A tutorial on RNA folding methods and resources

Transcription

1 A tutorial on RNA folding methods and resources Alain Denise, LRI/IGM, Université Paris-Sud with invaluable help from Yann Ponty, CNRS/Ecole Polytechnique 1 Master BIBS

2 Goals To help your work your way through the RNA data jungle. To introduce mature structure prediction/annotation tools and algorithms. Locate structural data Energy minimization Boltzmann Ensemble Pseudoknots Structural annotation Comparative methods 2 Master BIBS

3 RNA structure(s) 3 Master BIBS

4 RNA structure(s) 4 Master BIBS

5 How RNA folds G/C U/A U/G Canonical base-pairs 5s rrna (PDB ID: 1UN6) RNA folding = Hierarchical stochastic process driven by/resulting in the pairing (hydrogen bonds) of a subset of its bases. 5 Master BIBS

6 Secondary Structure representations 6 Master BIBS

7 Exercise Download the Java applet Varna ( [choose the Binaries file] Run it. See the two example structures, see how to switch from one to another. Put the following new sequence and structure: AAGGGCTTAGCTTAATTAAAGTAGTTGATTTGCATTCAGCAGCTGTAGGATAAAGTCTTGCAGTCCTTA (((((((..((((...)))).(((((...)))))...(((((...)))))))))))). Try the different representations (click right, Redraw, Algorithm) 7 A.Denise Y. Ponty M2 BIBS

8 Sources of RNA structural data Name Data type Scope Description File formats #Entries URL PDB All-atoms General RCSB Protein Data Bank Global repository for 3D molecular models PDB ~1,900 models NDB All-atoms, Secondary structures General Nucleic Acids Database Nucleic acids models and structural annotations. PDB, RNAML ~2,000 models RFAM Alignments, Secondary structures 3 General RNA FAMilies Multiple alignments of RNA as functional families. Features consensus secondary structures, either predicted and/or manually curated. STOCKHOLM, FASTA ~1,973 Alignments/ structures, 2,756,313 sequences STRAND Secondary structures General The RNA secondary STRucture and statistical ANalysis Database Curated aggregation of several databases CT, BPSEQ, RNAML, FASTA, Vienna 4,666 structures PseudoBase Secondary structures Pseudokn otted RNAs PseudoBase Secondary structure of known pseudonotted RNAs. Extended Vienna RNA 359 structures CRW Sequence alignments, Secondary structures Ribosoma l RNAs, Introns Comparative RNA Web Site Manually curated alignments and statistics of ribosomal RNAs. FASTA, ALN, BPSEQ 1,109 structures, 91,877 sequences 8 Master BIBS

9 Basic prediction Minimal free-energy folding 9 Master BIBS

10 Minimal Free-Energy (MFE) Folding Goal: Predict the functional (aka native) conformation of an RNA Hypothesis : it folds into a minimal free energy configuration Turner model associates free-energies to secondary structures The model is additive : the global energy is the sum of energies of secondary structure elements : basepair stackings terminal loops internal loops bulges Biological sequence analysis Durbin, Eddy, Krogh, Mitchison Cambridge Univ. Press Master BIBS

11 Minimal Free-Energy (MFE) Folding Several softwares do this work, notably RNAFold and Mfold. Most of them only consider secondary structures without pseudoknots. Almost all of them are based on a very powerful approach in algorithmics : dynamic programming. CAGUAGCCGAUCGCAGCUAGCGUA RNAFold, MFold 11 Master BIBS

12 Minimal Free-Energy (MFE) Folding So the folding problem is, given an energy function : Data : a sequence, Output : the folding which has the minimum free energy CAGUAGCCGAUCGCAGCUAGCGUA RNAFold, MFold 12 Master BIBS

13 Exercise In Rfam ( search for the microrna mir-263 family Once on the page of the family, click on alignments in the left menu. Ask to view the Seed alignment in FASTA (Ungapped format) : this can be done within the second group of choices : «Formatting options» Take the first two sequences: T.castaneum and D.virilis Fold them with RNAfold ( With Varna, draw and compare the two structures 13 Master BIBS

14 Exercise: some not easy cases Here are three trna sequences with their true structures. Fold them with RNAfold, and compare each of the predicted structure with the corresponding true one. Is it all right? >Artibeus jamaicensis, True Structure, trna Alanine AAGGGCTTAGCTTAATTAAAGTAGTTGATTTGCATTCAGCAGCTGTAGGATAAAGTCTTGCAGTCCTTA (((((((..((((...)))).(((((...)))))...(((((...)))))))))))). >Balaenoptera musculus, True Structure, trna Alanine GAGGATTTAGCTTAATTAAAGTGTTTGATTTGCATTCAATTGATGTAAGATATAGTCTTGCAGTCCTTA (((((((..((((...))))..((((...))))...(((((...)))))))))))). >Bos taurus, True Structure, trna Alanine GAGGATTTAGCTTAATTAAAGTGGTTGATTTGCATTCAATTGATGTAAGGTGTAGTCTTGCAATCCTTA (((((((..((((...)))).(((((...)))))...(((((...)))))))))))). 14 Master BIBS

15 Dynamic programming explained on a simpler (and unrealistic) energy model The first dynamic programming algorithm for RNA folding (Nussinov, Jacobson 1978) considered only the number of basepairs for the energy function: Data : a sequence Output : the secondary structure (without pseudonots) that has the largest number of basepairs. Very unrelevant energy model! Meanwhile this algorithm led to the best current folding methods (with much better energy functions) because it uses dynamic programming. 15 Master BIBS

16 Dynamic programming explained on a simpler (and unrealistic) energy model Dynamic programing is a very general optimization method, it is used for a lot of applications in computer science. The first step is to find a recurrence relation that allows to construct the objects of interest. Notation : γ(i,j) = number of basepairs in the best structure between bases i and j. δ(i,j) = 1 if bases i et j are complementary, 0 otherwise. 16 Master BIBS

17 Nussinov s algorithm (1978) Let i and j be two positions. Suppose that I know all the best possible structures within any interval located between i and j, but not equal to the interval (i,j) i+1 j-1 1 i n j How can I construct the best possible structure between i and j? 17 Master BIBS

18 Nussinov s algorithm (1978) i i+1 1. j i 2. j-1 j 3. i+1 j-1 i j i k k+1 j 4. How can I construct the best possible structure between i and j? There are 4 ways to do it. 18 Master BIBS

19 Nussinov s algorithm (1978) γ(i,j) = Max { i i+1 1. γ(i+1,j) j i j-1 2. γ(i,j-1) j i+1 j-1 i j 3. γ(i+1,j-1)+δ(i,j) i k k+1 j 4. Max i<k<j { γ(i,k) + γ(k+1,j)} } 19 Master BIBS

20 Recurrence relation γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } γ(i,i) = 0 for any i γ(i,j) = 0 if j<i 1 i j n [ ] With this recurrence, we can compute γ(1,n). the maximum number of basepairs in the whole sequence. We will construct the corresponding structure in a following step. 20 Master BIBS

21 C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 C C G G C A U G γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } 21 Master BIBS

22 C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 C C G G C A U G C 2 G 3 γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } 22 Master BIBS

23 C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 C C G G C A U G γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } 23 Master BIBS

24 C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 C C G G C A U G C 1 C 2 G 3 γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } 24 Master BIBS

25 C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 C C G G C A U G C 1 C 2 G 3 γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } 25 Master BIBS

26 C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 C C G G C A U G γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } 26 Master BIBS

27 C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 C C G G C A U G C 1 C 2 G 3 G 4 γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } 27 Master BIBS

28 C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 C C G G C A U G C 2 G 3 G 4 C 5 γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } 28 Master BIBS

29 C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 C C G G C A U G Exercise: complete the table. γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } 29 Master BIBS

30 C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 C C G G C A U G C 1 C 2 G 3 G 4 C 5 A 6 U 7 G 8 γ(i,j) = Max { γ(i+1,j) γ(i,j-1), γ(i+1,j-1)+δ(i,j) Max i<k<j { γ(i,k) + γ(k+1,j)} } 30 Master BIBS

31 Algorithmic complexity The complexity of an algorithm is a measure of its memory and time requirements, according to the size of the data. In many cases, it is given not precisely, but with an «order of magnitude». Here, according to n, the length of the sequence: Space complexity: O(n 2 ) Time complexity: O(n 3 ) 31 Master BIBS

32 A language-theoretical point of view γ(i,j) = Max { i i+1 1. γ(i+1,j) j i j-1 2. γ(i,j-1) j i+1 j-1 i j 3. γ(i+1,j-1)+δ(i,j) i k k+1 j 4. Max i<k<j { γ(i,k) + γ(k+1,j)} } 32 Master BIBS

33 A language-theoretical point of view Decomposition Context-free grammar S i i+1 NS j i SN j-1 j i+1 j-1 i j NSN i k k+1 j SS ε N a c g u } 33 Master BIBS

34 A language-theoretical point of view Decomposition Context-free grammar S NS SN NSN SS ε N a c g u S a N S c N S N g c N S N g N S a u N S N S g ε 34 Master BIBS

35 A language-theoretical point of view Decomposition Context-free grammar a S NS SN NSN SS ε N a c g u c c a N N S S S N N S N N u N S S g g The grammar can generate all possible sequences For any given sequence, it can generate all possible secondary structures: each derivation tree represents a structure. So the grammar has been made for being ambiguous The energy of a given structure can be computed with a system of attributes that are associated to the rules of the grammar. In fact, the Nussinov algorithm is a variant of CYK (see ITPP course). N S g ε 35 Master BIBS

36 Up-to-date algorithm: Zucker, Stiegler 1981 and its improvements The same general principle : dynamic programming. The same algorithmic complexity. But a much more realistic energy function. The parameters have been set by experimental measures (Turner, 1999, 2004). Softwares: RNAfold, UnaFold/mfold 36 Master BIBS

37 Probabilistic approaches in RNA folding RNA in silico paradigm shift: From single structure, minimal free-energy folding to ensemble approaches. CAGUAGCCGAUCGCAGCUAGCGUA UnaFold, RNAFold, Sfold Ensemble diversity? Structure likelihood? Evolutionary robustness? 37 Master BIBS

38 Probabilistic approaches indicate uncertainty and suggest alternative conformations Example: >ENA M10740 M Saccharomyces cerevisiae Phe-tRNA. : Location:1..76 GCGGATTTAGCTCAGTTGGGAGAGCGCCAGACTGAAGATTTGGAGGTCCTGTGTTCGATCCACAGAATTCGCACCA RNAFold -p Native structure «dot-plot» 38 Master BIBS

39 Prise en compte des liaisons non canoniques [Parisien, Major 2008] Séquence MC-Fold Structure secondaire (avec liaisons non canoniques) MC-Sym Structure 3D 39 Master BIBS

40 Prise en compte des liaisons non canoniques [Parisien, Major 2008] Modèle d énergie : décomposition de la structure similaire à Turner. Valeurs des paramètres estimés sur les structures connues (expérimentalement). Algorithme : heuristique basée en partie sur la programmation dynamique. 40 Master BIBS

41 Pseudoknots New practical tools (at last!) 41 Master BIBS

42 Pseudoknots Pseudoknots are complex topological models indicated by crossing interactions. Pseudoknots are largely ignored by computational prediction tools: Lack of accepted energy model Algorithmically challenging Yet heuristics can be sometimes efficient. Visualizing of secondary structure with pseudoknots is supported by: PseudoViewer VARNA 42 Master BIBS

43 Exercise Here is the native structure of a tmrna from the PseudoBase (ID: PKB210) CCGCUGCACUGAUCUGUCCUUGGGUCAGGCGGGGGAAGGCAACUUCCCAGGGGGCAACCCCGAACCGCAGCAGCGACAUUCACAAGGAAU :((((((::(((:::[[[[[[[::))):((((((((((::::)))))):((((::::)))):::)))):)))))):::::::]]]]]]]: Fold this sequence using RNAFold and compare the result to the native structure Fold this sequence using Pknots-RG (Program type: Enforcing PK) 43 Master BIBS

44 Predicting pseudoknots True structure pknotsrg RNAfold 44 Master BIBS

45 Predicting pseudoknots In fact, the general problem of predicting secondary structures with pseudoknots with a relevant energy function is practically intractable Formally, this problem belongs to the class of NP-hard problems, that is among the most difficult problems in computer science. Meanwhile, algorithms exist for some restricted classes of pseufoknots. This is the case of pknotsrg. But these algorithms are computationally expensive. 45 Master BIBS

46 A summary of prediction algorithms, with or without pseudoknots Without pseudoknots Year Authors Complexity 1981 Zuker, Stiegler O(n 4 ) 1999 Lingsǿ, Zucker, Pedersen O(n 3 ) RNAfold, mfold With pseudoknots 1999 Rivas, Eddy O(n 6 ) 2000 Lyngsǿ, Pedersen O(n 5 ) 2000 Akutsu, Uemura O(n 5 ) 2003 Dirks, Pierce O(n 5 ) 2004 Reeder, Giegerich O(n 4 ) pknotsrg 2009 Cao, Chen O(n 6 ) 46 Master BIBS

47 Prediction by Homology 47 Master BIBS

48 Prediction by homology Data : several homologous RNA sequences. Output : a consensus structure for this set of sequences. 48 Master BIBS

49 1. From sequence alignment 49 Master BIBS

50 Detecting covariations We start from a sequence alignment: GAGGACTGAGCTCAGTTAAAGTGCCTG AAGGGCCCCGCTGGGCAAAG--GCTG AAGGGGTCGGCTGACCTAAAGTAGTTG GAGGGGTGAG-GCAUCTAAAGTGTTTG GAGGACTGTGCTCAGTTAAAGTGTTTG...((((...))))... We search for sequence covariations They come from compensatory mutations during the evolution 50 Master BIBS

51 Detecting covariations We start from a sequence alignment: GAGGACTGAGCTCAGTTAAAGTGCCTG AAGGGCCCCGCTGGGCAAAG--GCTG AAGGGGTCGGCTGACCTAAAGTAGTTG GAGGGGTGAG-GCAUCTAAAGTGTTTG GAGGACTGTGCTCAGTTAAAGTGTTTG...((((...))))... Measure : mutual information between positions i and j : - Pr(i=a) Pr(j=b) log(pr(i=a j=b)) a,b where a and b are the different nucleotides. 51 Master BIBS

52 Two softwares based on this approach RNA-alifold (Hofacker et al. 2000) RNAz (Washietl et al. 2005) 52 Master BIBS

53 Application : trna Alanine >Artibeus_jamaicensis AAGGGCTTAGCTTAATTAAAGTAGTTGATTTGCATTCAGCAGCTGTAGGATAAAGTCTTGCAGTCCTTA >Balaenoptera_musculus GAGGATTTAGCTTAATTAAAGTGTTTGATTTGCATTCAATTGATGTAAGATATAGTCTTGCAGTCCTTA >Bos_taurus GAGGATTTAGCTTAATTAAAGTGGTTGATTTGCATTCAATTGATGTAAGGTGTAGTCTTGCAATCCTTA >Canis_familiaris GAGGGCTTAGCTTAATTAAAGTGTTTGATTTGCATTCAATTGATGTAAGATAGATTCTTGCAGCCCTTA >Ceratotherium_simum GAGGGTTTAGCTTAATTAAAGTGTTTGATTTGCATTCAGTTGATGTAAGATAGAGTCTTGCAGCCCTTA >Dasypus_novemcinctus GAGGACTTAGCTTAATTAAAGTGCCTGATTTGCGTTCAGGAGATGTGGGGCTAAATCTTGCAGTCCTTA >Equus_asinus AAGGGCTTAGCTTAATGAAAGTGTTTGATTTGCGTTCAATTGATGTGAGATAGAGTCTTGCAGTCCTTA >Erinaceus_europeus GAGGATTTAGCTTAAAAAAAGTGGTTGATTTGCATTCAATTGATATAGGAAATATAATCTTGTAATCCTTA >Felis_catus GAGGACTTAGCTTAATTAAAGTGTTTGATTTGCAATCAATTGATGTAAGATAGATTCTTGCAGTCCTTA >Hippopotamus_amphibius AGGGACTTAGCTTAATAAAAGCAGTTGAGTTGCATTCAATTGATGTGAGGTGCGGTCTTGCAGTCTCTA >Homo_sapiens AAGGGCTTAGCTTAATTAAAGTGGCTGATTTGCGTTCAGTTGATGCAGAGTGGGGTTTTGCAGTCCTTA 53 Master BIBS

54 Exercise 1. Compute an alignment of the previous sequences, by using ClustalW or ClustalO: (do not forget to put the «DNA» option) 2. Copy/paste the result in RNAalifold : 3. Look at the result. 54 Master BIBS

55 Application : trna H.sapiens >Homo_sapiensArg TGGTATATAGTTTAAACAAAACGAATGATTTCGACTCATTAAATTATGATAATCATATTTACCAA >Homo_sapiensAsn TAGATTGAAGCCAGTTGATTAGGGTGCTTAGCTGTTAACTAAGTGTTTGTGGGTTTAAGTCCCATTGGTCTAG >Homo_sapiensAsp AAGGTATTAGAAAAACCATTTCATAACTTTGTCAAAGTTAAATTATAGGCTAAATCCTATATATCTTA >Homo_sapiensCys AGCTCCGAGGTGATTTTCATATTGAATTGCAAATTCGAAGAAGCAGCTTCAAACCTGCCGGGGCTT >Homo_sapiensGln TAGGATGGGGTGTGATAGGTGGCACGGAGAATTTTGGATTCTCAGGGATGGGTTCGATTCTCATAGTCCTAG >Homo_sapiensGlu GTTCTTGTAGTTGAAATACAACGATGGTTTTTCATATCATTGGTCGTGGTTGTAGTCCGTGCGAGAATA >Homo_sapiensGly ACTCTTTTAGTATAAATAGTACCGTTAACTTCCAATTAACTAGTTTTGACAACATTCAAAAAAGAGTA >Homo_sapiensHis GTAAATATAGTTTAACCAAAACATCAGATTGTGAATCTGACAACAGAGGCTTACGACCCCTTATTTACC >Homo_sapiensIso AGAAATATGTCTGATAAAAGAGTTACTTTGATAGAGTAAATAATAGGAGCTTAAACCCCCTTATTTCTA >Homo_sapiensLeuCun ACTTTTAAAGGATAACAGCTATCCATTGGTCTTAGGCCCCAAAAATTTTGGTGCAACTCCAAATAAAAGTA 55 Master BIBS

56 Exercise The same as previously, but with these new sequences. 1. Compute an alignment of the previous sequences, by using ClustalW or ClustalO: (do not forget to put the «DNA» option) 2. Copy/paste the result in RNAalifold : 3. Look at the result. What happened? Why? 56 Master BIBS

57 Simultaneous folding and alignment 57 Master BIBS

58 Problem specification Data : a set of sequences Output : a sequence alignment, and a common secondary structure. 58 Master BIBS

59 Approaches The reference approach: Sankoff s algorithm (1985) Algorithmic approach: dynamic programming Complexity : n 3k for k sequences of length n Two implementations (with constraints) Foldalign (Gorodkin, Heyer, Stormo 1997, Havgaard, Lyngso, Stormo, Gorodkin 2005). Dynalign (Mathews, Turner 2002) Heuristics based on this algorithm : LocaRNA ( 59 Master BIBS

60 Exercise 1. Take the two previous sets of sequences (one after the other) and run LocARNA. Look at the results. 2. Consider the first set only. Run LocARNA with the first two sequences, then the first three, and so on. How many sequences do you need to get the right trna structure? 60 Master BIBS

61 Sankoff s algorithm in a few words : Data : a set of sequences Parameters : a score matrix, giving a score S ij,kl for each alignment of pairs of nucleotides. Output : a sequence alignment, and a common secondary structure. Method : dynamic programming. It is a bit complicated, so we will study a simplified version of the algorithm : Foldalign. Two sequences only No multiloop allowed in the secondary structure Simplified score matrix 61 Master BIBS

62 Recurrence relation for Foldalign 62 Master BIBS