????????F????? ?? ???a

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????????F????? ?????aµ???? ?????aµµat?sµ??

• ?a?te??? ?p?????

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???aµ???? ?????aµµat?sµ??

• St????s? (t?p???-?????)
• RNA secondary structure prediction
• ??aµeµß?a???? tµ?µata
• Hidden Markov Models
• ???e? efa?µ????

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St????s?

• ?????
• ??p???
• ??d???? pe??pt?se??

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???aµ???? p????aµµat?sµ??
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??? pe??pt?se?? st????se??
F(i,0)-id, F(0,j)-jd
F(i,0)0, F(0,j)0
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?????? ??a ta ?e?? (gap penalties)
?p?? p???? ??a ta ?e??
S???et? p???? ??a ta ?e??
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?a??de??µa
?st? d?? a???????e?
?? ????µe ??a ta ?e??
d1
??te ? ?a??te?? ????? st????s? ?a e??a?
A A G T T A G C A G C A G T A T C G C A -
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????? st????s?
A A G T T A G C A G C A G T A T C G C A -
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??p??? st????s?
A G T T A G C A A G T A T C G C A
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????? a??????µ??

• ?p?????? ep?s?? e?d???? pe??pt?se?? st????s??
  (p.?. p??sa?µ???)
• T????µe d??ad? ?a e?t?p?s??µe, µ?a µ????
  a???????a a? s??a?t?ta? se µ?a µe?a??te??
• ?st? ?t? ?????µe ?a a????e?s??µe a? st??
  a????????a t?? ????d??? lacI t?? E.coli ?p???e? ?
  ???st? a????????a t?? ?p?????t? (promoter). ?st?
  a??µa ?t? t? tµ?µa t?? ????d??? ??e? a????????a
• ?a? ? a????????a t?? ?p?????t? e??a?

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s????e?a
F(i,0)-id F(0,j)0.
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?a? ? a???????a t?? p??a??? ?p?????t? e??a?
C A T G A T
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RNA secondary structure prediction
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Nussinov
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??aµeµß?a???? tµ?µata
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?a 3 ßas??? e??t?µata se ??a ??? ...

• ??t?µ?s?
• ?ed?µ???? t?? µ??t????, p?? ?a ?p?????s??µe t??
  ????? p??a??t?ta µ?a? a???????a? s?µß????.
  P(x?)
• ?p???d???p???s?
• ??? ?a ß???µe t?? p?? p??a?? a????????a
  ?atast?se?? (path) ap? t?? ?p??a ??e? d????e? t?
  µ??t???, ??a ?a d?se? t?? s???e???µµ??? a???????a
  s?µß????.
• ??pa?de?s?
• ??? ?a t??p?p???s??µe t?? pa?aµ?t???? t??
  µ??t????, ?ts? ?ste ?a µe??st?p????e? ? s???????
  p??a??f??e?a t?? a?????????
• ?MLargmaxP(x?)

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... ?a? ?? apa?t?se?? t???

• ??t?µ?s?
• ???????µ?? FORWARD, a??????µ?? d??aµ????
  p????aµµat?sµ??, p?? ?p??????e? t?? s???????
  p??a??t?ta t?? a???????a?, ????? ?a d????e? ap?
  ??a ta d??at? µ???p?t?a (a????????e?
  ?atast?se??).
• ?p???d???p???s?
• ???????µ?? t?? VITERBI, a??????µ?? d??aµ????
  p????aµµat?sµ??, p?? µ?s? a?ad??µ?? (recursion)
  ?p??????e? t?? p?? p??a?? a????????a ?atast?se??
  ??a t? ded?µ??? a???????a ?a? t? ded?µ???
  µ??t???. (??a??a?t??? NBEST).
• ??pa?de?s?
• ???????µ?? t?? BAUM-WELCH (? a?????
  FORWARD-BACKWARD), e?d??? pe??pt?s? t??
  a??????µ?? ?? (Expectation-Maximization), ?
  ?p???? ?e????eta? ta ded?µ??a sa? ded?µ??a µe
  e??e?p?? t?µ?? (missing values) ?a? ?p??????e?
  ?.?.?. ??a t?? pa?aµ?t???? t?? µ??t????
  (??a??a?t??? Gradient Descent).

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???????µ?? Forward
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???????µ?? Viterbi
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?p???d???p???s? forward
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?? t?? ?st???? ap???d???p???s?
??a??a?t??? µp??e? ?a ?p?????s?e? ? p??a??t?ta
d??ad?, ? e? t?? ?st???? p??a??t?ta t?
s???e???µµ??? ?????e?t?d?? ?a p?????e ap? µ?a
?at?stas?
?????ta? ???s? t?? Forward ?a? Backward
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• ??e??e?t?µata
• st?? pe??pt?se?? p?? ta e?a??a?t??? µ???p?t?a
  ????? p??? µ????? d?af???? st?? p??ß?ep?µe?e?
  p??a??t?te?.
• ?ta? µ?a ?at?stas? ??e? p??? µ???? p??a??t?ta
  ?a? t? µ???p?t? µe t?? µ???st? p??a??t?ta, de?
  t?? ep?s??pteta? p?t?.

• ?e???e?t?µata
• ?p??e? ?a p??ß?ef?e? µ?a p??a??t?ta ? ?p??a de?
  e??a? ?????? ??a t? µ??t??? (µ?a µ? ep?t?ept?
  µet?ßas?).

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S???pt??? ? a??????µ??

• ?p?????sµ?? t?? ? ?a? ?
• ?p?????sµ?? t?? ???
• ?pa?????? µ???? ?a s??????e?

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??a pa??de??µa...
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s????e?a...
???a??t?te? µetaß?se?? 1 0 0.90
0.100.10 0.90 ???a??t?te? ?e???se?? ? ?
G C 0.70 0.10 0.10 0.100.25
0.25 0.25 0.25
1 0
1 0
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s????e?a...
?st? µ?a a???????a DNA, ? ?p??a p?????eta? ap? t?
pa?ap??? µ??t???
AAACAAGAATGCGCACACTACGCAAAAACAATTAGTCGCACTCACGATGA
AACAAATTACCACGGTGAA 111111111100000000000001111111
111100000000000000111111110000000000001   AACGAATA
AACCTCAGAGGCCCAGCGTATATAAACAAGATAAAAACCTAGTCAGCACT
CTGACCAGACG 11111111110000000000000000000001111111
1111111100000000000000000000000   AGCTCACGACTTGAGG
ATAAGAAAAAAACAACAGCTCACGACTTGAGGATAAGAAAAAAACA 000
00000000000001111111111111100000000000000000011111
111111111
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s????e?a...
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s????e?a...
?? ?µ?? ?? p??a??t?te? µetaß?se?? ???a?a?
???a??t?te? µetaß?se?? 1 0 0.98
0.020.03 0.97 ???a??t?te? ?e???se?? ? ?
G C 0.60 0.10 0.10 0.100.25
0.25 0.25 0.25
1 0
1 0
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s????e?a...
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Posterior-Viterbi decoding
??????ta? ?? ep?t?ept?? µetaß?se??
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Optimal Accuracy Posterior Decoding
?a?a??a?? t?? Posterior-Viterbi, ? ?p??a
?p??????e? t? µ???p?t?
S???????
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???e? efa?µ????

• Fold recognition
• Threading
• Domain recognition

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Fold recognition
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Threading

• Protein threading is the problem of aligning a
  protein sequence whose structure we want to
  elucidate (the target protein) with a protein
  sequence whose structure is known (the template
  protein) in such a way that mapping residues of
  the target onto a template according to the
  alignment affords an accurate model of the
  backbone structure of the target.

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Domain recognition
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Transformational Grammars
Colourless green ideas sleep furiously Choms
ky
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A transformational grammar consists of a number
of symbols and a number of rewriting rules
(productions) of the form a?b, where a and b
are both strings of symbols. i.e. C ? cN, C ?
E There are two types of symbols -abstract
nonterminal symbols -terminal (observable)
symbols)
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Production rules

• Regular grammars only productions of the form W
  ?aW or W ?a
• Context-free grammars productions of the form W
  ?ß. Left just one non-terminal, right any
  string
• Context-sensitive grammars productions of the
  form a1Wa2 ?a1ßa2
• Unrestricted grammars any production of the form
  a1Wa2 ??
• W any non terminal,
• a any terminal,
• a, ? any string of nonterminals and/or terminals
  including null string
• ß any string of nonterminals and/or terminals
  not including null string

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Regular Expressions
RK-G-EDRKHPCG-AGSCI-FY-LIVA-x-FYM
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?s?d??aµ?a

S ? rW1kW1 W1 ? gW2 W2 ? afilmnqrstvwyW3 W3
? agsciW4 W4 ? fW5yW5 W5 ? lW6iW6vW6aW6 W6
? acdefghiklmnpqrstvwyW7 W7 ? fym
RK-G-EDRKHPCG-AGSCI-FY-LIVA-x-FYM
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Stochastic Grammars? the notion probability of
a sentence is an entirely useless one, under
any known interpretation of this term. Noam
Chomsky (famed linguist) Every time I fire a
linguist, the performance of the recognizer
improves. Fred Jelinek (former head of IBM
speech recognition group)
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HMMs and Regular grammars
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Modeling (allowed) transitions explicitly B ?
L F E L ? L F E L ? L F E In the
notation of the grammars, these are the
nonterminal symbols Modeling emission explicitly
(no probab. here) in state F a c g t
in state L a c g t In the notation of
the grammars, these are the terminal symbols
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??a µa??

• Together Modelling each combination of state and
  transition explicitly
• B ? aL cL gL tL aF cF gF tF E
• L ? aL cL gL tL aF cF gF tF E
• F ? aL cL gL tL aF cF gF tF E
• P( B ? aL ) P(B) P(aL)
• P( L ? aF ) P(F L) P(aF)
• These are the so called rewriting rules

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• Thats all we need to define a stochastic regular
  grammar !
• Finite alphabet of terminal symbols
• (a,c,g,t)
• Finite set of nonterminal symbols
• (B,L,F,E)
• A set of rewriting rules
• (B -gt aF, L -gt cF, ...)
• Probabilities
• P(B-gtaL)

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Hidden states Non-terminals
Transition matrix Rewriting rules
Emission matrix Terminals
Probabilities Probabilities
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Example possible regular grammar N ? aF cF
gF tF aL cL gL tL E 0,1 0,1
0,3 ... B ? aF cF gF tF aL cL gL
tL E 0,2 0,1 0,2 ... C ? aF cF
gF tF aL cL gL tL E 0,1 0,3
0,2 ... An example derivation from the above
grammar is B ? aF ? aaL ? aacL ? aactF ?
aactE Finite State Automata Meale, Moore
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?d??aµ?e? t?? Regular Grammars

• Regular language
• a b a a a b
• Palindrome language
• a a b b a a
• Copy language
• a a b a a b

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?a???d??µe? G??sse?

• ????? ????????? ?? ????? ????.
• Doc, note. I dissent. A fast never prevents a
  fatness. I diet on cot.
• RNA secondary structure
• aggccuaaauagaucuag...
• ((()))...(((())))....

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Context-free grammars

• St? context-free grammar, st? a??ste?? s?????
  p??pe? ?a ????µe ??a ?a? µ??? non-terminal, a???
  st? a??ste?? ?p????d?p?te s??d?asµ? terminal ?a?
  non-terminal
• S ?aSabSbaabb
• S?aSa ?aaSaa ?aabSbaa ?aabaabaa
• To parsing ???eta? µe ta Push-down automata

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Context-free grammars for RNA
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Chomsky Normal form

• W1?W2W3 or W1?a
• ???e ??aµµat??? µp??e? ?a p??e? t? µ??f? a?t?
• ?d?a?te?a ???s?µ? ??a t??? a??????µ???

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Stochastic Context-free grammars (SCFGs)

• Se ???e ?a???a a?at??eta? µ?a p??a??t?ta
• ?as??? p?e????t?µa, ? p??fa??? ep??tas? ?a?
  e???pt??s? t?? ap?te?esµ?t?? (?p?? ??a pa??de??µa
  ap? Regular expression se ???)
• ?a??de??µa ?p??e? ?a ep?t??p??µe (µe
  d?af??et????, ?a? µ????? p??a??t?te?) t?
  ?a?eµ??? ?e?????µa G-U, C-A

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?a ßas??? e??t?µata se ??a SCFG

• ??? ?a ep?t????µe t?? ?a??te?? st????s? µ?a?
  a???????a? µe µ?a ??aµµat??? (alignment-parsing
  problem)
• ?p?????sµ?? t?? p??a??t?ta? µ?a? a???????a?
  ded?µ???? µ?a? ??aµµat???? (scoring problem)
• ???es? t?? ?a??te??? pa?aµ?t??? µ?a? ??aµµat????
  a? ?p?????? ???st? pa?ade??µata (training
  problem)

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?? apa?t?se?? t???

1. Cocke-Younger-Kasami (CYK) algorithm ???t?st?????
   t?? Viterbi sta ???
2. Inside (outside) algorithm ? ??t?st????? t??
   Forward (Backward)
3. Inside-Outside algorithm? ??t?st????? t??
   Baum-Welch (Forward-Backward)

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??t?st????e?
St???? ??? SCFG
???t?st? st????s? Viterbi CYK
P(x?) Forward Inside
EM algorithm Baum-Welch Inside-Outside
Memory complexity O(LM) O(L2M)
Time complexity O(LM2) O(L3M3)
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???e? p??se???se??

• Nusinov algorithm
• ?e??st?p??e? t? s????? t?? ?e??a???? ß?se??
• Zuker algorithm
• ?e??st?p??e? µ?a s????t?s? e????e?a? (?G), ?
  ?p??a ap?d?de? ?a??te?a
• ?a? ?? d?? a??????µ??, µp????? ?a ??af??? se µ?a
  ?s?d??aµ? µ??f? SCFG

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??d???? pe??pt?se??
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?e??pt?se?? pseudoknots
?pa?t???ta? e?d???? t??p?p???se?? ??a ?a
e?s?µat????? se ??a SCFG
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?pe?t?se??

• ????profile HMM
• SCFG?Covariance Model (CM)
• Eddy and Durbin, 1994

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?? ???eta? µe t?? p??te??e??
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?a?a??a???

• Ranked Node Rewriting Grammar (RNRG)
• Multi-Tape S-Attributed Grammars (MTSAG)

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Ranked Node Rewriting Grammar (RNRG)
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Ranked Node Rewriting Grammar (RNRG)
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Multi-Tape S-Attributed Grammars (MTSAG)
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?p?te??sµata

• Prediction of Bacteriorhodopsin (1AP9)
• QAQITGRPEWIWLALGTALMGLGTLYFLVKGMGVSDPDAKKFYAITTLVP
  AIAFTMYLSMLLGYGLTMVPFGGEQNPIYWARYADWLFTTPLLLLDLALL
  VDAD
• .......TTHHHHHHHHHHHTTHHHHHHHHSS..S.HHHHHHHHHHHHTH
  HHHHHHHHHHHTT.....SSS.SSS....STTHHHHTTTHHHHTTTTSTT
  TT..
• .........MMMMMMMMMMMMMMMMMMMMMMMMMM......PMMPMMPPM
  MPPMMPPMMPMMPMMPMMP........PPMPPMPPMPPMPPMMPPMPPMP
  P...
• .........PMMPMMPMMPMMPMMPMMPPMMPMMP......PMMPMMPPM
  MPPMMPPMMPPMMPPMMPP........PPMPPMPPMPPMPPMPPMMPMMP
  P...
• QGTILALVGADGIMIGTGLVGALTKVYSYRFVWWAISTAAMLYILYVLFF
  GFTSKAESMRPEVASTFKVLRNVTVVLWSAYPVVWLIGSEGAGIVPLNIE
  TLLF
• HHHHHHHHHHHHHHHHHHHHHHS..SSS.HHHHHHHHHHHHHHHHHHHTT
  TTTTT..TT.SHHHHTTHHHHHHHHHHHHHHHHHHTTTTSSSSSS.SHHH
  HHHH
• PPMPPMPPMPPMPPMMPMMPMMP.....PMMPMMPMMPMMPMMPPMMPPM
  PP..........PPMMPMMPMMPMMPMMPPMMPPMMP......PPMMPPM
  MPPM
• PMMPPMPPMPPMMPMMPMMPMMP.....PMMPMMPMMPMMPPMPPMMPPM
  MP..........PMMPMMPPMMPMMPPMMPPMPPMPP......MMMMMMM
  MMMM
• MVLDVSAKVGFGLILLRSRAIFGEAEAPEPSAGDGAAATS
• HHHHHHHTHHHHTTTT........................
• MPPMPPMMPMMPMMPP........................
• MMMMMMMMMMMMMMMM........................

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Software

• INFERNAL
• http//infernal.wustl.edu/
• RNACAD
• http//www.cse.ucsc.edu/mpbrown/rnacad/
• CONUS
• http//www.genetics.wustl.edu/eddy/people/robin/c
  onus/
• PKNOTS
• ftp//ftp.genetics.wustl.edu/pub/eddy/software/pk
  nots.tar.gz
• mtsag2c
• http//bioweb.pasteur.fr/docs/doc-gensoft/mtsag2c
  /
• RNAUI
• http//www.uga.edu/RNA-Informatics/software/rnaui
  0_2.tar