Survey of Sequence Matching and alignment algorithms

Presented by Jennifer
Johnstone


What is Bioinformatics?


Sequence Matching Problem


The Alignment Problem


Future Research

Bioinformatics is the application of computers in
Biology using algorithms, statistics and other
mathematical techniques to decipher the
language of DNA.


Given a string
s,

of size
n
, and a pattern
p
, of size
m,
for what indices
I
of
s

does
p

exactly match
s.

Example: Let p =
ABA

and s =
AABAAGTABA

then
I = {2, 8} since





A
ABA
AGTABA






ABA




and






AABAAGT
ABA






ABA



Naive String Matching Algorithm,
O(m*n).


String Matching with Finite Automata ,
O((m*|
Σ
|)+n).


Boyer
-
Moore Algorithm,
O(
m+n
) (
in practice).



String Matching with Compact Suffix Trees,
O(n log(n) + m*|
Σ
| +k).


String Matching using Suffix Arrays ,


O(
n+m

log(n) +k).

Given a pattern
p

=
aba

and a string
s

=
acbababa

we must first define the state function
δ
(
q,x
).



q

x

δ
(
焬x
⤠

0

a

1

0

b

0

0

c

0

1

a

1

1

b

2

1

c

0

2

a

3

2

b

0

2

c

0

3

a

1

3

b

2

3

c

0

i

s
i

State

1

a

δ
(0,a) = 1

2

c

δ
(1,c) = 0

3

b

δ
(0,b) = 0

4

a

δ
(0,a) = 1

5

b

δ
(1,b) = 2

6

a

δ
(2,a) = 3

7

b

δ
(3,b) = 2

8

a

δ
(2,a) = 3

Now we see that the match
condition is met for
i

= 6, 8.
Then the starting indexes are

j =
i

–

3+ 1, such that I ={ 4, 6 }.


Given two strings we want to generate an optimal
alignment. The alignment of two strings may
involve the insertion of gaps and
\
or the
acceptance of mismatched entries.

Example: Consider the following possible alignment of
the two strings
GACGGATTATG and
GATCGGAATAG:

GA

CGGA
T
TATG

GATCGGA
A
TA

G

Dynamic Approach


Computing Optimal Alignment using a
dynamic programming matrix and a scoring
function. (
O(m*n))

Heuristic Approach used in practice to speed up
search times on large databases. Consider the
Human genome which is over 3 billion
characters long for which you may need to
align only a small portion.


FASTP and FASTA Programs


BLAST Algorithm


Development of the Heuristic approaches is
constantly being improved upon and
researched as the algorithms themselves are
only 10
-
15 years old.


Development of tools that can perform a 10
-
way comparison of genomes.


Bioinformatics as a whole is an active field of
research that strongly needs qualified
professionals who have an aptitude for
computing and
\
or biology
.


B
ockenhauer
, Hans
-
Joachim and
Bongartz
, Dirk (2007)
Algorithmic Aspects of Bioinformatics. Berlin: Springer
pg.37
-
114


Haubold
, Bernhard and
Wiehe
, Thomas (2006)
Introduction to Computational Biology: An Evolutionary
Approach. Basel:
Birkh
auser

pg.65
-
85.


Jones, Neil C. and
Pevzner
,
Pavel

A. (2004)
An
Introduction to Bioinformatics Algorithms. Cambridge: The
MIT Press pg. 148
-
226 and 311
-
337.


Parida
,
Laxmi

(2008)
Pattern Discovery in Bioinformatics:
Theory & Algorithms. Boca Raton: Chapman & Hall/CRC
pg. 139
-
182 and 183
-
212.


Polanski,
Andrzej

and Kimmel,
Marek

(2007)
Bioinformatics. Berlin: Springer pg. 155
-
183 and 349
-
354.