Sequence comparison: Local alignment

1
Sequence comparison Local alignment

• Genome 559 Introduction to Statistical and
  Computational Genomics
• Prof. William Stafford Noble

2
One-minute responses

• It would be helpful to somehow get the solutions
  for the sample problems in our lecture printouts.
• You can see the solutions by visiting the class
  web page and opening the slides there.
• I am still a little confused about the difference
  between strings and lists.
• A string is like a tuple of characters. Unlike a
  string a list is (1) mutable and (2) may contain
  other objects besides characters.
• The Biotechniques paper went into a lot of detail
  -- how much of this should we understand?
• I intend the paper to provide background for
  those who are interested. You should be sure you
  understand just what I go over in lecture.
• I am slightly worried because I never seem to do
  things in the most straightforward way.
• This just takes practice. Often, there is no
  single best way.

3
One-minute responses

• There was perhaps a bit too much programming in
  this class.
• There was more class time for Python, which was
  nice.
• I really liked the sample problem times.
• Problem set is very reasonable.
• The examples and practice are most useful
  teaching methods for me at least. I am getting
  comfortable with the code through practice.
• I like the sample problems. In the last few
  classes I felt rushed to finish them, but this
  time I was able to do all 3. It's very
  satisfying when they work.

• I had somewhat more difficulty with today's
  exercises. I think it was due to the inherent
  complexity of adding new types to the repertoire.
• Class moved at a good speed today.
• I enjoyed the pace today.
• Today's pace was good.
• The pace was good -- it was helpful for me to
  have more time for problems.
• Good pace.
• Programming problems were a good speed today.
• The biostats portion was a little fast but
  manageable.

4
One-minute responses

• The cheat sheet really helped.
• I really liked the list of operations and methods
  on the back of the lecture notes.
• Lists of commands in slides were helpful.

• Reviewing the DP matrix was very helpful.
• I'm glad we reviewed the Needleman-Wunsch
  algorithm.
• The traceback review helped me realize I'd
  forgotten how to do it.

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Local alignment

• A single-domain protein may be homologous to a
  region within a multi-domain protein.
• Usually, an alignment that spans the complete
  length of both sequences is not required.

6
BLAST allows local alignments
Global alignment
Local alignment
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Global alignment DP

• Align sequence x and y.
• F is the DP matrix s is the substitution matrix
  d is the linear gap penalty.

8
Local alignment DP

• Align sequence x and y.
• F is the DP matrix s is the substitution matrix
  d is the linear gap penalty.

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Local DP in equation form
0
10
A simple example
Find the optimal local alignment of AAG and
AGC. Use a gap penalty of d-5.
A C G T
A 2 -7 -5 -7
C -7 2 -7 -5
G -5 -7 2 -7
T -7 -5 -7 2
A A G

A
G
C
0
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A simple example
Find the optimal local alignment of AAG and
AGC. Use a gap penalty of d-5.
A C G T
A 2 -7 -5 -7
C -7 2 -7 -5
G -5 -7 2 -7
T -7 -5 -7 2
A A G
0 0 0 0
A 0
G 0
C 0
0
12
A simple example
Find the optimal local alignment of AAG and
AGC. Use a gap penalty of d-5.
A C G T
A 2 -7 -5 -7
C -7 2 -7 -5
G -5 -7 2 -7
T -7 -5 -7 2
A A G
0 0 0 0
A 0
G 0
C 0
0
-5
2
0
-5
0
13
A simple example
Find the optimal local alignment of AAG and
AGC. Use a gap penalty of d-5.
A C G T
A 2 -7 -5 -7
C -7 2 -7 -5
G -5 -7 2 -7
T -7 -5 -7 2
A A G
0 0 0 0
A 0 2
G 0 ?
C 0 ?
0
14
A simple example
Find the optimal local alignment of AAG and
AGC. Use a gap penalty of d-5.
A C G T
A 2 -7 -5 -7
C -7 2 -7 -5
G -5 -7 2 -7
T -7 -5 -7 2
A A G
0 0 0 0
A 0 2 ? ?
G 0 0 ? ?
C 0 0 ? ?
0
15
A simple example
Find the optimal local alignment of AAG and
AGC. Use a gap penalty of d-5.
A C G T
A 2 -7 -5 -7
C -7 2 -7 -5
G -5 -7 2 -7
T -7 -5 -7 2
A A G
0 0 0 0
A 0 2 2 0
G 0 0 0 4
C 0 0 0 0
0
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Local alignment

• Two differences with respect to global alignment
• No score is negative.
• Traceback begins at the highest score in the
  matrix and continues until you reach 0.
• Global alignment algorithm Needleman-Wunsch.
• Local alignment algorithm Smith-Waterman.

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A simple example
Find the optimal local alignment of AAG and
AGC. Use a gap penalty of d-5.
A C G T
A 2 -7 -5 -7
C -7 2 -7 -5
G -5 -7 2 -7
T -7 -5 -7 2
A A G
0 0 0 0
A 0 2 2 0
G 0 0 0 4
C 0 0 0 0
0
AG AG
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Local alignment
Find the optimal local alignment of AAG and
GAAGGC. Use a gap penalty of d-5.
A C G T
A 2 -7 -5 -7
C -7 2 -7 -5
G -5 -7 2 -7
T -7 -5 -7 2
A A G
0 0 0 0
G 0
A 0
A 0
G 0
G 0
C 0
0
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Local alignment
Find the optimal local alignment of AAG and
GAAGGC. Use a gap penalty of d-5.
A C G T
A 2 -7 -5 -7
C -7 2 -7 -5
G -5 -7 2 -7
T -7 -5 -7 2
A A G
0 0 0 0
G 0 0 0 2
A 0 2 2 0
A 0 2 4 0
G 0 0 0 6
G 0 0 0 2
C 0 0 0 0
0
20
Local alignment
Find the optimal local alignment of AAG and
GAAGGC. Use a gap penalty of d-5.
A C G T
A 2 -7 -5 -7
C -7 2 -7 -5
G -5 -7 2 -7
T -7 -5 -7 2
A A G
0 0 0 0
G 0 0 0 2
A 0 2 2 0
A 0 2 4 0
G 0 0 0 6
G 0 0 0 2
C 0 0 0 0
AAG AAG
0
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Summary

• Local alignment finds the best match between
  subsequences.
• Smith-Waterman local alignment algorithm
• No score is negative.
• Trace back from the largest score in the matrix.