Introduction to Bioinformatics
Sequence Alignments
Sequence Alignments
 Cornerstone of bioinformatics
 What is a sequence?
• Nucleotide sequence
• Amino acid sequence
 Pairwise and multiple sequence alignments
• We will focus on pairwise alignments
 What alignments can help
• Determine function of a newly discovered gene sequence
• Determine evolutionary relationships among genes, proteins,
and species
• Predicting structure and function of protein
Intro to Bioinformatics – Sequence Alignment
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Acknowledgement: This notes is adapted from lecture notes of both Wright State University’s Bioinformatics Program and Professor Laurie Heyer of Davidson College with permission.
DNA Replication
 Prior to cell division, all the
genetic instructions must be
“copied” so that each new cell
will have a complete set
 DNA polymerase is the enzyme
that copies DNA
• Reads the old strand in the 3´ to 5´
direction
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Over time, genes accumulate mutations
 Environmental factors
• Radiation
• Oxidation
 Mistakes in replication or
repair
 Deletions, Duplications
 Insertions, Inversions
 Translocations
 Point mutations
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Deletions
 Codon deletion:
ACG ATA GCG TAT GTA TAG CCG…
• Effect depends on the protein, position, etc.
• Almost always deleterious
• Sometimes lethal
 Frame shift mutation:
ACG ATA GCG TAT GTA TAG CCG…
ACG ATA GCG ATG TAT AGC CG?…
• Almost always lethal
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Indels
 Comparing two genes it is generally impossible
to tell if an indel is an insertion in one gene, or
a deletion in another, unless ancestry is known:
ACGTCTGATACGCCGTATCGTCTATCT
ACGTCTGAT---CCGTATCGTCTATCT
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The Genetic Code
Substitutions are
mutations
accepted by
natural selection.
Synonymous:
CGC  CGA
Non-synonymous:
GAU  GAA
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Comparing Two Sequences
 Point mutations, easy:
ACGTCTGATACGCCGTATAGTCTATCT
ACGTCTGATTCGCCCTATCGTCTATCT
 Indels are difficult, must align sequences:
ACGTCTGATACGCCGTATAGTCTATCT
CTGATTCGCATCGTCTATCT
ACGTCTGATACGCCGTATAGTCTATCT
----CTGATTCGC---ATCGTCTATCT
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Why Align Sequences?
 The draft human genome is available
 Automated gene finding is possible
 Gene: AGTACGTATCGTATAGCGTAA
• What does it do?
 One approach: Is there a similar gene in
another species?
• Align sequences with known genes
• Find the gene with the “best” match
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Gaps or No Gaps
 Examples
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Scoring a Sequence Alignment
Given
 Match score:
+1
 Mismatch score:
+0
 Gap penalty:
–1
 Sequences
ACGTCTGATACGCCGTATAGTCTATCT
||||| |||
|| ||||||||
----CTGATTCGC---ATCGTCTATCT

 Matches: 18 × (+1)
 Mismatches: 2 × 0
Score
 Gaps: 7 × (– 1)
Intro to Bioinformatics – Sequence Alignment
= +11
11
Origination and Length Penalties
 Note that a bioinformatics computational model or
algorithm must be “biologically meaningful” or
even “biologically significant”
 We want to find alignments that are evolutionarily
likely.
 Which of the following alignments seems more
likely to you?
ACGTCTGATACGCCGTATAGTCTATCT
ACGTCTGAT-------ATAGTCTATCT
ACGTCTGATACGCCGTATAGTCTATCT
AC-T-TGA--CG-CGT-TA-TCTATCT


 We can achieve this by penalizing more for a new
gap, than for extending an existing gap
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Scoring a Sequence Alignment (2)
Given
 Match/mismatch score:
+1/+0
 Gap origination/length penalty: –2/–1
 Sequences
ACGTCTGATACGCCGTATAGTCTATCT
||||| |||
|| ||||||||
----CTGATTCGC---ATCGTCTATCT

 Matches: 18 × (+1)
 Mismatches: 2 × 0
Score
 Origination: 2 × (–2)
 Length: 7 × (–1)
= +7
 Caution: Sometime “gap extension” used instead of “gap
length” …
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How can we find an optimal alignment?
 Finding the alignment is computationally hard:
ACGTCTGATACGCCGTATAGTCTATCT
CTGAT---TCG-CATCGTC--T-ATCT
 C(27,7) gap positions = ~888,000 possibilities
 It’s possible, as long as we don’t repeat our
work!
 Dynamic programming: The Needleman &
Wunsch algorithm
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Dynamic Programming
 Technique of solving optimization problems
• Find and memorize solutions for subproblems
• Use those solutions to build solutions for larger
subproblems
• Continue until the final solution is found
 Recursive computation of cost function in a
non-recursive fashion
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Dynamic Programming
 Example
• Solving Fibonacci number f(n) = f(n-1) + f(n-2)
recursively takes exponential time

Because many numbers are recalculated
• Solving it using dynamic programming only takes a
linear time

Use an array f[] to store the numbers
f[0] = 1;
f[1] = 1;
for (i = 2; i <= n; i++)
f[i] = f[i – 1] + f[i – 2];
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Global Sequence Alignment
 Needleman-Wunsch algorithm
Di,j = max{ Di-1,j + d(Ai, –), Di,j-1 + d(–, Bj), Di-1,j-1 + d(Ai, Bj) }
B
i-1
A
i
j-1
j
 Suppose we are aligning:
Seq1
a with a …
Seq2 a
Intro to Bioinformatics – Sequence Alignment
0
-1
a
-1
17
Dynamic Programming (DP) Concept
 Suppose we are aligning:
CACGA
CGA
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DP – Recursion Perspective
 Suppose we are aligning:
ACTCG
ACAGTAG
 Last position choices:
G
G
+1
ACTC
ACAGTA
G
-
-1
ACTC
ACAGTAG
G
-1
ACTCG
ACAGTA
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What is the optimal alignment?
 ACTCG
ACAGTAG
 Match: +1
 Mismatch: 0
 Gap: –1
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Needleman-Wunsch: Step 1
 Each sequence along one axis
 Gap penalty multiples in first row/column
 0 in [1,1] (or [0,0] for the CS-minded)
A
C
A
G
T
A
G
0
-1
-2
-3
-4
-5
-6
-7
A
-1
1
Intro to Bioinformatics – Sequence Alignment
C
-2
T
-3
C
-4
G
-5
21
Needleman-Wunsch: Step 2
 Vertical/Horiz. move: Score + (simple) gap penalty
 Diagonal move: Score + match/mismatch score
 Take the MAX of the three possibilities
A
C
A
G
T
A
G
0
-1
-2
-3
-4
-5
-6
-7
A
-1
1
Intro to Bioinformatics – Sequence Alignment
C
-2
T
-3
C
-4
G
-5
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Needleman-Wunsch: Step 2 (cont’d)
 Fill out the rest of the table likewise…
a
a
c
a
g
t
a
g
0
-1
-2
-3
-4
-5
-6
-7
c
-1
1
Intro to Bioinformatics – Sequence Alignment
t
-2
0
c
-3
-1
g
-4
-2
-5
-3
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Needleman-Wunsch: Step 2 (cont’d)
 Fill out the rest of the table likewise…
a
a
c
a
g
t
a
g
0
-1
-2
-3
-4
-5
-6
-7
c
-1
1
0
-1
-2
-3
-4
-5
t
-2
0
2
1
0
-1
-2
-3
c
-3
-1
1
2
1
1
0
-1
g
-4
-2
0
1
2
1
1
0
-5
-3
-1
0
2
2
1
2
 The optimal alignment score is calculated in the
lower-right corner
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But what is the optimal alignment
 To reconstruct the optimal alignment, we must
determine of where the MAX at each step came
from…
a
a
c
a
g
t
a
g
0
-1
-2
-3
-4
-5
-6
-7
Intro to Bioinformatics – Sequence Alignment
c
-1
1
0
-1
-2
-3
-4
-5
t
-2
0
2
1
0
-1
-2
-3
c
-3
-1
1
2
1
1
0
-1
g
-4
-2
0
1
2
1
1
0
-5
-3
-1
0
2
2
1
2
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A path corresponds to an alignment

= GAP in top sequence

= GAP in left sequence

= ALIGN both positions
 One path from the previous table:
 Corresponding alignment (start at the end):
AC--TCG
ACAGTAG
Intro to Bioinformatics – Sequence Alignment
Score = +2
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Algorithm Analysis
 Brute force approach
• If the length of both sequences is n, number of
possibility = C(2n, n) = (2n)!/(n!)2  22n / (n)1/2,
using Sterling’s approximation of n! = (2n)1/2e-nnn.
• O(4n)
 Dynamic programming
• O(mn), where the two sequence sizes are m and n,
respectively
• O(n2), if m is in the order of n
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Practice Problem
 Find an optimal alignment for these two
sequences:
GCGGTT
GCGT
 Match: +1
 Mismatch: 0
 Gap: –1 g
c
g
t
g
0
-1
-2
-3
-4
Intro to Bioinformatics – Sequence Alignment
c
-1
g
-2
g
-3
t
-4
t
-5
-6
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Practice Problem
 Find an optimal alignment for these two
sequences:
GCGGTT
GCGT
g
c
g
g
t
t
g
c
g
t
0
-1
-2
-3
-4
-1
1
0
-1
-2
-2
0
2
1
0
-3
-1
1
3
2
GCGGTT
GCG-TIntro to Bioinformatics – Sequence Alignment
-4
-2
0
2
3
-5
-3
-1
1
3
-6
-4
-2
0
2
Score = +2
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Semi-global alignment
 Suppose we are aligning:
GCG
GGCG
 Which do you prefer?
G-CG
-GCG
GGCG
GGCG
g
g
g
c
g
0
-1
-2
-3
-4
c
-1
1
0
-1
-2
g
-2
0
1
1
0
-3
-1
1
1
2
 Semi-global alignment allows gaps at the ends
for free.
• Terminal gaps are usually the result of incomplete
data acquisition  no biologically significant
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Semi-global alignment
 Semi-global alignment allows gaps at the ends
for free.
g
g
g
c
g
0
0
0
0
0
c
0
1
1
0
1
g
0
0
1
2
1
0
1
1
1
3
 Initialize first row and column to all 0’s
 Allow free horizontal/vertical moves in last row
and column
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Local alignment
 Global alignments – score the entire alignment
 Semi-global alignments – allow unscored gaps
at the beginning or end of either sequence
 Local alignment – find the best matching
subsequence
 CGATG
AAATGGA
 This is achieved by allowing a 4th alternative at
each position in the table: zero.
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Local Sequence Alignment
 Why local sequence alignment?
• Subsequence comparison between a DNA sequence
and a genome
• Protein function domains
• Exons matching
 Smith-Waterman algorithm
Initialization: D1,j = , Di,1 = 
Di,j = max{
Di-1,j + d(Ai, –),
Di,j-1 + d(–,Bj),
Di-1,j-1 + d(Ai,Bj),
0}
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Local alignment
 Score: Match = 1, Mismatch = -1, Gap = -1
c
a
a
a
t
g
g
a
0
0
0
0
0
0
0
0
g
0
0
0
0
0
0
0
0
a
0
0
0
0
0
1
1
0
t
0
1
1
1
0
0
0
2
g
0
0
0
0
2
1
0
1
0
0
0
0
1
3
2
1
CGATG
AAATGGA
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Local alignment
 Another example
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More Example
 Align
ATGGCCTC
ACGGCTC
Mismatch  = -3
Gap
 = -4
Global
Alignment:
ATGGCCTC
ACGGC-TC
-A
T
G
G
C
C
T
C
Intro to Bioinformatics – Sequence Alignment
-0
-4
-8
-12
-16
-20
-24
-28
-32
A
-4
1
-3
-7
-11
-15
-19
-23
-27
C
-8
-3
-2
-6
-10
-10
-14
-18
-22
G
-12
-7
-6
-1
-5
-9
-13
-17
-21
G
-16
-11
-10
-5
0
-4
-8
-12
-16
C
-20
-15
-14
-9
-4
1
-3
-7
-11
T
-24
-19
-14
-13
-8
-3
-2
-2
-6
C
-28
-23
-18
-17
-12
-7
-2
-5
-1
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More Example
Local
Alignment:
ATGGCCTC
ACGG CTC
or
ATGGCCTC
ACGGC TC
Intro to Bioinformatics – Sequence Alignment
-A
T
G
G
C
C
T
C
-0
0
0
0
0
0
0
0
0
A
0
1
0
0
0
0
0
0
0
C
0
0
0
0
0
1
1
0
1
G
0
0
0
1
1
0
0
0
0
G
0
0
0
1
2
0
0
0
0
C
0
0
0
0
0
3
1
0
1
T
0
0
1
0
0
0
0
2
0
C
0
0
0
0
0
1
1
0
3
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Scoring Matrices for DNA Sequences
 Transition: A  G C  T
 Transversion: a purine (A or G) is replaced by a
pyrimadine (C or T) or vice versa
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Scoring Matrices for Protein Sequence
 PAM 250
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Scoring Matrices for Protein Sequence
 PAM (Percent Accepted Mutations)
 1 PAM unit can be thought of as the amount of time in which an
“average” protein mutates 1 out of every 100 amino acids.
 Perform multiple sequence alignment on a “family” of proteins that are
at least 85% similar. Find the frequency of amino acid i and j are aligned
to each other and normalize it.
 Entry mij in PAM1 represents the probability of amino acid i
substituted by amino acid j in 1 PAM unit
 PAM 2 = PAM 1 × PAM 1
 PAM n = (PAM 1)n, e.g., PAM 250 = (PAM 1)250
 Questions
 Why are values in a PAM matrix integers? Shouldn’t a probability be
between 0 and 1?
 Why is PAM250 possible? Shouldn’t a probability be less than or equal
to 100%?
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Scoring Matrices for Protein Sequence
 BLOSUM (BLOcks SUbstitution Matrix) 62
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Using Protein Scoring Matrices
 Divergence
BLOSUM 80
PAM 1
Closely related
Less divergent
Less sensitive
BLOSUM 62
PAM 120
 Looking for
BLOSUM 45
PAM 250
Distantly related
More divergent
More sensitive
• Short similar sequences → use less sensitive matrix
• Long dissimilar sequences → use more sensitive matrix
• Unknown → use range of matrices
 Comparison
• PAM – designed to track evolutionary origin of proteins
• BLOSUM – designed to find conserved regions of proteins
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Multiple Sequence Alignment
 Why multiple sequence alignment (MSA)
• Two sequences might not look very similar.
• But, some “similarity” emerges with more sequences,
however.
 Is dynamic programming still applicable?
 CLUSTALW
• One of most popular tools for MSA
• Heuristic-based approach
• Basic
1) Calculate the distance matrix based on pairwise alignments
2) Construct a guide tree
NJ (unrooted tree)  Mid-point (rooted tree)
3) Progressive alignment using the guide tree
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