1. C omputational ncRNA gene finding (& nc RNA structure prediction) Liming Cai (BINF8210@UGA, Fall 2015) nc RNA structure prediction (& computational ncRNA gene finding)

3. Non-coding RNAs Functions other than coding proteins, e.g., structural, catalytic, and regulatory factors functional RNAs = ncRNAs + UTR motifs (-) No strong statistical features, such as ORFs, or polyadenylated, demonstrated in coding genes (+) Transcribed ncRNA molecules can fold into secondary and tertiary structures (more conserved than sequences)

4. Sources of ncRNAs Non-coding RNA genes encode RNAs, e.g., miRNAs, rox1 and rox2 RNAs in male Drosophila melanogaster. In introns and intergenic regions, e.g., snoRNAs In 5’ and 3’ UTRs, e.g., regulatory motifs (functional RNAs)

5. Functions of ncRNAs rRNAs and tRNAs RNA maturation: snRNA in recognizing splicing sites RNA modification: snoRNA converting uridine to pseudo-uridine Regulation of gene expression and translation: e.g., miRNAs DNA replication: e.g., telomerase RNAs - template for addition of telomeric repeats Etc.

6. Classes of ncRNAs (Bompfunewerer, et al, 2005) ClassSizeFunctionPhylogenetic distribution tRNA70-80Translationubiquitous rRNA 16S/18S 28S+5.8S/23S 5S 1.5K 3K 130 translationubiquitous RNase P MRP 220-440 250-350 tRNA - maturation ubiquitous eukarya snoRNA telomerase 130 400-550 pseudouridinyl ation addition of repeats snRNA U1 ~ U6 100-600 130-140 Spliceosome mRNA maturation Eukarya Eukarya, archaea U7 7SK ~65 ~300 Histone mRNA Maturation Translational regulation Eukayotes vertebrata tmRNA300-400Tags protein For proteolysis bacteria miRNA~22Post-tran. Reg.Multi-cellular orgs

7. Some ncRNAs databases Rfam (280,000 regions of 379 families) NONCODE (109 transitional classes and 9 groups) RNAdb (800 mammalian ncRNAs, excluding tRNAs, rRNAs and snRNAs) Arabidposis small RNA Project (ASRP) Etc.

8. ncRNA gene finding strategies 1.Computational predictive methods 2.cDNA cloning to enrich ncRNAs 3.Detecting new transcripts with oligonucleotide microarrays

9. ncRNA gene finding: a computational challenge ncRNA genes do not have significant statistical signals large in number diverse, 20 nts to 22,000 nts - Not sure what to look for - Computationally intensive - Simply no good method - Methods compromising accuracy

10. Folded into 3D structure Difficulty to discover ncRNAs from genomes Unlike protein- coding genes: No strong statistical sequence signals (no ORF, no polyadenine) tRNA gene Transcribed to tRNA sequence

11. Computational ncRNA gene finding methods Specific (custom-designed) ncRNA search and annotation (e.g., tRNAscan, methylattion-guide snoRNA, miRNA, tmRNA) Reconfigurable search systems (e.g., Infernal, ERPIN, RNATOPS,FastR) –mechanism to profile the target ncRNA (structure) - need training data De novo ncRNA gene detection with –base composition (e.g., G+C %) –structure fold (e.g., RNAz) Comparative analysis (e.g., QRNA, EvolFold) - consensus structure ncRNA “holy grail” ?

12. Review literature in computational ncRNA gene finding and annotation A. Laederach (2007) Informatics challenges in Structural RNA, Brief Bioinformatics 8(5) 294-303. S. Eddy (2001) Non-coding RNA genes and modern RNA world, Nature Reviews Genetics, 2(12), 919-929. S. Griffiths-Jones (2007) Annotating noncoding RNA genes, Annual Rev. Genomics & Human Genetics, 8:279-298. Machado-Lima et al (2008) Computational methods in noncoding RNA research, Mathematical Biology, 56: 15-49.

13. 506 miRNAs Comparison between NUPACK and Triple 499 tRNAs Comparison between NUPACK and Triple Data were from Bonnet et al, 2004

14. 499 tRNA Comparisons between HG, Triple, NUPACK Data were from Bonnet et al, 2004 499 tRNA Comparisons between HG and NUPACK

15. What are in this lecture? RNA secondary structure prediction 1. ab initio structure prediction 2. consensus structure prediction 3. structural model-based prediction [Doudna,et al, 1999] [tRNA unfolding pathway] but why just secondary structure?

16. Tertiary structure: Less understood non-canonical interactions Only a small number of resolved structures Secondary structure: canonical base pairs (Well understood) Scaffolding tertiary structure Well studied, many known structures Measuring ncRNA secondary structure may be a feasible solution for ncRNA gene finding

19. What else are in this lecture? ncRNA gene finding and annotation 4. Structural profile-based ncRNA gene annotation 5. comparative analysis based ncRNA gene finding 6. ab initio ncRNA gene detection

20. Base pairings of RNAs Base pairings allow RNA to fold Watson-Crick base pairs: A-U, C-G Wobble pair G-U called canonical pairs for secondary structure Note: all 16 (including non-canonical) base pairs are possible for RNA tertiary structure

21. NN N O H H 5’-u-u-c-c-g-a-a-g-c-u-c-a-a-c-g-g-g-a-a-a-u-g-a-g-c-u-3’ P a P c 5’ 3’ P u a P g P CYTOSINE N N N O H H H N N GUANINE URACIL ADENINE NN O O H N N N N N HH

22. Secondary structure is important to tertiary structure

23. Stems in nested or parallel pattern aacguuccccucugg g gcagcccag a ugccc stem (double helix): stacked base pairs loop: strand of unpaired bases ac c gg u

24. Stems in crossing patterns aacguuccccucuac c gg g gcagcgg u ccag a ugcac c cc Pseudoknots: crossing patterns of stems

25. RNA secondary structure elements Hairpin loop Junction (Multiloop) Bulge Loop Single-Stranded Interior Loop Stem Image– Wuchty Pseudoknot

26. RNA stem-loop (pseudoknot-free) structure example

27. RNA secondary structure prediction 1.ab inito structure prediction to predict the structure of a single sequence 2. Consensus structure prediction to predict the structure shared by more than one sequences 3. Statistical model-based prediction and alignment to search for desirable structures on genomes or data bases

28. 1. ab initio structure prediction Hydrogen bonds consume energy contained in the molecule. The smaller the free energy is, the more stable the structure folded.

29. ab initio structure prediction (cont’) Consider only canonical base pairs A-U, C-G, and G-U. Base pairings reduce the amount of free energy contained in the molecule. Maximizing the number of base pairs would minimize the free energy in the molecule. (Only an approximate model)

30. ab initio structure prediction (cont’) But how to count? An RNA could be very long; there may be many possible ways that base pairs can be formed: e.g., ……ACGGUACGUC….. conflicting pairs A-U, A-U G-C, G-C etc. Even the number of non-conflicting combinations of base pairs is exponentially large.

31. ab initio structure prediction (cont’) i j (1) head paired with tail (2) tail is unpaired (3) head is unpaired (4) ik j two subfolds

32. looking at shorter (e.g., very short) subsequences in a long sequence ACGGU…ACGUC For subsequences of length 1, A, C, G, G, U, …, A, C, G, U, C #of base pairs 0, 0, 0, 0, 0, …, 0, 0, 0, 0, 0 For subsequences of length 2, AC, CG, GG, GU, …, AC, CG, GU, UC # 0, 1. 0, 1, …, 0, 1, 1, 0 For subsequence of length 3, ACG, CGG, GGU, …, UAC, ACG, CGU, GUC, UUC ?: e.g., GUC (1) G-C + U --> 1+0 =1 head-tail (2) G + UC --> 0+0 =0 head unpaired (3) GU + C --> 1+0 =1 tail unpaired (4) GU + C --> 1+0 =1 split (5) G + UC --> 0+0 =0 split

33. examine a little longer sequence …..ACGGUACGU….. i j ==> max of {cases 1, 2, 3, 4} 1.Head-tail paired, count = 1 + max count in subsequence CGGUACG i+1 j-1 2. Head unpaired, count = max count in subsequence CGGUACGU i+1 j 3.Tail unpaired, count = max count in subsequence ACGGUACG i j-1 4.Split (why needed and where to split ?) ACGGUACGU when k=i+2 i j ==> ACG + GUACGU count = max count in ACG + max count in GUACGU

34. Ab initio structure prediction (cont’) Maximizing the number of base pairs (Nussinov et al, 1978) simple model:  (i, j) = 1

35. GGGAAAUCC C i,j = 0 when i=j 0 0 0 0 0 0 0 0 G G G A A A U C C GGGAAAUCCGGGAAAUCC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 AU AAUC 0 0 1 1 1 GAAAUC 0 1 2 1 1 2 2 3 23

36. Example 2: ACGGUU subsequence of length 0: empty sequence, 0 pairs subsequences of length 1: A, C, G, G, U, U 0 0 0 0 0 0 pairs subsequences of length 2: AC, CG, GG, GU, UU 0 1 1 0 0 pairs subsequences of length 3: ACG, CGG, GGU, GUU 1 1 1 1 pairs Subsequences of length 4: ACGG, CGGU, GGUU 1 2 2pairs Subsequences of length 5: ACGGU, CGGUU 2 2pairs subsequence of length 6: ACGGUU 3pairs

37. Prediction Algorithm Web Server http://frontend.bioinfo.rpi.edu/applications/mfold/cgi-bin/rna-form1.cgi Sample sequence: (1) tRNA GGGGUCAUAGCUCAGUUGGUAGAGCGCUACAAUGGCAUUGUAGAGGUCAGCGG UUCGAUCCCGCUUGGCUCCACCA (2) a part of tmRNA CCUCUCUCCCUAGCCUCCGCUCUUAGGACGGGGAUCAAGAGAGGUCA AACCCAAAAGAGA Simple matrix, simple matrix with G-U pair Complex matrix Rfam database: http://www.sanger.ac.uk/Software/Rfam/http://www.sanger.ac.uk/Software/Rfam/

38. Thermodynamic energy based structure prediction Energy minimization algorithm predicts the correct secondary structure by minimizing the free energy (  G)  G calculated as sum of individual contributions of: –loops –base pairs –secondary structure elements

39. Free-energy values (kcal/mole at 37 o C ) Energies of stems calculated as stacking contributions between neighboring base pairs

40. Free-energy values (kcal/mole at 37 o C )

41. Zuker’s algorithm MFOLD: computing loop dependent energies

42. Assumptions in such algorithms Most likely structure corresponds to energetically most stable structure Energy associated with any position is only influenced by local sequence and structure Structure formed does not produce pseudoknots

43. RNA structure prediction web servers MFOLD http://www.bioinfo.rpi.edu/applications/mfold/rna/form1.cgihttp://www.bioinfo.rpi.edu/applications/mfold/rna/form1.cgi RNAfold ( a part of Vienna Package) http://rna.tbi.univie.ac.at/cgi-bin/RNAfold.cgi Examples: GCTTACGACCATATCACGTTGAATGCACGC CATCCCGTCCGATCTGGCAAGTTAAGCAAC GTTGAGTCCAGTTAGTACTTGGATCGGAGA CGGCCTGGGAATCCTGGATGTTGTAAGCT

44. RNA pseudoknot (tmRNAs) terminates translation errors Bacterial tmRNA consensus structure (Felden et al. 2001. NAR 29)

45. Functions of pseudoknots (TMV 3’ UTR) Promotes efficient translation Binds EF1A, cooperates with 5’UTR (Leathers et al. 1993 MCB 13 Zeenko et al. 2002 JVI 76)

46. Pseudoknots drastically increase computational complexity

47. RNA pseudoknot prediction web servers Pknots-RG: http://bibiserv.techfak.uni-bielefeld.de/pknotsrg/ Pknots-RE (the first pseudoknot prediction algorithm) Kinefold: http://kinefold.curie.fr/cgi-bin/form.pl ILM http://cic.cs.wustl.edu/RNA/

48. Computational complexity issues Pseudoknot-free structures: O(n 3 ) CUP time Pseudoknots: NP-hard, restricted cases O(n 5 ) Heuristics added: O(n 4 ) Difficult for search RNA structures in genomes

49. 2. Consensus structure prediction Covariance fact for RNAs: Variations in RNA sequence maintain base-pairing patterns for secondary structures When a nucleotide in one base changes, the base it pairs to must also change to maintain the same structure

50. Structure alignments (example) C A G A GC A A G A CG UA AU G A AG UG CA CU Query RNA structureB: nonhomologousA: structural homolog query: GGGGGCAACCCC A: AUCCGAAAGGAU     | | |    query: GGGGGCAACCCC B: CCUAGAAAGGAU     |  | |    query: GGGGGCAACCCC A: AUCCGAAAGGAU | | | | |  | | | | | | query: GGGGGCAACCCC B: CCUAGAAAGGAU     |  | |    primary sequence alignment scoring: structure + sequence alignment scoring: -6 +11-6

51. Mutlipel Structural Alignment of 13 tmRNA genes from the β-proteobacteria [Felden et al’01] Covariance

52. Dynamic programming approach (Sankoff 1984) This can be regarded as running ‘two Nussinov algorithms at the same time’ to simultaneously fold two RNAs i j pq ‘the coordinated fold’ is found through computing C i,j,p,q, needs: O(n 6 ) time for two sequences and O(n 3k ) for k seqs

53. Inferring structure by comparative sequence analysis (1) calculate a multiple sequence alignment Requires sequences to be similar enough so that they can be initially aligned Sequences should be dissimilar enough for covarying substitutions to be detected

54. Inferring structure by comparative sequence analysis (cont’) (2) compute Mutual Information f x i : frequency of a base x in column i f xiyj : joint (pairwise) frequency of base pair x-y between columns i and j If i and j are uncorrelated, mutual information is 0

55. Inferring structure by comparative sequence analysis (cont’) (3) use mutual information M i,j as pairing “energy” and treat the multiple alignment as a “generic” sequence apply a Nussinov’s algorithm-like process to find the most likely common structure

56. Inferring consensus structure by a graph- theoretic approach (ConRAN and RNASampler) Identify all stems in every sequence, assigning each stem a vertex in the graph Connect two stems in two different sequences with an edge if they are similar Connect two stems in the same sequence with an edge if they do not conflict The optimal consensus structure corresponds the maximum clique

57. Consensus structure prediction programs Dynalign http://rna.urmc.rochester.edu/dynalign.html Foldalign http://www.bioinf.au.dk/cgi-bin/webparser-1.5.pl ComRNA http://ural.wustl.edu/~yji/comRNA/ RNA sampler http://ural.wustl.edu/~xingxu/RNASampler/index.html Carnac http://bioinfo.lifl.fr/RNA/carnac/carnac.php

58. 3. Statistical model-based structure prediction and alignment Extension from HMM to include mechanisms that can describe (long-distance) base pairings Stochastic grammars can describe models defined by HMMs Stochastic grammars can describe models not definable by HMMs

59. Stochastic context-free grammar Covariance model (CM) [Eddy and Durbin’94] based on computational grammar systems M 2  a M’ 2 I 2  a I 2 D 2  I 2 M’ 2  I 2 I 2  M 3 D 2  M 3 M’ 2  D 3 I 2  D 3 D 2  D 3 A path in the HMM  a derivation in the grammar

60. a a cg u uc c u c ua g acc S S S S S  aSu L  aL S  uSaL  cL S  gSc L  a S  cSgL  c S  L Each derivation tree corresponds to a structure. Stochastic context-free grammar (cont’) Stochastic Context-free Grammars (SCFGs) L L L L [Lari and Young’90, Sakakibara et al’94]

61. S  aSu S  cSg S  gSc S  uSa S  a S  c S  g S  u S  SS 1. A CFG S  aSu  acSgu  accSggu  accuSaggu  accuSSaggu  accugScSaggu  accuggSccSaggu  accuggaccSaggu  accuggacccSgaggu  accuggacccuSagaggu  accuggacccuuagaggu 2. A derivation of “accuggacccuuagaggu” 3. Corresponding structure Stochastic context-free grammar (cont’)

62. What to do with SCFGs ? Structure prediction require the SCFG model to be flexible enough Structure search require the model to be specific Both need to do sequence-structure alignment

63. Structure prediction with SCFG S  aSu S  cSg S  gSc S  uSa S  aS S  cS S  gS S  uS S  Sa S  Sc S  Sg S  Su S  a S  c S  g S  u S  SS Probability parameter assignment: (1)Sum of probabilities of the same LHS =1 (2) Geometric distributions for loop and stem lengths (3) Parameters are obtained from training sequences with known structures Alignment score between model S and subsequence x[i..j] is computed, when x[i]=a, x[j]=u C(S, i, j) = max { C(S,i+1, j-1)*P(S -> aSu), C(S,i+1, j)*P(S -> aS), C(S, I,j-1)*P(S -> Su), max k { C(S,i,k)C(S,k+1,j)P(S->SS) }

64. Web servers for RNA Structure prediction with SCFG S  aSu S  cSg S  gSc S  uSa S  aS S  cS S  gS S  uS S  Sa S  Sc S  Sg S  Su S  a S  c S  g S  u S  SS Infernal: http://infernal.janelia.org/ Pfold: (multiple sequence + SCFG) http://www.daimi.au.dk/~compbio/rnafold/

65. RNA secondary structure prediction 1. ab initio structure prediction 2. consensus structure prediction 3. structural (SCFG) model-based prediction ncRNA gene finding and annotation 4. profile-based ncRNA gene annotation 5. comparative analysis based ncRNA gene finding 6. ab initio ncRNA gene prediction

66. 4. Structure profile based RNA gene annotation Secondary structure alone is not sufficient for predicting ncRNA genes, BUT it remains to be the best hope for an exploitable statistical signal To find RNA structures or genes, one can profile the structure to be searched. Often, SCFG is used as a modeling tool.

67. Structure profile based RNA gene annotation (cont’) Search for a specific family RNAs (structures) Need an effective mechanism to profile the family Need a fast structure-sequence alignment algorithm

68. model modeling e.g. CM SCFG profiling genome alignment scanning window (target sequence) RNA training sequences with annotated structures

69. CM is a profile-SCFG, position-specific, very effective Slow O(n 3 N)-time even for pseudoknot-free RNAs in genomes or large databases Cannot handle pseudoknots HMM based filtering to imprve speed Examples: tRNAscan-SE (http://lowelab.ucsc.edu/tRNAscan-SE/)http://lowelab.ucsc.edu/tRNAscan-SE/ infernal (http://infernal.janelia.org/)http://infernal.janelia.org/

70. 5. Comparative analysis based ncRNA gene finding Based on structure features of RNA Consider two or more genomes phylogenetically related Use sequence alignment tools (such as BLASTN) to find local alignment between the two Search with a sliding window Identify potential RNA fold within the window Computationally verify it to be putative RNA QRNA (Eddy group, 2001) EvoFold (Haussler group, 2006) RNAz (Stadler group, 2005)

71. QRNA (Eddy et al, 2001) detecting ncRNA genes with SCFGs given two aligned sequences, to test the pattern of substitutions observed in the pairwise alignment of two homologous sequences using a pair of SCFGs for ncRNAs (compensatory mutations) a pair HMM for protein-coding genes (conserved regions) a pair HMM for other regions (random evolution)

72. QRNA:

73. Probability parameters

75. Other software to detect RNA genes based on comparative analysis EvoFold multiple genomes use SCFG + phylogeny to predict consensus structure RNAz multiple genomes predict the consensus fold compare energy of the fold to background energy

76. 3. Ab initio prediction of ncRNA genes mainly based on base composition difference between real RNAs and the background, limited success. Unsuccessful by simply predicting the structure of RNAs Other methods?

77. Fold energy and fold certainty Methods based on folding energy do not seem to work [just like structure prediction] How do distinguish a real ncRNA from random sequences that fold to the same structure by chance [both could have the same energy] The difference seems to be the structure certainty But how to compute structure certainty?

78. Fold certainty For a real ncRNA sequence: Base pairs contributing to the real fold should not be everywhere. ‘overall strength’ of base pairs contributing to other, false folds should be weak. For a random sequence: either it does not fold or there is a low probability to form a certain fold

79. Fold certainty (cont’) Compute Shannon entropy En(S) = ∑Pij log Pij where Pij is the probability for bases i and j to pair Pij = (number of folds pair (i,j) is involved) / (number of folds) [simplified]

80. Fold certainty (cont’) We measured entropy Z-score of a real ncRNA based on the entropies of its random counterparts But the entropy Z-score performance on different ncRNAs is different miRNAs perform well while tRNAs do not What happened?

81. Readings and projects in RNA informatics www.uga.edu/RNA-Informatics/Readings www.uga.edu/RNA-Informatics/Projects www.uga.edu/RNA-Informatics/Projects/project-details.html

83. What about pseudoknots?

84. Tree decomposition based search algorithms Dynamic programming at the nucleotide level is time consuming Very Slow, O(n 6 N)-time even for restricted pseudoknot categories Pseudoknots are not very complex from graph-theoretic point of view

85. Tree decomposition based search algorithms (cont’s) profile each stem with SCFG, connecting the two halves with an edge profile each loop with HMM, connect two ends of the loop with a directed edge Produce a mxied graph H for the structure Preprocess target sequence with the profiles to obtain all potential candidates, construct a graph G for the sequence Structure-sequence alignment corresponding finding an optimal subgraph in G isomorphic to H

86. Tree decomposition based search algorithms (cont’s) H is decomposed as a tree representation Fast alignment algorithm can be obtained O(k t Nn) where t is the tree width of H, usually small for pseudoknotted RNAs, k is a parameter, small also Successful for RNA structures that belong to a well-defined family

87. Sequence-structure alignment Structure Structure graph Tree decomposition Sequence 1 Sequence graph 2 1 1. Construct graphs 2. Tree decompose the structure graph 3. Dynamic programming based on tree decomposition alignment subgraph isomorphism 3

88. st structure graph abb’cc’dd’a’ Structure graph Hidden Markov Model (HMM) Covariance Model (CM) aa’ b b’ c c’ d d’

89. structure graph For each stem, identify k candidates in the sequence genome sequence Sequence graph st abb’cc’dd’a’ a1a2 a’1a’2

90. structure graph For each stem, identify k candidates in the sequence genome sequence Sequence graph st abb’cc’dd’a’ a1a2 a’2a’1 b1b’1b2b’2

91. genome sequence t a1a’1b1b’1c1 c’1 a2a’2b2b’2c2 c’2 sequence graph s Sequence graph a’2a’1a1a2b1b’1d’2d’1d1d2b2b’2c1c’1c2c’2

92. Subgraph isomorphism structure graph aa’bb’cc’ a1a’1b1b’1c1 c’1 a2a’2b2b’2c2 c’2 Sequence-structure alignment becomes subgraph isomorphism sequence graph k=2 s s t t

93. aa’bb’cc’ a b a’b c’ a’ b b’ c’ b’ c c’ b d b’d d’ b’ dd’ st s a a’a a’ t Tree decomposition of structure graph (1) Pseudoknot-free structure graphs have tree width = 2

94. aa’bb’cc’dd’ (1) Pseudoknot-free structure graphs have tree width = 2 (2) Almost all pseudoknot structure graphs have small tree width x y a b a’b c’ a’ b b’ c’ y b’ c c’ y b d b’ y d d’ b’ y s a a’a a’ t c c’ y d d’ x y st Tree decomposition of structure graph (cont’d)

95. Tree width of tmRNA Tree width = 5

96. Tree decomposition based search algorithms (cont’s)

97. HI: Haemophilus influenzae NM: Neisseria meningitidis SC:Saccharomyces cerevisiae SB: Saccharomyces bayanus

98. RNA structure and gene search How to identify novel RNAs whose structure may deviate from the common structure of the family? - make a profile accommodate novel structures (This may mean to test more potential structures) - make the structure-sequence alignment fast enough