CSE 527 Lecture 17, 11/24/04 - University of Washington · •“Wobble Pair” G - U ~ 1 kcal/mole...
Transcript of CSE 527 Lecture 17, 11/24/04 - University of Washington · •“Wobble Pair” G - U ~ 1 kcal/mole...
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CSE 527Lecture 17, 11/24/04
RNA Secondary Structure Prediction
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Outline
• What is it
• How is it Represented
• Why is it important
• Examples
• Approaches
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RNA Structure
• Primary Structure: Sequence
• Secondary Structure: Pairing
• Tertiary Structure: 3D shape
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RNA Pairing
• Watson-Crick Pairing
• C - G ~ 3 kcal/mole
• A - U ~ 2 kcal/mole
• “Wobble Pair” G - U ~ 1 kcal/mole
• Non-canonical Pairs (esp. if modified)
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A tRNA 3d Structure
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tRNA - Alt.Representations
Anticodon loop
Anticodonloop
3’
5’
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tRNA - Alt.Representations
Anticodon loop
Anticodonloop
3’
5’
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Why?
• RNA’s fold,and function
• Nature useswhat works
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Importance
• Ribozymes (RNA Enzymes)
• Retroviruses
• Effects on transcription, translation,splicing...
• Functional RNAs: rRNA, tRNA, snRNA,snoRNA, micro RNA, RNAi, riboswitches,regulatory elements in 3’ & 5’ UTRs, ...
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AC
U
G
C
A
G
G
G
A
G
C
AA
G
C
GA
G
G CC
U
C
UGC A
A
UG
A C
G
GU
G
CA
U
GA
G
A G
C
G UCU UU
U
C
A
A
CA
C UG
U
UA
U
G
G
A
A
G U
UU
G
GC
UA
GC
G U
U CU
AG
A G
C U
G
UG
A
C
A
C
U
GC
CG
C
GA
C
G
G GA
A
A
G
U A A
C
GG
G
CGG
C
G
A
GU
AA
A
C C
C
GA
UC CC
G
GU
G
A
A
U
AG
CC
U GA
A
A
A
A
CA
A
A
GU
A
CA CGG
G
A
UAC
G
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RNA Pairing
• Watson-Crick Pairing
• C - G ~ 3 kcal/mole
• A - U ~ 2 kcal/mole
• “Wobble Pair” G - U ~ 1 kcal/mole
• Non-canonical Pairs (esp. if modified)
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Definitions• Sequence 5’ r1 r2 r3 ... rn 3’ in {A, C, G, T}
• A Secondary Structure is a set of pairs i•j s.t.
1. i < j-4
2. if i•j & i’•j’ are two pairs with i ≤ i’, then
A. i = i’ & j = j’, or
B. j < i’, or
C. i < i’ < j’ < j
First pair precedes 2nd,or is nested within it. No“pseudoknots.”}
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Nested
Pseudoknot
Precedes
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A Pseudoknot A-C / \3’ - A-G-G-C-U U U-C-C-G-A-G-G-G | C-C-C - 5’ \ / U-C-U-C
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Approaches toStructure Prediction
• Maximum Pairing+ works on single sequences+ simple- too inaccurate
• Minimum Energy+ works on single sequences- ignores pseudoknots- only finds “optimal” fold
• Partition Function+ finds all folds- ignores pseudoknots
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Approaches, II
• Comparative sequence analysis+ handles all pairings (incl. pseudoknots)- requires several (many?) aligned, appropriately diverged sequences
• Stochastic Context-free GrammarsRoughly combines min energy & comparative, butno pseudoknots
• Physical experiments (x-ray crystalography, NMR)
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Nussinov: Max Pairing
• B(i,j) = # pairs in optimal pairing of ri ... rj
• B(i,j) = 0 for all i, j with i ≥ j-4; otherwise
• B(i,j) = max of:
1. B(i+1,j)
2. B(i,j-1)
3. B(i+1,j-1) +(if ri pairs with rj then 1 else 0)
4. max { B(i,k)+B(k+1,j) | i < k < j }
Time: O(n3)
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3. they pair with each other,so 1 + best ri+1 ... rj-1
4.They pair, but not to each other;i pairs with k forsome i < k < j;so look at bestri ... rk + best rk+1 ... rj(don’t need to look atother k; why?)
“optimal pairing of ri ... rj” Several (overlapping, but exhaustive) possibilities
1.ri is unpaired; look at bestway to pair ri+1 ... rj
2.rj is unpaired; look at bestway to pair ri ... rj-1
i i+1
j
j
i
j-1
j
i+1
j-1
i
j
k
k+1
i
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Pair-based EnergyMinimization
• E(i,j) = energy of pairs in optimal pairing of ri ... rj
• E(i,j) = ∞ for all i, j with i ≥ j-4; otherwise
• E(i,j) = min of:
• E(i+1,j)
• E(i,j-1)
• E(i+1,j-1) + e(ri, rj)
• min { E(i,k)+E(k+1,j) | i < k < j }
Time: O(n3)
energy of one pair
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• Detailed experiments show it’smore accurate to model basedon loops, rather than just pairs
• Loop types1. Hairpin loop
2. Stack
3. Bulge
4. Interior loop
5. Multiloop
Loop-based EnergyMinimization
1
2
3
4
5
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thymine
cytosine
adenine
uracil
Base Pairs and Stacking
guanine
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LoopExamples
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Zuker: Loop-basedEnergy, I
• W(i,j) = energy of optimal pairing of ri ... rj
• V(i,j) = as above, but forcing pair i•j
• W(i,j) = V(i,j) = ∞ for all i, j with i ≥ j-4
• W(i,j) = min(W(i+1,j), W(i,j-1), V(i+1,j-1), min { E(i,k)+E(k+1,j) | i < k < j } )
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Zuker: Loop-basedEnergy, II
• V(i,j) =min(eh(i,j), es(i,j)+V(i+1,j-1), VBI(i,j), VM(i,j))
• VM(i,j) = min { W(i,k)+W(k+1,j) | i < k < j } )
• VBI(i,j) = min { ebi(i,j,i’,j’) + V(i’, j’) | i < i’ < j’ < j & i’-i+j-j’ > 2 }
hairpin stackbulge/
interiormulti-loop
Time: O(n4) O(n3) possible if ebi(.) is “nice”
bulge/interior
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Suboptimal Energy
• There are always alternate folds with near-optimalenergies. Thermodynamics predicts that populations ofidentical molecules will exist in different folds; individualmolecules even flicker among different folds
• Zuker’s algorithm can be modified to find suboptimalfolds
• McCaskill gives a more elaborate dynamic programmingalgorithm calculating the “partition function,” whichdefines the probability distribution over all these states.
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Two competing secondary structures for theLeptomonas collosoma spliced leader mRNA.
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Example ofsuboptimal
folding
Black dots: pairsin opt fold
Colored dots:pairs in folds2-5% worsethanoptimal fold
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A “Mountain” diagram