Flexible RNA design under structure and sequence constraints using a language theoretic approach

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1 Flexible RN design under structure and sequence constraints using a language theoretic approach Yu Zhou,, Yann Ponty Stéphane Vialette Jérôme Waldispühl Yi Zhang lain Denise LRI, niv. Paris-Sud, Orsay F-91405, France State Key Laboratory of Virology, Wuhan niversity, hina ellular and Molecular Medicine, niv. of alifornia San Diego, S LIX, NRS/Ecole Polytechnique, France + PIMS, Vancouver, anada LIM, niversité Paris-Est, France omputer Science, Mc ill niversity, anada Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 1 / 21

2 RN structure Primary structure Secondary structure Tertiary structure 5s rrn (PDBID: 1K73:B) RN Folding: Θ(n 3 ) Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 2 / 21

RN structure 1 10 20 30 40 50 60 70 80 90 100 110 120 122 Primary structure Secondary structure Tertiary structure 5s rrn (PDBID:

3 RN structure Primary structure Secondary structure Tertiary structure 5s rrn (PDBID: 1K73:B) RN Folding: Θ(n 3 ) RN Design: NP(-hard?) Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 2 / 21

4 Motivation for constrained design Motivation: Impact of structure on function of Exon Splicing Enhancers (ESE). Different structures Presence of ESE motif void other ESEs ( 1500!) Structural context of ESE motif in transcript was shown to affects its functionality. [Liu et al, FEBS Lett. 2010] ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 3 / 21

5 Design goals Positive design Optimize affinity of designed sequences towards target structure Negative design Limit affinity of designs towards alternative structures dditional constraints: Forbid motif list to appear anywhere in design Force motif list to appear each at least once Limit available alternatives for certain positions Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 4 / 21

6 Existing approaches for negative design Based on local search... RNInverse Info-RN RN-SSD NPack... genetic algorithms... RNFBinv FRNKenstein... or exact approaches RNIFold O4 Few algorithms support avoided/mandatory motifs none guarantees reasonable runtimes for any RN/motifs set. Typical reasons: Mandatory motifs Late deadends (Branch and Bound) Forbidden motifs Search space disconnection (Local Search) ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 5 / 21

7 Existing approaches for negative design Based on local search... RNInverse Info-RN RN-SSD NPack... genetic algorithms... RNFBinv FRNKenstein... or exact approaches RNIFold O4 Few algorithms support avoided/mandatory motifs none guarantees reasonable runtimes for any RN/motifs set. Typical reasons: Mandatory motifs Late deadends (Branch and Bound) Forbidden motifs Search space disconnection (Local Search) ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 5 / 21

8 Problem with local approaches: n example Simplified vocabulary {, } ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 6 / 21

9 Problem with local approaches: n example Simplified vocabulary {, } + Forbidden motifs F = {,} F may disconnect search space (holds for any move set!) ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 6 / 21

10 lobal Sampling [Levin et al, NR 12] Boltzmann Distribution (BD) based on affinity towards target S enerate at random candidate sequences w.r.t. BD Refold generated sequences and compare to target Boltzmann factor: B(s) := e E(s) RT Partition function: 10 B(s) 20 1 Z = s Boltzmann probability: p(s) := B(s) Z 30 Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 7 / 21

11 lobal Sampling [Levin et al, NR 12; Reinharz et al, ISMB 13] ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 8 / 21

12 lobal Sampling [Levin et al, NR 12; Reinharz et al, ISMB 13] omplementarity: + Diversity + Flexible composition - ccuracy ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 8 / 21

13 local approach [Reinharz et al, ISMB 13] Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB 13 9 / 21

14 Outline se formal language constructs to constrain global sampling Forced motifs voided motifs Structure compatibility + Positional constraints + Energy Model Regular language L Reg Weighted ontext-free Lang L S FL Folklore theorem (constructive): Reg (W)FL (W)FL Build weighted context-free grammar for L L S + Random generation lobal sampling under constraints Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

15 Outline se formal language constructs to constrain global sampling Forced motifs voided motifs Structure compatibility + Positional constraints + Energy Model Regular language L Reg Weighted ontext-free Lang L S FL Folklore theorem (constructive): Reg (W)FL (W)FL Build weighted context-free grammar for L L S + Random generation lobal sampling under constraints Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

16 Outline se formal language constructs to constrain global sampling Forced motifs voided motifs Structure compatibility + Positional constraints + Energy Model Regular language L Reg Weighted ontext-free Lang L S FL Folklore theorem (constructive): Reg (W)FL (W)FL Build weighted context-free grammar for L L S + Random generation lobal sampling under constraints ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

17 Outline se formal language constructs to constrain global sampling Forced motifs voided motifs Structure compatibility + Positional constraints + Energy Model Regular language L Reg Weighted ontext-free Lang L S FL Folklore theorem (constructive): Reg (W)FL (W)FL Build weighted context-free grammar for L L S + Random generation lobal sampling under constraints Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

18 Building the Finite State utomaton Forbidden motifs F = {f 1, f 2...} Mandatory motifs M = {m 1, m 2...} voiding a single word Linear automaton voiding multiple words Efficient ho-orasick construct Forcing a single word Linear automaton (omplemented) Forcing several words disjunctively ho-orasick Example: void (L ),,, ε Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

19 Building the Finite State utomaton Forbidden motifs F = {f 1, f 2...} Mandatory motifs M = {m 1, m 2...} voiding a single word Linear automaton voiding multiple words Efficient ho-orasick construct Forcing a single word Linear automaton (omplemented) Forcing several words disjunctively ho-orasick Example: void + (L L ) ε,,, ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

20 Building the Finite State utomaton Forbidden motifs F = {f 1, f 2...} Mandatory motifs M = {m 1, m 2...} voiding a single word Linear automaton voiding multiple words Efficient ho-orasick construct Forcing a single word Linear automaton (omplemented) Forcing several words disjunctively ho-orasick Example: Forcing (L ),,, ε ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

21 Building the Finite State utomaton Forbidden motifs F = {f 1, f 2...} Mandatory motifs M = {m 1, m 2...} voiding a single word Linear automaton voiding multiple words Efficient ho-orasick construct Forcing a single word Linear automaton (omplemented) Forcing several words disjunctively ho-orasick Example: Forcing or (L L ) ε ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

22 Building the Finite State utomaton To force multiple words, keep track of generated words: reate disjunctive automaton for each M M Reroute accepting states ccepting state = no forced word remaining (ε in ) Forbidden words can be added to sub-automata #States: O (2 M ( i f i + j m j )) Example: M = {, } ε {} ε M ε,,, ε {} Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

23 Building the Finite State utomaton To force multiple words, keep track of generated words: reate disjunctive automaton for each M M Reroute accepting states ccepting state = no forced word remaining (ε in ) Forbidden words can be added to sub-automata Example: M = {, } ε ε M ε #States: {} ε {} O (2 M ( i f i + j m j )),,, Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

24 Building the Finite State utomaton To force multiple words, keep track of generated words: reate disjunctive automaton for each M M Reroute accepting states ccepting state = no forced word remaining (ε in ) Forbidden words can be added to sub-automata #States: O (2 M ( i f i + j m j )) Example: M = {, }; F = {} ε ε ε,, ε ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

25 Building the grammar Input: Secondary Structure S + Positional constraints reate Parse Tree for secondary structure B Translate Parse Tree into single-word grammar Expand grammar to instantiate compatible base/base-pairs D Restrict to bases/base-pairs allowed at each position ( ( (. ) ) (.. ) ) Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

26 Building the grammar Input: Secondary Structure S + Positional constraints reate Parse Tree for secondary structure B Translate Parse Tree into single-word grammar Expand grammar to instantiate compatible base/base-pairs D Restrict to bases/base-pairs allowed at each position S 1 S 2 S 4 S 3 S 8 S 9 S10 S 5. ( ( (. ) ) (.. ) ) Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

27 Building the grammar Input: Secondary Structure S + Positional constraints reate Parse Tree for secondary structure B Translate Parse Tree into single-word grammar Expand grammar to instantiate compatible base/base-pairs D Restrict to bases/base-pairs allowed at each position S 1. S 2 S 2 ( S 3 ) S 3 ( S 4 ) S 8 S 4 ( S 5 ) S 5. S 8 ( S 9 ) S 9. S 10 S 10. ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

28 Building the grammar Input: Secondary Structure S + Positional constraints reate Parse Tree for secondary structure B Translate Parse Tree into single-word grammar Expand grammar to instantiate compatible base/base-pairs D Restrict to bases/base-pairs allowed at each position V 1 V 2 V 2 V 2 V 2 V 2 V 3 V 3 V 3 V 3 V 3 V 3 V 3 V 4 V 8 V 4 V 8 V 4 V 8 V 4 V 8 V 4 V 8 V 4 V 8 V 4 V 5 V 5 V 5 V 5 V 5 V 5 V 5 V 8 V 9 V 9 V 9 V 9 V 9 V 9 V 9 V 10 V 10 V 10 V 10 V 10 ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

29 Building the grammar Input: Secondary Structure S + Positional constraints reate Parse Tree for secondary structure B Translate Parse Tree into single-word grammar Expand grammar to instantiate compatible base/base-pairs D Restrict to bases/base-pairs allowed at each position V 1 V 2 V 2 V 2 V 2 V 2 V 3 V 3 V 3 V 3 V 3 V 3 V 3 V 4 V 8 V 4 V 8 V 4 V 8 V 4 V 8 V 4 V 8 V 4 V 8 V 4 V 5 V 5 V 5 V 5 V 5 V 5 V 5 V 8 V 9 V 9 V 9 V 9 V 9 V 9 V 9 V 10 V 10 V 10 V 10 V 10 ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

30 Random generation ombine F and automaton F (Multiplying #Rules by Q 3 ) (W)F Recurrence on #words (resp. weight) of each NT enrens [Ponty et al, Bioinformatics 06]: Precomputes #words for each non-terminal Random eneration w.r.t. weighted distribution niform distribution:,, or anywhere 1 or e 1/RT Nussinov energy model: or e 2/RT or e 3/RT E XY Stacking-pairs model (Turner 2004) WX YZ e WZ /RT (Based on refined, yet similar, grammar) Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

31 omplexity utomaton: Time #States Q O (2 M ( i f i + j m j )) Initial F: #Rules #Non Term. Θ(n) Final F: #Non Term. N O(n Q 2 ), #Rules R O(n Q 3 ) Random generation: ny NT fully determines the length of its produced words. Preprocessing: Θ( R ) time/θ( N ) space eneration: Θ(n Q ) time for each design omplete algorithm has linear overall complexity but total length of motifs impacts preprocessing stage. Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

32 Time benchmark 350 Running time (second) Length of structure (nt) Random realistic secondary structures [Denise et al, TS 10] Mandatory motifs M = {} Forbidden motifs F = {,, } Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

33 FRND vs NPK: k design Benchmark: Random target structure + Design k sequences Refold design + Structural Sensitivity using RNFold (Turner 2001) Proportion Struct. Sens. distribution FRND (uniform) Struct. Sens. 0-50% 50-75% 75-90% 90-99% 100% Length (nts) Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

34 FRND vs NPK: k design Benchmark: Random target structure + Design k sequences Refold design + Structural Sensitivity using RNFold (Turner 2001) Proportion Struct. Sens. distribution FRND (weighted) Struct. Sens. 0-50% 50-75% 75-90% 90-99% 100% Length (nts) Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

35 FRND vs NPK: k design Benchmark: Random target structure + Design k sequences Refold design + Structural Sensitivity using RNFold (Turner 2001) Proportion Struct. Sens. distribution NPK Struct. Sens. 0-50% 50-75% 75-90% 90-99% 100% Length (nts) Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

36 FRND vs NPK: Same time consumption For RNs up to 100 nts, #perfect/correct/decent designs are favorable to FRND if given same amount of time as NPK (inc. refolding) Struct. Sens. 100% - NPK 90-99% - NPK 75-90% - NPK 100% - FRND (weighted) 90-99% - FRND (weighted) 75-90% - FRND (weighted) Population Structures Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

37 FRND vs NPK: Same time consumption For RNs up to 100 nts, #perfect/correct/decent designs are favorable to FRND if given same amount of time as NPK (inc. refolding) Population Struct. Sens. 100% - NPK 90-99% - NPK 75-90% - NPK 100% - FRND (weighted) 90-99% - FRND (weighted) 75-90% - FRND (weighted) Structures Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

38 onclusion/perspectives Done: Linear time algorithm for positive design under constraints Practical runtime complexity Standalone Python implementation + Webserver ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

39 onclusion/perspectives Done: Linear time algorithm for positive design under constraints Practical runtime complexity Standalone Python implementation + Webserver To Dos: ombined with soft constraints (Boltzmann sampling) for compositional control Full Turner energy model Investigation of constrained glocal approach Better products for grammars/automata ann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

40 cknowledgments oauthors Yu Zhou (SD) Stéphane Vialette (LIM) Jérôme Waldispühl (Mcill) Yi Zhang (Wuhan, hina) lain Denise (LRI/IM) James Regis (Polytechnique) for technical help Vlad Reinharz (Mcill) You for your attention! Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

41 cknowledgments oauthors Yu Zhou (SD) Stéphane Vialette (LIM) Jérôme Waldispühl (Mcill) Yi Zhang (Wuhan, hina) lain Denise (LRI/IM) James Regis (Polytechnique) for technical help Vlad Reinharz (Mcill) You for your attention! Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

42 ombining grammar and automaton Ideas: Simulate run in automaton while generating word in grammar Each new non-terminal commits to connecting two states Terminal rules check if commitment is fulfilled Some non-terminals may become unproductive clean-up V t V = V q q t V δ(q,t) q V t V t = V q q t V δ(q,t) q t s.t. δ(q, t ) = q V t V t V = V q q t V δ(q,t) q t V { Vq q t if δ(q, t) = q V t = otherwise δ(q,t ) q Yann Ponty (NRS/Polytechnique, France) Flexible RN design Sept. 22 th M-BB / 21

Towards firm foundations for the rational design of RNA molecules

39 28 4 8 282 28 98 32 3 36 68 3 82 : (405)-43-> 43 42 4 40 8 25 37 46 26 36 24 27 E23_9 34 22 3 33 32 E23_2 2 48 o 9 Towards firm foundations for the rational design of RN molecules 47 2 E23_6 E23_ 45