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B IOCHEM ISTRY

1Department of Biochemistry Stanford University School of Medicine Stanford CA94305 USA 2Biophysics Program Stanford University Stanford CA 94305 USA3Department of Chemistry and Biochemistry Biomolecular Science and Engineer-ing Program University of California at Santa Barbara Santa Barbara CA 93106USA 4Department of Physics Stanford University Stanford CA 94305 USAPresent address RNA Biology Laboratory Center for Cancer Research NationalCancer Institute Frederick MD 21702 USAdaggerCorresponding author Email rhijustanfordedu

Watkins et al Sci Adv 20184 eaar5316 25 May 2018

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Blind prediction of noncanonical RNA structureat atomic accuracyAndrew M Watkins1 Caleb Geniesse12 Wipapat Kladwang1 Paul Zakrevsky3Luc Jaeger3 Rhiju Das124dagger

Prediction of RNA structure from nucleotide sequence remains an unsolved grand challenge of biochemistry andrequires distinct concepts from protein structure prediction Despite extensive algorithmic development in recentyears modeling of noncanonical base pairs of new RNA structural motifs has not been achieved in blind challengesWe report a stepwiseMonte Carlo (SWM)methodwith a unique add-and-deletemove set that enables predictions ofnoncanonical base pairs of complex RNA structures A benchmark of 82 diverse motifs establishes the methodrsquosgeneral ability to recover noncanonical pairs ab initio including multistrand motifs that have been refractory toprior approaches In a blind challenge SWM models predicted nucleotide-resolution chemical mapping and com-pensatory mutagenesis experiments for three in vitro selected tetraloopreceptors with previously unsolvedstructures (C72 C710 and R1) As a final test SWM blindly and correctly predicted all noncanonical pairs of a Zikavirus double pseudoknot during a recent community-wide RNA-Puzzle Stepwise structure formation as encoded inthe SWMmethod enables modeling of noncanonical RNA structure in a variety of previously intractable problems

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INTRODUCTIONSignificant success in proteinmodeling has been achieved by assumingthat the native conformations of a macromolecule have the lowest freeenergy and that the free energy function can be approximated by a sumof hydrogen bonding van derWaals electrostatic and solvation termsthat extend over angstrom-scale distances Computational methodsthat subject large pools of low-resolutionproteinmodels to an all-atomMonte Carlominimization guided by these free energy functions haveachieved nearndashatomic accuracy predictions in the CASP (Critical As-sessment of Structure Prediction) community-wide blind trials (1)When adapted to RNA structure modeling analogous methods haveconsistently achieved nucleotide resolution in the RNA-Puzzle blindtrials but have not yet reached atomic accuracy aside from previouslysolved motifs that happen to recur in new targets (2) A disappointingtheme in recent RNA-Puzzle assessments is that the rate of accurateprediction of noncanonical base pairs is typically 20 or lower evenfor models with correct global folds (2) Without recovery of thesenoncanonical pairs RNA computational modeling will not be ableto explain evolutionary data predict molecular partners or be pro-spectively tested by compensatory mutagenesis for the myriadbiological RNAs that are being discovered at an accelerating pace

The lag between the protein and RNAmodeling fields is partly ex-plained by differences in how protein and RNA molecules fold Pro-tein structures are largely defined by how a helices and b sheets packtogether As abundant data exist on these regular protein elements andtheir side-chain interactions proteinmodels with reasonable accuracycan often be assembled from fragments of previously solved structuresLess regular loops interconnecting a and b elements are less criticalfor defining protein folds Those loops are typically not recovered athigh accuracy even in the most exceptional blind predictions (3ndash5)

By contrast predictable and the geometrically regular elements ofRNA folding are Watson-Crick helices that sequester their sidechains and therefore cannot be positioned by direct side-chain inter-actions Instead the RNA loops interconnecting those helices formintricate noncanonical base pairs that define an RNArsquos global helixarrangement The RNA structure prediction problemmore so than theprotein problem depends on discovering these irregular loop confor-mations and their associated noncanonical base pairs ab initio Un-fortunately discovering the lowest free energy conformations of newnoncanonical loop motifs has not generally been tractable becauseof the vast number of deep local minima in the all-atom folding freeenergy landscape of even the smallest such motifs Essentially allthree-dimensional (3D) RNA modeling methods including MC-SymMC-Fold Rosetta FARFAR iFoldRNA SimRNA and Vfold3D usecoarse-grained modeling stages that allow for smoother conforma-tional search but generally return conformations too inaccurate to be re-fined to atomic accuracy by Monte Carlo minimization or moleculardynamics refinement (6ndash10)

To address this challenge we have developed Rosettamethods thatattempt to remove barriers in conformational search through the ad-dition of residues one at a time rather than through low-resolutioncoarse-graining or through small perturbations to fully built conforma-tions We previously described how step-by-step buildup of an RNAstructure enforcing low-energy conformations for each added nucleo-tide could lead to atomic accuracy models of irregular single-strandedRNA loops (11) The calculation instantiated in the Rosetta modelingframework involved a deterministic enumeration over buildup pathsanalogous to classic dynamic programming methods developed for ca-nonical RNA secondary structure prediction (11 12) This enumerativestepwise assembly (SWA)method guaranteed a unique solution for thefinal conformational ensemble but necessitated large expenditures ofcomputational power For example calculations for even small loopsof 5 to 7 nucleotides (nt) required tens of thousands of CPU (centralprocessing unit) hours (11) junctions involving multiple interactingstrands would further increase computational cost to many millionsof CPU hours which is currently prohibitive

In the hope of reducing this computational expense we hypothe-sized that the stepwise addition moves developed for SWAmight still

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be effective at producing high-accuracy models if implemented aspart of a stochastic sampling scheme rather than deterministic enu-meration To test this hypothesis we have developed stepwiseMonteCarlo (SWM) a Monte Carlo optimization method whose primarymoves are the stepwise addition moves of SWA Here we report thatSWMenables significant increases in the computational speed of ab initiostructure prediction and describe applications of SWM to previously in-tractable noncanonical RNA structures Tests of SWM include strin-gent blind evaluation through prospective experimental tests and anRNA-Puzzle community-wide structure prediction challenge

RESULTSEfficient implementation of SWMFigure 1 illustrates the SWMprocedure which has been implementedin the Rosetta framework (13) and is also freely available through anonline ROSIE (Rosetta Online Server that Includes Everyone) server

Watkins et al Sci Adv 20184 eaar5316 25 May 2018

(see Materials and Methods) (14) In realistic 3D RNAmodeling pro-blems RNAhelices are typically known a priori from secondary struc-ture predictionmethods Themain goal is therefore to infer lowest freeenergy conformations of loops that connect these helices such as thefour nucleotides GCAA closing a hairpin (Fig 1A) or two strandseach with a single guanosine in the GG mismatch motif (Fig 1B)Our previous work (11 15 16) introduced stepwise addition movesthat allow building of these nucleotides one at a time starting fromconformations with helices only (Start Fig 1 A and B) Conceptuallyeach addition was proposed to simulate the stepwise formation ofwell-defined structure from ldquorandom coilrdquondashlike ensembles (dottedlines Fig 1 A and B)

Here we stochastically carry out these addition moves choosingrandom positions on which to prepend or append new nucleotides(Add Fig 1 A and B) rather than enumerating these additions at allpossible positions [as was implemented previously (11 15)] Thesestochastic moves are accepted if they lower the computed free energy

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Fig 1 SWM efficiently searches the complex energy landscapes of noncanonical RNA loops (A and B) SWM trajectories solve a GCAA tetraloop [Protein Data Bank(PDB) ID 1ZIH) (A) and a two-strand GG-mismatch two-way junction (1F5G) (B) in 10moves or less (left) Final structures achieve low free energies and sub-angstrom RMSDaccuracies numerous such structures appear in simulations involving 100 models (right-hand panels) (C) Significantly reduced CPU time is required for convergence ofSWM compared to enumeration by SWA (11) except for loops drawn from the 23S ribosomal RNA (rRNA) (red) (D to F) SWMmodels for J23 (D) from group II intron (3G78)modeled with the energy function previously used for SWA and 23S rRNA loop (1S72) (E) and L2 loop (F) of viral pseudoknot (1L2X) both modeled with updated Rosettafree energy function illustrate sub-angstrom recovery of irregular single-stranded loops excised from crystal structures

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of the model or if the free energy increment is lower than a thermalfluctuation energy as set by the Metropolis criterion (17) To main-tain detailed balance in theMonte Carlo scheme the moves intermixthese additions with deletions of single residues again chosen ran-domly and accepted on the basis of the Metropolis criterion (DeleteFig 1A) These deletion moves simulate the transient unstructuringof nucleotides at the edges of loops To allow buildup of multistrandmotifs we developedmoves tomerge and split independent regions ofRNA such as regions associated with the different helices of multi-helix junctions (Merge Fig 1B) Last we allowed resampling of ran-domly chosen internal degrees of freedom maintaining chain closurewith robotics-inspired kinematic closure algorithms (Resample Fig 1A)(18 19) These resampling moves could not be incorporated into theprevious enumerative SWA because of the large number of increasedmodeling pathways that would need to be enumerated

Before testing SWM it was unclear whether a stochastic searchmight allow for efficient ab initio recovery of RNA loop conforma-tions In our previous work on enumerative SWA we posited thatldquoan inability to guarantee exhaustive conformational sampling hasprecluded the consistent prediction of biomolecular structure at highresolutionrdquo (11) Nevertheless in our test cases SWM did achieve effi-cient search over the free energy landscape despite the lack of a guar-antee of exhaustive conformational sampling Figure 1 (A and B)illustrates the recovery of the sub-angstrom accuracy conformationsof theGCAA tetraloop andGGmismatchmotifs using less than 3 hoursof computation on a singlemodern laptop computer to create 100modelsFurthermore these runs were ldquoconvergentrdquo Different simulationsindependently achieved the same low-energy configurations repeat-edly (numerous models within 2 Aring of experimental structures rightpanels in Fig 1 A andB) suggesting highly efficient sampling For com-parison modeling of these small loops by SWA enumeration re-quired use of many thousands of CPU hours due to the requirementof enumerating multiple loop conformations over multiple builduppathways

Ab initio recovery of complex single-stranded RNA loopsAfter preliminary tests on simple loops we carried out SWMmodelingon a set of 15 single-strandedRNA loops excised fromcrystal structurespreviously used to benchmark the enumerative SWA method (11)These loops were specifically chosen because of their irregularity theyeach harbor nonndashA-form backbone conformations form noncanonicalpairs with surrounding residues and span different helices in functionalRNAs We confirmed that for nearly all these trans-helix cases SWMproduces conformations that give computed free energies and accura-cies as low as those achieved by SWA [median energy gap and rootmean squared deviation (RMSD) values table S1 and Fig 1 C and D]In many cases the computational cost for achieving convergent andaccurate modeling was reduced by up to two orders of magnitude (seeSupplementaryMethods and Fig 1C) Exceptions to this speed increasewere loops that needed to be rebuilt into the 23S ribosomal RNA(rRNA) (red points Fig 1C) which featured a particularly large num-ber of surrounding nucleotides and concomitantly many viable inter-acting conformations This observation suggested that SWMwould beparticularly efficient for ab initiomodeling ofmotifs that primarily formnoncanonical interactions within the motif as is typically the case forRNA junctions and tertiary contacts (see below) but not for the longestribosomal loops Furthermore through its increased speed SWMallowed us to confirm that recent updates to the Rosetta free energyfunction (20) and estimation of conformational entropy of unstructured

Watkins et al Sci Adv 20184 eaar5316 25 May 2018

segments generally improved modeling accuracy for single-strandedRNA loops (tables S1 and S2) The improvements included rescue ofsome 23S rRNA loops (Fig 1E) and solution of a loop from a beet west-ern yellow virus frameshifting pseudoknot that was previously not solv-able by SWA (Fig 1F and table S3) (11) Supplementary Text provides amore detailed description of energy function updates and results on thistrans-helix loop benchmark

Ab initio recovery across complex noncanonical motifsTo more broadly evaluate SWM we expanded the 15 single-strandedloop benchmark to a larger set of 82 complex multistranded RNAmo-tifs that we encountered in previous RNA-Puzzles and other modelingchallenges (table S3 and fig S1) Because of the efficiency of SWMmodeling we could test a benchmark that was nearly three times largerthan ourmost extensive previous efforts (8)Over the entire benchmarkSWM achieved a mean and median RMSD accuracy (over the top fivecluster centers) of 215 and 149 Aring and mean and median recovery ofnonndashWatson-Crick pairs of 76 and 96 respectively (Table 1 table S3and fig S2) We observed numerous cases in which the SWM modeland experimental structure were nearly indistinguishable by eye(Fig 2) Examples included two-strandedmotifs that required ordersof magnitude higher computational expense with the prior enumer-ative SWA method (16) such as the most conserved domain of thesignal recognition particle (126 Aring RMSD five of five noncanonicalpairs recovered Fig 2A) and the first RNA-Puzzle challenge a humanthymidylate synthetase mRNA segment (096 Aring one noncanonicalpair and one extrahelical bulge recovered Fig 2B) (2) For several testcases there was experimental evidence that formation of stereotypedatomic structures required flanking helices to be positioned by thebroader tertiary context If the immediately flanking helix contextwas provided the median RMSD accuracy and nonndashWatson-Crickbase pair recovery in these cases were excellent (119 Aring and 100Table 1 fig S2 and table S3) as illustrated by the J55a hinge fromthe P4-P6 domain of theTetrahymena group I intron (055 Aring RMSDall four noncanonical pairs and all three extrahelical bulges recov-ered Fig 2C) (21)

Perhaps the most striking models were recovered for multi-helixjunctions and tertiary contacts whichhave largely eludedRNAmodel-ing efforts seeking high resolution (6 8) SWM achieves high accuracymodels for the P2-P3-P6 three-way junction from the Varkud satelliteribozyme previously missed by all modelers in the RNA-Puzzle 7challenge (113 Aring RMSD three of three noncanonical pairs recoveredFig 2D) a highly irregular tertiary contact in a hammerhead ribozyme(116 Aring RMSD two of three noncanonical pairs and one extrahelicalbulge recovered Fig 2E) a complex between a GAAA tetraloop andits 11-nt receptor (064 Aring RMSD all four noncanonical pairs recov-ered when flanking helix context was provided Fig 2F) and thetRNAphe T-loop a loop-loop tertiary contact stabilized by chemicalmodifications at 5-methyluridine pseudouridine and N1-methyl-adenosine (133 Aring accuracy when flanking context was provided Fig2G)Motifs without any flankingA-formhelices offered particularly strin-gent tests for ab initiomodeling and could also be recovered at high accu-racy by SWM as illustrated by the inosine tetradndashcontaining quadruplex(287 Aring RMSD overall 046 Aring RMSD if the terminal uracils which makecrystal contacts are excluded Fig 2H) For comparison we also carriedout modeling with Fragment Assembly of RNA with Full Atom Refine-ment (FARFAR)on these 82motifs taking care to removepossible homo-logs from the methodrsquos fragment library to mimic a realistic ab initioprediction scenario (we could not carry out fair comparisons to other

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methods due to the unavailability of similar homolog exclusion optionsin those methods Supplementary Methods) SWM strongly outper-formed these FARFAR models in terms of recovery of noncanonicalpairs (P lt 5 times 10minus5) and RMSD accuracy (P lt 2 times 10minus4) (P values arebased onWilcoxon ranked-pairs test n = 82 fig S3 Table 1 and tablesS3 and S4)

In some benchmark cases SWMdid not exhibit nearndashatomic accu-racy recovery and illuminated challenges remaining for computationalRNAmodeling While a few discrepancies between SWMmodels andx-ray structures could be explained by crystallographic interactions(for example edge nucleotides making crystal contacts Fig 3H) mostproblems were better explained by errors in the energy function For9 of the 14 cases in which the SWMmodeling RMSDwas worse than30Aring (and thus definitively not achieving atomic accuracy) the energyof the lowest free energy SWM model was lower than that of the op-timized experimental structure often by several units of free energy[calibrated here to correspond to kBT (20) table S3] One clue forthe source of this issue came from cases where the fragment-basedmethod (FARFAR) outperformed SWM if assessed by RMSD butnot by the fraction of base pairs recovered (Table 1) The existenceof these FARFAR models with native-like backbones but incorrectbase pairs suggested that conformational preferences implicitly en-coded in database fragments in FARFAR might need to be bettercaptured during SWM One possible route to improving SWMmight be to update the RNA torsional potential of the Rosetta freeenergy function which currently does not model correlations acrossmost backbone torsions Results on the hepatitis C virus internal ribo-some entry site the sarcin-ricin loop and other test cases suggest thata modified torsional potential as well as inclusion of metal ions mayeventually address these residual problems (fig S4)

Watkins et al Sci Adv 20184 eaar5316 25 May 2018

Stringent tests of SWM models for new RNA-RNA tertiarycontact motifsAs we began to see significant improvements of modeling accuracy inthe 82-motif benchmark we hypothesized that SWMmight be able topredict noncanonical base pairs in motifs that have been refractory tonuclear magnetic resonance and crystallographic analysis Success inthe 11-nt tetraloopreceptor benchmark test case (Fig 2F) a classicmodel system and ubiquitous tertiary contact in natural RNAs en-couraged us to model alternative tetraloopreceptor complexes selectedfor use inRNAengineeringWe applied SWMto these complexes whosestructures have not yet been solved experimentally (2 22) and we de-signed stringent experimental tests to validate or falsify thesemodels

A detailed sequencefunction analysis previously suggested similari-ties between the GAAAC72 GAAAC710 and GGAAR(1) interac-tions discovered through in vitro evolution (22) and the classic GAAA11-nt receptor which has been crystallized in numerous contexts It hasnot been clear however whether this similarity holds at the structurallevel due to the unavailability of high-resolution structures of the threeartificial tetraloopreceptors For example prior literature analysesconflicted in the proposal of which C72 receptor nucleotides if anymight form a ldquoplatformrdquo (lime Fig 3A) analogous to A4-A5 platformin the 11-nt receptor [G4 and A6 with an intervening bulge in thestudies of Sripakdeevong et al (11) and Costa and Michel (23)and G4 andU5 in the study of Geary et al (22)] Similarly a proposedhomology of C9 in R(1) to A8 in the 11-nt receptor (22) has not beentested by structure modeling or experiments

We carried out SWM modeling to explore possible structuralhomologies of these four receptors In the SWM runs the stem andbasal G-A sugar-Hoogsteen pair of the GNRA tetraloop and theirdocking site into the GGCC stem of the receptor were seeded on

Table 1 Benchmark of SWM compared to previous Rosetta FARFAR over different classes of RNA structure motifs

Category

Motif properties

Best of five cluster centers

RMSD (Aring)

FNWCdagger

No of motifs

Length

Strands

SWM

FARFAR

SWM

FARFAR

Single helix or multiple helices with crystallographic context provided

Trans-helix loop

15

6

1

083

329

100

077

Apical loop

4

45

1

114

296

100

100

Two-way junction

14

75

2

074

115

100

100

Multi-helix junction

5

11

3

191

193

080

033

Tertiary contact

10

85

2

125

178

083

050

Multiple helices without crystallographic context provided

Two-way junction

15

7

2

159

140

100

055

Multi-helix junction

5

10

3

260

345

040

020

Tertiary contact

8

85

2

289

213

036

020

Non-helix embedded

5

10

4

281

430

080

071

Overall

82

7

2

149

193

096

067

Median values reported Mean values given in tables S3 and S4 daggerFraction of nonndashWatson-Crick pairs from experimental structure observed incomputational model

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Fig 2 SWM recovers noncanonical base pairs ab initio for complex RNA motifs From left to right in each panel 2D diagram with problem definition 2D diagramwith experimental noncanonical base pairs experimental 3D model SWM 3D model and 3D overlay (experimental marine SWM model salmon) (A to H) Motifs are (A)most conserved domain of human signal-recognition particle (PDB ID 1LNT) (B) noncanonical junction from human thymidylate synthase regulatory motif RNA-Puzzle1 (PDB ID 3MEI) (C) irregular J55a hinge from the P4-P6 domain of the Tetrahymena group I self-splicing intron (PDB ID 2R8S) (D) P2-P3-P6 three-way A-minor junctionfrom the Varkud satellite nucleolytic ribozyme RNA-Puzzle 7 (PDB ID 4R4V) (E) tertiary contact stabilizing the Schistosoma hammerhead nucleolytic ribozyme (PDB ID2OEU) (F) tetraloopreceptor tertiary contact from the P4-P6 domain of the Tetrahymena group I self-splicing intron (PDB ID 2R8S) (G) T-looppurine interaction from yeasttRNAphe involving three chemically modified nucleotides (PDB ID 1EHZ) and (H) RNA quadruplex including an inosine tetrad (PDB ID 2GRB) Colors indicate accuratelyrecovered noncanonical features (pastel colors) accurately recovered extrahelical bulges (wheat with white side chains) flanking helices built de novo (violet) parts ofexperimental structure used for modeling but allowed to minimize (dark violet) fixed context from experimental structure (black in 2D and white in 3D) and additionalhelical context not included in modeling (gray in 2D and white in 3D)

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Fig 3 SWM modeling and prospective experimental tests of previously unsolved tetraloopreceptor motifs (A) Ab initio SWM models for canonical 11-nttetraloopreceptor motif and alternative motifs discovered through in vitro selection that have resisted crystallization Lavender salmon lime and teal coloringshighlight homologous structural features During modeling the bottom flanking helix (white) was allowed to move relative to the top helices of the receptor andtetraloop (gray) which were held fixed (B) Canonical 11-nt tetraloop receptor module from the P4-P6 domain of the Tetrahymena group I self-splicing intron (PDB ID2R8S) In (A) and (B) red asterisks mark uracil residues predicted to be bulged (C) CMCT mapping of the receptors installed into the P4-P6 domain of the Tetrahymenaribozyme (tetraloop and receptor indicated by black boxes) supports the bulged uracils in the predicted models (black asterisks) (D) Selective tests of each R(1)receptor base pair by compensatory mutagenesis in tectoRNA dimer Rescue by double and triple mutants (black bars) was compared to energetic perturbations predictedbased on the sum of effects (white bars) of component mutations or more conservatively to the single mutants P lt 005 P lt 0001 and P lt 1 times 10minus6 (computed byStudentrsquos t test for difference of means) ns not significant (E) Overall 3D model of tectoRNA dimer with SWM model for R(1) receptor WT wild-type

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the basis of one crystal structure of theGAAA11-nt receptor [see con-siderations of A-minor geometries discussed byGeary et al (22)] Theremaining 10 nucleotides and receptor stem were modeled ab initioSWM modeling of all four of these receptors achieved convergencewith 8 of the top 10 models clustered within 2 Aring RMSD of each otherThe modeling recovered the known GAAA11-nt structure at 080 AringRMSD and reproduced a previous C72 model that involved SWAenumeration of only 3 nucleotides (G4-U5-A6) rather than rebuildingab initio the complete tetraloopreceptor interaction

SWM models for all four tetraloopreceptors exhibited not onlystriking structural homology to each other but also noncanonicalfeatures (extrahelical bulges and pairs) that were not anticipated fromprior manual modeling efforts (see Fig 3A Supplementary Text andmodels provided in the Supplementary Materials) Three featureswere preserved across loops First models for all receptors exhibiteda docking site for the second nucleotide of the tetraloop (salmonFig 3A) In GAAA11-nt GAAAC72 and GAAAC710 where thesecond tetraloop nucleotide is A the receptor docking site was pre-dicted to be an adenosine that is part of a Watson-CrickHoogsteenU-A pair In GGAAR(1) where the second tetraloop nucleotide is Gthe receptor docking site was predicted to be U3 part of a non-canonical Watson-Crick U3-U10 pair Second SWM models for allreceptors exhibited a platform involving two same-strand base-pairednucleotides that stack under the tetraloop (lime Fig 3A) The se-quence varies however between A-A in the 11-nt receptor G-U inthe C710 receptor G-A in the C72 receptor [supporting the modelsby Sripakdeevong et al (11) and Costa and Michel (23) but not themodel in Geary et al (22)] and G-U in the R(1) receptor In the R(1)receptor C9 was predicted by SWM to form a stabilizing C-G basepair with a platform nucleotide While C9 was previously proposedto be homologous to A8 in the 11-nt receptor based on mutagenesisdata indicating its importance (22) the new model also explains priorbinding data that implicated C9 as forming core interactions in R(1)Third all receptors show a noncanonical pair involving Watson-Crickedges needed to transition between the platform region and the lowerstem of the receptor (teal Fig 3A) The sequence is a G-A pair in R(1)and a GsdotU wobble in the others Overall given the sequence mappingbetween receptors revealed by the SWM models each noncanonicalpairing in the naturally occurring GAAA11-nt structure had a homologalbeit one that was difficult to predict (and in some cases differentlypredicted) in each of the three non-native tetraloop receptors

We tested these features using prospective experiments TheSWM models predicted different single uridines to be bulged outof each tetraloop receptor Reaction to CMCT [N-cyclohexyl-Nprime-(2-morpholinoethyl)carbodiimide tosylate] followed by reverse tran-scription allows singlendashnucleotide resolution mapping of unpaireduridines that bulge out of structure and expose their Watson-Crickedges to solution We therefore installed the tetraloopreceptors intothe P4-P6 domain of the Tetrahymena ribozyme (Fig 3B) which alsodisplays other bulged uridines that served as positive controls (aster-isks in Fig 3C) These experiments verified extrahelical bulging ofsingle-nucleotide uridines predicted by SWM at different positionsin the different receptors and disfavored prior manual models (seeFig 3C and Supplementary Text)

We carried out further prospective experiments to incisively testbase pairs newly predicted by SWM modeling In particular the R(1)receptor model included numerous unexpected noncanonical featuresespecially a base triple involving a newWatson-Crick singlet base pairG4-C9 and a dinucleotide platform at G4-U5 These features were

Watkins et al Sci Adv 20184 eaar5316 25 May 2018

stringently evaluated via compensatory mutagenesis Chemical mappingon the P4-P6 domain confirmed the G4-C9 base pair but was not sensi-tive enough to test other compensatory mutants (fig S5) We thereforecarried out native gel assembly measurements in a different system thetectoRNAdimerwhich enables precise energeticmeasurements spanning5 kcalmol (Fig 3 D and E) Observation of energetic disruption by in-dividual mutations and then rescue by compensatory mutants confirmedthe predicted interactions of G4-C9 the base triple G4-U5-C9 and non-canonical pairG6-A7 (Plt001 in all cases Fig 3D) aswell as other featuresof the model (see Supplementary Text and fig S6) Overall these exper-imental results falsified bulge predictions and base pairings previouslyguessed for these tetraloopreceptors (11 22 23) and strongly supportedthe models predicted by SWM Our structural inference and mutagene-sis-based validation of noncanonical pairs would have been intractablewithout the SWM-predicted models because of the large number of pos-sible mutant pair and triple combinations that would have to be tested

Blind prediction of all noncanonical pairs of acommunity-wide RNA-PuzzleThe community-wide modeling challenge RNA-Puzzle 18 providedan opportunity to further blindly test SWM and to compare it to bestefforts of other state-of-the-art algorithms (Fig 4) This problemwasof mixed difficulty On the one hand the 71-nt target sequence wasreadily identified via PDB-BLAST (Basic Local Alignment SearchTool) (24) to be a Zika virus RNA homologous to a molecule witha previously solved x-ray structure an Xrn1 endonuclease-resistant(xrRNA) fragment of Murray Valley Encephalitis virus (PDB ID4PQV) (25) However the crystallographic environment of the priorstructure disrupted a pseudoknot (between L3 and J14 Fig 4A)expected from sequence alignments so that nearly half of the priorstructure could not be trusted as a template for homology modelingIntermolecular crystal contacts produced an open single-strandedregion in the asymmetric unit where the pseudoknot was expectedand interleaved regions from separate molecules the scale of theseconformational perturbations was as large as the dimensions of themolecule itself (fig S7) Further complicating the modeling twoWat-son-Crick pairs within stem P3 changed to or fromGsdotUwobble pairsMoreover previous literature analysis (25) suggested extension of thishelix by two furtherWatson-Crick pairs (U29-A37 and U30-A36) al-beit without direct evidence fromphylogenetic covariation and in par-tial conflict with dimethyl sulfate (DMS) probing Ab initio modelingat a scale inaccessible to the prior enumerative SWAmethod was nec-essary for modeling the RNA and we therefore carried out SWM (seeFig 4B and Materials and Methods)

The lowest free energy SWM models for RNA-Puzzle 18 con-verged to a tight ensemble of intricate structures with one submittedSWMmodel shown in Fig 4C TheWatson-Crick pairs U29-A37 andU30-A36 predicted in the literature did not occur in the models In-stead several other features were consistently observed across theSWMmodels [colored in Fig 4 A (right) and C] coaxial arrangementof the pseudoknot helix (purple) on P3 (light violet) a noncanonicaltrans Watson-Crick base pair between A37 and U51 stacking underP1 (green) a UA-handle (26) formed by U29-A36 (turquoise) andlack of pairing by U30 A35 A52 and A53 (sand and orange) Thesefeatures were not uniformly presentmdashor not predicted at allmdashinmodels created by FARFAR or as it later turned out in modelssubmitted by other RNA-Puzzle participants (fig S8)

The subsequent release of the crystal structure (Fig 4 D and E)(27) confirmed all base pairs predicted by SWM modeling (100

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Fig 4 Blind prediction of a complex RNA tertiary fold during RNA-Puzzle 18 (A) Two-dimensional diagram of the RNA-Puzzle 18 (Zika xrRNA) modeling problemhighlighting motifs that needed to be built de novo in red (left) and SWM-predicted pairings (pastel colors right) WC Watson-Crick HG Hoogsteen (B) Structures discoveredby SWM (green) are lower in energy and ~4 Aring from models from conventional fragment assembly (FARFAR blue) note that x axis is RMSD to the lowest free energy SWMmodel not the experimental structure (unavailable at the time of modeling) (C and D) Magnified view of noncanonical region built de novo for SWM model submitted forRNA-Puzzle competition (C) and the subsequently released crystal structure (D) (E) and (F) give overlays in magnified and global views respectively (SWM salmon crystalmarine) (G) Fraction of noncanonical base pairs recovered and RMSD to native model obtained by Rosetta modeling (black larger and smaller symbols are SWM and FARFARrespectively) and other laboratories (gray) for RNA-Puzzle 18 Points recovering zero noncanonical pairs are given a small vertical perturbation to appear visually distinct

Watkins et al Sci Adv 20184 eaar5316 25 May 2018 8 of 12

SC I ENCE ADVANCES | R E S EARCH ART I C L E

nonndashWatson-Crick recovery) The only structural deviation involvedA53 (sand Fig 4C) which was predicted in SWM models to be un-paired and stacked on neighbor A52 (orange Fig 4C) In the crystalA53 was unpaired but bulged out of the core to form a contact with acrystallographic neighbor while a 16-hexanediol molecule from thecrystallization buffer took its place (white sticks Fig 4C) this arrange-ment was noted independently to be a likely crystallographic artifact(27) There is striking overall fold agreement (308 Aring RMSD and 190Aring over just themost difficult noncanonical region nucleotides 5 and 626 to 40 49 to 59 and 70 and 71 Fig 4 C andD)much better than the~10 Aring best-case agreement seen in previous RNA-Puzzles of compa-rable difficulty (2) Furthermore SWM accurately predicted all non-canonical base pairs (FNWC = 1 Fig 4G)While one blind model fromanother method achieved somewhat comparable RMSD to the crystalstructure (361Aring) it predicted only one of six nonndashWatson-Crick basepairs (Fig 4G) and left a ldquoholerdquo in the central noncanonical region(RMSD of 367 Aring in that region fig S8)

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DISCUSSIONWe have developed an algorithm for modeling RNA structures calledstepwiseMonte Carlo (SWM) which uniquely allows for the additionand deletion of residues during modeling guided by the Rosetta all-atom free energy function The minima of the energy landscape areefficiently traversed by this method allowing the ab initio recovery ofsmall RNA loop structures in hours of CPU time (Fig 1) On an exten-sive benchmark SWM enables quantitative recovery of noncanonicalpairs in cases that include prior RNA-Puzzle motifs junctions andtertiary contacts involving numerous strands and motifs without anyA-form helices (Fig 2 and Table 1) We applied SWM to modelstructures of three previously unsolved tetraloopreceptors and pro-spectively validated thesemodels through chemicalmapping and exten-sive compensatory mutagenesis (Fig 3) Last SWM achieved blindprediction of all noncanonical pairs of a recent RNA-Puzzle an intri-cately folded domain of the Zika RNA genome whose pairings weremissed by other methods applied by our group and by other modelinggroups (Fig 4) Themost striking aspect of the SWMmodels is the highrecovery of noncanonical pairs which have largely eluded previous al-gorithms when tested in blind challenges These results support stepwisenucleotide structure formation as a predictive algorithmic principle forhigh-resolution RNA structure modeling We expect SWM to be usefulin the ab initio modeling and if extended to sequence optimization thediscovery of novel motifs for RNA architectonic design (28 29)

The results above focused on solving individual noncanonical mo-tifsWhile these problems arise frequently in real-worldmodeling (forexample the unsolved tetraloop receptors) most functional RNAstructures harbor multiple junctions and tertiary contacts whose foldsbecome dependent on each other through the lever armndashlike effects ofinterconnecting helices SWM is currently too computationally expen-sive to simultaneously simulate all motifs and helices in these mole-cules It may be necessary to better parallelize the current algorithm toallow concomitant modeling of multiple motifs on multiprocessorcomputers as is routine inmolecular dynamics simulations (30) Alter-natively modeling may benefit from iterating back and forth betweenhigh-resolution SWM and complementary low-resolution modeling ap-proaches likeMC-SymMC-Fold Rosetta FARFAR iFoldRNA SimRNAand Vfold3D (6ndash10) similar to iterative approaches in modeling largeproteins (5) In addition we note that SWM relies heavily on the as-sumed free energy function for folding and several of our benchmark

Watkins et al Sci Adv 20184 eaar5316 25 May 2018

cases indicate that even the most recently updated Rosetta free energyfunction is still not accurate when SWM enables deep sampling There-fore a critical open question is whether residual free energy functionproblemsmight be corrected by improved RNA torsional potentials treat-ment of electrostatic effects or use of energy functions independentlydeveloped for biomolecular mechanics and refinement (5 30 31)

MATERIALS AND METHODSStepwise Monte CarloSWM was implemented in C++ in the Rosetta codebase The sourcecode and the stepwise executable compiled for different environmentsare beingmade available inRosetta release 36 and later releases free toacademic users at wwwrosettacommonsorg Full documentation in-cluding example command lines tutorial videos and demonstrationcode is available at wwwrosettacommonsorgdocslatestapplication_documentationstepwisestepwise_monte_carlostepwise

The full set of benchmark cases including the 82 central to thisworkis available at httpsgithubcomDasLabrna_benchmark The reposi-tory contains input files for each benchmark case scripts for setting upbenchmark runs using either SWM or fragment assembly includingautomated job submission for multiple cluster job schedulers andscripts for creating analysis figures and tables Finally SWM is avail-able through a web server on ROSIE at httprosierosettacommonsorgstepwise Supplementary Methods gives detailed descriptions of SWMSWA and fragment assembly ofRNAwith FARFARmodeling evaluationof RMSD and energetic sampling efficiency and PDB accession IDs forexperimental structures

Chemical mappingChemical mapping was carried out as in the study of Kladwang et al(32) Briefly DNA templates for the P4-P6 RNA were producedthrough polymerase chain reaction assembly of oligonucleotides oflength 60 nucleotides or smaller (IntegratedDNATechnologies) usingPhusion polymerase (Finnzymes) DNA templateswere designedwiththe T7 RNA polymerase promoter (5prime-TTCTAATACGACTCACTA-TA-3prime) at their 5prime ends A custom reverse transcription primer-binding site (5prime-AAAGAAACAACAACAACAAC-3prime) was includedat the 3prime terminus of each template RNA transcribed with T7 RNApolymerase (New England Biolabs) was purified using RNACleanXP beads (Beckman Coulter) RNA modification reactions were per-formed in 20-ml reactions containing 12 pmol of RNA RNAs wereincubated with 50 mMNa-Hepes (pH 80) at 90degC for 3 min and thencooled to room temperatureMgCl2 at 0 or 10mM final concentrationwas then added followed by incubation at 50degC for 30 min and thenroom temperature before chemical mapping Chemical probes wereused at the following final concentrations DMS (0125 vv) CMCTin water (26 mgml) and 1M7 (1-methyl-7-nitroisatoic anhydride)[105 mgml in anhydrous dimethyl sulfoxide (DMSO) with finalDMSO concentration of 25] Chemical probes were allowed to reactfor 15min before quenching 1M7andCMCTreactionswere quenchedwith 50ml of 05Msodium2-(N-morpholino)ethanesulfonate (Na-MES)(pH 60) while the DMS reaction was quenched with 30 ml of 3MNaCl50 ml of b-mercaptoethanol 15 ml of oligo-dT beads [poly(A)purist Am-bion] and 025 ml of a 025 mM 5prime-FAM-A20-Tail2 primer whichcomplements the reverse transcription primer-binding site at theRNA 3prime ends The quench mixture was incubated at room temperaturefor 15 min and the purification beads were pulled down with a 96 postmagnetic stand and washed with 100 ml of 70 ethanol twice for RNA

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purification RNAs were reverse-transcribed with SuperScript III re-verse transcriptase at 48degC for 40 min (Life Technologies) RNAtemplate was subsequently hydrolyzed for 3 min at 90degC in 02 MNaOH After pH neutralization complementary DNA (cDNA) onoligo-dT beads was pulled down by magnetic stand and washed withethanol as above cDNAs were eluted into 10 ml of ROX 350 standardladder in Hi-Di Formamide (Life Technologies) using 1 ml of ROX350 in 250 ml of Hi-Di Formamide ABI 3700 sequencers were usedfor electrophoresis of cDNA Capillary electrophoresis data werequantitated with HiTRACE (33) Data from these P4-P6 RNA experi-ments have been posted to the RNA Mapping Database (34) at thefollowing accession IDs

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Native gel shift experimentsGel shifts were performed as previously described (22) Briefly equi-molar amounts of each RNAmonomer at various concentrations (upto 20 mM final concentration) were mixed in water and denatured at95degC for 1 min Mixtures were cooled on ice for 2 min and annealed at30degC for 5 min before the addition of Mg2+ buffer [9 mM tris-borate(pH 83) and 15 mM Mg(OAc)2 final concentration] After 30-minincubation at 30degC samples were incubated at 10degC for 15 min beforenative gel analysis [7 (291) polyacrylamide gels in Mg2+ buffer at10degC] One of the monomers contained a fixed amount of 3prime end [32P]pCp-labeled RNA (~025 to 05 nM final concentration) Monomerand dimer bands were quantifiedwith ImageQuant and dimer forma-tion was plotted against RNA concentration Kdrsquos (dissociation con-stant) were determined as the concentration at which half of theRNA molecules were dimerized and converted to DG (relative to1 M standard state) through the formula DG = kBT ln(Kd1 M) wherekB is the Boltzmann constant and T is the temperature

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at httpadvancessciencemagorgcgicontentfull45eaar5316DC1Supplementary TextSupplementary Methodsfig S1 Illustrated descriptions and modeling constraints of all 82 benchmark test casesfig S2 Rosetta free energy versus RMSD summaries of SWM modeling runs for 82 complexRNA motifsfig S3 Comparison of model accuracy between SWM and fragment assembly of RNA withFARFAR over an 82 motif benchmarkfig S4 Potential routes to overcome limitations in Rosetta free energy functionfig S5 Compensatory mutagenesis of the R(1) receptor read out through chemical mappingfig S6 Comprehensive single mutant analysis of the tetraloop receptor R(1)fig S7 Global fold changes between the template viral xrRNA and the Zika xrRNA structureprediction challengefig S8 Other models of RNA-Puzzle 18 (Zika xrRNA)table S1 A comparison of the SWA and SWM methods using the same energy function as theoriginal SWA benchmark set of trans-helix single-stranded loops and SWM results using theupdated Rosetta free energy function (SWM)table S2 Updates to the Rosetta energy function

Watkins et al Sci Adv 20184 eaar5316 25 May 2018

table S3 Detailed performance of the stepwise Monte Carlo algorithm on 82 benchmark casestable S4 Detailed performance of the FARFAR algorithm on 82 benchmark casestable S5 Measurements of interaction free energy between R(1) mutant tetraloop receptorsand GGAA tetraloopdata file S1 Three-dimensional SWM models canonical 11-ntGAAA R(1)GGAA C72GAAAand C710GAAA tetraloopreceptors in PDB formatReferences (35ndash87)

REFERENCES AND NOTES1 P Bradley K M S Misura D Baker Toward high-resolution de novo structure prediction

for small proteins Science 309 1868ndash1871 (2005)2 Z Miao R W Adamiak M Antczak R T Batey A J Becka M Biesiada M J Boniecki

J M Bujnicki S-J Chen C Y Cheng F-C Chou A R Ferreacute-DrsquoAmareacute R Das W K DawsonF Ding N V Dokholyan S Dunin-Horkawicz C Geniesse K Kappel W KladwangA Krokhotin G E Łach F Major T H Mann M Magnus K Pachulska-WieczorekD J Patel J A Piccirilli M Popenda K J Purzycka A Ren G M Rice J Santalucia JrJ Sarzynska M Szachniuk A Tandon J J Trausch S Tian J Wang K M WeeksB Williams II Y Xiao X Xu D Zhang T Zok E Westhof RNA-Puzzles Round III 3D RNAstructure prediction of five riboswitches and one ribozyme RNA 23 655ndash672 (2017)

3 P-S Huang K Feldmeier F Parmeggiani D A F Velasco B Houmlcker D Baker De novodesign of a four-fold symmetric TIM-barrel protein with atomic-level accuracy Nat ChemBiol 12 29ndash34 (2016)

4 S Ovchinnikov D E Kim R Y-R Wang Y Liu F DiMaio D Baker Improved de novostructure prediction in CASP11 by incorporating coevolution information into RosettaProteins 84 (suppl 1) 67ndash75 (2016)

5 S Ovchinnikov H Park D E Kim F DiMaio D Baker Protein structure prediction usingRosetta in CASP12 Proteins 86 (suppl 1) 113ndash121 (2018)

6 M Parisien F Major The MC-Fold and MC-Sym pipeline infers RNA structure fromsequence data Nature 452 51ndash55 (2008)

7 A Krokhotin K Houlihan N V Dokholyan iFoldRNA v2 Folding RNA with constraintsBioinformatics 31 2891ndash2893 (2015)

8 R Das J Karanicolas D Baker Atomic accuracy in predicting and designingnoncanonical RNA structure Nat Methods 7 291ndash294 (2010)

9 C Zhao X Xu S-J Chen Predicting RNA structure with Vfold Methods Mol Biol 16543ndash15 (2017)

10 M J Boniecki G Lach W K Dawson K Tomala P Lukasz T Soltysinski K M RotherJ M Bujnicki SimRNA A coarse-grained method for RNA folding simulations and3D structure prediction Nucleic Acids Res 44 e63 (2016)

11 P Sripakdeevong W Kladwang R Das An enumerative stepwise ansatz enablesatomic-accuracy RNA loop modeling Proc Natl Acad Sci USA 108 20573ndash20578(2011)

12 S R Eddy How do RNA folding algorithms work Nat Biotechnol 22 1457ndash1458 (2004)13 R Das D Baker Macromolecular modeling with Rosetta Annu Rev Biochem 77 363ndash382

(2008)14 R Moretti S Lyskov R Das J Meiler J J Gray Web-accessible molecular modeling with

Rosetta The Rosetta Online Server that Includes Everyone (ROSIE) Protein Sci 27259ndash268 (2018)

15 R Das Four small puzzles that Rosetta doesnrsquot solve PLOS ONE 6 e20044 (2011)16 P Sripakdeevong M Cevec A T Chang M C Erat M Ziegeler Q Zhao G E Fox X Gao

S D Kennedy R Kierzek E P Nikonowicz H Schwalbe R K O Sigel D H TurnerR Das Structure determination of noncanonical RNA motifs guided by 1H NMR chemicalshifts Nat Methods 11 413ndash416 (2014)

17 J Ferkinghoff-Borg in Bayesian Methods in Structural Bioinformatics T HamelryckK Mardia J Ferkinghoff-Borg Eds (Springer Berlin Heidelberg 2012) pp 49ndash93

18 D J Mandell E A Coutsias T Kortemme Sub-angstrom accuracy in protein loopreconstruction by robotics-inspired conformational sampling Nat Methods 6 551ndash552(2009)

19 F-C Chou P Sripakdeevong S M Dibrov T Hermann R Das Correcting pervasive errorsin RNA crystallography through enumerative structure prediction Nat Methods 1074ndash76 (2013)

20 R F Alford A Leaver-Fay J R Jeliazkov M J OrsquoMeara F P DiMaio H ParkM V Shapovalov P D Renfrew V K Mulligan K Kappel J W Labonte M S PacellaR Bonneau P Bradley R L Dunbrack Jr R Das D Baker B Kuhlman T KortemmeJ J Gray The Rosetta all-atom energy function for macromolecular modeling and designJ Chem Theory Comput 13 3031ndash3048 (2017)

21 A A Szewczak T R Cech An RNA internal loop acts as a hinge to facilitate ribozymefolding and catalysis RNA 3 838ndash849 (1997)

22 C Geary S Baudrey L Jaeger Comprehensive features of natural and in vitro selectedGNRA tetraloop-binding receptors Nucleic Acids Res 36 1138ndash1152 (2008)

23 M Costa F Michel Rules for RNA recognition of GNRA tetraloops deduced by in vitroselection Comparison with in vivo evolution EMBO J 16 3289ndash3302 (1997)

TRP4P6_WT2_0000

DMS CMCT and 1M7 for GAAA11-nt(wild type) receptor

TRP4P6_C72_0000

DMS CMCT and 1M7 for GAAAC72 receptor

TRP4P6_C7X_0000

DMS CMCT and 1M7 for GAAAC710 receptor

TRP4P6_R1J_0000

DMS CMCT and 1M7 for GAAAC72 receptor

TRP4P6_R1J_0001

R(1) compensatory mutants tested by 1M7 and DMS

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24 P W Rose A Prlić A Altunkaya C Bi A R Bradley C H Christie L D CostanzoJ M Duarte S Dutta Z Feng R K Green D S Goodsell B Hudson T KalroR Lowe E Peisach C Randle A S Rose C Shao Y-P Tao Y Valasatava M VoigtJ D Westbrook J Woo H Yang J Y Young C Zardecki H M Berman S K BurleyThe RCSB protein data bank Integrative view of protein gene and 3D structuralinformation Nucleic Acids Res 45 D271ndashD281 (2017)

25 J S Kieft J L Rabe E G Chapman New hypotheses derived from the structure ofa flaviviral Xrn1-resistant RNA Conservation folding and host adaptation RNA Biol 121169ndash1177 (2015)

26 L Jaeger E J Verzemnieks C Geary The UA_handle A versatile submotif in stable RNAarchitectures Nucleic Acids Res 37 215ndash230 (2009)

27 B M Akiyama H M Laurence A R Massey D A Costantino X Xie Y Yang P-Y ShiJ C Nix J D Beckham J S Kieft Zika virus produces noncoding RNAs using amulti-pseudoknot structure that confounds a cellular exonuclease Science 3541148ndash1152 (2016)

28 C Geary A Chworos E Verzemnieks N R Voss L Jaeger Composing RNA nanostructuresfrom a syntax of RNA structural modules Nano Lett 17 7095ndash7101 (2017)

29 J D Yesselman D Eiler E D Carlson A N Ooms W Kladwang X Shi D A CostantinoD Herschlag M C Jewett J S Kieft R Das Computational design of asymmetricthree-dimensional RNA structures and machines bioRxiv 2017 223479 (2017)

30 L Heo M Feig What makes it difficult to refine protein models further via moleculardynamics simulations Proteins 86 (suppl 1) 177ndash188 (2018)

31 D Tan S Piana R M Dirks D E Shaw RNA force field with accuracy comparable tostate-of-the-art protein force fields Proc Natl Acad Sci USA 115 E1346ndashE1355 (2018)

32 W Kladwang T H Mann A Becka S Tian H Kim S Yoon R Das Standardization ofRNA chemical mapping experiments Biochemistry 53 3063ndash3065 (2014)

33 S Yoon J Kim J Hum H Kim S Park W Kladwang R Das HiTRACE High-throughputrobust analysis for capillary electrophoresis Bioinformatics 27 1798ndash1805 (2011)

34 J D Yesselman S Tian X Liu L Shi J B Li R Das Updates to the RNA mappingdatabase (RMDB) version 2 Nucleic Acids Res 46 D375ndashD379 (2017)

35 L Kinch S Yong Shi Q Cong H Cheng Y Liao N V Grishin CASP9 assessment of freemodeling target predictions Proteins 79 (suppl 10) 59ndash73 (2011)

36 O Russakovsky J Deng H Su J Krause S Satheesh S Ma Z Huang A KarpathyA Khosla M Bernstein A C Berg L Fei-Fei ImageNet large scale visual recognitionchallenge Int J Comput Vis 115 211ndash252 (2015)

37 B Kuhlman G Dantas G C Ireton G Varani B L Stoddard D Baker Design of a novelglobular protein fold with atomic-level accuracy Science 302 1364ndash1368 (2003)

38 J M Blose M L Manni K A Klapec Y Stranger-Jones A C Zyra V Sim C A GriffithJ D Long M J Serra Non-nearest-neighbor dependence of the stability for RNAbulge loops based on the complete set of group I single-nucleotide bulge loopsBiochemistry 46 15123ndash15135 (2007)

39 C E Longfellow R Kierzek D H Turner Thermodynamic and spectroscopic study ofbulge loops in oligoribonucleotides Biochemistry 29 278ndash285 (1990)

40 P Thulasi L K Pandya B M Znosko Thermodynamic characterization of RNA triloopsBiochemistry 49 9058ndash9062 (2010)

41 H Kleinert Path Integrals in Quantum Mechanics Statistics Polymer Physics and FinancialMarkets (World Scientific ed 5 2009) pp 1015ndash1024

42 R Tarjan Depth-first search and linear graph algorithms SIAM J Comput 1 146ndash160 (1972)43 T Xia J SantaLucia Jr M E Burkard R Kierzek S J Schroeder X Jiao C Cox D H Turner

Thermodynamic parameters for an expanded nearest-neighbor model for formationof RNA duplexes with WatsonndashCrick base pairs Biochemistry 37 14719ndash14735 (1998)

44 F-C Chou W Kladwang K Kappel R Das Blind tests of RNA nearest-neighbor energyprediction Proc Natl Acad Sci USA 113 8430ndash8435 (2016)

45 I W Davis L W Murray J S Richardson D C Richardson MOLPROBITY Structurevalidation and all-atom contact analysis for nucleic acids and their complexesNucleic Acids Res 32 W615ndashW619 (2004)

46 C Y Cheng F-C Chou R Das Modeling complex RNA tertiary folds with RosettaMethods Enzymol 553 35ndash64 (2015)

47 F L Murphy T R Cech GAAA tetraloop and conserved bulge stabilize tertiary structureof a group I intron domain J Mol Biol 236 49ndash63 (1994)

48 P D Renfrew E J Choi R Bonneau B Kuhlman Incorporation of noncanonicalamino acids into Rosetta and use in computational protein-peptide interface designPLOS ONE 7 e32637 (2012)

49 R Das Atomic-accuracy prediction of protein loop structures through an RNA-inspiredansatz PLOS ONE 8 e74830 (2013)

50 J A Ippolito T A Steitz The structure of the HIV-1 RRE high affinity rev binding site at16 Aring resolution J Mol Biol 295 711ndash717 (2000)

51 H Shi P B Moore The crystal structure of yeast phenylalanine tRNA at 193 Aring resolutionA classic structure revisited RNA 6 1091ndash1105 (2000)

52 M E Burkard D H Turner NMR structures of r(GCAGGCGUGC)2 and determinantsof stability for single guanosinendashguanosine base pairs Biochemistry 39 11748ndash11762(2000)

Watkins et al Sci Adv 20184 eaar5316 25 May 2018

53 J H Cate A R Gooding E Podell K Zhou B L Golden C E Kundrot T R CechJ A Doudna Crystal structure of a group I ribozyme domain Principles of RNA packingScience 273 1678ndash1685 (1996)

54 B Pan Y Xiong K Shi J Deng M Sundaralingam Crystal structure of an RNA purine-richtetraplex containing adenine tetrads Implications for specific binding in RNA tetraplexesStructure 11 815ndash823 (2003)

55 M Egli G Minasov L Su A Rich Metal ions and flexibility in a viral RNA pseudoknot atatomic resolution Proc Natl Acad Sci USA 99 4302ndash4307 (2002)

56 J Deng Y Xiong B Pan M Sundaralingam Structure of an RNA dodecamer containing afragment from SRP domain IV of Escherichia coli Acta Crystallogr Sect D Biol Crystallogr59 1004ndash1011 (2003)

57 M Wu D H Turner Solution structure of (rGCGGACGC)2 by two-dimensional NMR andthe iterative relaxation matrix approach Biochemistry 35 9677ndash9689 (1996)

58 J E Wedekind D B McKay Crystal structure of the leadzyme at 18 Aring resolution Metalion binding and the implications for catalytic mechanism and allo site ion regulationBiochemistry 42 9554ndash9563 (2003)

59 B Pan Y Xiong K Shi M Sundaralingam Crystal structure of a bulged RNA tetraplex at11 Aring resolution Implications for a novel binding site in RNA tetraplex Structure 111423ndash1430 (2003)

60 C C Correll J Beneken M J Plantinga M Lubbers Y-L Chan The common and thedistinctive features of the bulged-G motif based on a 104 Aring resolution RNA structureNucleic Acids Res 31 6806ndash6818 (2003)

61 D J Klein P B Moore T A Steitz The roles of ribosomal proteins in the structureassembly and evolution of the large ribosomal subunit J Mol Biol 340 141ndash177 (2004)

62 M P Robertson H Igel R Baertsch D Haussler M Ares Jr W G Scott The structureof a rigorously conserved RNA element within the SARS virus genome PLOS Biol 3 e5(2005)

63 A Serganov Y-R Yuan O Pikovskaya A Polonskaia L Malinina A T Phan C HobartnerR Micura R R Breaker D J Patel Structural basis for discriminative regulation ofgene expression by adenine- and guanine-sensing mRNAs Chem Biol 11 1729ndash1741(2004)

64 J SantaLucia Jr D H Turner Structure of (rGGCGAGCC)2 in solution from NMR andrestrained molecular dynamics Biochemistry 32 12612ndash12623 (1993)

65 F M Jucker H A Heus P F Yip E H M Moors A Pardi A network of heterogeneoushydrogen bonds in GNRA tetraloops J Mol Biol 264 968ndash980 (1996)

66 S C Ha K Lowenhaupt A Rich Y-G Kim K K Kim Crystal structure of a junctionbetween B-DNA and Z-DNA reveals two extruded bases Nature 437 1183ndash1186 (2005)

67 R K Montange R T Batey Structure of the S-adenosylmethionine riboswitchregulatory mRNA element Nature 441 1172ndash1175 (2006)

68 B Pan K Shi M Sundaralingam Crystal structure of an RNA quadruplex containinginosine tetrad Implications for the roles of NH2 group in purine tetrads J Mol Biol 363451ndash459 (2006)

69 S Nozinovic B Fuumlrtig H R A Jonker C Richter H Schwalbe High-resolution NMRstructure of an RNA model system The 14-mer cUUCGg tetraloop hairpin RNANucleic Acids Res 38 683ndash694 (2010)

70 Y V Lerman S D Kennedy N Shankar M Parisien F Major D H Turner NMR structureof a 4 times 4 nucleotide RNA internal loop from an R2 retrotransposon Identificationof a three purinendashpurine sheared pair motif and comparison to MC-SYM predictionsRNA 17 1664ndash1677 (2011)

71 S D Kennedy R Kierzek D H Turner Novel conformation of an RNA structural switchBiochemistry 51 9257ndash9259 (2012)

72 M Martick T-S Lee D M York W G Scott Solvent structure and hammerhead ribozymecatalysis Chem Biol 15 332ndash342 (2008)

73 M P Robertson W G Scott The structural basis of ribozyme-catalyzed RNA assemblyScience 315 1549ndash1553 (2007)

74 Q Zhao Q Han C R Kissinger T Hermann P A Thompson Structure of hepatitis C virusIRES subdomain IIa Acta Crystallogr Sect D Biol Crystallogr 64 436ndash443 (2008)

75 C E Dann III C A Wakeman C L Sieling S C Baker I Irnov W C Winkler Structure andmechanism of a metal-sensing regulatory RNA Cell 130 878ndash892 (2007)

76 S D Gilbert R P Rambo D Van Tyne R T Batey Structure of the SAM-II riboswitchbound to S-adenosylmethionine Nat Struct Mol Biol 15 177ndash182 (2008)

77 J-D Ye V Tereshko J K Frederiksen A Koide F A Fellouse S S Sidhu S KoideA A Kossiakoff J A Piccirilli Synthetic antibodies for specific recognition andcrystallization of structured RNA Proc Natl Acad Sci USA 105 82ndash87 (2008)

78 C C Correll B Freeborn P B Moore T A Steitz Metals motifs and recognition in thecrystal structure of a 5S rRNA domain Cell 91 705ndash712 (1997)

79 A L Feig W G Scott O C Uhlenbeck Inhibition of the hammerhead ribozyme cleavagereaction by site-specific binding of Tb(III) Science 279 81ndash84 (1998)

80 S Thore C Frick N Ban Structural basis of thiamine pyrophosphate analogues bindingto the eukaryotic riboswitch J Am Chem Soc 130 8116ndash8117 (2008)

81 J Wang Inclusion of weak high-resolution x-ray data for improvement of a group IIintron structure Acta Crystallogr Sect D Biol Crystallogr 66 988ndash1000 (2010)

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SC I ENCE ADVANCES | R E S EARCH ART I C L E

82 R T Byrne A L Konevega M V Rodnina A A Antson The crystal structure ofunmodified tRNAPhe from Escherichia coli Nucleic Acids Res 38 4154ndash4162 (2010)

83 S Dibrov J McLean T Hermann Structure of an RNA dimer of a regulatory elementfrom human thymidylate synthase mRNA Acta Crystallogr Sect D Biol Crystallogr67 97ndash104 (2011)

84 L Huang A Serganov D J Patel Structural insights into ligand recognition by a sensingdomain of the cooperative glycine riboswitch Mol Cell 40 774ndash786 (2010)

85 N Safaee A M Noronha D Rodionov G Kozlov C J Wilds G M Sheldrick K GehringStructure of the parallel duplex of poly(A) RNA Evaluation of a 50 year-old predictionAngew Chem Int Ed Engl 52 10370ndash10373 (2013)

86 M Meyer H Nielsen V Olieacuteric P Roblin S D Johansen E Westhof B MasquidaSpeciation of a group I intron into a lariat capping ribozyme Proc Natl Acad Sci USA111 7659ndash7664 (2014)

87 N B Suslov S DasGupta H Huang J R Fuller D M J Lilley P A Rice J A PiccirilliCrystal structure of the Varkud satellite ribozyme Nat Chem Biol 11 840ndash846(2015)

Acknowledgments We thank F-C Chou for early discussions and Stanford ResearchComputing Center for expert administration of the BioX3 clusters (supported by NIH

Watkins et al Sci Adv 20184 eaar5316 25 May 2018

1S10RR02664701) and Sherlock clusters Funding We acknowledge financial supportfrom the Burroughs Wellcome Fund [CASI (Career Awards at the Scientific Interface) to RD]NIH grants R21 CA219847 R35 GM122579 and R21 GM102716 (to RD) intramural researchgrants from the University of California Santa Barbara Academic Senate (to LJ) and aRosettaCommons grant Author contributions AMW CG LJ and RD designed theresearch AMW CG WK PZ and RD carried out the research AMW LJ and RDwrote the manuscript All authors reviewed the manuscript Competing interests Theauthors declare that they have no competing interests Data and materials availabilityAll data and computer code needed to evaluate the conclusions in this paper are availableat links described in Materials and Methods Additional data related to this paper maybe requested from the authors

Submitted 19 November 2017Accepted 17 April 2018Published 25 May 2018101126sciadvaar5316

Citation A M Watkins C Geniesse W Kladwang P Zakrevsky L Jaeger R Das Blindprediction of noncanonical RNA structure at atomic accuracy Sci Adv 4 eaar5316 (2018)

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Blind prediction of noncanonical RNA structure at atomic accuracyAndrew M Watkins Caleb Geniesse Wipapat Kladwang Paul Zakrevsky Luc Jaeger and Rhiju Das

DOI 101126sciadvaar5316 (5) eaar53164Sci Adv

ARTICLE TOOLS httpadvancessciencemagorgcontent45eaar5316

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