Table Of ContentMethods in
Molecular Biology 2586
Risa Karakida Kawaguchi
Junichi Iwakiri Editors
RNA Structure
Prediction
M M B
ETHODS IN OLECULAR IO LO GY
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JohnM.Walker
School of Lifeand MedicalSciences
University of Hertfordshire,Hatfield
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RNA Structure Prediction
Edited by
Risa Karakida Kawaguchi
Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, USA
Junichi Iwakiri
Department of Computational Biology and Medical Sciences, Graduate School of Frontier Sciences,
The University of Tokyo, Chiba, Japan
Editors
RisaKarakidaKawaguchi JunichiIwakiri
ColdSpringHarborLaboratory DepartmentofComputationalBiology
ColdSpringHarbor,NY,USA andMedicalSciences
GraduateSchoolofFrontierSciences
TheUniversityofTokyo
Chiba,Japan
ISSN1064-3745 ISSN1940-6029 (electronic)
MethodsinMolecularBiology
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Preface
Sincethe1960s,RNAsecondarystructureanalysishasbeenperformedforawidevarietyof
groupsofRNAs,includingrRNAsandRNAvirusgenomes[1],andthishasbeenfollowed
byRNA3Dstructureanalysis[2].OwingtotheinstabilityofRNAstructures,thenumber
of the detected structures is much smaller for RNAs than for proteins, specifically 1523
RNA-only structures compared with 151,577 protein-only structures in the Protein Data
Bank(PDB)[3]asof2020.Insilicostructurepredictionis,therefore,apowerfulapproach
toovercomingtheselimitationsandrevealingacomprehensiveviewofRNAstructures.The
mostprevalentandhigh-performancestructurepredictionmethodisbasedonathermody-
namic model that takes the primary sequence as an input and predicts a representative
structureaccordingtoitsstability.Freeenergychangesareestimatedasametricofstructure
stabilitybyapproximationofthoseforeachsub-structureusingthemeltingtemperaturefor
shortoligosorbasedonstructuresindatabases[4–6].TocomputetheprobabilityofRNA
secondarystructuresbasedonthermodynamicmodels,itisnecessarytocomputethesumof
P
the exponential of the free energy changes. This is formulated as edGðζ,xÞ=RT, where
ζ∈ΩðxÞ
dG(ζ,x)isthefreeenergychangeofsequencexandstructureζ,Risthegasconstant,Tis
theabsolutetemperature,andΩ(x)representsthesetofallpossiblestructuresofsequencex.
dG(ζ,x) for every possible subsequence x can be efficiently computed by a dynamic pro-
graming (DP) technique using the subproblems dG(ζ,x0), where x0 is a subsequence of x.
AftercomputingtheDPvariablesobtainedforthefullsequence,thepartitionfunctionand
probability of the structure can be computed following a canonical distribution. Previous
benchmark studies have carried out the comprehensive assessment of RNA secondary and
3Dpredictiontoolswithmultiplestructuredatabases[7,8],indicatingnotonlysufficiently
high prediction accuracy but also computational limitation in robustness and performance
stabilityfor manypredictionmethods.
In terms of accuracy and computational time, one of the main limitations of in silico
structureanalysisisthepredictionoflongRNAs.Forexample,theestimationoffreeenergy
changesisassumedtoshowlowaccuracyfordistantbasepairsbecausemodelsarefittedto
results obtained from short RNAs. The rapid exponential increase in possible structures
relativetosequencelengthisalsoacriticalproblemforfeasibility.Whiletheimprovementof
applicability and performance has been actively studied for in silico structure analysis [9],
experimentaltechniqueshavealsobeenappliedtosolvethoseproblemsatthesametime,for
example, high-throughput structure probing methods including SHAPE-seq [10] and
DMS-seq [11].These methods utilize high-throughput sequencing to capture cleavage or
modification events introduced by chemical reagents or enzymes as a signature of reactive
sites regardless of the length or condition of RNA samples. This is based on the principle
that the probability of these events is correlated with the probability of being unpaired in
RNAsecondarystructures.Bycomparingthedeterminedandpredictedaccessibilities,both
scores have been found to be consistent at a transcriptome-wide level [9]. Owing to the
varioussourcesofbiologicalandtechnicalnoise,thereisachallengeinextractingreproduc-
ible results from high-throughput data including such noise [12, 13]. However, the inte-
gration of multiple datasets relying on different techniques may uncover the true
transcriptome-wideRNAstructurelandscapebyovercomingdata-specificbiases[14].
v
vi Preface
Moreover, high-throughput structure probing methods can be applied to a variety of
conformational analyses. A careful selection of reagents and experimental settings can
further enhance the comprehensiveness of detectability of base reactivity within a specific
time range [15]. For the detection of the co-accessibility of multiple bases, a structure
probingmethodvariantcalledmutationalprofilinghasbeendeveloped(e.g.,SHAPE-MaP
[16]andDMS-MaP[17]).Insuchmethods,themutationsonthesamereadareusedasa
cluetodeterminewhichstructureorcombinationofstructuresisobservedinvivo[18,19].
The secondarystructure isknownto spontaneouslyfold in amannerdeeply dependenton
the primary sequence but to be perturbed by triggers that can include other molecules’
binding, modification, and different cell states (e.g., temperature, pH, or metal ion; [11,
19,20]).Analyzingtheinconsistencybetweenthepredictedstructuresand experimentally
determined reactivities is, therefore, an efficient approach to discover the existence of
in vivo-specific regulation that causes structure disruption. Recently, a probing method
thatcapturesthefoldingofgrowingnascentRNAduringtranscriptionhasbeendeveloped
[21, 22]. Because RNA secondary structure is formed simultaneously during transcription
[23],thestructurecomparisonbetweennascentandmaturedRNAspotentiallyrevealsthe
formation of a structure differing from the initial or stable form, suggesting that the
influenceofthermodynamicfluctuationsmayaffectRNAfoldingkinetics.
Compared with RNA secondary structure prediction, RNA 3D structure prediction is
recognized as a more challenging problem due to the more numerous degrees of freedom
for3Dstructures,suchasdistancesandanglesofeachbasepair,resultinginhighcomputa-
tional demand. Despite such difficulties, improvements in RNA structure prediction have
been attempted for 3D structures using information from experimentally validated struc-
turesviaX-crystallographyandcryo-EM.TheaccumulationofRNA3Dstructureinforma-
tion is also expected to help clarify the kinetic mechanisms of RNA and protein
binding[24].
For both RNA secondary structure and 3D structure analyses, machine learning has
focused on combining classical structure prediction methods with the vast amounts of
experimental structure data recently obtained. One successful example has utilized deter-
minedRNAstructuresinorder toimprovepredictionaccuracyofexistingRNAsecondary
structurepredictionmethods.Whilesomestudieshaveappliedsuchdatatoimprovingthe
parameters in thermodynamic models [25–27], another strategy cooperatively improves
prediction models by aligning the predicted base pairs and detected accessibilities to be
consistent[28].Theapplicationofdeeplearningmodelshasenabledtheimplementationof
a new strategy to tackle complex problems, such as high-resource demands or high-
dimensionality input features. For example, a deep neural network model achieved a
dramatic advancement of binding motif identification required for RNA interaction deter-
mination. By considering the higher-order influences of base combinations for RNA and
protein binding, this model enables accurate binding site prediction as well as a deeper
elucidationofRNAbindingregulationmechanisms[29].Assuch,machinelearningmeth-
ods, accumulated data, and their resulting accurate structure predictions have a strong
synergistic effect in moving the field of RNA biology forward by expanding the targets of
RNAstructureanalysis,fromshortnon-codingRNAs(ncRNAs)tolongorcodingRNAs,
withavarietyofgoals.
Preface vii
Organization of This Book
Inthisseries,weintroducerecentprogressinRNAstructurepredictionanditsapplication
fromabroadviewpoint,particularlyoverthelastseveralyears.Here,weintroducethetopics
covered by 16 chapters and discuss some additional topics that are closely related to RNA
structureprediction,suchasRNAinversefolding.Becauseofadvancementsinexperimental
protocolsanddevices(e.g.,nanoporesequencing[30]),theintegrationofnewtypesofdata
aswellasnewanalysistechniquesisnecessary.Hence,thevarietyoftopicscontainedinthis
series is hoped to serve as a simple guide for both experimental and computational RNA
researchers.
RNASecondaryStructurePrediction
RNAsecondarystructurepredictionisaproblemthatinvolvespredictingthecombinations
ofbasepairingbetweencomplementarybases,namelyAwithUandGwithC,aswellasfor
G–Uwobblepairs.Thegold-standardmethodforRNAsecondarystructurepredictionisa
thermodynamicmodelinwhichthefreeenergychangeofthestructureisapproximatedby
the experimentally obtained parameters for each partial structure. The highly stable struc-
tureisthenselectedasthebestpredictionresultthattakesintoaccountthelandscapeofall
possiblestructuresthroughuseofadifferentmetric,suchasminimumfreeenergy(MFE),
maximum expected accuracy, and centroid structure computation [31]. Because of the
enormousnumberofpossiblebasepairs,reliablesecondarystructurepredictionisobtained
inexchangefortheconsiderablecomputationtimerequiredtofindstablestructureswhose
freeenergychangesaresubstantiallysmall.Forexample,onecanassumethateachbaseofa
sequenceof100nucleotidesisrandomlysampledfromfourtypesofbases.Ifabasecanbind
toitscomplementarybaseatanyposition,eachpaircanformabasepairwithaprobabilityof
6/16¼ 0.375.Giventhis probability, theorderofall possiblestructuresfora sequenceof
100basescanreachroughly1055.Inathermodynamicmodel,however,theprobabilityof
the unstable structures or base pairs is low enough that they rarely affect the results of the
structureprediction.Onestrategythatignoresthoselow-probabilitystructurescanreduce
thecomputationareatobeexploredwhilemaintainingtheprecisionofstructureprediction.
An efficient enumeration of all possible structures can be conducted by DP. The
computational time of a DP algorithm depends on the sequence length but can be varied
depending on the structure types to be included. For example, pseudoknot structures
consistofbasepairscrossingovereachother.ThecomputationaltimeofDP-basedstructure
predictionwithpseudoknotsisO(N6)whilethecomputationaltimeforstructureswithout
pseudoknots is O(N3), where N is the sequence length [32]. This makes it difficult to
analyzeRNAslongerthanseveraltensofnucleotides,althoughpseudoknotscanfunctionas
a key motif for biological regulation [33]. Kimchi et al. (2019) tackled this problem by
developingLandscapeFold,whichenumeratesstructuresincludingpseudoknotsbasedona
polymerphysicsmodel[34].ItcanpredicttheMFEstructureaswellasthedistributionof
freeenergychangesforallpossiblestructuresratherthanutilizingaDPalgorithmbasedon
thermodynamic models. The structure analysis of LandscapeFold can be a powerful
approach to analyze the structures of functional short RNAs, such as ligands or aptamers.
In addition to theprediction ofstructuresincluding pseudoknots,another problem isthat
an appropriate metric is required to compare multiple RNA structures. The novel tool
planeGraph2tree clusters RNA structures with pseudoknots based on the PEELING
viii Preface
algorithm [35]. Its input is a plane graph obtained from each RNA secondary structure.
planeGraph2treeidentifiesatopologicalcentroidofthegraphandconstructsatopological
centroidtree.Thedistancebetweentwostructuresisthenobtainedbytheminimumcostof
editingoperations.
For the structure analysis of long RNAs, even the prediction of pseudoknot-free
structuresisinfeasiblebecauseofthecomputationaltimeandprecisionproblem.Computa-
tion of local structuresinstead ofglobal structures isa solution to accelerate DP computa-
tion.Rfoldisamodelinwhichamaximumconstraintissetforthebasepairdistanceinorder
to analyze the local structure stability of RNA [36]. The model can be applied for the
computationofavarietyofstructuremetrics:stemprobability,accessibility,andeachloop-
type probability. However, the problems of over- and underflow as well as computational
timeexistforlongRNAsincludingmRNAsandpre-mRNAs.ParasoRisanalgorithmbased
ontheRfoldmodel,anditsDPalgorithmismodifiedanddistributedtomultiplecomputa-
tional nodes for a local structure analysis [9]. Similar to global structure prediction, it can
compute a variety of structure scores for all possible structures under the constraint of a
maximumspanforbasepairs.ThisplatformisalsoappliedtoanefficientsimulationofRNA
secondary structures, for example, a dynamic conformational change caused by a single
point mutation. Radiam has been developed to detect mutations that can disrupt a large
partofasecondarystructure,calledriboSNitches[37],evenwithinlongRNAs.Tofurther
improvethecomputationofglobalstructurepredictionbasedonaDPalgorithm,Linear-
Fold accelerates MFE structure prediction using beam search, which ignores only the
low-probability results to avoid a substantial decrease in prediction accuracy [38]. The
acceleration depends on the beam size that defines the stack size of the partial structures
to be considered for the next DP computation. The computational complexity of Linear-
FoldMFEstructurepredictionisO(Nblogb),whereNisthesequencelengthandbisthe
user-definedbeamsize. Thisstrategycan alsobeappliedto RNA–RNAinteractionpredic-
tionasimplementedinLinearCofold,whichisintroducedinthisseries.
As such, a wide variety of RNA secondary structure prediction tools have been devel-
opedintermsoftheirpossiblestructures,metricstoevaluatethestructures,orapproaches
to extract representative structures. Several platforms have been developed for structure
analysis using multiple tools simultaneously, including ViennaRNA [39], Freiburg RNA
Tools [40], and Rtools [5]. Rtools is a web server that can analyze a query sequence with
eight different applications for RNA secondary structure analysis. CentroidFold and Cen-
troidHomfoldpredicttherepresentativestructureforthequeryaccordingtotheγ-centroid
estimators. RintD and RintW are tools to visualize the distribution of the secondary
structuresovertheHammingdistancefromthereferencestructures,indicatingthestability
ofthereferencestructuresdespitethermodynamicfluctuation.Someotherworkbenchesfor
RNA-seqanalysisalsoprovidetoolsforRNAsecondarystructureanalysis,andthesecanbe
usedfor thequickanalysisoftargettranscriptsaswellasncRNAs[41].
While existing structure prediction models can achieve accurate prediction in general,
theaccuracyofstructurepredictionmayoccasionallybedecreasedforcertainRNAs,suchas
long RNAs or RNAs in vivo. Previous studies have attempted to improve models and
parameters through machine-learning approaches. The classical thermodynamic models
contain several thousands of parameters, for example, with 7850 parameters used in the
fullTurnermodel[42].Optimizingthosemodelswithalargenumberofparametersposesa
riskofoverfitting.MXfoldisamethodtotrainmodelparametersforthefreeenergychange
approximation based on a structured support vector machine [43]. Combining with L1
regularization, MXfold has been shown to produce the best prediction accuracy while
Preface ix
avoidingoverfitting.OtherthanthestructureofsingleRNAs,thepredictionofRNA–RNA
interactions has been actively studied because those interactions are tightly related to the
functionofncRNAs,suchasmiRNAs,siRNAs,andlongncRNAs.Whilethereissubstantial
spacetoexploreforpotentialbindingregionsgenome-wide,RIblastandRIsearch2applya
seed-and-extend-basedalignmentstrategytospeedupandimprovethediscoveryofhighly
complementary regions that can form a stable structure with the queried RNA [44]. By
changingthesettingfortheseedsearchsteptouseafastcomputationlibrary,itenablesthe
efficientdiscoveryofthecandidateregionsthatcanformstablestructureswithbasepairs.As
anintroductionofvariousRNA-RNAinteractionpredictions,Fukunagaetal.haveprovided
acomprehensivesurveyonthepredictionwebservicesincludingtheirLncRRIsearch[45].
ApplicationofRNASecondaryStructurePrediction
Thanksto highlyaccuratestructureprediction,the comparisonofpredictedstructurescan
be further applied to the functional analysis of RNAs. In particular, the comparison of
predicted structure stability with experimentally determined accessibility has the potential
torevealtheexistenceoftheexternalfactorsthatcausestructurealterationincludingRNA
bindingproteinsorbasemodification[46].WhileRNAsecondarystructurecanbeexperi-
mentally determined by several approaches (e.g., X-ray crystal structure analysis, cryo-
electron microscopy, and NMR), they require the appropriate concentrations of a single
RNAandsufferfromproblemsoffeasibilityandthroughputlimitations.Ahigh-throughput
structure probing method is an approach that can overcome the throughput and coverage
problems of existing conformational analysis methods. By using a high-throughput
sequencing technique, this method detects RNA modification at reactive sites. Takizawa
has introduced a means of inferring the reactivity of each base from high-throughput
structure probing data using the computational methods PROBer [47], BUMHMM
[48], and reactIDR [13]. In Chap. 13, the author applied these pipelines to discover the
structuralconstraintsontheRNAgenomeofinfluenzavirus[14].
Similarly, the combination of RNA binding protein (RBP) pulldown and high-
throughputRNAsequenceanalysishasbeenwidelyappliedattranscriptome-widetoreveal
the mechanism of RBP and (m)RNA. However, this strategy is susceptible to biased back-
grounds and false positives derived from the pulldown assay step, even when UV cross
linking is included, as is used in CLIP-seq and its alternatives [49]. For the accurate
inference of sequential and structural RBP binding motifs, an artificial library of random
short RNAs is utilized in SELEX [50] and RNAcompete [51], enabling an efficient motif
analysis with high coverage. These methods solve the practical problem of capturing the
desiredaptamerswithabindingaffinitythatishighenoughforthetargetRBPamongapool
ofrandomRNAs.ResidualBind,introducedinthisseries,isadeeplearningframeworkfor
inferring RBP binding motifs from experimental RBP binding data [52]. The outstanding
characteristic of ResidualBind is that it can perform a global importance analysis for the
existenceofmotifstoimprovethemodelinterpretabilityoftheirdeeplearningmodel.
The functional domains of RNAs, particularly of ncRNAs, have been discovered by
examiningtheconservationofnotonlysequencesbutalsosecondarystructuresrequiredto
interact with other molecules to perform biological roles. One example of the potential
conservation signature is a pattern found in RNA structure-aware alignment [53]. Specifi-
cally,itisdefinedasaco-occurrenceoftwomutationsatpairedbasesthatdoesnotdisrupt
theirpairing[54].WalterCostaetal.(2019)developedanovelapproach,calledSSS-test,to
evaluate the significance of positive and negative selection on RNA structures based on
