Beyond ab initio modelling… Comparative and Boltzmann equilibrium Yann Ponty, CNRS/Ecole Polytechnique with invaluable help from Alain Denise, LRI/IGM,

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Beyond ab initio modelling… Comparative and Boltzmann equilibrium Yann Ponty, CNRS/Ecole Polytechnique with invaluable help from Alain Denise, LRI/IGM, Université Paris-Sud M2 Bioinfo Paris-Saclay

Prediction by homology M2 Bioinfo Paris-Saclay  Data : several homologous RNA sequences.  Output : a consensus structure for this set of sequences.

Prediction by Homology From sequence alignment 3M2 Bioinfo Paris-Saclay

Detecting covariations M2 Bioinfo Paris-Saclay  We start from a sequence alignment: GAGGACTGAGCTCAGTTAAAGTGCCTG AAGGGCCCCGCTGGGCAAAG--GCTG- AAGGGGTCGGCTGACCTAAAGTAGTTG GAGGGGTGAG-GCAUCTAAAGTGTTTG GAGGACTGTGCTCAGTTAAAGTGTTTG  Look for sequence covariations

Detecting covariations M2 Bioinfo Paris-Saclay  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

Detecting covariations M2 Bioinfo Paris-Saclay  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

Detecting covariations M2 Bioinfo Paris-Saclay  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.

Two softwares based on this approach M2 Bioinfo Paris-Saclay  RNA-alifold (Hofacker et al. 2000)  RNAz (Washietl et al. 2005)

RNAalifold 9M2 Bioinfo Paris-Saclay

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 10M2 Bioinfo Paris-Saclay

Exercise M2 Bioinfo Paris-Saclay Compute an alignment of the previous sequences, by using MAFFT: (do not forget to set the Nucleic Acid option) 2. Copy/paste the result in RNAalifold : 3. Look at the result.

MAFFT alignment >Artibeus_jamaicensis AAGGGCTTAGCTTAATTAAAGTAGTTGATTTGCATTCAGCAGCTGTAGG--ATAAAGTCTTGCAGTCCTTA >Balaenoptera_musculus GAGGATTTAGCTTAATTAAAGTGTTTGATTTGCATTCAATTGATGTAAG--ATATAGTCTTGCAGTCCTTA >Bos_taurus GAGGATTTAGCTTAATTAAAGTGGTTGATTTGCATTCAATTGATGTAAG--GTGTAGTCTTGCAATCCTTA >Canis_familiaris GAGGGCTTAGCTTAATTAAAGTGTTTGATTTGCATTCAATTGATGTAAG--ATAGATTCTTGCAGCCCTTA >Ceratotherium_simum GAGGGTTTAGCTTAATTAAAGTGTTTGATTTGCATTCAGTTGATGTAAG--ATAGAGTCTTGCAGCCCTTA >Felis_catus GAGGACTTAGCTTAATTAAAGTGTTTGATTTGCAATCAATTGATGTAAG--ATAGATTCTTGCAGTCCTTA >Equus_asinus AAGGGCTTAGCTTAATGAAAGTGTTTGATTTGCGTTCAATTGATGTGAG--ATAGAGTCTTGCAGTCCTTA >Homo_sapiens AAGGGCTTAGCTTAATTAAAGTGGCTGATTTGCGTTCAGTTGATGCAGA--GTGGGGTTTTGCAGTCCTTA >Hippopotamus_amphibius AGGGACTTAGCTTAATAAAAGCAGTTGAGTTGCATTCAATTGATGTGAG--GTGCGGTCTTGCAGTCTCTA >Dasypus_novemcinctus GAGGACTTAGCTTAATTAAAGTGCCTGATTTGCGTTCAGGAGATGTGGG--GCTAAATCTTGCAGTCCTTA >Erinaceus_europeus GAGGATTTAGCTTAAAAAAAGTGGTTGATTTGCATTCAATTGATATAGGAAATATAATCTTGTAATCCTTA 12M2 Bioinfo Paris-Saclay

RNAalifold 13M2 Bioinfo Paris-Saclay

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 14M2 Bioinfo Paris-Saclay

Exercise M2 Bioinfo Paris-Saclay 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 ?

MAFFT alignment >Homo_sapiensArg TGGTATATAGT---TTAAACAAAACGAATGATTTCGACTCATTAAAT---TATGATAA---TCATATTTACCAA >Homo_sapiensGly ACTCTTTTAGT---ATAAATAGTACCGTTAACTTCCAATTAACTAGT---TTTGACAACATTCAAAAAAGAGTA >Homo_sapiensHis GTAAATATAGT---TTAACCAAAACATCAGATTGTGAATCTGACAAC--AGAGGCTTACGACCCCTTATTTACC >Homo_sapiensIso AGAAATATGTC---TGATAAAAGAGTTACTTTGATAGAGTAAATAAT--AGGAGCTTAAACCCCCTTATTTCTA >Homo_sapiensGlu GTTCTTGTAGT---TGAAATACAACGATGGTTTTTCATATCATTGGT--CGTGGTTGTAGTCCGTGCGAGAATA >Homo_sapiensLeuCun ACTTTTAAAGG---ATAACAGCTATCCATTGGTCTTAGGCCCCAAAAATTTTGGTGCAACTCCAAATAAAAGTA >Homo_sapiensAsn TAGATTGAAGCCAGTTGATTAGGGTGCTTAGCTGTTAACTAAGTGTT-TGTGGGTTTAAGTCCCATTGGTCTAG >Homo_sapiensGln TAGGATGGGGTGTGATAGGTGGCACGGAGAATTTTGGATTCTCAGGG--ATGGGTTCGATTCTCATAGTCCTAG >Homo_sapiensCys AGCTCCGAGGT-----GATTTTCATATTGAATTGCAAATTCGAAGAA---GCAGCTTCAAACCTGCCGGGGCTT >Homo_sapiensAsp AAGGTATTAGA---AAAACCATTTCATAACTTTGTCAAAGTTAAATT---ATAGGCTAAATCCTATATATCTTA 16M2 Bioinfo Paris-Saclay

RNAalifold 17M2 Bioinfo Paris-Saclay RNAalifold finds a common but much less conserved structure.

Prediction by Homology Simultaneous folding and alignment 18M2 Bioinfo Paris-Saclay

Problem specification  Data : a set of sequences  Output : a sequence alignment, and a common secondary structure. 19M2 Bioinfo Paris-Saclay

Approaches  The reference approach: Sankoff’s algorithm (1985)  Algorithmic approach: dynamic programming  Complexity : n 3k for k sequences of length n  There are several implementatons, herer are two of them (with constraints):  Foldalign (Gorodkin, Heyer, Stormo 1997, Havgaard, Lyngso, Stormo, Gorodkin 2005).  Dynalign (Mathews, Turner 2002)  Heuristics based on this algorithm :  LocaRNA ( freiburg.de:8080/LocARNA.jsp). freiburg.de:8080/LocARNA.jsp 20M2 Bioinfo Paris-Saclay

Exercise M2 Bioinfo Paris-Saclay Take the two previous sets of sequences (one after the other) and run LocARNA. Look at the results 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?

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 22M2 Bioinfo Paris-Saclay

23M2 Bioinfo Paris-Saclay

Recurrence relation for Foldalign 24M2 Bioinfo Paris-Saclay

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30M2 Bioinfo Paris-Saclay

From energy minimization to Boltzmann equilibrium? M2 Bioinfo Paris-Saclay

Optimization methods can be overly sensitive to fluctuations of the energy model Example:  Get RFAM seed alignment for D1-D4 domain of the Group II intron  Extract A. capsulatum ( Acidobacterium_capsu.1 ) sequence  Run RNAFold on sequence using default parameters  Rerun RNAFold using latest energy parameters Denise Ponty - Tuto ARN - Stability (Turner 2004) RNA ACGAUCGCGA CUACGUGCAU CGCGGCACGA CUGCGAUCUG CAUCGGA... Stability (Turner 1999) <ε<ε

Probabilistic approaches in RNA folding  RNA in silico paradigm shift:  From single structure, minimal free-energy folding…  … to ensemble approaches. …CAGUAGCCGAUCGCAGCUAGCGUA… Ensemble diversity? Structure likelihood? Evolutionary robustness? UnaFold, RNAFold, Sfold… M2 Bioinfo Paris-Saclay

Probabilistic approaches indicate uncertainty and suggest alternative conformations Example: >ENA|M10740|M Saccharomyces cerevisiae Phe-tRNA. : Location:1..76 GCGGATTTAGCTCAGTTGGGAGAGCGCCAGACTGAAGATTTGGAGGTCCTGTGTTCGATCCACAGAATTCGCACCA M2 Bioinfo Paris-Saclay Native structure RNAFold -p « dot-plot »

ij i+1j-1 i i+1 j j i j-1 i kk+1 j Nussinov’s algorithm (1978) Partition function algorithms can be adapted from non-ambiguous* DP scheme Is this decomposition ambiguous? * Ambiguous = Multiple ways to generate a structure 35M2 Bioinfo Paris-Saclay