Bioinformatics PhD. Course

1
Bioinformatics PhD. Course
Summary (approximate)

• 1. Biological introduction

• 2. Comparison of short sequences (lt10.000 bps)

• 3 Comparison of large sequences (up to 250 000
  000)

• 4 Sequence assembly

• 5 Efficient data search structures and algorithms

• 6 Proteins...

2
3. Comparison of large sequences
Summary (more or less)

• 3.1 Overview
• 3.2 Suffix trees
• 3.3 MUMs

3
Suffix trees
Algorithms on strings, trees and sequences, Dan
Gusfield Cambridge University Press http//seque
nce.rutgers.edu/st/
4
Suffix trees
Given string ababaas
Suffixes
3 abaas
1 ababaas
4 baas
2 babaas
What kind of queries can we do?
5
Applications of Suffix trees
1. Exact string matching

• Does the sequence ababaas contain any ocurrence
  of the patterns abab, aab, and ab?

6
Applications of Suffix trees
2. Finding the repeats within a sequence.

7
Queries on Suffix trees

• Does the sequence ababaas contain any ocurrence
  of patterns abab, aab, and ab?

• Find repeats within the sequence ababaas.

8
Quadratic Insertion algorithm
Given the string ababaabbs
9
Quadratic Insertion algorithm
Given the string ababaabbs
ababaabbs,1
10
Quadratic Insertion algorithm
Given the string ababaabbs
ababaabbs,1
babaabbs,2
11
Quadratic Insertion algorithm
Given the string ababaabbs
babaabbs,2
12
Quadratic Insertion algorithm
Given the string ababaabbs
babaabbs,2
13
Quadratic Insertion algorithm
Given the string ababaabbs
14
Quadratic Insertion algorithm
Given the string ababaabbs
ba
baabbs,2
15
Quadratic Insertion algorithm
Given the string ababaabbs
ba
baabbs,2
16
Quadratic Insertion algorithm
Given the string ababaabbs
ba
baabbs,2
17
Quadratic Insertion algorithm
Given the string ababaabbs
ba
ba
baabbs,2
18
Quadratic Insertion algorithm
Given the string ababaabbs
ba
baabbs,2
19
Quadratic Insertion algorithm
Given the string ababaabbs
ba
baabbs,2
20
Quadratic Insertion algorithm
Given the string ababaabbs
21
Quadratic Insertion algorithm
Given the string ababaabbs
22
Quadratic Insertion algorithm
Given the string ababaabbs
23
Generalizad suffix tree
A suffix tree of many strings
is called a generalized suffix tree
and is the suffix tree of the concatenation of
strings.
For instance,
24
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
Given the suffix tree of ababaaba
25
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
26
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
ab
a
ba,5
27
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
ab
a
ba,5
28
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
aaß,1
ab
a
ba,5
b
a
bba,3
a
baabba,1
29
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
aaß,1
ab
a
ba,5
b
a
bba,3
a
baabba,1
30
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
aaß,1
ab
a
ba,5
ß,2
b
a
bba,3
a
b
baabba,1
a
a
bba,4
baabba,2
31
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
aaß,1
ab
a
ba,5
ß,2
b
a
bba,3
a
b
baabba,1
a
a
bba,4
baabba,2
32
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
aaß,1
a
b
a
ba,5
ß,2
b
a
bba,3
a
b
baabba,1
ß,3
a
a
bba,4
baabba,2
33
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
aaß,1
a
b
a
ba,5
ß,2
b
a
bba,3
a
b
baabba,1
ß,3
a
a
bba,4
baabba,2
34
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
ß,4
ß,4
aaß,1
a
b
a
ba,5
ß,2
b
a
bba,3
a
b
baabba,1
ß,3
a
a
bba,4
baabba,2
35
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
ß,4
ß,4
aaß,1
a
b
a
ba,5
ß,2
b
a
bba,3
a
b
baabba,1
ß,3
a
a
bba,4
baabba,2
36
Generalizad suffix tree
Construction of the suffix tree of
ababaabbaaabaaß
ß,4
ß,4
aaß,1
ß,4
a
b
a
ba,5
ß,2
b
a
bba,3
a
b
baabba,1
ß,3
a
a
bba,4
baabba,2
37
Generalizad suffix tree
Generalized suffix tree of ababaabbaaabaaß
What kind of queries can we do?
38
Applications of Suffix trees
1. The substring problem for a database of
patterns DB

• Does the DB contain any ocurrence of patterns
  abab, aab, and ab?

39
Applications of Suffix trees
2. The longest common substring of two strings
40
Applications of Suffix trees
3. Finding MUMs.
41
Linear Insertion algorithm
Given the string ......
P1 the leaves of suffixes from ? have been
inserted
P2 the string ? is the longest string that can
be spelt through the tree.
42
Insertion algorithm example
Given the string ababaababb...
43
Linear Insertion algorithm
Given the string ......
P1 the leaves of suffixes from ? have been
inserted
P2 the string ? is the longest string that
P3 there is a pointer,called suffix pointer
between any node and its longest no proper suffix
node.
44
Insertion algorithm example
45
Insertion algorithm example
46
Insertion algorithm example
47
Insertion algorithm example
48
Insertion algorithm example
49
Insertion algorithm example
?
Given the string ababaababb...
8
?
ababb...,5
ababb...,3
ba
ba
ababb...,4
50
Insertion algorithm improving time
we have pointed to the following nodes
51
Insertion algorithm improving time
we have pointed to the following nodes
ba
baababb...,1
ba
baababb...,2
52
Suffix tree implementationsuffix-links
Given sequence ababaas
?
a?
53
Suffix links
Given Suffix tree of ababaas
54
Insertion algorithm
Given the string ababaabbs
55
Insertion algorithm
Given the string ababaabbs
56
Insertion algorithm
Given the string ababaabbs
57
Insertion algorithm
Given the string ababaabbs
58
Insertion algorithm
Given the string ababaabbs
babaabbs,2
59
Insertion algorithm
Given the string ababaabbs
60
Insertion algorithm
Given the string ababaabbs
61
Insertion algorithm
Given the string ababaabbs
62
Insertion algorithm
Given the string ababaabbs
baabbs,1
63
Insertion algorithm
Given the string ababaabbs
64
Insertion algorithm
Given the string ababaabbs
65
Insertion algorithm
Given the string ababaabbs
66
Insertion algorithm
Given the string ababaabbs
67
Insertion algorithm
Given the string ababaabbs
68
Insertion algorithm
Given the string ababaabbs