CS5263%20Bioinformatics

1
CS5263 Bioinformatics

• Lecture 21
• RNA Secondary Structure Prediction

2
Road map

• Biological roles for RNA
• Whats secondary structure?
• How is it represented?
• Why is it important?
• How to predict?

3
Central dogma
The flow of genetic information
transcription
translation
DNA
RNA
Protein
Replication
4
Classical Roles for RNA

• mRNA - Message RNA
• tRNA - Transfer RNA (61 kinds, 75nt)
• rRNA - Ribosomal RNA (4 kinds, 120-5k nt)

RNA
Protein
Ribosome
5
Classical Roles for RNA

• mRNA
• tRNA
• rRNA

Ribosome
6
Semi-classical RNA

• snRNA - small nuclear RNA (splicing U1, etc,
  60-300nt)
• RNaseP - tRNA processing (300 nt)
• SRP - signal recognition particle membrane
  targeting (100-300 nt)
• tmRNA - resetting stalled ribosomes, destroy
  aberrant mRNA
• Telomerase - (200-400nt)
• snoRNA - small nucleolar RNA (many varieties
  80-200nt)

7
New Roles for RNA

• Riboswitch an mRNA regulates its own activity
• siRNA (Nobel prize 2006, Fire Mello)
• microRNAs
• saRNA small activating RNA
• Hundreds of families
• Rfam release 1, 1/2003 25 families, 55k
  instances
• Rfam release 7, 3/2005 503 families, 300k
  instances

8
Example Riboswitch
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Non-coding RNAs

• Dramatic discoveries in last 5 years
• 100s of new families
• Many roles regulation, transport, stability,
  catalysis,
• 1 of DNA codes for
• protein, but 30 of it is copied into RNA, i.e.
• ncRNA gtgt mRNA

10
Take-home message

• RNAs play many important roles in the cell beyond
  the classical roles
• Many of which yet to be discovered
• RNA functions are determined by structures

11
RNA structure

• Primary sequence
• Secondary base-pairing
• Tertiary 3D shape

12
RNA base-pairing

• Watson-Crick Pairing
• C-G 3kcal/mole
• A-U 2kcal/mole
• Wobble Pair G U 1kcal/mole
• Non-canonical Pairs

13
tRNA structure
14
Secondary structure prediction

• Given CAUUUGUGUACCU.
• Goal
• How can we compute that?

15
Terminology
Hairpin Loops
Interior loops
Stems
Multi-branched loop
Bulge loop
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Pseudoknot
ucgacuguaaaaaagcgggcgacuuucagucgcucuuuuugucgcgcgc
5-
-3
10
20
30
40

• Makes structure prediction hard. Not considered
  in most algorithms.

17
The Nussinov algorithm

• Goal maximizing the number of base-pairs
• Idea Dynamic programming
• Loop matching
• Nussinov, Pieczenik, Griggs, Kleitman 78
• Too simple for accurate prediction, but
  stepping-stone for later algorithms

18
The Nussinov algorithm

• Problem
• Find the RNA structure with the maximum
  (weighted) number of nested pairings
• Nested no pseudoknot

ACCACGCUUAAGACACCUAGCUUGUGUCCUGGAGGUCUAUAAGUCAGACC
GCGAGAGGGAAGACUCGUAUAAGCG
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The Nussinov algorithm

• Given sequence X x1xN,
• Define DP matrix F(i, j) maximum number of
  base-pairs if xixj folds optimally
• Matrix is symmetric, so let i lt j

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The Nussinov algorithm

• Can be summarized into two cases
• (i, j) paired optimal score is 1 F(i1, j-1)
• (i, j) unpaired optimal score is
• maxk F(i, k) F(k1, j)
• a number of other ways to summarize, all
  equivalent

21
The Nussinov algorithm

• F(i, i) 0
• F(i1, j-1) S(xi, xj)
• F(i, j) max
• maxk F(i, k) F(k1, j)
• S(xi, xj) 1 if xi, xj can form a base-pair, and
  0 otherwise
• Generalize S(A, U) 2, S(C, G) 3, S(G, U) 1
• Or other types of scores (later)
• F(1, N) gives the optimal score for the whole seq

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How to fill in the DP matrix?

• F(i1, j-1) S(xi, xj)
• F(i, j) max
• maxk F(i, k) F(k1, j)

0
0
0 (i, j)
0
0
0
0
0
0
0
i
i1
j1
j
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How to fill in the DP matrix?

• F(i1, j-1) S(xi, xj)
• F(i, j) max
• maxk F(i, k) F(k1, j)

0
0
0
0
0
0
0
0
0
0
j i 1
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How to fill in the DP matrix?

• F(i1, j-1) S(xi, xj)
• F(i, j) max
• maxk F(i, k) F(k1, j)

0
0
0
0
0
0
0
0
0
0
j i 2
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How to fill in the DP matrix?

• F(i1, j-1) S(xi, xj)
• F(i, j) max
• maxk F(i, k) F(k1, j)

0
0
0
0
0
0
0
0
0
0
j i 3
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How to fill in the DP matrix?

• F(i1, j-1) S(xi, xj)
• F(i, j) max
• maxk F(i, k) F(k1, j)

0
0
0
0
0
0
0
0
0
0
j i N - 1
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Minimum Loop length

• Sharp turns unlikely
• Let minimum length of hairpin loop be 1
• F(i, j) 0 for j i lt 2

0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0
U ? A G ? C C ? G G
C
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Algorithm

• Initialization
• F(i, i) 0 for i 1 to N
• F(i, i1) 0 for i 1 to N-1
• Iteration
• For L 1 to N-1
• For i 1 to N l
• j min(i L, N)
• F(i1, j -1) s(xi, xj)
• F(i, j) max
• max i ? k lt j F(i, k) F(k1, j)
• Termination
• Best score is given by F(1, N)
• (Need to trace back refer to the Durbin book)

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Complexity

• For L 1 to N-1
• For i 1 to N l
• j min(i L, N)
• F(i1, j -1) s(xi, xj)
• F(i, j) max
• max i ? k lt j F(i, k) F(k1, j)
• Time complexity O(N3)
• Memory O(N2)

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Example

• RNA sequence GGGAAAUCC
• Only count of base-pairs
• A-U 1
• G-C 1
• G-U 1
• Minimum hairpin loop length 1

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G G G A A A U C C
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0
G G G A A A U C C
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G G G A A A U C C
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0
0
G G G A A A U C C
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G G G A A A U C C
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 1
0 0 1 1
0 0 0 0
0 0 0
0 0
0
G G G A A A U C C
34
G G G A A A U C C
0 0 0 0 0
0 0 0 0 0
0 0 0 0 1
0 0 0 1 1
0 0 1 1 1
0 0 0 0
0 0 0
0 0
0
G G G A A A U C C
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G G G A A A U C C
0 0 0 0 0 0 1 2 3
0 0 0 0 0 1 2 3
0 0 0 0 1 2 2
0 0 0 1 1 1
0 0 1 1 1
0 0 0 0
0 0 0
0 0
0
G ? U G ? C G ? C
AAA
G G G A A A U C C
A ? U G ? C G ? C G
A ? U G G ? C G ? C
AA
AA
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G G G A A A U C C
0 0 0 0 0 0 1 2 3
0 0 0 0 0 1 2 3
0 0 0 0 1 2 2
0 0 0 1 1 1
0 0 1 1 1
0 0 0 0
0 0 0
0 0
0
G ? U G ? C G ? C
AAA
G G G A A A U C C
A ? U G ? C G ? C G
A ? U G G ? C G ? C
AA
AA
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G G G A A A U C C
0 0 0 0 0 0 1 2 3
0 0 0 0 0 1 2 3
0 0 0 0 1 2 2
0 0 0 1 1 1
0 0 1 1 1
0 0 0 0
0 0 0
0 0
0
G ? U G ? C G ? C
AAA
G G G A A A U C C
A ? U G ? C G ? C G
A ? U G G ? C G ? C
AA
AA
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G G G A A A U C C
0 0 0 0 0 0 1 2 3
0 0 0 0 0 1 2 3
0 0 0 0 1 2 2
0 0 0 1 1 1
0 0 1 1 1
0 0 0 0
0 0 0
0 0
0
G ? U G ? C G ? C
AAA
G G G A A A U C C
A ? U G ? C G ? C G
A ? U G G ? C G ? C
AA
AA
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Energy minimization

• For L 1 to N-1
• For i 1 to N l
• j min(i L, N)
• E(i1, j -1) e(xi, xj)
• E(i, j) min
• min i ? k lt j E(i, k) E(k1, j)
• e(xi, xj) represents the energy for xi base pair
  with xj
• Energy are negative values. Therefore
  minimization rather than maximize.
• More complex energy rules energy depends on
  neighboring bases

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Terminology
Hairpin Loops
Interior loops
Stems
Multi-branched loop
Bulge loop
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The Zuker algorithm main ideas

1. Instead of base pairs, pairs of base pairs (more
   accurate)
2. Separate score for bulges
3. Separate score for different-size composition
   of loops
4. Separate score for interactions between stem
   beginning of loop
5. Use additional matrix to remember current state.
   similar to affine-gap alignment.

42
Two popular implementation

• mFold by Zuker
• RNAfold in the Vienna package (Hofacker)
• Includes several useful utilities, such as
  structure comparison, searching, base-paring
  probability from partition functions, etc.

43
Accuracy

• 50-70 for sequences up to 300 nt
• Not perfect, but useful
• Possible reasons
• Energy rule not perfect 5-10 error
• Many alternative structures within this error
  range
• Alternative structure do exist
• Structure may change in presence of other
  molecules

44
Comparative structure prediction

• Given K homologous aligned RNA sequences
• Human aagacuucggaucuggcgacaccc
• Mouse uacacuucggaugacaccaaagug
• Worm aggucuucggcacgggcaccauuc
• Fly ccaacuucggauuuugcuaccaua
• Orc aagccuucggagcgggcguaacuc
• If ith and jth positions are always base paired
  and covary, then they are likely to be paired

45
Mutual information

• fab(i,j) of times the pair a, b are in
  positions i, j
• fa (i) of times the base a is in positions i

aagacuucggaucuggcgacaccc uacacuucggaugacaccaaagug
aggucuucggcacgggcaccauuc ccaacuucggauuuugcuaccaua
aagccuucggagcgggcguaacuc
fgc(3,13) 3/5 fcg(3,13) 1/5 fau(3,13) 1/5
fg(3) 3/5 fc(3) 1/5 fa(3) 1/5
fc(13) 3/5 fg(13) 1/5 fu(13) 1/5
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Mutual information

• Also called covariance score
• M is high if base a in position i always follow
  by base b in position j
• Does not require a to base-pair with b
• Advantage can detect non-canonical base-pairs
• However, M 0 if no mutation at all, even if
  perfect base-pairs

aagacuucggaucuggcgacaccc uacacuucggaugacaccaaagug
aggucuucggcacgggcaccauuc ccaacuucggauuuugcuaccaua
aagccuucggagcgggcguaacuc
One way to get around is to combine covariance
and energy scores
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Comparative structure prediction

• Given a multiple alignment, can infer structure
  that maximizes the sum of mutual information, by
  DP
• However, alignment is hard, since structure often
  more important than sequence

48
Comparative structure prediction

• In practice
• Get multiple alignment
• Find covarying bases deduce structure
• Improve multiple alignment (by hand)
• Go to 2
• A manual EM process!!

49
Comparative structure prediction

• Align then fold
• Align and fold
• Fold then align

50
Context-free Grammar for RNA Secondary Structure

• S SS aSu cSg uSa gSc L
• L aL cL gL uL ?

S
ag u cg
aaacgg ugcc
S
S
S
L
S
S
a L
L
L
a
?
a c g g a g u g c c c g u
51
Stochastic Context-free Grammar (SCFG)

• Probabilistic context-free grammar
• Probabilities can be converted into weights
• CFG vs SCFG is similar to RG vs HMM
• S SS
• S aSu uSa L
• S cSg gSc L
• S uSg gSu L
• L aL cL gL uL ?

0
e(xi, xj) F(i1, j-1) F(i, j) max
L(i, j) maxk (F(i, k) F(k1,
j)) L(i, j) 0
2
3
1
0
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SCFG Decoding

• Decoding given a grammar (SCFG/HMM) and a
  sequence, find the best parse (highest
  probability or score)
• CYK algorithm (Viterbi)
• The Nussinov and Zuker algorithms are essentially
  special cases of CYK
• CYK and SCFG are also used in other domains (NLP,
  Compiler, etc).

53
SCFG Evaluation

• Given a sequence and a SCFG model
• Estimate P(seq is generated by model), summing
  over all possible paths
• Inside-outside algorithm
• Analogous to forward-background
• Inside bottom-up parsing (P(xi..xj))
• Outside top-down parsing (P(x1..xi-1 xj1..xN))
• Can calculate base-paring probability
• Analogous to posterior decoding
• Essentially the same idea implemented in the
  Vienna RNAfold package

54
SCFG Learning

• Covariance model similar to profile HMMs
• Given a set of sequences with common structures,
  simultaneously learn SCFG parameters and
  optimally parse sequences into states
• EM on SCFG
• Inside-outside algorithm
• Efficiency is a bottleneck
• Have been successfully applied to predict tRNA
  genes and structures
• tRNAScan

55
Future directions

• Structure prediction
• Secondary
• Tertiary
• Structural comparison tools
• Structural alignment
• Structure search tools
• RNA-BLAST
• Structural motif finding
• RNA-MEME