Combinatorial pattern discovery in biological sequences: the TEIRESIAS algorithm

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Combinatorial pattern discovery in biological
sequences the TEIRESIAS algorithm
Bioinformatics 1998
Authors Isidore Rigoutsos
Aris Floratos

• Speaker Minghua ZHANG

March. 12, 2003
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Content

• Background
• Problem definition
• Algorithm
• Performance
• Future work
• Conclusion

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Background

• The development of biology provides us with a lot
  of information previously unknown.
• DNA sequences, protein sequences
• One way to make use of the information discovery
  patterns in biological sequences.
• Application
• Classification
• Given a protein family, if we find a pattern P of
  the family
• Later when a new protein comes in, if the protein
  matches P, if is very likely the new protein also
  belongs to the same family.
• Function prediction.

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Problem Definition

• ? the alphabet of the characters
• E.g for DNA sequences, ?A,C,G,T.
• Pattern
• A sequence of characters in ?, and wild-cards
  (.)
• Wild-card cannot be at the beginning or end of
  the sequence.
• E.g A..G is a pattern AG. is not.

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Problem Definition (contd)

• Given a pattern P
• Its length P No. of characters and wild-cards
  in P.
• char(P) No. of characters in P.
• E.g. A.G.T5, char(A.G.T)3.
• Its subpattern a substring of P, which itself is
  a pattern.
• A.G is a subpattern of A.G.T while A.G. is not.
• Its language G(P) p p is a pattern obtained
  by replacing all wild-cards in P with characters
  in ?
• E.g. G(A.G) AAG, ACG, AGG, ATG .

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Problem Definition (contd)

• Given a character sequence s, we say it matches a
  pattern P in position y
• if a substring of s is in G(P) and
• the substring begins from offset y in s.
• E.g if SACGATCA, PCG.T, then s matches P in
  position 2.
• Given a sequence database Ds1, s2, , sn
• support(P) No. of sequences in D that match P.
• List(P) (x,y) sx matches P in position y
• Frequent
• If support (P) K

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Problem Definition (contd)

• pattern
• L, W are 2 integers, 0
• P is an pattern
• ? subpattern Q of P with char(Q)L, we have Q W.
• E.g A.G.C.T is a pattern, A..G.C.T is not
  a pattern.

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Problem Definition (contd)

• Pattern P is more specific than P
• P is obtained from P by
• Replacing some wild-cards to characters, and/or
• Appending a string to the left/right of P
• E.g PA..G, P1AC.G, or P2A..GT.
• List(P)
• Given a set of patterns, a pattern P is maximal
  if
• ?p, p is more specific than p
• we have List(p)
• E.g PA.GT, PACGT, if List(P)List(P)(1,1),
  (2,2), (3,1), then P is not maximal.

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Problem Definition (contd)

• Problem
• Inputs
• A character sequence database D
• Support threshold K
• parameters L, W.
• Outputs
• p p is an pattern p is frequent p
  is maximal char(p)L.

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Algorithm

• Two parts
• 1. Find elementary patterns.
• Frequent patterns having exactly L
  characters
• 2. Find required patterns.

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Algorithm part 1

• Find the set of elementary patterns EP

EPempty Scan D For all c in ? if
support(c) K Extend(c) Algorithm

• Extend(pattern P)
• If char(P)L add P to EP return
• For i0 to W- P - L char(P)
• P P i dots
• for all (x,y) in List(P)
• if (y P i )
• a SX y P i
• update List(P a)
• For all c in ?
• if List( Pc ) K
• Extend ( Pc )
• Function

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Algorithm part 2

• Terminologies
• Given a pattern P with char(P) L,
• Prefix(P) its subpattern containing the first
  L-1 characters.
• Suffix(P) its subpattern containing the last L-1
  characters.
• E.g L3, prefix(A.G.TG)A.G, suffix(A.G.TG)TG

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Algorithm part 2 (contd)

• Terminologies
• Convolution
• If suffix(P) prefix(Q), then
• conv(P, Q) PQ (Qprefix(Q)Q)
• E.g PAC.G, QC.GT, then QT, conv(P,Q)AC.GT
• If Rconv(P,Q), then
• List(R) (x,y) (x,y) in List(P) (x, y P
  - suffix(P)) in List(Q)

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Algorithm part 2 (contd)

• Terminologies
• Partial orders on a set of patterns
• prefix_wise less than (
• Align two patterns along their left-most columns
• Find the first column with a . and a character
• The pattern with character in the column is
  smaller.
• E.g A . G T
• A G T . C
• So AGT.C

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Algorithm part 2 (contd)

• Terminologies
• Partial orders on a set of patterns
• suffix_wise less than (
• E.g A . G T
• A G T . C
• So A.GT

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Algorithm part 2 (contd)

• Works on a stack
• At first, push all elementary patterns into the
  stack.
• Prefix-wise less patterns are pushed later, so
  that they are closer to the top of the stack.
• Deal with the top pattern one by one
• until the stack is empty

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Algorithm part 2 (contd)

• P is on top of the stack
• Extend P to the right
• find elementary patterns whose prefix is the same
  as suffix(P).
• convolution P with the patterns one by one with
  prefix-wise less pattern first.
• If Rconv(P,Q).
• If List( R ) List(P), pop stack.
• If support(R) K and R is maximal push R,
  starts over again.
• Extend P to the left.
• Pop P from stack. If P is maximal, report it.

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Performance

• Experiments
• effectiveness
• real data
• successfully find patterns previously known by
  biologist.
• efficient
• synthetic data

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Performance (contd)

• Core histones H3 and H4
• Database 13 proteins from H3 family, 7 from H4.
• L3, W35
• Find 9 patterns in all 20 proteins
• For those patterns with the largest No. of
  characters

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Performance (contd)

• Synthetic data generation
• Use the generator in http//www.expasy.ch/sprot/ra
  ndseq.html to get
• A random protein P of 400 amino acids
• Obtain 20 derivative proteins from P
• With a X similarity to P

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Performance (contd)

• Synthetic data
• X40, 50, 60, 70, 80, 90
• L3, W10 (15)
• K12, 14, 16, 18, 20
• Results
• The algorithm is efficient.
• The running time is almost linear on the actual
  size of the output.

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Performance (contd)

• Algorithm analysis
• Bad factors
• ACGT and GTA will generate ACGTA. However, CGTA
  may be infrequent. More candidates are generated.
  
• Good factors
• By use partial order of specific patterns will be generate before less
  specific patterns.
• E.g ACG is considered before AC.T ? ACGTG is
  generated before AC.TG ? If AC.TG is not maximal
  due to ACGTG, it will not be pushed into stack
  for further candidate generations
• When R is generated from P, if List( R )
  List(P), P will be popped out of the stack.
• Reduce no. of candidates

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Performance (contd)

• A simple comparison
• Compared with an Apriori-like algorithm, which
  finds all patterns, not only maximal ones.
• X90, L3, W10, K16

( Running time does not include time to output
patterns )
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Future work

• Find more flexible patterns
• Pattern with ambiguous characters
• E.g. ACGT means a pattern, which can match both
  ACT and AGT. (IALYD2000)
• Pattern with flexible gaps
• Gap one or several consecutive wild-cards
• E.g In A..G, .. is a gap of length 2
• Flexible gap
• A-x(3,5)-G
• A--G.

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Conclusion

• TEIRESIAS can find patterns composed of
  characters and wild-cards.
• It can successfully find out patterns from
  biological sequences.
• Its running time is roughly linear to the size of
  the output.
• Future research discover more flexible patterns.

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Reference

• IA1998 Combinatorial pattern discovery in
  biological sequences the TEIRESIAS algorithm.
  Isidore Rigoutsos, etal. Bioinformatics, Vol 14,
  No. 1, 1998, 55-67.
• IALYD2000 The emergence of pattern discovery
  techniques in computational biology. Isidore
  Rigoutsos, etal. Metabolic Engineering 2, 159-177
  (2000)
• AI On the time complexity of the TEIRESIAS
  algorithm. Aris Floratos, etal. IBM research
  report.

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