Longer, deeper and affordable kisses. · Folding kissing hairpins Stefan Janssen (Bielefeld...

Longer, deeper and affordable kisses.

Corinna Theis, Stefan Janssen and Robert Giegerich

Faculty of Technology & Center for BiotechnologyBielefeld University, Germany

sjanssen@TechFak.Uni-Bielefeld.DE

LIX Bioinformatics Colloquium,8-10th November 2010,

Ecole Polytechnique, Paris

Stefan Janssen (Bielefeld University) Longer, deeper and affordable kisses. LIX 2010, Paris 1 / 28

Folding nested structures

maximizing base-pairs

minimizing free energy

O(n3) time

O(n2) space

Folding crossed structures

general pseudoknotfolding is NP-hard[Lyngsø 2000, Akutsu 2000]

polynomial algorithmsfor special classes

Folding simple pseudoknots

Folding simple recursive pseudoknots

loop regions may contain substructures ...

... even simple recursive pseudoknots

already computed

Folding simple recursive pseudoknots

8 moving boundaries

→ O(n8) time→ O(n2) space

too much computing time

→ canonization= pknotsRG

[Reeder & Giegerich 2004]

Folding canonical simple recursive pseudoknots

Three rules of canonization1 perfect helices: no loops, no bulges

2 maximal helices

3 helices must not overlap

The clue

optimal helices can beprecomputed in O(n2) time andspace

pknotsRG: 4 moving boundaries

What canonization might miss

Folding kissing hairpins

12 moving boundaries

way too high compute time

12 moving boundaries

way too high compute time

with canonization

Kissing hairpin as an overlay of two pseudoknots

Problem 1: Violating Bellman’s Principle

Bellman’s Principle: Monotonicity of scoring wrto optimizationE (Kiss) = E (left PK ) + E (right PK )− E (overlap)

Problem 2: Incompatible pseudoknots

Strategy A

Summary Strategy A

Strategy A is correct, symmetric and heuristic:

1 Assume left PK optimal and find best consistent right PK

2 Assume right PK optimal and find best consistent left PK

3 Return better overlay structure

Strategy B

Strategy C

l = boundaryleft (rpk (k))rpk(k) = min (E (PKh,k+2,m,j) , rpk(k + 1))

Relating strategies

Strategies A,B,C are heuristic, but increasingly general.For any sequenxe x :

SearchspaceA(x) ⊆ SearchspaceB(x) ⊆ SearchspaceC (x) ⊂ SearchspacecsrKH(x)

O(n4) O(n4) O(n5) O(n6) timeO(n2) O(n3) O(n2) O(n2) space

2.4% 5.5% 2.4% 0% missed opt.csrKH

1 1.2 11.2 508.0 time1 9.2 1.3 4.5 space

Evaluation

Evaluation in terms of Pseudobase:61 pseudoknotted structures, including (only) 6 kissing hairpin motifsAgreement of strategies:

C 6= B 6= A C = B 6= A C = B = A

2 2 57

Correctness of predictions:

A,B,C agree and correctly predict the 6 true kissing hairpins

for 7 simpler pseudoknots, a kissing hairpin is predicted

Co-transcriptional folding

Strategy A: in all cases, it is the left PK which is locally optimal

→ double speed of Strategy A, by dropping symmetric case?

→ more complex motifs as successive overlays in O(n4) / O(n2)?

Co-transcriptional folding

Strategy A: in all cases, it is the left PK which is locally optimal

→ double speed of Strategy A, by dropping symmetric case?

→ more complex motifs as successive overlays in O(n4) / O(n2)?

Thanks for your attention

Problem with Strategy B

Extra Heuristic for Strategy B

Longer, deeper and affordable kisses. · Folding kissing hairpins Stefan Janssen (Bielefeld...

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