alain denise bioinformatique lri orsay umr cnrs 8623 université paris-sud 11 algorithmes pour la...
TRANSCRIPT
![Page 1: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/1.jpg)
Alain DeniseBioinformatiqueLRI OrsayUMR CNRS 8623Université Paris-Sud 11
Algorithmes pour la comparaison des structures secondaires d’ARNAlgorithmes pour la comparaison des structures secondaires d’ARN
![Page 2: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/2.jpg)
© Ebbe Sloth Andersen
Les multiples rôles de l’ARNLes multiples rôles de l’ARN
![Page 3: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/3.jpg)
© Ebbe Sloth Andersen
Les multiples rôles de l’ARNLes multiples rôles de l’ARN
![Page 4: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/4.jpg)
Why RNA ?Why RNA ?
Present in all cellular processes The only molecule which can be genome as well
as catalyser Origin of life (?): RNA world Frequent target for antibiotics
© E.Westhof 2005
![Page 5: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/5.jpg)
RNA structure: tRNARNA structure: tRNA
Primary structure
Tertiary structure Secondary structure
GCGGAUUUAGCUCAGUUGGGAGAGCGCCAGACUGAAUAUCUGGAGGUCCUGUGUUCGAUCCCACAGAAUUCGCACCA
![Page 6: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/6.jpg)
RNA structure levelsRNA structure levelsRNA structure ~ Graph of bounded degree,
containing a (known) hamiltonian path.
Arc-annotated sequences
General (Tertiary structure)
Crossing (Secondary structure
with pseudoknots)
Nested (Secondary structurewithout pseudoknots)
Plain (Primary structure)
![Page 7: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/7.jpg)
RNA « Bio-Algorithmics » RNA « Bio-Algorithmics »
Structure prediction (given sequence) Design: sequence prediction (given structure) Structural pattern-matching Comparison of two or several structures
![Page 8: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/8.jpg)
Why to compare RNA structures ?Why to compare RNA structures ?
• How much are they similar (or different?)
classification phylogeny
• Which parts are the more similar between the two structures?
• Is the small one similar to a part of the large one?
Comparison score + correspondence between the structures
![Page 9: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/9.jpg)
Edition and alignmentEdition and alignment
We are given a set of basic operations and a score function associated to each of them.
Data : two structures S1 and S2.
• Edit(S1,S2) : find a best-scoring sequence of operations which changes S1 into S2.
• Align(S1,S2) : find a structure S which contains S1 and S2 as substructures, in such a way to maximize
Score(Edit(S1,S)+Edit(S2,S)).
![Page 10: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/10.jpg)
Example: sequence comparisonExample: sequence comparison
Deux séquences v = v1v2…vn et w = w1w2…wm
Opérations d’édition : • ins(x,i) • suppr(x,i)• subs(x,y,i)
CHAT - suppr(C,1) HAT - subs(H,R,1) RAT
(Pour les séquences : édition ~ alignement : CHAT - RAT)
![Page 11: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/11.jpg)
Example: tree comparisonExample: tree comparison
![Page 12: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/12.jpg)
Edition vs AlignmentEdition vs Alignment
Alignment
EditionIns( )Del( )
Subs( , )
Ancestor relations are conserved
![Page 13: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/13.jpg)
The nested caseThe nested case
Secondary structures (without pseudokots) Tree comparison
![Page 14: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/14.jpg)
Tree comparisonTree comparison
![Page 15: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/15.jpg)
Tree edition algorithmTree edition algorithmZhang, Shasha 1989
![Page 16: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/16.jpg)
Tree edition algorithmTree edition algorithmScore( (f) , ’(f’) ) = Max
Subs(, ’) + Score(f,f’)
Ins(’) + Score((f) , f’ )
Del() + Score( f , ’(f’) )
Score( [(f) o t1 o … o tp] , [’(f’), t’1 o … o t’q] ) = Max
Score((f), ’(f’)) + Score([t1 o … o tp], [t’1 o … o t’q])
Ins(’) + Score( [(f) o t1 o … o tp] , [ f’, t’1 o … o t’q])
Del() + Score([ f o t1 o … o tp] , [’(f’) o t’1,… o t’q])
f t1 t2 … tp
Zhang, Shasha 1989
O(n3logn) [Klein 1998]
![Page 17: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/17.jpg)
Score( (f) , ’(f’) ) = Max
Subs(, ’) + Score(f,f’)
Ins(’) + Score((f) , f’ )
Del() + Score( f , ’(f’) )
Tree alignment algorithmTree alignment algorithm
Score((f) o t1 o … o tp ; ’(f’) o t’1 o … o t’q ) = Max
Score((f); ’(f’)) + Score(t1 o … o tp ; t’1 o … o t’q)
Ins(’) + Maxi { Score((f) o … o ti ; f’ ) + Score(ti+1 o … o tp ; t’1 o … o t’q) }
Del() + Maxj { Score( f ; ’(f’) o t’1 o … o t’j) + Score(t1 o … o tp; t’j+1 o … o t’q) }
f t1 t2 … tp
Jiang, Wang, Zhang 1995
O(n4)
![Page 18: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/18.jpg)
Edition vs AlignmentEdition vs AlignmentScore( [(f), t1,…,tp] , [’(f’), t’1,…,t’q] ) = Max
…
Ins(’) + Score( [(f), t1,…,tp] , [ f’, t’1,…,t’q])
…
Score( [(f), t1,…,tp] , [’(f’), t’1,…,t’q] ) = Max
…
Ins(’) + Maxi { Score( [(f), …ti] , f’ ) + Score([ti+1,…, tp], [t’1,…,t’q]) }
…
![Page 19: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/19.jpg)
Edition vs AlignmentEdition vs AlignmentScore( , ) = Max
…
Ins( ) + Score( , )
…
Score( , ) = Max
…
Ins( ) + Maxi { Score( , ) + Score( , ) }
…
i+1i
![Page 20: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/20.jpg)
Edition vs AlignmentEdition vs AlignmentScore( , ) = Max
…
Ins( ) + Score( , )
…
Score( , ) = Max
…
Ins( ) + Maxi { Score( , ) + Score( , ) }
…
i+1i
Can be inserted anywhere
![Page 21: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/21.jpg)
Complexity Complexity
Edition [Zhang, Shasha 1989, Klein 1998]
• Worst-case : O(n4) [Zhang-Shasha 1989] O(n3logn) [Klein 1998,
Dulucq-Touzet 2003]
• In average : O(n3) [Dulucq-Tichit 2003]
Alignment [Jiang, Wang, Zhang 1995]
• Worst-case : O(n4)
![Page 22: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/22.jpg)
3 operations!
AU AU
GCGC
GUGU
UAU U
Delete( )
Insert( )
Insert( )
Edition operations: problemEdition operations: problem
A-UU-AG-CC-U
A-UU U
G-CC-U
AUGG…….UCAU AUGG…….UCUU
![Page 23: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/23.jpg)
Opérations on bases: Substitution:
Deletion / Insertion:
Operations on arcs:Arc-substitution:
Arc-deletion / Arc-insertion:
Arc-breaking / :
Arc-altering / :
A C
A
C G U A
C G
C G C G
C G C -
Edition operations on RNAEdition operations on RNA
New
![Page 24: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/24.jpg)
A first solutionA first solution
A-UU-AG-CC-U
A-UU A
G-CC-U
AUGG…….UCAU AUGG…….UCAU
A
U
G
C
U
A
C
U
A
U
G
C
U
A
C
U
But this implies some constraints on the scores. For example:
Arc-deletion = Arc-Breaking + 2 Base-Deletion
Höchsmann, Töller, Gierich, Kurtz 2003(RNAforester)
![Page 25: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/25.jpg)
Edition operations on RNAEdition operations on RNA
Opérations on bases: Substitution:
Deletion / Insertion:
Operations on arcs:Arc-substitution:
Arc-deletion / Arc-insertion:
Arc-breaking / :
Arc-altering / :
A C
A
C G U A
C G
C G C G
C G C -
![Page 26: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/26.jpg)
General
Crossing
Nested
Plain
Complexity of the edition problemComplexity of the edition problem
![Page 27: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/27.jpg)
General Crossing Nested Plain
General NP-complete
Crossing NP-complete
Nested NP-complete O(nm3)
Plain O(nm / logn)
• Jiang, Lin, Ma, Zhang 2002• Blin, Fertin, Rusu, Sinoquet 2003• Crochemore, Landau, Ziv-Ukelson 2002
If 2Score(Arc-altering) = Score(Arc-breaking) + Score (Arc-removing), then algorithm in O(n3m) or Edit(crossing,nested) et Edit(nested,nested)
Complexity of the edition problemComplexity of the edition problem
![Page 28: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/28.jpg)
Complexity of 2ary struct. comparisonComplexity of 2ary struct. comparison
Tree operations RNA operations
Edition O(n3logn)[Zhang-Shasha 1989, Klein 1998]
NP-complete[Blin, Fertin, Sinoquet, Rusu 2003]
Alignment O(n4) [Jiang, Wang, Zhang 1995] ?
![Page 29: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/29.jpg)
Secondary structure alignmentSecondary structure alignment
A-BCD-EFGABB-DF-FG
AB---CDEFGABBDF---FG
ABCDEFG ABBDFFG
Edition Alignment
![Page 30: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/30.jpg)
New edition operations on treesNew edition operations on trees
Arc-breaking / :
Arc-altering / :
C G C G
C G C -
![Page 31: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/31.jpg)
Alignment algorithm (1/5)Alignment algorithm (1/5)
f
![Page 32: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/32.jpg)
Alignment algorithm (2/5) Alignment algorithm (2/5)
f t
![Page 33: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/33.jpg)
Alignment algorithm (2/5) Alignment algorithm (2/5)
f t
![Page 34: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/34.jpg)
Alignment algorithm (2/5)Alignment algorithm (2/5)
f t
![Page 35: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/35.jpg)
Alignment algorithm (2/5)Alignment algorithm (2/5)
f t
![Page 36: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/36.jpg)
Alignment algorithm (2/5)Alignment algorithm (2/5)
f t
![Page 37: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/37.jpg)
Alignment algorithm (3/5)Alignment algorithm (3/5)
f t
![Page 38: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/38.jpg)
Alignment algorithm (3/5)Alignment algorithm (3/5)
f t
![Page 39: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/39.jpg)
Alignment algorithm (3/5)Alignment algorithm (3/5)
f t
![Page 40: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/40.jpg)
Alignment algorithm (3/5)Alignment algorithm (3/5)
f t
![Page 41: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/41.jpg)
Alignment algorithm (3/5)Alignment algorithm (3/5)
f t
![Page 42: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/42.jpg)
Alignment algorithm (4/5)Alignment algorithm (4/5)
f t
![Page 43: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/43.jpg)
Alignment algorithm (5/5)Alignment algorithm (5/5)
f t
![Page 44: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/44.jpg)
Alignment algorithm (5/5) Alignment algorithm (5/5)
f t
![Page 45: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/45.jpg)
Alignment algorithm (5/5) Alignment algorithm (5/5)
f t
![Page 46: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/46.jpg)
Tree operations RNA operations
Edition O(n3logn)[Zhang-Shasha 1989, Klein 1998]
NP-complete[Blin, Fertin, Sinoquet, Rusu 2003]
Alignment O(n4) [Jiang, Wang, Zhang 1995]
O(n4) [Herrbach, AD, Dulucq, Touzet 2005]
Complexity of 2ary struct. comparisonComplexity of 2ary struct. comparison
![Page 47: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/47.jpg)
Tree operations RNA operations
Edition O(n3logn)[Zhang-Shasha 1989, Klein 1998]
NP-complete[Blin, Fertin, Sinoquet, Rusu 2003]
Alignment O(n4) [Jiang, Wang, Zhang 1995]
O(n4) [Herrbach, AD, Dulucq, Touzet 2005]
Complexity of 2ary struct. comparisonComplexity of 2ary struct. comparison
Complexity of the alignment problem for the other structure
levels: [Blin, Touzet 2006]
![Page 48: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/48.jpg)
Example: two tRNAsExample: two tRNAs
Homo sapiens Bacillus subtilis
Drawing: Tulip (David Auber et al., LaBRI)
Base-subs / Arc-subs
Deletions / Insertions
Arc-breaking
Arc-altering
![Page 49: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/49.jpg)
Et dans la vraie vie ? Et dans la vraie vie ?
![Page 50: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/50.jpg)
Alignement de RNAses PAlignement de RNAses P
![Page 51: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/51.jpg)
Alignement de RNAses PAlignement de RNAses P
![Page 52: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/52.jpg)
Alignement de RNAses PAlignement de RNAses P
![Page 53: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/53.jpg)
Alignement de RNAses PAlignement de RNAses P
![Page 54: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/54.jpg)
To do…To do…• Biological validation :
• Test on real data• Comparison with other softwares (RNAForester, MiGal [J.Allali,
M.F.Sagot])• Combined approaches ([J.Allalli, A.Ouangraoua-P.Ferraro]) • Parameters : substitution matrices etc.• Statistical evaluation of results
Relevant algorithms and parameters Useful and user-friendly programs
• Sequence/Structure alignment• Multiple alignment • …
![Page 55: Alain Denise Bioinformatique LRI Orsay UMR CNRS 8623 Université Paris-Sud 11 Algorithmes pour la comparaison des structures secondaires dARN Algorithmes](https://reader035.vdocuments.site/reader035/viewer/2022062511/55142247550346ec488b58b3/html5/thumbnails/55.jpg)
CréditsCrédits
• Julien Allali• David Auber • Serge Dulucq• Claire Herrbach• Rym Kachouri• Yann Ponty• Michel Termier• Laurent Tichit• Hélène Touzet• Eric Westhof