Download Lecture 3: Sequence Alignment

Introduction to
Bioinformatics
1
Introduction to Bioinformatics.
LECTURE 3: SEQUENCE ALIGNMENT
*
Chapter 3: All in the family
2
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
3.1 Eye of the tiger
* In 1994 Walter Gehring et alum (Un. Basel) turn the
gene “eyeless” on in various places on Drosophila
melanogaster
* Result: on multiple places eyes are formed
* ‘eyeless’ is a master regulatory gene that controls +/2000 other genes
* ‘eyeless’ on induces formation of an eye
3
Eyeless Drosophila
4
Mutant Drosophila melanogaster: gene ‘EYELESS’ turned on
5
LECTURE 3: SEQUENCE ALIGNMENT
Homeoboxes and Master regulatory genes
6
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
HOMEO BOX
A homeobox is a DNA sequence found within
genes that are involved in the regulation of
development (morphogenesis) of animals, fungi
and plants.
7
LECTURE 3: SEQUENCE ALIGNMENT
Drosophila melanogaster: HOX homeoboxes
8
LECTURE 3: SEQUENCE ALIGNMENT
Drosophila melanogaster: PAX homeoboxes
9
LECTURE 3: SEQUENCE ALIGNMENT
Homeoboxes and Master regulatory genes
10
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
3.2 On sequence alignment
Sequence alignment is the most important task in
bioinformatics!
11
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
3.2 On sequence alignment
Sequence alignment is important for:
* prediction of function
* database searching
* gene finding
* sequence divergence
* sequence assembly
12
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
3.3 On sequence similarity
Homology: genes that derive from a common ancestor-gene
are called homologs
Orthologous genes are homologous genes in different
organisms
Paralogous genes are homologous genes in one organism
that derive from gene duplication
Gene duplication: one gene is duplicated in multiple copies
that therefore free to evolve and assume new functions
13
LECTURE 3: SEQUENCE ALIGNMENT
HOMOLOGOUS and PARALOGOUS
14
LECTURE 3: SEQUENCE ALIGNMENT
HOMOLOGOUS and PARALOGOUS
15
LECTURE 3: SEQUENCE ALIGNMENT
HOMOLOGOUS and PARALOGOUS versus ANALOGOUS
16
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT: sequence similarity
Causes for sequence (dis)similarity
mutation:
a nucleotide at a certain location is replaced by
another nucleotide (e.g.: ATA → AGA)
insertion:
at a certain location one new nucleotide is
inserted inbetween two existing nucleotides
(e.g.: AA → AGA)
deletion:
at a certain location one existing nucleotide
is deleted (e.g.: ACTG → AC-G)
indel:
an insertion or a deletion
17
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
3.4 Sequence alignment: global and local
Find the similarity between two (or more)
DNA-sequences by finding a good
alignment between them.
18
The biological problem of
sequence alignment
DNA-sequence-1
tcctctgcctctgccatcat---caaccccaaagt
|||| ||| ||||| |||||
||||||||||||
tcctgtgcatctgcaatcatgggcaaccccaaagt
DNA-sequence-2
Alignment
19
Sequence alignment - definition
Sequence alignment is an arrangement of two or more sequences,
highlighting their similarity.
The sequences are padded with gaps (dashes) so that wherever possible,
columns contain identical characters from the sequences involved
tcctctgcctctgccatcat---caaccccaaagt
|||| ||| ||||| |||||
||||||||||||
tcctgtgcatctgcaatcatgggcaaccccaaagt
20
Algorithms
Needleman-Wunsch
Pairwise global alignment only.
Smith-Waterman
Pairwise, local (or global) alignment.
BLAST
Pairwise heuristic local alignment
21
Pairwise alignment
Pairwise sequence alignment methods are concerned with finding the bestmatching piecewise local or global alignments of protein (amino acid) or DNA
(nucleic acid) sequences.
Typically, the purpose of this is to find homologues (relatives) of a gene or geneproduct in a database of known examples.
This information is useful for answering a variety of biological questions:
1. The identification of sequences of unknown structure or function.
2. The study of molecular evolution.
22
Global alignment
A global alignment between two sequences is an alignment in which all the
characters in both sequences participate in the alignment.
Global alignments are useful mostly for finding closely-related sequences.
As these sequences are also easily identified by local alignment methods global
alignment is now somewhat deprecated as a technique.
Further, there are several complications to molecular evolution (such as domain
shuffling) which prevent these methods from being useful.
23
Global Alignment
Find the global best fit between two sequences
Example: the sequences s = VIVALASVEGAS and
t = VIVADAVIS align like:
A(s,t) =
V I V A L A S V E G A S
| | | |
|
|
|
V I V A D A - V - - I S
indels
24
The Needleman-Wunsch algorithm
The Needleman-Wunsch algorithm (1970, J Mol Biol.
48(3):443-53) performs a global alignment on two
sequences (s and t) and is applied to align protein or
nucleotide sequences.
The Needleman-Wunsch algorithm is an example of
dynamic programming, and is guaranteed to find the
alignment with the maximum score.
25
The Needleman-Wunsch algorithm
Of course this works for both DNA-sequences
as for protein-sequences.
26
Alignment scoring function
The cost of aligning two symbols xi and yj is the
scoring function σ(xi,yj )
27
Alignment cost
The cost of the entire alignment:
c
M    ( xi , yi )
i 1
28
A simple scoring function
σ(-,a) = σ(a,-) = -1
σ(a,b) = -1 if a ≠ b
σ(a,b) = 1 if a = b
29
The substitution matrix
A more realistic scoring function is given by the
biologically inspired substitution matrix :
A
G
C
T
A
10
-1
-3
-4
G
-1
7
-5
-3
C
-3
-5
9
0
T
-4
-3
0
8
Examples:
* PAM (Point Accepted Mutation) (Margaret Dayhoff)
* BLOSUM (BLOck SUbstitution Matrix) (Henikoff and Henikoff)
30
Scoring function
The cost for aligning the two sequences s =
VIVALASVEGAS and t = VIVADAVIS :
V I V A L A S V E G A S
|
|
|
A(s,t) = | | | |
V I V A D A - V - - I S
is:
M(A) = 7 matches + 2 mismatches + 3 gaps
=7
–2
–3
=2
31
Optimal global alignment
The optimal global alignment A* between two sequences s
and t is the alignment A(s,t) that maximizes the total
alignment score M(A) over all possible alignments.
A* = argmax M(A)
Finding the optimal alignment A* looks a combinatorial
optimization problem:
i. generate all possible allignments
ii. compute the score M
iii. select the alignment A* with the maximum score M*
32
Local alignment
Local alignment methods find related regions within sequences - they can
consist of a subset of the characters within each sequence.
For example, positions 20-40 of sequence A might be aligned with positions
50-70 of sequence B.
This is a more flexible technique than global alignment and has the advantage
that related regions which appear in a different order in the two proteins (which is
known as domain shuffling) can be identified as being related.
This is not possible with global alignment methods.
33
The Smith Waterman algorithm
The Smith-Waterman algorithm (1981) is for determining similar regions
between two nucleotide or protein sequences.
Smith-Waterman is also a dynamic programming algorithm and improves
on Needleman-Wunsch. As such, it has the desirable property that it is
guaranteed to find the optimal local alignment with respect to the scoring
system being used (which includes the substitution matrix and the gapscoring scheme).
However, the Smith-Waterman algorithm is demanding of time and
memory resources: in order to align two sequences of lengths m and n,
O(mn) time and space are required.
As a result, it has largely been replaced in practical use by the BLAST
algorithm; although not guaranteed to find optimal alignments, BLAST is
34
much more efficient.
Optimal local alignment
The optimal local alignment A* between two
sequences s and t is the optimal global alignment
A(s(i1:i2), t(j1:j2) ) of the sub-sequences s(i1:i2) and
t(j1:j2) for some optimal choice of i1, i2, j1 and j2.
35
Sequence alignment - meaning
Sequence alignment is used to study the evolution of the sequences
from a common ancestor such as protein sequences or DNA
sequences.
Mismatches in the alignment correspond to mutations,
and gaps correspond to insertions or deletions.
Sequence alignment also refers to the process of constructing
significant alignments in a database of potentially unrelated sequences.
36
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
3.5 Statistical analysis of alignments
This works identical to gene finding:
* Generate randomized sequences based on the
second string
* Determine the optimal alignments of the first
sequence with these randomized sequences
* Compute a histogram and rank the observed
score in this histogram
* The relative position defines the p-value.
37
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT: statistical analysis
Histogram of scores of randomly
generated strings using permutation
of original sequence t
original sequence s
38
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
3.6 BLAST:
fast approximate alignment
• Fast but heuristic
• Most used algorithm in bioinformatics
• Verb: to blast
39
40
41
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
3.7 Multiple sequence alignment:
Determine the best alignment between multiple
(more than two) DNA-sequences.
42
Multiple alignment
Multiple alignment is an extension of pairwise alignment to
incorporate more than two sequences into an alignment.
Multiple alignment methods try to align all of the sequences
in a specified set.
The most popular multiple alignment tool is CLUSTAL.
Multiple sequence alignment is computationally difficult and
is classified as an NP-Hard problem.
43
Multiple alignment
44
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
3.8 Computing the alignments
* NW and SW are both based on Dynamic
Programming (DP)
* A recursive relation breaks down the computation
45
Dynamic Programming Approach to
Sequence Alignment
The dynamic programming approach to sequence alignment always tries to
follow the best prior-result so far.
Try to align two sequences by inserting some gaps at different locations, so as to
maximize the score of this alignment.
Score measurement is determined by "match award", "mismatch penalty" and
"gap penalty". The higher the score, the better the alignment.
If both penalties are set to 0, it aims to always find an alignment with maximum
matches so far.
Maximum match = largest number matches can have for one sequence by
allowing all possible deletion of another sequence.
It is used to compare the similarity between two sequences of DNA or Protein, to
predict similarity of their functionalities.
Examples: Needleman-Wunsch(1970), Sellers(1974), Smith-Waterman(1981)46
The Needleman-Wunsch algorithm
The Needleman-Wunsch algorithm (1970, J Mol Biol. 48(3):443-53) performs a
global alignment on two sequences (A and B) and is applied to align protein or
nucleotide sequences.
The Needleman-Wunsch algorithm is an example of dynamic programming,
and is guaranteed to find the alignment with the maximum score.
Scores for aligned characters are specified by the transition matrix σ (i,j) :
the similarity of characters i and j.
47
The Needleman-Wunsch algorithm
For example, if the substitution matrix was
A
G
C
T
A
10
-1
-3
-4
G
-1
7
-5
-3
C
-3
-5
9
0
T
-4
-3
0
8
then the alignment:
AGACTAGTTAC
CGA---GACGT
with a gap penalty of -5, would have the following score...
48
The Needleman-Wunsch algorithm
1. Create a table of size (m+1)x(n+1) for sequences s and t of lengths m and n,
2. Fill table entries (m:1) and (1:n) with the values:
i
j
k 1
k 1
M i ,1   (s k ,), M1, j   (, t k )
3. Starting from the top left, compute each entry using the recursive relation:
M i, j
M i 1, j 1   (s i , t j )


 max  M i 1, j   (s i ,) 
M



(

,
t
)
j 
 i , j 1
4. Perform the trace-back procedure from he bottom-right corner
49
The Needleman-Wunsch algorithm
Once the F matrix is computed, note that the bottom right hand corner of the
matrix is the maximum score for any alignments. To compute which alignment
actually gives this score, you can start from the bottom left cell, and compare the
value with the three possible sources(Choice1, Choice2, and Choice3 above) to
see which it came from. If it was Choice1, then A(i) and B(i) are aligned, if it was
Choice2 then A(i) is aligned with a gap, and if it was Choice3, then B(i) is aligned
with a gap.
50
The Needleman-Wunsch algorithm
51
52
The Smith-Waterman algorithm
1. Create a table of size (m+1)x(n+1) for sequences s and t of lengths m and n,
2. Fill table entries (1,1:m+1) and (1:n+1,1) with zeros.
3. Starting from the top left, compute each entry using the recursive relation:
M i, j
M i 1, j 1   (s i , t j )
 M

 i 1, j   (s i ,) 
 max 

 M i , j 1   (, t j ) 


0
4. Perform the trace-back procedure from the maximum element in the table to
the first zero element on the trace-back path.
53
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
EXAMPLE: Eyeless Gene Homeobox
Compare the gene eyeless of Drosophila Melanoganster with the human gene
aniridia. They are master regulatory genes producing proteins that control large
cascade of other genes. Certain segments of genes eyeless of Drosophila
melanogaster and human aniridia are almost identical. The most important of
such segments encodes the PAX (paired-box) domain, a sequence of 128 amino
acids whose function is to bind specific sequences of DNA. Another common
segment is the HOX (homeobox) domain that is thougth to be part of more than
0.2% of the total nummber of vertebrate genes.
54
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
55
Introduction to Bioinformatics
LECTURE 3: GLOBAL ALIGNMENT
56
Introduction to Bioinformatics
LECTURE 3: GLOBAL ALIGNMENT
57
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
58
END of LECTURE 3
59
Introduction to Bioinformatics
LECTURE 3: SEQUENCE ALIGNMENT
60
61