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RNA-RNA Interaction Prediction with Stochastic Grammars Sebastian Wild Markus Nebel Anika Scheid {s_wild,nebel}@cs.uni-kl.de Fachbereich Informatik 5. October 2012 10. Herbstseminar der Bioinformatik Sebastian Wild RNA-RNA Interaction

  1. RNA-RNA Interaction Prediction with Stochastic Grammars Sebastian Wild Markus Nebel Anika Scheid {s_wild,nebel}@cs.uni-kl.de Fachbereich Informatik 5. October 2012 10. Herbstseminar der Bioinformatik Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 1 / 12

  2. RNA secondary structure: model primary structure: � � word over a, c, g, u secondary structure: � � parentheses word ( , | , ) gcccugauagcguagucacuagcgagucuguauucuaagaagaucacugaggguucgcgggg | ( ( ( ( ( | ( ( ( ( | | | ) ) ) ) | | ( ( | | ( ( ( | | | | ) ) ) ) ) | | | ( ( | | ( ( | | | | | ) ) | ) ) | | ) ) ) ) ) Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 2 / 12

  3. RNA also interacts! C G C C G C G A U G 5' U U G C A A U U A A U U A G A G C C G C C U A 41 nt C A U G A U A G A U C C G C G G G G C U U A C U bacterial antisense RNA A U C G U A U 3' A A U G A C C G G C G C U A U U A C G OxyS G A interact non-trivally, A U U A A C G C G C C G A U G C C A U U A A U U U U A C G U “knotted” structure U A A U A U C C G A U C A C U A A U G C C C A G A U A U U A U C G A G A U U CopT C A G U G U U A C U A U C G G C CopA G A C G U goal: predict whole G C C G G C G G U A U U G C C G G U G G G CC C A U G C C G G C C C C A G U A U interaction structure, C C G G C U A A U A C G U C A U A C U A A C G U A U A G not only interaction sites C U U 5' C G 3' C G U C fhlA A U A U G A C G G C A C U A G U 5' A U AUACACCGA U G C 3' 29bp 3' 5' Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 3 / 12

  4. RNA-RNA interaction problem (RIP) two RNA molecules interact, i. e. form a joint secondary structure predict the “best” one possible RIP in general NP -complete � restrict structure Exclude pseudo knots (internal & external) 1 Exclude Zig-Zags : 2 Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 4 / 12

  5. Example joint secondary structure � joint structure can be encoded as “2D-word” : pair of upper and lower word matching ( ) � internal bond matching [ ] � external bond (between two molecules) | � unpaired base [ [ [ [ [ � � ( ( | | ) ) ( ( ) ) ( ( ||) ) [ [ [ ( ( [ [ ) ) � ( ] ] ] ( ( ] ] ) ) ) ( ( ( ) ) ) ] ] ] ] ] Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 5 / 12

  6. Stochastic CFG Stochastic Context-free Grammars G = ( N, Σ, R, S, P ) nonterminals N terminal alphabet Σ � ⋆ � rule set R ⊂ N × N ∪ Σ start nonterminal S ∈ N P : R → [ 0, 1 ] : rule probabilities Probability of a derivation tree : Product of used rules’ probabilities For structure prediction: � � Σ = | b , ( b , ) b : b ∈ { a, c, g, u } unambiguous w. r. t. structure Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 6 / 12

  7. Structure Prediction with Formal Grammars training data Grammar prediction data ggcggugcca terminals ACGU auggugggugccaa structure annotations ( ( ( | | | ) ) ) | induces compute parametric parse trees stochastic model rel. rule freq. for secondary str. training phase compute most likely parse tree for sequence most likely structure auggugggugccaa | ( ( ( ( | | | | ) ) ) ) | Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 7 / 12

  8. Structure Prediction with Formal Grammars training data Grammar prediction data ggcggugcca terminals ACGU auggugggugccaa structure annotations ( ( ( | | | ) ) ) | induces compute parametric parse trees stochastic model rel. rule freq. for secondary str. training phase compute most likely parse tree for sequence Both can all be done with the same stochastic parser . most likely structure auggugggugccaa | ( ( ( ( | | | | ) ) ) ) | Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 7 / 12

  9. Stochastic CFG Stochastic Context-free Grammars G = ( N, Σ, R, S, P ) nonterminals N terminal alphabet Σ � ⋆ � rule set R ⊂ N × N ∪ Σ start nonterminal S ∈ N P : R → [ 0, 1 ] : rule probabilities Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 8 / 12

  10. 2 -dimensional CFG 2 -dimensional Context-free Grammars G = ( N, Σ, R, S, P ) nonterminals N terminal alphabet Σ N ∪ ( Σ ⋆ ) 2 � ⋆ � rule set R ⊂ N × start nonterminal S ∈ N P : R → [ 0, 1 ] : rule probabilities Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 8 / 12

  11. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: S Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  12. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: � | � S Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  13. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: � | �� � � � S S ( ) Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  14. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: � | �� �� � � �� � S S ( ( ) ) Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  15. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: �� [ � | �� �� � � �� � S S ( ( ) ) ] Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  16. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: �� [ �� [ � | �� �� � � �� � S S ( ( ) ) ] ] Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  17. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: �� [ �� [ �� [ � | �� �� �� �� � S ( ( ) ) ] ] ] Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  18. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: �� [ �� [ �� [ � | �� �� �� �� �� | � S ( ( ) ) ] ] ] Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  19. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: �� [ �� [ �� [ � | �� �� �� �� �� | �� | � ( ( ) ) ] ] ] Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  20. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: �� [ �� [ �� [ � | �� �� �� �� �� | �� | � ( ( ) ) ] ] ] Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  21. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: [ [ [ | | | ( ( ] ] ] ) ) Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

  22. A Simplistic Grammar for RIP � | � � | � � ( � � ) � � ( � � ) � S → , S → S, S → S , S → S S � � � � � � � � � � � � S → , S → S, S → S , S → S S | | ( ) ( ) � [ � [ � � S → , S → S ] ] Example: � |[ [ [ || � ((] ] ] )) Sebastian Wild RNA-RNA Interaction Prediction 2012/10/05 9 / 12

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