RNA Abstract Shape Analysis

Transcription

1 ourse: iegerich RN bstract nalysis omplete shape iegerich enter of Biotechnology Bielefeld niversity ourse on omputational RN Biology, Tübingen, March 2006 iegerich ourse:

2 ourse: iegerich omplete shape omplete shape package iegerich ourse:

3 RN ene Prediction via Structure... ourse: iegerich omplete shape Is this sequence an RN gene? Does it have a known functional structure? When sequence conservation is low or no homologs are known: STEP 1: MFE folding (Mfold, RNfold, pknotsr) STEP 2: Structure comparison against known functional structures iegerich ourse:

4 RN ene Prediction via Structure... ourse: iegerich omplete shape Is this sequence an RN gene? Does it have a known functional structure? When sequence conservation is low or no homologs are known: STEP 1: MFE folding (Mfold, RNfold, pknotsr) STEP 2: Structure comparison against known functional structures It is not that easy... iegerich ourse:

5 ccuracy of MFE folding... ourse: iegerich omplete shape adequacy of thermodynamic parameters...? interaction with other molecules...? RN sequence processing...? folding kinetics (co-transcriptional folding)...? physical properties of the folding space...! iegerich ourse:

6 Recent Mfold Evaluation by utell Lab ourse: iegerich omplete shape Doshi KJ, annone JJ, obaugh W, utell RR.: Evaluation of the suitability of free-energy minimization using nearest-neighbor energy parameters for RN secondary structure prediction. BM Bioinformatics ug 5;5:105. ompares MFE foldings to structures derived by comparative and proven by experimental techniques. Findings: base pair accuracy of about 20% - 71% no improvement from recently updated thermodynamic parameters note: did not check for good near-optimal solutions iegerich ourse:

7 (1) ourse: iegerich omplete shape The folding space of a given sequence is LRE: number of foldings is exponential in sequence length number of near-optimal foldings is exponential in energy window Look at the 111 best structures for a trn (using the tool RNmovies). iegerich ourse:

8 (2) ourse: iegerich omplete shape What we observe from RNmovie: LRE number of close-to-optimal foldings FEW structural classes holding many similar foldings an we reduce the folding space to the representatives of these classes? iegerich ourse:

9 RN structure prediction based on thermodynamics ourse: iegerich omplete shape Even with the best possible model parameters: MFE structure is often wrong Some near-optimal structure is always right The number of near-optimals is exponential Most are similar, but some quite distinct Bulge Loop (right) Bulge Loop (left) Multiple Loop Stacking Region Is there a shape LIKE this... or NOT like this...? Hairpin Loop Internal Loop iegerich ourse:

10 Formalizing the notion of () shape ourse: iegerich omplete shape ion retains nesting and adjacency of stems iegerich ourse:

11 Formalizing the notion of () shape ourse: iegerich omplete shape ion retains nesting and adjacency of stems ion disregards all sizes (of stems, loops,... ) iegerich ourse:

12 Formalizing the notion of () shape ourse: iegerich omplete shape ion retains nesting and adjacency of stems ion disregards all sizes (of stems, loops,... ) ion may retain or disregard presence and type of bulges and internal loops iegerich ourse:

13 Levels of ion (1) ourse: iegerich omplete shape ((((((...(((..(((...))))))...(((..((...))..))))))))).. Level 5: [[][]] Level 4: [[][[]]] Level 3: [[[]][[]]] Level 2: [[ []][ [] ]] Level 1: [ [ [ ]] [ [ ] ]] iegerich 20 * * * * * * * * * ourse: * * * * * * 56 * 1 *

14 Levels of ion (2) ourse: iegerich Level 0 Level 1 Full structure ll types of loops Level 3 ll helix interruptions Level 4 Multi and internal loops, no bulges Level 5 Stem arrangement only omplete shape iegerich ourse:

15 ion mathematics ourse: iegerich omplete shape eneral: tree-like domains of structures F and P tree homomorphism π : F P For each sequence s: folding space of sequence s: F (s) of sequence s: P(s) = π(f (s)) shape class of p in F (s): f (x, p) = {x x F (S), π(x) = p} shape representative structure: shrep = class member of minimal free energy, formally shrep(s, p) iegerich ourse:

16 trees and shape strings ourse: iegerich omplete shape Level 0 Level 3 Level 5 c c c sr sr sr ml g g g a a u sr c g sr sr c g c sr g sr c g c g uuuu bl aua sr c g ccc L ((((.(((...)))((...(...))))))) [ [ ] [ [ ] ] ] [ [ ] [ ] ] iegerich L D L L ourse: L L D L

17 algorithmics ourse: iegerich omplete shape Implementation of shape : shape are tree homomorphisms integrate well with DP algorithms allows for a priori rather than a posteriori compute in parallel with energy perform analyses on per-shape basis iegerich ourse:

18 lgorithmics: more detailed ourse: iegerich omplete shape Implementation in DP: Define shape mapping π in algebra Then, fold grammar ( *** mfe *** pp) computes for every shape its mfe structure naively implemented O(n 3 P(s) ) time iegerich ourse:

19 lgorithmics: more detailed ourse: iegerich omplete shape Implementation in DP: Define shape mapping π in algebra Then, fold grammar ( *** mfe *** pp) computes for every shape its mfe structure naively implemented O(n 3 P(s) ) time Faster: apply k-best filter Wrong: fold grammar ( *** mfe k *** pp) Why? iegerich ourse:

20 lgorithmics: more detailed ourse: iegerich omplete shape Implementation in DP: Define shape mapping π in algebra Then, fold grammar ( *** mfe *** pp) computes for every shape its mfe structure naively implemented O(n 3 P(s) ) time Faster: apply k-best filter Wrong: fold grammar ( *** mfe k *** pp) Why? Better: fold grammar ( /// mfe k *** pp) alg1 /// alg2 = use classification scheme of alg1, but apply choice function of alg2 O(n 3 P k ) time iegerich ourse:

21 lgorithmics: even more detailed ourse: iegerich omplete shape Optimal efficiency with 3-pass strategy: 1 fill Matrices as usual with energy score only 2 suboptimal backtrace: annotate each cell with its difference to global optimal path 3 Bottom-up calculation of ( *** mfe *** pp) for all cells with diff < threshold O(n 3 + n P k ) time, since are only computed for cells leading to a structure with energy below threshold iegerich ourse:

22 Properties of and shreps ourse: iegerich omplete shape shape classes are disjoint shreps are interesting have sequence-independent representation are meaningful across different sequences (of different length) and shreps can be computed efficiently iegerich ourse:

23 nalysis with ourse: iegerich omplete shape The three top shreps of the aforementioned trn: [] (((((((((((((((.((((...(((((((...))))))).)))))))))))...)))))))) kcal/mol [[][]] ((((((((...((.((((...(((((((...))))))).))))))(((...))).)))))))) kcal/mol [[][][]] ((((((...((((...)))).(((((((...)))))))...(((((...))))).)))))) kcal/mol iegerich ourse:

24 ourse: iegerich omplete shape iegerich ourse:

25 ourse: iegerich omplete shape iegerich ourse:

26 ourse: iegerich omplete shape iegerich ourse:

27 Statistics ourse: iegerich omplete shape Is the really smaller than the folding space? See some statistics within 5% kcal/mol of MFE: iegerich ourse:

28 ourse: iegerich Structures omplete shape Nr. of Structures/ Sequence length [nt] iegerich ourse:

29 ourse: iegerich 1e Structures omplete shape Nr. of Structures/ Sequence length [nt] iegerich ourse:

30 ourse: 1 iegerich omplete shape Ratio of to Structures Sequence length [nt] iegerich ourse:

31 ourse: iegerich omplete shape Ratio of to Structures e Energy range above mfe [kcal/mol] iegerich ourse:

32 ourse: iegerich 1e+18 1e+16 1e+14 Structures * N * N omplete shape Nr. of Structures/ 1e+12 1e+10 1e+08 1e Sequence length N [nt] iegerich ourse:

33 Variation within shape ourse: How homogenous are shape classes? iegerich omplete shape iegerich ourse:

34 Variation within shape ourse: How homogenous are shape classes? iegerich omplete shape iegerich ourse:

35 : Best k shreps ourse: iegerich omplete shape R N s h a p e s [] [[][]] [[][][]] iegerich ourse:

36 ourse: iegerich omplete shape classifies structures by shape computes a small number of representative structures no heuristics involved as fast as traditional RN folding vailable at iegerich ourse:

37 omplete shape ourse: iegerich How much would you trust a structure with a probability of , even when it is optimal? omplete shape iegerich hip Lawrence, Benasque 2003 ourse:

38 From energy to probability ourse: iegerich omplete shape ccording to Boltzmann statistics, sequence s has structure x with probability Prob(x) = (e Ex /RT )/Q where T is temperature, R universal gas constant, and Q the partition function, Q = /RT e Ex x F (s) ccumulated shape probabilities Prob(p) = π(x)=p Prob(x) for all p P(s) iegerich ourse:

39 package ourse: Overtaking: probabilities contradict energy ranking iegerich omplete shape [ ] E= kcal/mol P= ets 2 nd iegerich [ ][ ][ ] E= kcal/mol P= ets 1 st ets 3 rd ourse: [ ][ ] E= kcal/mol P= Björn Voß

40 propos complete ourse: iegerich omplete shape probabilities give full information about folding space we cannot compute only the k most likely only feasible up to 300 nts iegerich ourse:

41 lgorithmics ourse: iegerich omplete shape omplete shape requires a non-ambiguous grammar with correct dangles at all places and partition function algebra pf applies classified dynamic programming compute per class partition function: fold grammar ( *** pf) s divide by overall partition function: fold grammar pf s takes time O( P(s) n n 3 ) where n = s and P(s) = 1.1 for π 5 iegerich ourse:

42 Results from complete ourse: iegerich omplete shape Some observations: Sequence 1 Prob. 2 Prob. lin-4 precursor [] trn-ala [] [[]] typical mrn [][[][]] [[[][]][]] HIV-1 Leader [][[][[][]]]] [][[[][[][]]][]] iegerich ourse:

43 References on shape ourse: iegerich omplete shape bstract of RN by iegerich, Voss, Rehmsmeier. Nucleic cids Research 2004, Vol. 32, No 15, 1-9. omplete Probabilistic nalysis of RN bstract by Voss, iegerich, Rehmsmeier. BM Biology, 2006, Feb 15;4(1):5 : an integrated RN package based on. Steffen P, Voss B, Rehmsmeier M, Reeder J, iegerich R. Bioinformatics 2006, Feb 15;22(4): iegerich ourse:

44 The End ourse: iegerich Thanks for your attention. omplete shape iegerich ourse: