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Day 1 " Last lecture: ! RNA Search and ! many biologically interesting roles for RNA " Motif Discovery " Today: " Covariance Models (CMs) represent CSE 527 ! conserved RNA sequence/structure motifs " Computational Biology

  1. Day 1 " Last lecture: ! RNA Search and ! many biologically interesting roles for RNA " Motif Discovery " Today: " Covariance Models (CMs) represent CSE 527 ! conserved RNA sequence/structure motifs " Computational Biology " 2 Computational Problems " How to predict secondary structure " How to model an RNA “motif” ! (I.e., sequence/structure pattern) " Given a motif, how to search for instances " Given (unaligned) sequences, find motifs " How to score discovered motifs " How to leverage prior knowledge " 3 4

  2. RNA Motif Models " “Covariance Models” (Eddy & Durbin 1994) " aka profile stochastic context-free grammars " Motif Description " aka hidden Markov models on steroids " Model position-specific nucleotide preferences and base-pair preferences " Pro: accurate " Con: model building hard, search sloooow " 10 What " Main Results " A probabilistic model for RNA families " Very accurate search for tRNA " The “Covariance Model” " (Precursor to tRNAscanSE - current favorite) " ! A Stochastic Context-Free Grammar " Given sufficient data, model construction A generalization of a profile HMM " comparable to, but not quite as good as, ! Algorithms for Training " human experts " From aligned or unaligned sequences " Some quantitative info on importance of Automates “comparative analysis” " pseudoknots and other tertiary features " Complements Nusinov/Zucker RNA folding " Algorithms for searching " 11 12

  3. Example: searching for Probabilistic Model Search " tRNAs ! As with HMMs, given a sequence, you calculate likelihood ratio that the model could generate the sequence, vs a background model " You set a score threshold " Anything above threshold " a “hit” " Scoring: " “Forward” / “Inside” algorithm - sum over all paths " Viterbi approximation - find single best path ! (Bonus: alignment & structure prediction) " 13 14 How to model an RNA “Motif”? " How to model an RNA “Motif”? " Add “column pairs” and pair emission probabilities Conceptually, start with a profile HMM: " for base-paired regions " from a multiple alignment, estimate nucleotide/ insert/delete preferences for each position " given a new seq, estimate likelihood that it could be generated by the model, & align it to the model " <<<<<<< >>>>>>> paired columns … … mostly G ins all G del 16 17

  4. Profile Hmm Structure " CM Structure " A: Sequence + structure " B: the CM “guide tree” " C: probabilities of letters/ pairs & of indels " Think of each branch being an HMM emitting both sides of a helix (but M j : " Match states (20 emission probabilities) " 3’ side emitted in I j : " Insert states (Background emission probabilities) " reverse order) " D j : " Delete states (silent - no emission) " 18 24 Overall CM CM Viterbi Alignment ! Architecture " (the “inside” algorithm) " One box (“node”) per node = i th letter of input of guide tree " x i BEG/MATL/INS/DEL just x ij = substring i ,..., j of input like an HMM " T yz = P (transition y " z ) MATP & BIF are the key y E x i , x j = P (emission of x i , x j from state y ) additions: MATP emits pairs of symbols, modeling base- y S ij = max # log P ( x ij gen'd starting in state y via path # ) pairs; BIF allows multiple helices " 25 26

  5. CM Viterbi Alignment ! (the “inside” algorithm) " y = max " log P ( x ij generated starting in state y via path " ) S ij % z y max z [ S i + 1, j # 1 + log T yz + log E x i , x j ] match pair ' y ] z max z [ S i + 1, j + log T yz + log E x i match/insert left ' ' y = y ] z S ij & max z [ S i , j # 1 + log T yz + log E x j match/insert right ' z max z [ S i , j + log T yz ] delete ' y left + S k + 1, j y right ] ' max i < k $ j [ S i , k bifurcation ( Time O(qn 3 ), q states, seq len n Time O(qn 3 ), q states, seq len n compare: O(qn) for profile HMM 27 29 Covariation is strong evidence for base pairing mRNA leader Mutual Information " f xi , xj " M ij = f xi , xj log 2 ; 0 # M ij # 2 f xi f xj xi , xj Max when no seq conservation but perfect pairing " MI = expected score gain from using a pair state " mRNA leader switch? Finding optimal MI, (i.e. opt pairing of cols) is hard(?) " Finding optimal MI without pseudoknots can be done by dynamic programming " 30 31

  6. M.I. Example (Artificial) " * 1 2 3 4 5 6 7 8 9 * MI: 1 2 3 4 5 6 7 8 9 A G A U A A U C U 9 0 0 0 0 0 0 0 0 A G A U C A U C U 8 0 0 0 0 0 0 0 A G A C G U U C U 7 0 0 2 0.30 0 1 A G A U U U U C U 6 0 0 1 0.55 1 A G C C A G G C U 5 0 0 0 0.42 A G C G C G G C U 4 0 0 0.30 A G C U G C G C U 3 0 0 A G C A U C G C U 2 0 A G G U A G C C U 1 A G G G C G C C U A G G U G U C C U A G G C U U C C U Cols 1 & 9, 2 & 8: perfect conservation & might be A G U A A A A C U base-paired, but unclear whether they are. M.I. = 0 A G U C C A A C U A G U U G C A C U Cols 3 & 7: No conservation, but always W-C pairs, A G U U U C A C U so seems likely they do base-pair. M.I. = 2 bits. Cols 7->6: unconserved, but each letter in 7 has A 16 0 4 2 4 4 4 0 0 only 2 possible mates in 6. M.I. = 1 bit. " C 0 0 4 4 4 4 4 16 0 G 0 16 4 2 4 4 4 0 0 32 35 U 0 0 4 8 4 4 4 0 16 MI-Based Structure-Learning ! Primary vs Secondary Info " Find best (max total MI) subset of column pairs among i…j, subject to absence of pseudo-knots ! $ S i , j = max S i , j " 1 j unpaired % max i # k < j " 4 S i , k " 1 + M k , j + S k + 1, j " 1 j paired & “Just like Nussinov/Zucker folding” " disallowing allowing BUT, need enough data---enough sequences at right pseudoknots phylogenetic distance " # n & % " ( /2 max j M i , j $ ' i = 1 36 37

  7. Comparison to TRNASCAN " tRNAScanSE " Fichant & Burks - best heuristic then " Uses 3 older heuristic tRNA finders as evaluation criteria Slightly different 97.5% true positive " prefilter " 0.37 false positives per MB " Uses CM built as described for final scoring " CM A1415 (trained on trusted alignment) " Actually 3(?) different CMs " > 99.98% true positives " " eukaryotic nuclear " < 0.2 false positives per MB " Current method-of-choice is “tRNAscanSE”, a CM- " prokaryotic " based scan with heuristic pre-filtering (including " organellar " TRNASCAN?) for performance reasons. " Used in all genome annotation projects " 40 41 Rfam – an RNA family DB ! Griffiths-Jones, et al., NAR ’03, ’05, ’08 " Biggest scientific computing user in Europe - An Important Application: ! 1000 cpu cluster for a month per release " Rfam " Rapidly growing: " Rel 1.0, 1/03: 25 families, 55k instances " Rel 7.0, 3/05: 503 families, >300k instances " Rel 9.0, 7/08: 603 families, 896k instances ! Rel 9.1, 1/09: 1372 families, ??? instances " 43

  8. Rfam database ! Example Rfam Family " http://www.sanger.ac.uk/Software/Rfam/ ! (Release 7.0, 3/2005) " IRE (partial seed alignment): ! Input (hand-curated): " 503 ncRNA families � Hom.sap. GUUCCUGCUUCAACAGUGUUUGGAUGGAAC MSA “seed alignment” " Hom.sap. UUUCUUC.UUCAACAGUGUUUGGAUGGAAC 280,000 annotated ncRNAs � Hom.sap. UUUCCUGUUUCAACAGUGCUUGGA.GGAAC SS_cons " Hom.sap. UUUAUC..AGUGACAGAGUUCACU.AUAAA Score Thresh T " Hom.sap. UCUCUUGCUUCAACAGUGUUUGGAUGGAAC Hom.sap. AUUAUC..GGGAACAGUGUUUCCC.AUAAU 8 riboswitches, 235 small nucleolar RNAs, Window Len W " Hom.sap. UCUUGC..UUCAACAGUGUUUGGACGGAAG Hom.sap. UGUAUC..GGAGACAGUGAUCUCC.AUAUG 8 spliceosomal RNAs, 10 bacterial Output: " Hom.sap. AUUAUC..GGAAGCAGUGCCUUCC.AUAAU antisense RNAs, 46 microRNAs, 9 Cav.por. UCUCCUGCUUCAACAGUGCUUGGACGGAGC CM " Mus.mus. UAUAUC..GGAGACAGUGAUCUCC.AUAUG ribozymes, 122 cis RNA regulatory Mus.mus. UUUCCUGCUUCAACAGUGCUUGAACGGAAC scan results & “full Mus.mus. GUACUUGCUUCAACAGUGUUUGAACGGAAC elements, … � alignment” " Rat.nor. UAUAUC..GGAGACAGUGACCUCC.AUAUG Rat.nor. UAUCUUGCUUCAACAGUGUUUGGACGGAAC SS_cons <<<<<...<<<<<......>>>>>.>>>>> 44 46 Day 2 ! Rfam – key issues "" " 5 slide synopsis of last lecture Overly narrow families " Covariance Models (CMs) represent conserved RNA sequence/structure motifs " Variant structures/unstructured RNAs " Spliced RNAs " They allow accurate search " RNA pseudogenes " But " Human ALU is SRP related w/ 1.1m copies " " a) search is slow " Mouse B2 repeat (350k copies) tRNA related " " b) model construction is laborious " Speed & sensitivity " Motif discovery " 48 49

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