SPIRE2005

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Normalized Similarity of RNA Sequences
Rolf Backofen Danny Hermelin Gad M. LandauOren
Weimann
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RNA sequences
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RNA sequences
C G
C G
G C
C
A U
U A
C G
A
G
U
A
G
U
C
G
U
A
G
U
A
C
C
A
C
A
G
U
U
G
C
G
G
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LCS of Strings
S1
C
G
U
A
G
U
A
C
C
A
C
A
G
U
G
U
G
G
C
S2
A
G
C
A
G
C
C
U
C
G
G
G
C
G
G
A
A
U
U
Global LCS
Hirschberg 1977
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LCS of RNA sequences
Left arc match
Right arc match
RNA Global LCS Klein
1998
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Global Similarity - LCS
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Local Similarity Normalized LCS

• Report the most similar substring pair according
  to some scoring scheme.
• In our case, we look for the substrings
  (with their arcs) that maximize
• Can be viewed as measure of the density of the
  matches.

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Local Similarity in Strings

• Local edit distance O(nm) Smith Waterman 1981
• Normalized LCS O(mnlogn) Arslan Pevzner 2001
• Normalized LCS for sparse matrices O(rLloglogn)
• Efraty Landau 2004

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Our Result

• A novel local similarity metric for comparing RNA
  sequences.
• An time algorithm for computing
  this metric.
• As fast as the global algorithm (in contrast to
  the case of strings).

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Definitions

• A chain is a sequence of matches that is strictly
  increasing in rows and columns.

• The length of a chain from (i,j) to match (i,j)
  is i-ij-j.

• A k-chain(i,j) is the shortest chain of k
  matches starting from (i,j).

• The normalized value of k-chain(i,j) is k
  divided by its length. ( )

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• General idea - Construct (k1)-chain(i,j) by
  concatenating (i,j) to k-chain(i,j) .

a b c a d e c f h c
a
g
g
b
f
h
e
c
g
g
g
f
d
e
f
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Decomposing k-Chains
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Decomposing k-Chains (non arc match)
Best (k-1)-Chain
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Decomposing k-Chains (mismatch)
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Decomposing k-Chains (right arc match)
Best k-Chain
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Decomposing k-Chains (left arc match)
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Decomposing k-Chains (left arc match I)
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Example 2-Chain
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Decomposing k-Chains (left arc match II)
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Decomposing k-Chains (left arc match II)
k lcs
Best (k-lcs)-Chain
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Decomposing k-Chains (left arc match III)
k lcs
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Example 3-Chain
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The Algorithm (Given R1,R2)

• Run Kleins algorithm to get LCS of every arc in
  R1 with every arc in R2.
• For k1,2,,n
• Construct all k-chains from
• bottom right to top left using DP.
• Report best k-chain.
• Total of - as fast as
  global LCS

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The DP
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Muchas Gracias por la atencion