from Figure 1a. In fact, no
helices exclusive to the ligand-bound model are even sampled. Interestingly, the ligand-binding domain is
clearly thermodynamically favorable if the kinetics of folding are simulated by sequential Boltzmann sam-
pling for sequence prexes. This indicates that it just might be possible to identify kinetic riboswitches by
Boltzmann sampling as well, but a great many challenges remain.
Hence, we nd that the original assumption holds for the kinetic riboswitch considered, but is violated by
the thermodynamic ones. In the best/simplest case, the predicted modalities for the latter are in good agree-
ment with the experimental models. This supports proling of Boltzmann sample predictions as a useful
method for identifying the conformational changes of simple thermodynamic riboswitches. For a more com-
plex case, there is still a strong correlation between prediction and experiment, but the agreement is not quite
as good — most likely because of the quality of the NNTM approximation independent of the ligand-binding
question. This highlights that thermodynamic riboswitch identication based on the structural modes pre-
dicted by RNAStructProling is possible, but additional work is needed for longer sequences and/or more
complex switches.
2Materials and Methods
2.1 Riboswitches
Figure 2:
Two visualizations of the same RNA secondary structure: arc diagram (left) and planar model (right). Runs of consecu-
tive base pairs, called helices, are both colored and numbered to indicate their correspondence. The helix
{(i,j),...,(i+k−
1,j−k+ 1)}
which begins with the base pairing between nucleotides in positions
i
and
j
and has total length
k
will be denoted
by the triple (i,j,k). Hence, the four helices pictured are (1,63,5),(9,29,6),(38,56,5), and (68,78,4) respectively.
A riboswitch is a segment of a messenger RNA (mRNA) molecule that regulates gene expression through
a conformational change induced by the binding of a small molecule ligand. The structure of a riboswitch
consists of two parts: an aptamer domain and an expression platform. Ligand binding to the aptamer domain
causes the expression platform to change its conformation, resulting in the regulation of gene expression [6,
47]. Regulation can occur by controlling transcription (synthesis of RNA from DNA) or translation (synthesis of
proteins from RNA). Transcriptional riboswitches control the formation of a terminator stem, whose presence
causes transcription termination [32, 40]. On the other hand, translational riboswitches control the exposure
of key regulatory elements like the Shine-Dalgarno (SD) sequence and the AUG start codon.
Riboswitches can be categorized into thermodynamic and kinetic switches [2]. Thermodynamic switches
exist as a mix of conformations whose energies are similar to the minimum free energy [28]. Ligand bind-
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Towards an understanding of RNA structural modalities |51
ing stabilizes a particular conformation. Moreover, thermodynamic switches can switch back and forth be-
tween conformations depending on the concentration of the ligand. Kinetic switches, on the other hand, are
riboswitches whose conformations have a large energy dierence [11]. RNA folding can occur faster than tran-
scription, and ligand binding to the RNA during co-transcriptional folding allows the RNA to fold into a high
energy state.
RNA conformations and their changes can manifest in dierent ways. We focus here on dierences in
the base-pairing of the secondary structures. We will compare the predicted structural modes identied by
proling to putative models obtained via NMR spectroscopy or uorescence spectroscopy. Each model will
be presented in secondary structure visualizations, using both arc diagrams and planar models, as in Figure
2. We compute the free energy change under the nearest neighbor thermodynamic model (NNTM) using GT-
fold [38], and the relative probability, which is the ratio of sampling probability of the model and sampling
probability of the MFE structure, according to Equation 2 with T= 310K.
2.2 Boltzmann sample
A popular approach for RNA secondary structure prediction [22, 25, 30, 41] is to nd a unique minimum free
energy (MFE) structure under the nearest neighbor thermodynamic model (NNTM). However, since the NNTM
is only an approximation to the folding biophysics, prediction accuracy has long been increased by consid-
ering suboptimal structures [48, 49] and/or base pairing probabilities under the Boltzmann partition func-
tion [12, 23, 26]. The ability to sample from the Boltzmann ensemble [5] allows one to examine structural
alternatives to the MFE structure in proportion to their estimated probability under the NNTM. Hence, it can
be used to search for signals of multimodality in RNA secondary structures [9, 20, 31, 33, 43].
A Boltzmann sample is a set of structures, typically of size 1000, sampled from the Boltzmann (i.e., Gibbs)
ensemble [5]. In this distribution, a structure Swith energy ϵ(S)exists with probability
P(S) = exp[−ϵ(S)/RT]
Z,(1)
where Ris the Boltzmann constant, Tis the absolute temperature, and Zis the partition function Z=
PS∈Ωexp[−ϵ(S)/RT]summed over all possible states (in this case, secondary structures for the given se-
quence) S∈Ω.
Since the sampling probability is exponential in energy, a small dierence in energy leads to a much
larger dierence in sampling probability. Given two structures S1and S2with energies ϵ1and ϵ2, the ratio of
their sampling probabilities is
P(S1)
P(S2)=exphϵ2−ϵ1
RT i.(2)
When T= 310K, a decrease in energy by 1 kcal/mol leads to approximately 5 fold increase in sampling
probability. Hence, one of the many distinct structures which is 4 kcal/mol above MFE prediction is unlikely
to be sampled at all since the relative probabilities would 1.4*10−3: 1.
2.3 Proling
Intuitively, we consider a mode in a Boltzmann sample to be a set of similar structures whose collective fre-
quency is high enough to be considered “signal” rather than “noise.” More precisely, we will consider each
(selected) prole identied by the cluster analysis method RNAStructProling [31] to be a structural mode. In
contrast to other cluster analysis methods [3, 17, 36], proling is explicit about ltering the thermodynamic
noise from the stochastic sampling. Additionally, proling facilitates comparisons between dierent clusters
in the Boltzmann sample by highlighting structural similarities and dierences in the summary prole graph,
like the one pictured in Figure 3.
Given a Boltzmann sample, typically with 1000 structures, proling rst identies the helix classes
present. A helix class is an equivalence class of helices which are all subsets of the same maximal helix.
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52 |Hee Rhang Yoon et al.
Figure 3:
A prole graph for the sequence from Figure 2 up to position 78. Proling identied 5 distinct structural modes
present in the Boltzmann sample, corresponding to the ve rectangles/selected proles listed. The table lists the feature
locations by
(i,j,k)
triple and sampled frequencies. For instance, pairings from the purple helix (which is maximal) are the
rst feature and occurred in 968 of the structures sampled. The four colored helices from Figure 2 correspond to the prole
[3[1][2]][6], where the brackets indicate the nesting relationship. This selected prole appears in the bottom left rectangle. It
diers from the selected prole above by the sixth feature. The prole [3[1][2]] has a specic frequency of 239, and a general
frequency of 430 since the latter includes the structures from the [3[1][2]][6] prole.
A helix is maximal if the run of base pairings cannot be extended any further. Next, proling selects high
frequency helix classes as features. The frequency cuto is determined by maximizing the average Shannon
information entropy. After feature selection, the next step identies the proles present in the Boltzmann
sample. A prole is an equivalence class of sampled structures which have the same set of features. Some
proles may have been sampled with very low frequency, so the Shannon entropy method is again used to
select only the most informative. The relationships among these selected proles are then presented in the
summary prole graph.
The summary prole graph is generated by computing a transitive reduction on the set of selected pro-
les, which are drawn as rectangles. If additional vertices are needed to connect the graph, as in Figure 4
on page 53, these “intersection” proles are drawn in dashed ovals. The “root” node, which is the oval at
the top of the graph, indicates the prole common to all sampled structures. In this example, there were no
features common to all sampled structures, so this is the empty prole. The “numerator” indicates the num-
ber of structures with exactly this prole, called the specic frequency. The “denominator” gives the number
of structures which contain at least this set of features, called the general frequency. In this example, 132 of
the 1000 structures sampled contained only the features 1 and 2, along with other lower frequency pairings,
whereas 963 contained those plus other additional features. Directed edges are labeled by the features which
are added as the proles grow larger, progressing down through the graph from the root node. Although the
graph pictured in Figure 3 is a tree, this is by no means a requirement.
The web version of proling is available at http://rnaproling.gatech.edu/. The code is freely available at
https://github.com/gtDMMB/RNAStructProling. By default, proling samples 1000 suboptimal structures
using Turner 99 energy parameters [24] and dangle option d2, which adds dangling energies for nucleotides
on the ends of multi-loops and external loops.
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Towards an understanding of RNA structural modalities |53
Figure 4:
Proling graph of SAM-III riboswitch showing the three structural modes identied. The arc diagrams visualize the
featured base pairings for each selected prole. Recall that the dashed oval is an intersection prole, included to connect the
graph.
3Analysis and Results
We use proling to identify predicted structural modalities for three riboswitches, two whose regulation is
thermodynamically controlled and one kinetic. We note that a second kinetic switch was analyzed, but results
were essentially the same. Some additional details are given at the end of Section 3.3.
3.1 SAM-III riboswitch: thermodynamic switch
The SAM-III riboswitch regulates metK gene expression in bacteria by controlling translation initiation. In
the absence of the ligand, the riboswitch folds so that the Shine Dalgarno (SD) sequence is exposed, allow-
ing translation to take place. Upon binding of S-adenosylmethionine (SAM), the riboswitch refolds into an
alternate conformation in which the SD sequence is sequestered [46].
Proling found 28 helix classes present in the Boltzmann sample generated, and selected 7 as features.
With these features, the sampled structures partitioned into 8 proles, and 3 had signicant enough presence
to be selected as structural modes. Note that prole [3[4][1]][2] includes the MFE structure.
The summary prole graph displayed in Figure 4 illuminates the relationship among these 3 modes. In
particular, one can see that the primary distinction is between structures which contain features 3 and 4
versus 6 and 7. Among the former, there are two types, depending on the presence of feature 5 which is a
short (maximal) helix of length 2.
Comparing this analysis to putative models of the SAM-III riboswitch shows that proling captures the
important conformation change. Table 1 illustrates NMR spectroscopy based models of the unbound and
ligand-bound structures presented in [46], along with the MFE structure.
Selected prole [6[7[1]][2]] which was found in 10.1% of the Boltzmann sample coincides exactly with
the proposed ligand-bound model whereas the unbound structure has the prole [3[1]]. Although this exact
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54 |Hee Rhang Yoon et al.
Table 1:
The two NMR-based models (unbound and ligand-bound) proposed in [
46
] and minimum free energy (MFE) prediction
of SAM-III riboswitch. The helices are labeled to match Figure 4, and the prole is also given. Energies were computed using
GTfold [
38
]. The dierence of
+0.60
kcal/mol between the ligand-bound and MFE structures results in a relative sampling
probability of 0.38:1 according to Equation 2 with
T= 310K.
The
+1.7
kcal/mol dierence from the MFE gives a 0.06:1 relative
sampling probability for the unbound structure.
Structure Structure representations Energy
unbound -24.90
kcal/mol
ligand-
bound
-26.00
kcal/mol
MFE -26.60
kcal/mol
combination of features was not identied, 85.9% of the Boltzmann sample included features 1 and 3, along
with 2 and 4. Since these dierences are all short (maximal) helices with length 2, we understand proles
[3[4][1]][2] and [3[5[4][1]][2] as variants on the unbound model whose energies were lowered via the additional
base pairings.
To appreciate why prole [3[1]] was not among the selected structural modes, we have only to consider
the predicted free energy changes under the NNTM listed in Figure 4. In the Boltzmann distribution, each
1 kcal/mol dierence is a factor of ∼5 in probability. Given the dierence of 1.7 kcal/mol from the MFE, the
probability of sampling exactly features 1 and 3 is quite low. This is an aspect of how thermodynamic opti-
mization methods can over-predict base pairs, although one which is easily addressed since the additional
pairings are all short helices.
In other words, the recall is excellent, but the precision could be improved. Here, the recall of 1 is being
computed as the ratio of “true positive” helices shared by predicted features and proposed models to the total
number of helices in the proposed model. The precision of 0.71 is being computed as the ratio of the same
true positive helices to the total number of predicted features.
Nonetheless, for the SAM-III riboswitch, proling identies that structures closely related to the proposed
unbound model dominant the Boltzmann sample, while the ligand-bound model is a signicant alternative
structural mode. This analysis provides a proof-of-principle result that thermodynamic riboswitches can be
detected from the dierent structural modalities identied by proling from a Boltzmann sample prediction.
3.2 add-riboswitch: thermodynamic switch
The adenine sensing riboswitch is found on chromosome II of Vibrio vulnicus. In the absence of the ligand,
the SD sequence and the AUG start codon are sequestered, thereby repressing translation. The ligand binding
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Towards an understanding of RNA structural modalities |55
changes the riboswitch conformation so that SD sequence and the AUG start codon are exposed, allowing
translation initiation [29].
The previous SAM-III analysis is a best case, with a clear correspondence between predicted structural
modes and putative base pairing models. However, the add-riboswitch is a more complicated example. To be-
gin, its length is 112 nucleotides, compared to the 59 length SAM-III sequence. This additional 53 nucleotides
substantially increases the number of low energy suboptimal secondary structures possible and hence the
structural diversity in the predicted Boltzmann sample.
For this riboswitch, proling nds 193 helix classes (versus 28 for SAM-III) present in the Boltzmann sam-
ple. However, nearly all are low or very low frequency, since only 9 (versus 7 before) are selected as features.
With these features, the sampled structures are partitioned in 41 proles (versus 8). Again, though, nearly all
are low frequency, since only 5 (versus 3) have signicant enough presence to be selected as structural modes.
Figure 5:
Proling graph of add-riboswitch showing the ve structural modes identied. In this case, four intersection proles
were needed to connect the graph. The arc diagrams visualize the three selected proles with the most featured pase pairings.
As before, the summary prole graph displayed in Figure 5 illuminates the relationship among these 5
modes. All selected proles include features 1, 2, and 3, which nest as [3[2[1]]]. All but one also contain the two
base pairs from feature 5, which are inserted into this run as [3[2[5[1]]]]. If this extended helix is considered a
structural unit, then the structural variation identied by proling is due to features 4, 6, 8, and 9.
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56 |Hee Rhang Yoon et al.
All but one of the modes contain feature 4. Since it is present in 75.7% of the sample, but the feature
threshold cuto is below 14.6%, we know that alternatives are lower frequency. Features 6, 8, and 9 are all
competing for base pairings in the sequence region from nucleotides 1 to 34. From this we understand that
thermodynamic optimization predicts a stable helix in this region, but the NNTM cannot resolve exactly which
pairings are involved. Hence, although proling predicts 5 structural modes, they are all closely related since
88.3% of the sample contained features 1, 2, and 3, and 61.9% contained 4 as well.
We note that no proles containing feature 7 were selected as structural modes. Under closer inspection of
the Boltzmann sample, this seems reasonable since the two most frequent were [7[4]] which had 37 structures
and [7[6][4][3[2[5[1]]]]] with 36. However, we also observed that feature 7 can be considered an alternative to
feature 3 since their maximal helices overlap; of the 166 structures without #3, 118 contain #7. (There were
108 structures which contained pairings from both #3 and #7.) This indicates that it may be useful to consider
low frequency alternatives to high probability pairings.
Table 2:
The three NMR spectroscopy based models (apoB, apoA, and holo) and the MFE predicted structure for the add-
riboswitch. According to the NNTM and Equation 1, the relative probabilities of sampling the proposed models versus the
MFE prediction are 0.0021,6.7*10−4, and 1.5*10−4, respectively.
Structure Structure representation Energy
apoB -20.30
kcal/mol
apoA -19.60
kcal/mol
holo -18.70
kcal/mol
MFE -24.1
kcal/mol
As with our previous SAM-III analysis, we compare the features identied by proling with the putative
helices in the NMR spectroscopy based models. Of the 9 features listed in Figure 5, all but 2 (#7 and #8) are
present in the model. Conversely, of the 9 helices in the putative models from Table 2, all but 2 (P1 and P2B)
are predicted features. Hence, the recall and precision are both 0.78.
Since 3 of 4 helices from the proposed ligand-bound model are featured, we conclude that proling nds
evidence for this conformation. Under further inspection, we will see that the remaining ligand-bound helix
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Towards an understanding of RNA structural modalities |57
is present in the Boltzmann sample, and hence that the original assumption captured by Figure 1a on page 49
is too strong. Since apoA mediates the transition from apoB to holo, it would seem that Figure 1b is a better
approximation to the folding landscape for this riboswitch — subject to the NNTM approximation to folding
biophysics.
As illustrated in Figure 6, it is not possible to increase this recall without substantially decreasing the
precision. Of the two “false negative” helices, the critical missing one is P1. This helix is a crucial dierence
between the two proposed unbound structures, apoB and apoA, since it forms the aptamer domain, which
persists in the ligand-bound holo conformation. However, P1 was only sampled in 36 structures (out of 1000),
and there are 20 other helix classes with higher frequency which were also not featured by proling.
This low frequency is a result of P1 being in direct competition with features 3 and 7. The maximal helix
for P1 is (1, 69, 8) which also overlaps with feature 2. However, we see from the proposed apoA structure that
portions of the P1 and feature 2 maximal helices can coexist as (3, 67, 4) and (68, 104, 4). Given the relative
probabilities, these ‘apoA’-like structures were only 2.7% of the sample. In contrast, no structures containing
both P1 and either feature 3 or 7 were sampled, although features 3 and 7 coexisted in 10.8% of the structures.
Similarly, only 5 ‘holo’-like structures were sampled which contained P1 and features 1 but not 2. (Ev-
ery structure which contained P1 also contained #4 and #6.) These structures all contained additional base
pairings, and each was assigned its own prole. Hence, unlike the SAM-III riboswitch, there is no structural
signal for the proposed ligand-bound holo conformation in the Boltzmann sample.
In contrast, though, ‘apoB’-like structures which contain features 3, 4, and 9 account for 14.5% of the
sample. (All but 1 of 834 structures which contain #3 also contain #1 and #2.) Of these, 6.7% contain P2B,
10.6% contain #5, and 1.9% contain P2B but not #5. Both P2B and #5 are short helices of length 2.
Figure 6:
Distribution of helix classes with frequency 30 or higher in the Boltzmann sample prediction for the add-riboswitch
analyzed. P1 is 30th with frequency 36, and P2B is 19th with 82. Taking the helices of the putative model as the target and
the proling features as the prediction, 7 (blue) are “true positives”, 2 (green) are “false positives,” and 2 (yellow) are “false
negatives.” This yields a recall, a precision, and an F1-score (harmonic mean of precision and recall) of 0.78. Increasing the
recall to 0.89 by including helix classes up to P2B (resp. 1 for P1) as features decreases the precision to 0.42 (resp. 0.3) and
reduces the F1-score from 0.78 to 0.57 (resp. 0.42). Hence, proling achieves a good balance between these two competing
objectives.
Finally, we note that all of the helices in the MFE structure occur in one or more of the putative models, as
illustrated in Figure 7. This supports the general understanding that high probability base pairings are most
likely to be a true structural signal while illustrating that the open challenge is to identify which of the lower
probability ones are also.
Given the precision and recall of the predicted features for the add-riboswitch, proling is clearly extract-
ing biologically relevant information from the Boltzmann ensemble. In this case, though, the correspondence
between the structural modes selected and the proposed models based on NMR spectroscopy is less good than
the SAM-III riboswitch. A particular challenge is to identify pairings like P1 that characterize structural modes
but which are only sampled at very low frequency. Since the critical missing helix also occurs in an unbound
model, other factors besides ligand-binding (such as folding kinetics) are more likely to be the cause of the
lower accuracy. To increase recall without decreasing precision, approaches for improving the NNTM approx-
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58 |Hee Rhang Yoon et al.
Figure 7:
Venn diagram highlighting the similarities and dierences among helix classes for the add-riboswitch base pairing
models with the MFE structure’s prole. Frequencies are given as specic / general. Recall that the specic frequency is the
number of sampled structures with exactly that prole while the general is the number which contain at least those helix
classes (and possibly others).
imation to folding biophysics — such as including auxiliary information from SHAPE and other footprinting
data — may well be needed.
3.3 pbuE riboswitch: kinetic switch
We now turn from riboswitches whose regulation is classied as “thermodynamic” to a “kinetic” one. The
pbuE riboswitch found in Bacillus subtilis is also adenine sensing. Unlike the previous two switches, pbuE
regulates transcription, and not translation. By default, a long terminator stem forms, resulting in transcrip-
tion attenuation. However, ligand binding during co-transcriptional folding stabilizes an alternative struc-
ture, disrupting formation of the terminator stem and allowing transcription to continue [21].
The pbuE sequence has length 102, and its structural diversity does fall between the SAM-III and add-
riboswitch. The Boltzmann sample has 73 helix classes reduced to 6 features, and 5 structural modes selected
from 7 proles. In this case, however, the prole graph given in Figure 8 reveals that 4 of these modes are very
closely related.
Unsurprisingly, all structures sampled included features 1 and 2, which is the transcription-attentuating
terminator stem with 22 base pairs. The proles then split on feature 3. Features 4 and 5 are almost identical.
Feature 6 explicitly lls in 3 additional base pairs, however structures belonging to the 2 related proles
without #6 do sometimes include pairings in the region 1,.. . ,17 — just with much lower frequency. Hence,
this is probably not a signicant structural dierence.
On further review, then, the Boltzmann sample has at most two signicant structural modes. Additional
analysis reveals that all but one structure in the prole [1[2]] also contains pairings from helix class #7 which
has frequency 58 and triplet (9, 29, 6). This is interesting because it is the helix P0 from the putative models.
Table 3 illustrates the uorescence spectroscopy based models of the pbuE riboswitch proposed in [21].
The unbound model consists of the terminator stem along with the helix P0 just discussed. When the aptamer
domain, which consists of the rst 63 nucleotides, has been transcribed, the riboswitch folds into a three-way
junction formed by helices P0, P1, and P2 which can be stabilized by ligand-binding. Since the helices P1 and
P2, whose maximal triples are (1, 63, 5) and (38, 56, 5), directly conict with feature 1, ligand binding disrupts
the terminator stem formation and transcription can proceed.
In comparing the predicted structural modes to the putative models, we did nd the unbound model
present in 5.8% of the sample, although manual inspection of low frequency alternatives was necessary to
identify the P0 pairings as the (9, 29, 6) helix in the [1[2]] prole. Clearly, the terminator stem dominates the
sample, and this is consistent with the kinetics of co-transcriptional regulation as well as Figure 1a on page 49.
The P1 and P2 aptamer helices are not sampled at all, which agrees with the negligible probability of
the ligand-bound structure relative to the MFE one. Interestingly, though, these helices are clearly present
when we simulate the transcription process. To do this, we generated a Boltzmann sample and proled it for
initial prexes of the pbuE sequence from length 65 up to length 101. For each of the 37 new samples, plus
the original full sequence, we tracked whether the helices P0, P1, and P2 were selected as features and also
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Towards an understanding of RNA structural modalities |59
Figure 8: Proling graph of the Boltzmann sample of pbuE riboswitch with ve modes identied from the Boltzmann sample.
whether the terminator stem helices (now denoted TS1 and TS2) were. Figure 9 demonstrates that the aptamer
domain helices are featured up to length 85, at which point the terminator stem begins to dominate.
Figure 9:
Graph indicating pbuE prex length at which helices from the aptamer domain (P0, P1, and P2) and the terminator
stem (now denoted TS1 and TS2) are either featured (solid), sampled (broken), or nonexistent (blank). The broken line shows
if the given helix is present in at least one of the sampled structures. A clear transition occurs as the transcription simulation
proceeds from position 80 to 90. We conclude that this is the critical window for ligand-binding to stabilize the apatmer
domain and prevent transcription attenuation.
In fact, when we examine the proling graphs for prexes of length 65 to 77, the prole [P1[P0][P2]] is
the dominant structural mode. For lengths 78 to 85, proles with this three-way junction were selected as
structural modes, along with other ones in which it was disrupted. For lengths 86 to 91, all structural modes
contained the terminator stem helices. Beyond 92, the results were very similar to Figure 8.
As we had expected, our proling analysis of the pbuE riboswitch shows that Boltzmann sampling does
not take into account folding kinetics, especially when mediated by ligand-binding. A novel outcome, how-
ever, was the simplicity with which the co-transcriptional folding process could be simulated and analyzed,
yielding useful insights.
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60 |Hee Rhang Yoon et al.
Table 3:
Fluorescence spectroscopy based models (unbound and ligand-bound) and MFE prediction for the pbuE riboswitch.
Given the dierences in free energy with the MFE, the relative probability of sampling the unbound structure is 0.012:1 while
the ligand-bound is 6.8*10−15:1.
Structure Structure representation Energy
unbound -32.30
kcal/mol
ligand-bound -14.90
kcal/mol
MFE -35.00
kcal/mol
As remarked, we analyzed a second kinetic switch, the thiM riboswitch from E.coli (TPP riboswitch),
and the results were suciently similar to pbuE not to report separately. In particular, we simulated the co-
transcriptional folding process by proling the initial prexes of the TPP sequence from length 80. Initially,
proling featured helices from the putative ligand-bound model. However, as the length of the sequence in-
creased, such helices ceased to be features as helices from the unbound model started to dominate.
4Discussion
We draw several conclusions from our RNAStructProling cluster analysis of Boltzmann sample predictions
for three dierent riboswitches whose conformational change under ligand-binding is manifested at the base
pairing level, resulting in dierent secondary structures from the unbound model.
First, in agreement with Figure 1a on page 49, we should not expect thermodynamic optimization meth-
ods to detect “kinetic” riboswitches like pbuE — at least not from a single Boltzmann sample prediction. This
is because the conformational change is fundamentally dependent on the folding dynamics mediated by
ligand-binding as the sequence is transcribed. Nonetheless, we were intrigued that the pbuE aptamer do-
main helices were featured by the proler for initial sequence prexes. This suggests that it may be possible
to simulate folding kinetics for riboswitch detection with this sequential sampling and proling approach.
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Towards an understanding of RNA structural modalities |61
It would certainly be interesting to compare against existing methods for detecting locally stable secondary
structure motifs [13, 16, 34].
Conversely, though, our results indicate that Figure 1b is a better representation for the two thermody-
namic riboswitches studied since all helices from the proposed ligand-bound models were suciently fa-
vorable under the NNTM to appear in the Boltzman sample predictions. However, the potential for proling
to identify the (approximate) structural modes for thermodynamic riboswitches is dependent on the diver-
sity of the Boltzmann sample, which in turn correlates with sequence length and switch complexity. As re-
marked, the SAM-III riboswitch is a best case. Nonetheless, we expect that other short, 2-state thermodynamic
riboswitches might well be equally successful.
In contrast, our second thermodynamic riboswitch was almost twice as long, as well having a proposed
3-state system. Out of the 9 features predicted by proling, 7 agreed with the putative model (which has 9
proposed helices). As remarked, this is both good precision and good recall at the helix level. To improve the
accuracy of the predicted structural modes, however, it would be necessary to identify the critical missing
P1 base pairings, which is one of at least 20 other low energy helices. To solve this needle/haystack prob-
lem, it is likely that additional computational approaches like recent advances in nonredundant Boltzmann
sampling [27] and in sampling with SHAPE data [35] may be needed to improve the quality of the NNTM
approximation to folding biophysics.
Acknowledgement: The authors would like to thank Professor Shan Zhao and the Department of Mathemat-
ics at the University of Alabama for hosting the excellent 2019 NSF-CBMS Conference: Mathematical Molec-
ular Bioscience and Biophysics, Professor Guowei Wei for his inspirational lectures at that meeting, and the
Computational and Mathematical Biophysics journal for organizing this special issue. Thanks also are due to
the anonymous reviewers whose thoughtful feedback signicantly improved the paper.
This work was supported by funds from the National Institutes of Health (R01GM126554 to CH,
R01GM101237 to AL, and F31GM130040 to AC) and the National Science Foundation (DMS1344199 to CH).
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