1. Computational ncRNA gene finding ncRNA structure prediction
Liming Cai
Fall 2010)

3. Non-coding RNAs
Functions other than coding proteins, e.g., structural, catalytic, and regulatory factors
functional RNAs = ncRNAs + UTR motifs
(-) No strong statistical features, such as ORFs, or polyadenylated, demonstrated in coding genes
(+) Transcribed ncRNA molecules can fold into secondary and tertiary structures (more conserved than sequences)

4. Sources of ncRNAs
Non-coding RNA genes encode RNAs, e.g., miRNAs, rox1 and rox2 RNAs in male Drosophila melanogaster.
In introns and intergenic regions, e.g., snoRNAs
In 5’ and 3’ UTRs, e.g., regulatory motifs (functional RNAs)

5. Functions of ncRNAs rRNAs and tRNAs
RNA maturation: snRNA in recognizing splicing sites
RNA modification: snoRNA converting uridine to pseudo-uridine
Regulation of gene expression and translation: e.g., miRNAs
DNA replication: e.g., telomerase RNAs - template for addition of telomeric repeats
Etc.

6. Classes of ncRNAs (Bompfunewerer, et al, 2005)
Size
Function
Phylogenetic
distribution
tRNA
70-80
Translation
ubiquitous
rRNA
16S/18S
28S+5.8S/23S 5S
1.5K 3K
130
translation
RNase P
MRP
tRNA -maturation
eukarya
snoRNA
telomerase
pseudouridinylation
addition of repeats
snRNA
U1 ~ U6
Spliceosome
mRNA maturation
Eukarya
Eukarya, archaea U7
7SK
~65
~300
Histone mRNA
Maturation
Translational
regulation
Eukayotes
vertebrata
tmRNA
Tags protein
For proteolysis
bacteria
miRNA
~22
Post-tran. Reg.
Multi-cellular orgs

7. Some ncRNAs databases Rfam (280,000 regions of 379 families)
NONCODE (109 transitional classes and 9 groups)
RNAdb (800 mammalian ncRNAs, excluding tRNAs, rRNAs and snRNAs)
Arabidposis small RNA Project (ASRP)
Etc.

8. ncRNA gene finding strategies
Computational predictive methods
cDNA cloning to enrich ncRNAs
Detecting new transcripts with oligonucleotide microarrays

9. ncRNA gene finding: a computational challenge
ncRNA genes do not have significant statistical signals
large in number
diverse, 20 nts to 22,000 nts
Not sure what to look for
Computationally intensive
- Simply no good method
- Methods compromising accuracy

10. Computational ncRNA gene finding methods
Specific (custom-designed) ncRNA search and annotation
(e.g., tRNAscan, methylattion-guide snoRNA, miRNA, tmRNA)
Reconfigurable search systems
(e.g., Infernal, ERPIN, RNATOPS,FastR)
mechanism to profile the target ncRNA (structure)
- need training data
De novo ncRNA gene detection with
base composition (e.g., G+C %)
structure fold (e.g., RNAz)
Comparative analysis (e.g., QRNA, EvolFold)
- consensus structure
ncRNA “holy grail” ?

11. Review literature in computational ncRNA gene finding and annotation
A. Laederach (2007) Informatics challenges in Structural RNA, Brief Bioinformatics 8(5)
S. Eddy (2001) Non-coding RNA genes and modern RNA world, Nature Reviews Genetics, 2(12),
S. Griffiths-Jones (2007) Annotating noncoding RNA genes, Annual Rev. Genomics & Human Genetics, 8:
Machado-Lima et al (2008) Computational methods in noncoding RNA research, Mathematical Biology, 56:

12. Comparison between NUPACK and Triple
506 miRNAs
Comparison between NUPACK and Triple
499 tRNAs
Comparison between
NUPACK and Triple
Data were from
Bonnet et al, 2004

13. 499 tRNA Comparisons between HG, Triple, NUPACK 499 tRNA
HG and NUPACK
Data were from
Bonnet et al, 2004

14. What are in this lecture?
RNA secondary structure prediction
1. ab initio structure prediction
2. consensus structure prediction
3. structural model-based prediction
but why just secondary structure?
[Doudna,et al, 1999]
[tRNA unfolding pathway]

16. What else are in this lecture?
ncRNA gene finding and annotation
4. Structural profile-based ncRNA gene annotation
5. comparative analysis based ncRNA gene finding
6. ab initio ncRNA gene detection

17. Base pairings of RNAs Base pairings allow RNA to fold
Watson-Crick base pairs: A-U, C-G
Wobble pair G-U
called canonical pairs for secondary structure
Note: all 16 (including non-canonical) base pairs
are possible for RNA tertiary structure

18. 5’-u-u-c-c-g-a-a-g-c-u-c-a-a-c-g-g-g-a-a-a-u-g-a-g-c-u-3’P u a P g P a P c N O H N O H
CYTOSINE
GUANINE N O H N H
URACIL
ADENINE

19. Secondary structure is important
to tertiary structure

20. Stems in nested or parallel patternc
guu
aga
aac c
ucu
cccc
acc gc
gca
ggg
ugc
ggu cc
stem (double helix): stacked base pairs
loop: strand of unpaired bases

21. Stems in crossing patterns
guu
aga
aac c
ucu
cccc
acc gc
gca
ggg
ugc
acc
ggu cc
Pseudoknots: crossing patterns of stems

22. RNA secondary structure elements
Pseudoknot
Stem
Interior Loop
Single-Stranded
Bulge Loop
Junction (Multiloop)
Hairpin loop
Image– Wuchty

23. RNA stem-loop (pseudoknot-free) structure example

24. RNA secondary structure prediction
ab inito structure prediction
to predict the structure of a single sequence
2. Consensus structure prediction
to predict the structure shared by more than one sequences
3. Statistical model-based prediction and alignment
to search for desirable structures on genomes or data bases

25. 1. ab initio structure prediction
Hydrogen bonds consume energy contained in the molecule.
The smaller the free energy is, the more stable the structure folded.

26. ab initio structure prediction (cont’)
Consider only canonical base pairs
A-U, C-G, and G-U.
Base pairings reduce the amount of free energy contained in the molecule.
Maximizing the number of base pairs would minimize the free energy in the molecule.
(Only an approximate model)

27. ab initio structure prediction (cont’)
But how to count?
An RNA could be very long; there may be many possible ways that base pairs can be formed:
e.g., ……ACGGUACGUC…..
conflicting pairs A-U, A-U
G-C, G-C
etc.
Even the number of non-conflicting combinations of base pairs
is exponentially large.

28. ab initio structure prediction (cont’)j
(1)
head paired with tail
(2)
tail is unpaired
(3)
head is unpaired
(4) i k j
two subfolds

29. looking at shorter (e.g., very short) subsequences
in a long sequence ACGGU…ACGUC
For subsequences of length 1,
A, C, G, G, U, …, A, C, G, U, C
#of base pairs 0, 0, 0, 0, 0, …, 0, 0, 0, 0, 0
For subsequences of length 2,
AC, CG, GG, GU, …, AC, CG, GU, UC
# 0, , 1, …, 0, 1, 1, 0
For subsequence of length 3,
ACG, CGG, GGU, …, UAC, ACG, CGU, GUC, UUC
?: e.g., GUC (1) G-C + U --> 1+0 =1 head-tail
(2) G + UC --> 0+0 =0 head unpaired
(3) GU + C --> 1+0 =1 tail unpaired
(4) GU + C --> 1+0 =1 split
(5) G + UC --> 0+0 =0 split

30. examine a little longer sequence …..ACGGUACGU…..
i j ==> max of {cases 1, 2, 3, 4}
Head-tail paired, count = 1 + max count in subsequence
CGGUACG
i j-1
2. Head unpaired, count = max count in subsequence
CGGUACGU
i j
Tail unpaired, count = max count in subsequence
ACGGUACG
i j-1
Split (why needed and where to split ?)
ACGGUACGU when k=i+2
i j ==> ACG + GUACGU
<---- k ---> count = max count in ACG
+ max count in GUACGU

31. Ab initio structure prediction (cont’)
Maximizing the number of base pairs (Nussinov et al, 1978)
simple model:
(i, j) = 1

32. G G G A A A U C C G A U C 1 1 1 1 1 2 1 2 3 Ci,j = 0 when i=jG A U C 1 1 1 1 1 2 1 2 3
GGGAAAUCC
Ci,j = 0 when i=j
GAAAUC
AAUC AU

33. Example 2: ACGGUU subsequence of length 0: empty sequence, 0 pairs
subsequences of length 1: A, C, G, G, U, U
pairs
subsequences of length 2: AC, CG, GG, GU, UU
pairs
subsequences of length 3: ACG, CGG, GGU, GUU
pairs
Subsequences of length 4: ACGG, CGGU, GGUU
pairs
Subsequences of length 5: ACGGU, CGGUU
pairs
subsequence of length 6: ACGGUU
3 pairs

34. Prediction Algorithm Web Server
Sample sequence:
(1) tRNA GGGGUCAUAGCUCAGUUGGUAGAGCGCUACAAUGGCAUUGUAGAGGUCAGCGGUUCGAUCCCGCUUGGCUCCACCA
(2) a part of tmRNA CCUCUCUCCCUAGCCUCCGCUCUUAGGACGGGGAUCAAGAGAGGUCAAACCCAAAAGAGA
Simple matrix,
simple matrix with G-U pair
Complex matrix
Rfam database:

35. Thermodynamic energy based structure prediction
Energy minimization algorithm predicts the correct secondary structure by minimizing the free energy (G)
G calculated as sum of individual contributions of:
loops
base pairs
secondary structure elements

36. Free-energy values (kcal/mole at 37oC )
Energies of stems calculated as stacking contributions between neighboring base pairs

37. Free-energy values (kcal/mole at 37oC )

38. Zuker’s algorithm MFOLD: computing loop dependent energies

39. Assumptions in such algorithms
Most likely structure corresponds to energetically most stable structure
Energy associated with any position is only influenced by local sequence and structure
Structure formed does not produce pseudoknots

40. RNA structure prediction web servers
MFOLD
RNAfold ( a part of Vienna Package)
Examples:
GCTTACGACCATATCACGTTGAATGCACGC
CATCCCGTCCGATCTGGCAAGTTAAGCAAC
GTTGAGTCCAGTTAGTACTTGGATCGGAGA
CGGCCTGGGAATCCTGGATGTTGTAAGCT

41. RNA pseudoknot (tmRNAs)
Bacterial tmRNA consensus structure
(Felden et al NAR 29)
terminates translation errors

42. Functions of pseudoknots (TMV 3’ UTR)
Promotes efficient translation
Binds EF1A, cooperates with 5’UTR
(Leathers et al MCB 13
Zeenko et al JVI 76)

43. Pseudoknots drastically increase computational complexity

44. RNA pseudoknot prediction web servers
Pknots-RG:
Pknots-RE (the first pseudoknot prediction algorithm)
Kinefold:
ILM

45. Computational complexity issues
Pseudoknot-free structures: O(n3) CUP time
Pseudoknots: NP-hard, restricted cases O(n5)
Heuristics added: O(n4)
Difficult for search RNA structures in genomes

46. 2. Consensus structure prediction
Covariance fact for RNAs:
Variations in RNA sequence maintain base-pairing patterns for secondary structures
When a nucleotide in one base changes, the base it pairs to must also change to maintain the same structure

47. Structure alignments (example)
C A
G A
G•C
A A
G A
C•G
U•A
A•U
G A
G A
AG
UG
CA
CU
Query RNA structure
A: structural homolog
B: nonhomologous
primary sequence alignment scoring:
query: GGGGGCAACCCC
A: AUCCGAAAGGAU
    | | |   
query: GGGGGCAACCCC
B: CCUAGAAAGGAU
    |  | |    -6 -6
structure + sequence alignment scoring:
query: GGGGGCAACCCC
A: AUCCGAAAGGAU
| | | | |  | | | | | |
query: GGGGGCAACCCC
B: CCUAGAAAGGAU
    |  | |   
+11 -6

48. Covariance
Mutlipel Structural Alignment of 13 tmRNA genes from
the β-proteobacteria [Felden et al’01]

49. Dynamic programming approach
(Sankoff 1984)
This can be regarded as running ‘two Nussinov algorithms at the same time’ to simultaneously fold two RNAs i j p q
‘the coordinated fold’ is found through computing Ci,j,p,q,
needs: O(n6) time for two sequences and O(n3k) for k seqs

50. Inferring structure by comparative sequence analysis
(1) calculate a multiple sequence alignment
Requires sequences to be similar enough so that they can be initially aligned
Sequences should be dissimilar enough for covarying substitutions to be detected

51. Inferring structure by comparative sequence analysis (cont’)
(2) compute Mutual Information
fxi : frequency of a base x in column i
fxiyj : joint (pairwise) frequency of base pair x-y between columns i and j
If i and j are uncorrelated, mutual information is 0

52. Inferring structure by comparative sequence analysis (cont’)
(3) use mutual information Mi,j as pairing “energy” and treat the multiple alignment as a “generic” sequence
apply a Nussinov’s algorithm-like process to find the most likely common structure

53. Inferring consensus structure by a graph-theoretic approach (ConRAN and RNASampler)
Identify all stems in every sequence, assigning each stem a vertex in the graph
Connect two stems in two different sequences with an edge if they are similar
Connect two stems in the same sequence with an edge if they do not conflict
The optimal consensus structure corresponds the maximum clique

54. Consensus structure prediction programs
Dynalign
Foldalign
ComRNA
RNA sampler
Carnac

55. 3. Statistical model-based structure prediction and alignment
Extension from HMM to include mechanisms that can describe (long-distance) base pairings
Stochastic grammars can describe models defined by HMMs
Stochastic grammars can describe models not definable by HMMs

56. Stochastic context-free grammar
Covariance model (CM) [Eddy and Durbin’94]
based on computational grammar systems
M2  a M’2 I2  a I2 D2  I2 M’2 I2 I2  M3 D2  M3
M’2 D3 I2  D3 D2  D3
A path in the HMM  a derivation in the grammar

57. Stochastic context-free grammar (cont’)
Stochastic Context-free Grammars (SCFGs)
[Lari and Young’90, Sakakibara et al’94] S
S  aSu L  aL
S  uSa L  cL
S  gSc L  a
S  cSg L  c
S  L S S L L L L c
g u u
a g a
a a c c
u c u
c c c c
Each derivation tree corresponds to a structure.

58. Stochastic context-free grammar (cont’)
S  aSu
S  cSg
S  gSc
S  uSa
S  a
S  c
S  g
S  u
S  SS
1. A CFG
S  aSu
 acSgu
 accSggu
 accuSaggu
 accuSSaggu
 accugScSaggu
 accuggSccSaggu
 accuggaccSaggu
 accuggacccSgaggu
 accuggacccuSagaggu
 accuggacccuuagaggu
2. A derivation of “accuggacccuuagaggu”
3. Corresponding structure

59. What to do with SCFGs ? Both need to do sequence-structure alignment
Structure prediction
require the SCFG model to be flexible enough
Structure search
require the model to be specific
Both need to do sequence-structure alignment

60. Structure prediction with SCFG
S  aSu
S  cSg
S  gSc
S  uSa
S  aS
S  cS
S  gS
S  uS
S  Sa
S  Sc
S  Sg
S  Su
S  a
S  c
S  g
S  u
S  SS
Probability parameter assignment:
Sum of probabilities of the same LHS =1
(2) Geometric distributions for loop and stem lengths
(3) Parameters are obtained from training sequences with known structures
Alignment score between model S and subsequence x[i..j] is computed, when x[i]=a, x[j]=u
C(S, i, j) = max { C(S,i+1, j-1)*P(S -> aSu),
C(S,i+1, j)*P(S -> aS),
C(S, I,j-1)*P(S -> Su),
maxk { C(S,i,k)C(S,k+1,j)P(S->SS) }

61. Web servers for RNA Structure prediction with SCFG
S  aSu
S  cSg
S  gSc
S  uSa
S  aS
S  cS
S  gS
S  uS
S  Sa
S  Sc
S  Sg
S  Su
S  a
S  c
S  g
S  u
S  SS
Web servers for RNA Structure prediction with SCFG
Infernal:
Pfold: (multiple sequence + SCFG)

62. RNA secondary structure prediction
1. ab initio structure prediction
2. consensus structure prediction
3. structural (SCFG) model-based prediction
ncRNA gene finding and annotation
4. profile-based ncRNA gene annotation
5. comparative analysis based ncRNA gene finding
6. ab initio ncRNA gene prediction

63. 4. Structure profile based RNA gene annotation
Secondary structure alone is not sufficient for
predicting ncRNA genes, BUT it remains to be
the best hope for an exploitable statistical signal
To find RNA structures or genes, one can profile
the structure to be searched. Often, SCFG is used
as a modeling tool.

64. Structure profile based RNA gene annotation (cont’)
Search for a specific family RNAs (structures)
Need an effective mechanism to profile the family
Need a fast structure-sequence alignment algorithm

65. RNA training sequences with annotated structures
modeling
e.g. CM
SCFG
profiling
model
alignment
genome
scanning window
(target sequence)

66. CM is a profile-SCFG, position-specific, very effective
Slow O(n3N)-time even for pseudoknot-free RNAs in genomes or large databases
Cannot handle pseudoknots
HMM based filtering to imprve speed
Examples:
tRNAscan-SE (
infernal (

67. 5. Comparative analysis based ncRNA gene finding
Based on structure features of RNA
Consider two or more genomes phylogenetically related
Use sequence alignment tools (such as BLASTN) to find local alignment between the two
Search with a sliding window
Identify potential RNA fold within the window
Computationally verify it to be putative RNA
QRNA (Eddy group, 2001)
EvoFold (Haussler group, 2006)
RNAz (Stadler group, 2005)

68. detecting ncRNA genes with SCFGs
QRNA (Eddy et al, 2001)
detecting ncRNA genes with SCFGs
given two aligned sequences, to test the pattern
of substitutions observed in the pairwise alignment of
two homologous sequences using
a pair of SCFGs for ncRNAs (compensatory mutations)
a pair HMM for protein-coding genes (conserved regions)
a pair HMM for other regions (random evolution)

69. QRNA:

70. Probability parameters

72. Other software to detect RNA genes based on comparative analysis
EvoFold
multiple genomes
use SCFG + phylogeny to predict consensus structure
RNAz
predict the consensus fold
compare energy of the fold to background energy

73. 3. Ab initio prediction of ncRNA genes
mainly based on base composition difference between real RNAs and the background, limited success.
Unsuccessful by simply predicting the structure of RNAs
Other methods?

74. Fold energy and fold certainty
Methods based on folding energy do not seem to work [just like structure prediction]
How do distinguish a real ncRNA from random sequences that fold to the same structure by chance [both could have the same energy]
The difference seems to be the structure certainty
But how to compute structure certainty?

75. Fold certainty For a real ncRNA sequence:
Base pairs contributing to the real fold should not be everywhere.
‘overall strength’ of base pairs contributing to other, false folds should be weak.
For a random sequence:
either it does not fold
or there is a low probability to form a certain fold

76. Fold certainty (cont’)
Compute Shannon entropy
En(S) = ∑Pij log Pij
where Pij is the probability for bases i and j to pair
Pij = (number of folds pair (i,j) is involved) / (number of folds)
[simplified]

77. Fold certainty (cont’)
We measured entropy Z-score of a real ncRNA based on the entropies of its random counterparts
But the entropy Z-score performance on different ncRNAs is different
miRNAs perform well while tRNAs do not
What happened?

78. Readings and projects in RNA informatics

80. What about pseudoknots?

81. Tree decomposition based search algorithms
Dynamic programming at the nucleotide level is time consuming
Very Slow, O(n6N)-time even for restricted pseudoknot categories
Pseudoknots are not very complex from graph-theoretic point of view

82. Tree decomposition based search algorithms (cont’s)
profile each stem with SCFG, connecting the two halves with an edge
profile each loop with HMM, connect two ends of the loop with a directed edge
Produce a mxied graph H for the structure
Preprocess target sequence with the profiles to obtain all potential candidates, construct a graph G for the sequence
Structure-sequence alignment corresponding finding an optimal subgraph in G isomorphic to H

83. Tree decomposition based search algorithms (cont’s)
H is decomposed as a tree representation
Fast alignment algorithm can be obtained O(kt Nn)
where t is the tree width of H, usually small for pseudoknotted RNAs, k is a parameter, small also
Successful for RNA structures that belong to a well-defined family

84. Sequence-structure alignment
1. Construct graphs 1 1
Structure graph
Sequence graph
subgraph
isomorphism
2. Tree decompose
the structure graph 2
Now we come back to RNA gene search. The core part of RNA gene search is Sequence-structure alignment. First from the structure we want to search
in genome, we construct structure graph and sequence graph. Then we tree decompose the structure graph.
Finally find the sequence-structure alignment based on the tree.
I will explain each step in detail in the following slides. 3
3. Dynamic programming
based on tree decomposition
Tree decomposition

85. Structure graph structure graph Hidden Markov Model (HMM) a a’
Covariance Model (CM) d’ b d b’ c’ c s a b b’ c c’ d d’ a’ t
First, we construct structure graph from structure. Each vertex is a half stem. And follow the order, connect two neighboring vertices with a directed edge for a loop. And a stem with a non-directed edge.
structure graph

86. Sequence graph structure graphb b’ c c’ d d’ a’ t
For each stem, identify k candidates in the sequence
Then we construct sequence graph. On the target genome sequence, we choose k candidates for each vertex. In this example,
k is two. a1 a2
a’1
a’2
genome sequence

87. Sequence graph structure graphb b’ c c’ d d’ a’ t
For each stem, identify k candidates in the sequence
We do that same thing for other stems. a1 a2 b1 b2
b’1
b’2
a’1
a’2
genome sequence

88. Sequence graph genome sequence sequence graph t s a1 a2 b1 b2 b’1 b’2d1 d2
d’2
d’1
a’1
a’2
sequence graph
Finally, we can get all possible structures in the sequence, so we get a sequence graph. a1 b1
b’1 c1
c’1
a’1 t s a2 b2
b’2 c2
c’2
a’2

89. Subgraph isomorphism structure graph
Sequence-structure alignment becomes
subgraph isomorphism
sequence graph k=2
So now we have both structure graph and sequence graph. To find the optimal sequence-structure alignment is to find the optimal subgraph in the sequence graph that is isomorphic to the structure graph! a1 b1
b’1 c1
c’1
a’1 s t a2 b2
b’2 c2
c’2
a’2

90. Tree decomposition of structure graphb d d’ b’ c c’ a’ t
b b’ c’
s a a’
a a’ t
a b a’
b c’ a’
b’ c c’
To get the optimal alignment, we do the second step: tree decompose the structure graph.
This is an example of the graph of a pseudoknot-free structure. For pseudoknot-free graph representations, the tree width is always 2.
b d b’
d d’ b’
(1) Pseudoknot-free structure graphs have tree width = 2

91. Tree decomposition of structure graph (cont’d)x y s a b d d’ b’ c c’ a’ t
b b’ c’ y
b’ c c’ y
s a a’
a a’ t
a b a’
b c’ a’
c c’ y
If we add a crossing stem in it, the tree width is only increased by 1. For all RNA structures with pseudoknots, the tree widths only increase slightly.
b d b’ y
d d’ b’ y
d d’ x y
(1) Pseudoknot-free structure graphs have tree width = 2
(2) Almost all pseudoknot structure graphs have small tree width

92. Tree width of tmRNA
Tree width = 5

93. Tree decomposition based search algorithms (cont’s)

94. Tree decomposition based search algorithms (cont’s)
HI: Haemophilus influenzae
NM: Neisseria meningitidis
SC:Saccharomyces cerevisiae
SB: Saccharomyces bayanus

95. RNA structure and gene search
How to identify novel RNAs whose structure may
deviate from the common structure of the family?
- make a profile accommodate novel structures
(This may mean to test more potential structures)
- make the structure-sequence alignment fast enough