Sequence comparison: More dynamic programming

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Sequence comparison More dynamic programming

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

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One-minute responses

• WAY TOO FAST. Please walk around more during
  sample problems. I was completely lost.
• Today I felt a bit lost. Most times I was still
  trying to figure out one slide or problem, while
  the class was on the next one.
• It was fast today, but after the reading I was
  prepared to take things more quickly and I
  understood things much better today.
• I enjoyed class today. I thought it moved at a
  great pace.
• I thought the pace was good today.
• I liked the pace of the lecture even though you
  said we spent too much time on the dynamic
  programming, it gave me time to understand.
• The pace is great and gives me time to explore.
• I thought this lecture built nicely on the last
  lecture. I struggled last class but it clicked
  today.

3
One-minute responses

• The matrix exercise was very helpful, even though
  Im not fully clear on how it works yet.
• I found todays class time much more
  understandable.
• I struggled a little bit to grasp the matrix, but
  by the end I had it. The pace and numerous
  examples helped.
• The DP matrix was simple to grasp after computing
  one or two matrix values, so the portion of the
  lecture could go faster.
• I like the sample problems.
• Dynamic programming reminded me of sudoku, which
  was fun.
• Going through the alignment table helped a lot.
• It was nice to do examples with DNA sequences.
• Im feeling a lot better about it all. I really
  like going through examples.
• Again, the small steps with programming problems
  helped, although the first problem was overly
  challenging (when explained in a different way it
  was fine).
• I was a little confused when writing the program.
  I think more practice is required. The practice
  problems will help.
• Todays class was much better since we had
  appropriate reading first. The sample problems
  were interesting since they actually relate to
  biology.

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One-minute responses

• Is there a place to get more samples of simple
  code to use to help see patterns of how this
  works? Or is there plenty in the book?
• There are lots of examples in the book. And of
  course, you can easily find lots of examples on
  the web. For a reference book with examples, try
  Python Cookbook, by Martelli, Ravenscroft and
  Ascher.
• Im a little fuzzy about how dynamic programming
  differs from other sorts of programming, but
  everything else was really clear.
• The term dynamic programming predates
  computers. There is no relationship between this
  use of the word programming and what we are
  learning to do in Python.

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DP matrix
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
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Three legal moves

• A diagonal move aligns a character from the left
  sequence with a character from the top sequence.
• A vertical move introduces a gap in the sequence
  along the top edge.
• A horizontal move introduces a gap in the
  sequence along the left edge.

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DP matrix
GA-ATC CATA-C
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
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DP matrix
GAAT-C CA-TAC
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
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DP matrix
GAAT-C C-ATAC
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
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DP matrix
GAAT-C -CATAC
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
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Multiple solutions

• When a program returns a sequence alignment, it
  may not be the only best alignment.

GA-ATC CATA-C
GAAT-C CA-TAC
GAAT-C C-ATAC
GAAT-C -CATAC
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DP in equation form

• 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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DP in equation form
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A simple example
Find the optimal 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
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A simple example
Find the optimal 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
A
G
C
16
A simple example
Find the optimal 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 -5 -10 -15
A -5
G -10
C -15
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A simple example
Find the optimal 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 -5 -10 -15
A -5 2 -3 -8
G -10 -3 -3 -1
C -15 -8 -8 -6
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Traceback

• Start from the lower right corner and trace back
  to the upper left.
• Each arrow introduces one character at the end of
  each aligned sequence.
• A horizontal move puts a gap in the left
  sequence.
• A vertical move puts a gap in the top sequence.
• A diagonal move uses one character from each
  sequence.

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A simple example
Find the optimal alignment of AAG and AGC. Use a
gap penalty of d-5.

• Start from the lower right corner and trace back
  to the upper left.
• Each arrow introduces one character at the end of
  each aligned sequence.
• A horizontal move puts a gap in the left
  sequence.
• A vertical move puts a gap in the top sequence.
• A diagonal move uses one character from each
  sequence.

A A G
0 -5
A 2 -3
G -1
C -6
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A simple example
Find the optimal alignment of AAG and AGC. Use a
gap penalty of d-5.

• Start from the lower right corner and trace back
  to the upper left.
• Each arrow introduces one character at the end of
  each aligned sequence.
• A horizontal move puts a gap in the left
  sequence.
• A vertical move puts a gap in the top sequence.
• A diagonal move uses one character from each
  sequence.

A A G
0 -5
A 2 -3
G -1
C -6
AAG- AAG- -AGC A-GC
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Traceback problem 1
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
Write down the alignment corresponding to the
circled score.
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Solution 1
GA CA
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
Write down the alignment corresponding to the
circled score.
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Traceback problem 2
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
Write down three alignments corresponding to the
circled score.
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Solution 2
GAATC CA---
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
Write down three alignments corresponding to the
circled score.
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Solution 2
GAATC CA---
GAATC C-A--
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
Write down three alignments corresponding to the
circled score.
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Solution 2
GAATC CA---
GAATC C-A--
GAATC -CA--
G A A T C
0 -4 -8 -12 -16 -20
C -4 -5 -9 -13 -12 -6
A -8 -4 5 1 -3 -7
T -12 -8 1 0 11 7
A -16 -12 2 11 7 6
C -20 -16 -2 7 11 17
Write down three alignments corresponding to the
circled score.