Lecture 8: Bioinformatic Algorithms - Sequence Alignment and Suffix Trees, Study notes of Computer Science

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CMSC423: Bioinformatic Algorithms,

Databases and Tools

Lecture 8

Sequence alignment:

exact alignment

inexact alignment

dynamic programming, gapped

alignment

Suffix trees for matching

• Suffix trees use O(n) space

• Suffix trees can be constructed in O(n) time

• Is CAT part of ATCATG?

• Match from root, char by char

• If run out of query – found match

• otherwise, there is no match

• intuition: CAT is the prefix

of some suffix

AT1, G$6,7 T2,2 CATG$3,

G$6,7 CATG$3,7 (^) G$ 6,

CATG$3,

4 1

6

5 2

3

$7, 7

Other uses

• Finding repeats

• internal nodes with multiple children – DNA that occurs in multiple places in the genome

• Longest common substring of two strings

• build suffix tree of both strings. Find lowest internal node that has leaves from both strings
• or: build suffix tree on one string and use suffix links to find longest match

• Note: running time for matching is O(|Pattern|),

not O(|Pattern| + |Text|)

(though O(|Text|) was spent in pre-processing

Why do we care?

• Suffix trees are used for

• mapping reads to a genome (e.g. personal genomics)
• comparing genomes (comparative genomics)
• finding repeats
• identifying genome signatures

• Exact matching – what to expect on exams

• build a suffix tree for a string
• answer some questions about one of the algorithms, e.g. for Z algorithm – is it necessary j be the farthest reaching Z- value or just any Z value extending past i?
• do something with the help of some of the algorithms (e.g. look for repeats that occur exactly twice, etc.)

Suffix arrays and compression

• Burrows-Wheeler transform

BANANA

BANANA$

ANANA$B

NANA$BA

ANA$BAN

NA$BANA

A$BANAN

$BANANA

$ BANANA

A$ BANAN

ANA$ BAN

ANANA$ B

BANANA$

NA$ BANA

NANA$ BA

sort (^) ANNB$AA compress

character before the suffix BWT

Note: characters in last column occur in same order as in first column Useful for matching within BWT

BWT – string matching

• Look for “BANA”
• Start at end (match right to left)
• Find character in rightmost column
• Identify corresponding range in first column
• Switch back to last column
• ...
• How do we know the first A in the pattern is the 2nd/3rd from the top of the matrix?
• Note: add'l data needed:

  of times each letter appears

  before every pos'n
• Running time? O(len(P)) operations. Each may cost O(log(len(T)))

ABN$

$ BANANA

A$ BANAN

ANA$ BAN

ANANA$ B

BANANA$

NA$ BANA

NANA$ BA

A N

A

A (^) B