Alignment methods

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Alignment methods

• April 21, 2009
• Quiz 1-April 23 (JAM lectures through today)
• Writing assignment topic due Tues, April 23
• Hand in homework 3
• Why has HbS stayed in the population?
• Learning objectives- Understand difference
  between global alignment and local alignment.
  Understand the Needleman-Wunsch algorithm.
  Understand the Smith-Waterman algorithm in global
  alignment mode.
• Workshop-Perform alignment of two nucleotide
  sequences
• Homework 4 due Tues, April 23

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Evolutionary Basis of Sequence Alignment
Why are there regions of identity when comparing
protein sequences? 1) Conserved function-amino
acid residues participate in reaction. 2)
Structural (For example, conserved cysteine
residues that form a disulfide linkage) 3)
Historical-Residues that are conserved solely due
to a common ancestor gene.
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Identity Matrix
1
A
1
0
C
1
0
0
I
1
0
0
0
L
L
I
C
A
Simplest type of scoring matrix
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Similarity
It is easy to score if an amino acid is identical
to another (the score is 1 if identical and 0 if
not). However, it is not easy to give a score
for amino acids that are somewhat similar.
CO2-
CO2-
NH3
NH3
Isoleucine
Leucine
Should they get a 0 (non-identical) or a 1
(identical) or Something in between?
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One is mouse trypsin and the other is crayfish
trypsin. They are homologous proteins. The
sequences share 41 identity.
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Evolutionary Basis of Sequence Alignment (Cont. 2)
Note it is possible that two proteins share a
high degree of similarity but have two different
functions. For example, human gamma-crystallin
is a lens protein that has no known enzymatic
activity. It shares a high percentage of
identity with E. coli quinone oxidoreductase.
These proteins likely had a common ancestor but
their functions diverged.
Analogous to railroad car and diner. Both have
the same form but different functions.
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Global Alignment Method
For example, the two hypothetical sequences
abcdefghajklm abbdhijk could be aligned like
this abcdefghajklm
abbd...hijk As shown, there are 6 matches, 2
mismatches, and one gap of length 3.
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Global Alignment Method Scored
The alignment is scored according to a payoff
matrix payoff match gt match,
mismatch gt mismatch,
gap_open gt gap_open,
gap_extend gt gap_extend For correct
operation, an algorithm is created such that the
match must be positive and the other payoff
entities must be negative.
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Global Alignment Method (cont. 3)
Example Given the payoff matrix payoff
match gt 4, mismatch gt
-3, gap_open gt -2,
gap_extend gt -1
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Global Alignment Method (cont. 4)
The sequences abcdefghajklm abbdhijk are
aligned and scored like this a b
c d e f g h a j k l m
a b b d . . . h i j k
match 4 4 4 4 4 4
mismatch -3 -3 gap_open
-2 gap_extend -1-1-1 for a total
score of 24-6-2-3 13.
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Global Alignment Method (cont. 5)
The algorithm should guarantee that no
other alignment of these two sequences has
a higher score under this payoff matrix.
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Lets align the following with a simple payoff
matrix ABCNJRQCLCRPM and AJCJNRCKCRBP Where
match 1 mismatch 0 gap 0 gap extension
0
Alignment A Sequence 1 ABCNJ-RQCLCR-PM
Sequence 2 AJC-JNR-CKCRBP- Score
101010101011010 Total Score 8 Alignment B
Sequence 1 ABC-NJRQCLCR-PM Sequence 2
AJCJN-R-CKCRBP- Score 101010101011010 Total
Score 8
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Three steps in Dynamic Programming
1. Initialization 2. Matrix fill or scoring 3.
Traceback and alignment
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Initialization step
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Matrix Fill (bottom two rows)
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Matrix Fill (bottom three rows)
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Matrix Fill (entire matrix)
Sequence 1 ABC-NJRQCLCR-PM Sequence 2
AJCJN-R-CKCRBP- Score 101010101011010 Total
Score 8
Sequence 1 ABCNJ-RQCLCR-PM Sequence 2
AJC-JNR-CKCRBP- Score 101010101011010 Total
Score 8
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Smith-Waterman algorithm
Mi,j MAXIMUM Mi-1, j-1 si,,j (match or
mismatch in the diagonal), Mi, j-1 w (gap in
sequence 1), Mi-1, j w (gap in sequence
2), 0 Where Mi-1, j-1 is the value in the
cell diagonally juxtaposed to Mi,j. (The i-1,
j-1 cell is up and to the left of mi,nj). Where
si,j is the value for the match or mismatch in
the minj cell. Where Mi, j-1 is the value in
the cell above Mi,j. Where w is the value for
the gap penalty. Where Mi-1, j is the value in
the cell to the left of Mi,j.
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Initialization step Create Matrix with M 1
columns and N 1 rows. M number of letters in
sequence 1 and N number of letters in sequence
2. First column (M-1) and first row (N-1) will
be filled with 0s.
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Matrix fill step Each position Mi,j is defined
to be the MAXIMUM score at position i,j Mi,j
MAXIMUM Mi-1, j-1 si,,j (match or mismatch
in the diagonal) Mi, j-1 w (gap in sequence
1) Mi-1, j w (gap in sequence 2)
row
column
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Sequence 1 ABCNJ-RQCLCR-PM Sequence 2
AJC-JNR-CKCRBP- Score 8