RNA folding on the 3D triangular lattice. Joel Gillespie, Martin Mayne and Minghui Jiang
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1 RNA folding on the 3D triangular lattice Joel Gillespie, Martin Mayne and Minghui Jiang University of Waterloo Alan Tsang July 19, 2010
2 Deoxyribonucleic Acid (DNA) Sequence of bases: Adenine (A) Cytosine (C) Guanine (G) Thymine (T) CGACAGGTACTGTGTCACC Base pairing: Adenine-Thymine (A=T) Cytosine-Guanine (C G) Forms the basis of double helix structure Cellular Blueprint
3 Sequence of bases: Adenine (A) Cytosine (C) Guanine (G) Uracil(U) Thymine (T) Ribonucleic Acid (RNA) Single stranded copy of DNA template CGACAGGUACUGUGUCACC Base pairing: Adenine-Uracil(A=U) Cytosine-Guanine (C G) Single stranded structure is unstable; bases seek pairing within the molecule
4 Ribonucleic Acid (RNA) Base pairing: Adenine-Uracil(A=U) Cytosine-Guanine (C G) Single stranded structure is unstable; bases seek pairing within the molecule This causes the RNA molecule to adopt specific shapes (conformations)
5 RNA Secondary Structure CGACAGGUACUGUGUCACC AAUGUCCAUGACGACAGCU Helix Structure
6 RNA Tertiary Structure
7 Form is Function Sequence Form Function
8 Our Problem Given the primary sequence of an RNA molecule: CGACAGGUACUGUGUCACC Predict its tertiary structure:
9 Our Problem Given the primary sequence of an RNA molecule. Predict its tertiary structure Find an arrangement that minimizes free energy (maximizes base pairing) Need to avoid: Self collision Sharp turns Continual motion Geometric constraints
10 Lattice Embedding Approximate 3D space with a triangular lattice. 2D triangular lattice
11 Lattice Embedding Approximate 3D space with a triangular lattice. Layered triangular lattice
12 Lattice Embedding Approximate 3D space with a triangular lattice. Layered triangular lattice
13 Lattice Embedding Approximate 3D space with a triangular lattice.
14 Triangular Lattice Advantages Density: each point has coordinate number = 12 Regularity: all points are equivalent Parity equivalence: cubic lattice cannot pair up bases of the same parity
15 Simulated Annealing Goal: Model the physical motion ( folding ) of the molecule as it settles into its final form ( conformation )
16 Simulated Annealing A move set define all valid ways of modifying our embedded molecule: Flip Moves are reversible.
17 Simulated Annealing A move set define all valid ways of modifying our embedded molecule: Pivot Moves are reversible.
18 Simulated Annealing A move set define all valid ways of modifying our embedded molecule: Pull Moves are reversible.
19 Simulated Annealing Our move set covers all possible rearrangements of the molecule: any conformation can be stretched out to a linear form using our moves, and the moves are reversible
20 Simulated Annealing Move towards state of lowest free energy Do not get stuck at local minima
21 Simulated Annealing Pick a random move P Current conformationv i with free energy score s(v i ) Determine the resulting conformation v i+1 Calculate the free energy score s(v i+1 ) If s(v i+1 ) s(v i ), then acceptmove
22 Simulated Annealing Pick a random move P Current conformationv i with free energy scores(v i ) Determine the resulting conformation v i+1 Calculate the free energy score s(v i+1 ) If s(v i+1 )<s(v i ), then accept move with probability Pr = 2 s + ( vi ) s( vi 1) T i where T i is a decreasing temperature value
23 Simulated Annealing Free Energy Score = score(i) bases i where score(i) = min( score(i,j) ) for all complementary bases j neighbouring i
24 Simulated Annealing Free Energy Score score(i,j) is boosted by neighbour stacking to encourage long strings of matches
25 Simulated Annealing Constructing helices Anneal procedure produces a series of complementary base pairs; group consecutive ones into candidate helices Rate each helix in terms of their free energy score
26 Simulated Annealing Constructing helices Accept helices greedily! Cropping unaccepted helices to prevent overlap Rate each helix in terms of their free energy score
27 Simulated Annealing Constructing helices Accept helices greedily! Cropping unaccepted helices to prevent overlap Rate each helix in terms of their free energy score
28 Simulated Annealing Constructing helices Discard unfit helices Resulting helices form a predicted secondary structure!
29 Tertiary Structure Use same annealing algorithm, with different scoring: Match bonus: positive score for each base pairing from secondary structure that is realized by the conformation
30 Tertiary Structure Use same annealing algorithm, with different scoring: Sharp turn penalty: small negative score for each base that forms a 60⁰ or 90⁰ turn. 90⁰ 60⁰ 120⁰ 180⁰
31 Tertiary Structure
32 Results DeltaIS versus HotKnot Runtimes DeltaIS(one randomized run) HotKnot hours a few minutes
33 Results DeltaIS versus HotKnot on sensitivity, selectivity, and accuracy. Sensitivity Selectivity Accuracy DeltaIS (best of 66 runs) DeltaIS (average ± stdev) 80.20% 78.37% 65.67% ± 0.82% ± 0.83% ± 1.09% HotKnot 71.69% 78.47% 59.90%
34 Results DeltaIS versus HotKnot Perfect Matches Perfect Secondary Structure (of 252 sequences) DeltaIS(all 66 runs) 47 DeltaIS(at least 1 run) 82 HotKnot 36
35 Results A scatter plot of the prediction accuracies of DeltaIS( ) and HotKnot( ) on individual sequences.
36 Results Randomized nature of algorithm allows detection of RNA switches : GGCCCCUUUGGGGGCCAGACCCCUAAAGGGGUC ((((((((((((((:::::)))))))))))))) ((((((::::)))))):((((((::::))))))
37 ~ FIN ~
38 Central Dogma of Molecular Biology DNA RNA Protein
39 Central Dogma of Molecular Biology DNA RNA Protein
40 Central Dogma of Molecular Biology DNA RNA Protein
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