RNA Structure Prediction and Comparison. RNA folding

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1 RNA Structure Prediction and Comparison Session 3 RNA folding Faculty of Technology robert@techfak.uni-bielefeld.de Bielefeld, WS 2013/2014

2 Base Pair Maximization This was the first structure prediction algorithm by [Nussinov et al. 1978]: In M i,j we compute the maximum number of base pairs in a sequence r = r 1 r 2...r n : { } M i,j+1 = max M i,j, max [M i,k M k+1,j ] ρ(r k, r j+1 ) i k (j 3) r k, r j+1 {A, U, G, C} and ρ(r k, r j+1 ) = { 1 when rk and r j+1 can form a base pair, 0 otherwise. Note: This is an improved version of the original recurrences.

3 Nussinov ambiguity The recurrences originally given by Nussinov are highly ambiguous: The algorithm finds each structure many times. This does not preclude finding an optimal structure, but we cannot ask for ALL optimal structures an exponential number of redundant structures would be generated we cannot sensibly ask for near-optimal structures

4 An improved energy model Instead of maximizing pase pairs, we can maximize hyrdogen bonds: C G: 3 A U: 2 G U: 1 This is sometimes called the Nussinov-Jacobson energy model It favours lonely pairs, especially C G. Lonely pairs are not stable because they lack base pair stacking.

5 Exercise 1 Design a basepair maximization algorithm that avoids lonely pairs. 2 Modify the Nussinov algorithm such that not the number of base pairs is maximized, but the number of basepair-stackings. Why is this a good idea? 3 Is (1) and (2) above the same problem?

6 Computing the structure of minimal free energy Similar recurrences (in principle) as with base pair maximization Adding up local energy contributions from loops and stacking regions Minimization of energy (rather than base pair maximization). Traditionally, free energy in physics is negative; the unfolded state has energy 0. A grammar describing structures (cf. Session 2) must be much more sophisticated to accomodate the thermodynamic energy model.

7 Nearest neighbour energy computation G C G A A C C C U A U A C U A G G G U G A U G A A Energy = hairpinloop(cg, CUAG) + stackedpair(cg, UG) + stackedpair(ug, AU) + internalloop(4, 1) + stackedpair(ua, AU) + stackedpair(au, CG)

8 Zuker s algorithm and Mfold Zuker and Stiegler (1981) introduced the thermodynamic model, which still applies (in a much refined form) today their recurrences distinguish closed (V) from any kind (W) of structure the underlying grammar is ambiguous (but not as badly as Nussinov s) near-optimal structures can be sampled in a clever, but ad-hoc fashion Zuker s program Mfold has been continuously updated and used since 1981(!) until it was recently replaced by UnaFold

9 Exercise 1 Play with Zuker s algorithm using the ADP pages

10 RNA-Folding in the WWW (running out) http: //bibiserv/techfak.uni-bielefeld.de/rnashapes The Vienna RNA package today is the most widely used program. It is open source and contains RNAfold, RNAsubopt, RNAalifold and many other RNA-related programs.

11 Algebraic Dynamic Programming (Preview) In the next semester, we will study a particular convenient way to implement RNA folding and other related algorithms: Algebraic Dynamic Programming Describe problem decomposition by tree grammar Describe scoring rules by evaluation algebra Use ASCII notation for tree grammar Compile via Bellman s GAP Grammar + algebra = excutable code

12 Structures as trees Recall the tree representation: sr A C G U sr br sr sr hl U G G C A A A C G UUUA

13 A non-ambiguous grammar without lonely pairs wuchty98 Z = struct struct str str str block strong bl comps ul nil region strong singlestrand empty comps cons ul cons singlestrand ss block comps block block ul region singlestrand strong sr sr ( ) with basepairing base strong base base weak base weak hl sr sr ( base region3 base base bl base base br base region strong strong region ml sr base cons base base il base ) with basepairing block comps region strong region region3 region with minsize 3

14 Exercise Consider the sequence and the two structures ((...))(...). CGAAACGAUUGUG ((.((...)).)) and construct a tree for each structure (if possible)

15 Tree grammar in GAP-L A part of the above tree grammar written in GAP-L strong = sr(base,strong,weak) with basepairing sr(base,weak,base) with basepairing # h weak = hl(base,region3,base) with basepairing sr(base,bl(region,strong),base) with basepairing... ml(base,cons(block,comps),base) with basepairing # h

16 Four evaluation algebras Ans enum = T Σ enum = (str,..., h) where str(s) = Str s ss((i,j)) = Ss (i,j) hl(a,(i,j),b) = Hl a (i,j) b sr(a,s,b) = Sr a s b bl((i,j),s) = Bl (i,j) s br(s,(i,j)) = Br s (i,j) il((i,j),s,(i,j )) = Il (i,j) s (i,j ) ml(a,s,b) = Ml a s b nil((i,j)) = Nil (i,j) cons(s,s ) = Cons s s ul(s) = Ul s h([s 1,..., s r ]) = [s 1,..., s r ] Ans bpmax = IN bpmax = (str,..., h) where str(s) = s ss((i,j)) = 0 hl(a,(i,j),b) = 1 sr(a,s,b) = s + 1 bl((i,j),s) = s br(s,(i,j)) = s il((i,j),s,(i,j )) = s ml(a,s,b) = s + 1 nil((i,j)) = 0 cons(s,s ) = s + s ul(s) = s h([]) = [] h([s 1,..., s r ]) = [ max i ] 1 i r Ans pretty = dot-bracket strings pretty = (str,..., h) where str(s) = s ss((i,j)) = dots(j-i) hl(a,(i,j),b) = ( ++dots(j-i)++ ) sr(a,s,b) = ( ++s++ ) bl((i,j),s) = dots(j-i)++s br(s,(i,j)) = s++dots(j-i) il((i,j),s,(i,j )) = dots(j-i)++s++ dots(j -i ) ml(a,s,b) = ( ++s++ ) nil((i,j)) = cons(s,s ) = s++s ul(s) = s h([s 1,..., s r ]) = [s 1,..., s r ] Ans count = IN count = (str,..., h) where str(s) = s ss((i,j)) = 1 hl(a,(i,j),b) = 1 sr(a,s,b) = s bl((i,j),s) = s br(s,(i,j)) = s il((i,j),s,(i,j )) = s ml(a,s,b) = s nil((i,j)) = 1 cons(s,s ) = s * s ul(s) = s h([]) = [] h([s 1,..., s r ]) = [s 1 + Bielefeld + s r ] University

17 Remark on a simplification The shown grammar and its evaluation algebras are a little too simple for energy minimization:

18 Remark on a simplification The shown grammar and its evaluation algebras are a little too simple for energy minimization: the same funktion bl is used for attaching an unpaired region to a block in a multiloop forming a left bulge, i.e. an unpaired region left of a closed substructure the enegy model has different energy contributions for these cases You find a proper RNA folding grammar at

19 Model refinement: Dangling bases Dangling bases are a refinement of thr energy model, which is not always implemented fully in folding programs. Unpaired bases neighboring stacks can be integrated into the stack. The energy contribution can be almost as good as with another base pair....((u((...(((a((..))a)))...((b((...))b)).))u))... How many dangles?

20 Model refinement: Dangling bases Dangling bases are a refinement of thr energy model, which is not always implemented fully in folding programs. Unpaired bases neighboring stacks can be integrated into the stack. The energy contribution can be almost as good as with another base pair....((u((...(((a((..))a)))...((b((...))b)).))u))... How many dangles?...a((u((b..c(((a((..))a)))d.e((b((...))b))f))u))g... a or g dangles to U (outside) c or d dangles to A e or f dangles to B b or f dangles to U (inside) f can dangle either to B or to U ambiguous dangle Each possible dangle has a different energy contribution, the best combination must be determined.

21 The problem of dangles Dangling bases are a problem not from the thermodynamic point of view, but algorithmically: Given a concrete structure, it is easy to evaluate the best dangles and their energy contribution In structure prediction, the search space explodes when dangles/no-dangles are considered alternative structures

22 Dangling options in RNAfold Pragmatics in RNAfold: -d0: NoDangle no dangling energies -d1: Microstate all dangling alternatives considered as different structures -d2: Overdangle all possible dangles are calculated everywhere (including some impossible ones); folding energies are corrected after MFE prediction; the true MFE structure may NOT be found. We will come back to the dangle problem in the Session on probabilistic shape analysis.

23 Sneak preview Next topic: Abstract shape analysis computing a representative set of near-optimal structures