Dynamic programming is used for sequence alignment and other bioinformatics tasks. It works by breaking problems down into smaller subproblems. Needleman-Wunsch introduced an algorithm for global sequence alignment using dynamic programming that maximizes matches between sequences. The algorithm involves initializing a matrix, filling it using scoring schemes, and backtracking to trace alignments. Local alignment follows a similar approach but replaces negative values in the matrix with zeros to restrict alignments.

1. MARYAM BIBI
FA12-BTY-011
TOPIC : DYNAMIC PROGRAMING
SUBJECT : BIOINFIRMATICS

2. Alignment
used to uncover homologies between sequences
combined with phylogenetic studies
can determine orthologous and paralogous
relationships
Global Alignments
compares one whole sequence with other entire
sequence
computationally expensive
Local Alignment
uses a subset of a sequence and attempts to align it
to subset of other sequences
computationally less expensive

3. Dynamic Programming:
dynamic programing is solving complex
prblems by breaking them into a simpler
subproblems.
Problem can be divided into many smaller
parts.
Needleman and Wunsch were the first to
propose this method.

4. Needleman and Wunsch describes general
algorithm for sequence aignment.
Maximize a score of similarity to give maximun
match.
Maximun match= largest number of nucleotides
that can be match with others.
That want to quantify sequence similarity
between two sequences.

5. Dynamic programming in bioinformatics
Dynamic programming is widely used in
bioinformatics for the tasks such as sequence
alignment, protein folding, RNA structure
prediction and protein-DNA binding.
First dynamic programming algorithms for
protein-DNA binding were developed in the 1970s
independently by Charles Delisi in USA
and Georgii Gurskii and Alexanderr
zasedatelev in USSR.

6. Dynamic Programming in sequence alignment
There are three steps in dynamic programing.
1. initialization.
The first step in the global alignment dynamic programming
approach is to create a matrix with M + 1 columns and N + 1
rows where M and N correspond to the size of the sequences to
be aligned.
2. Matrix filling(scoring)
We fill the matrix with highest possible score.
To align with diagnol ( align in next position.)
Allign in off-diagonal requires inserion of crossponding gaps
3. Traceback and aligning
Move from last corner and follow arrow.

7. Global alignment via dynamic programing
1st column and 1st row will be empty.
Fill 1st block with zero
Then fill 1st row and 1st coulmn with gap penality multiples.
While filling the matrix there are three possible values
 horizental: score+ gap penality
 Verticle: score+ gap penality
 Diagonal: score+(match/mismatch)
We have to write max score from these values in a
cell
Let ,
match = + 1
mismatch= -1
gap penality= -2

8. Lets
Seq# 1 A A A C
Seq# 2 A G C -

9. A A T C
0 -2 -4 -6 -8
A -2
( 1) ( -4)
1
(-4)
-1 -6
-1
-1
-3 -5
G -4
-1 0 -2 -4
C -6
-3 -2 -1 -1

10. Backward tracking
In backward tracking we have to move
from last cell( lower corner) and follows
arrow from which cell the current cell’s
values come from and go ahead.

11. A A T C
0 -2 -4 -6 -8
A -2 1 -1 -3 -5
G -4
-1 0 -2 -4
C -6
-3 -2 -1 -1

12. A A T C
0 -2 -4 -6 -8
A -2 1 -1 -3 -5
G -4
-1 0 -2 -4
C -6
-3 -2 -1 -1
Path 1
Path 2

13. Backtracking
Now we have to allign this sequence.
For alligning there are 2 rules.
1. If the value come from column we will have
to write two sequences
2. If value come from horizontal or vertical
then we will have to write perpendicular
and add gap to other side.

14. Backtracking
Here we have two paths. So we will get two
possible sequences.
We will write sequence from 3’-end.
Path 1:
Seq#1 A A T C
Seq#2 - A G C

15. Backtracking
Path 2
Seq# 1 A A T C
Seq# 2 A G - C
Hense , we do global allignment in this way.

16. Local alignment via dynamic programing
Algorithim is same as in global alignment,
but there are some changes.
We fill 1st column and 1st row with zero.
If the value comes in negative number than
it is replaced by zero.
Backtracking will be start from maximun
value.

17. Local alignment
Let,
Match = 1
Mismatch = 0
Gap penality= 0
And sequence#1 GAATTCAGTTA
Squence#2 GGATCGA

18. G A A T T C A G T T A
0 0 0 0 0 0 0 0 0 0 0 0
G 0 1 1 1 1 1 1 1 1 1 1 1
G 0 1 1 1 1 1 1 1 2 2 2 2
A 0 1 2 2 2 2 2 2 2 2 2 3
T 0 1 2 2 3 3 3 3 3 3 3 3
C 0 1 2 2 3 3 4 4 4 4 4 4
G 0 1 2 2 3 3 4 4 5 5 5 5
A 0 1 2 3 3 3 3 4 5 5 5 6

19. Bactracking
After the matrix fill step, the maximum alignment
score for the two test sequences is 6. The traceback
step determines the actual alignment(s) that result
in the maximum score.

20. G A A T T C A G T T A
0 0 0 0 0 0 0 0 0 0 0 0
G 0 1 1 1 1 1 1 1 1 1 1 1
G 0 1 1 1 1 1 1 1 2 2 2 2
A 0 1 2 2 2 2 2 2 2 2 2 3
T 0 1 2 2 3 3 3 3 3 3 3 3
C 0 1 2 2 3 3 4 4 4 4 4 4
G 0 1 2 2 3 3 4 4 5 5 5 5
A 0 1 2 3 3 3 3 4 5 5 5 6

21. Backtracking
Rule will be same for this as in global
alignment
Sequence alignment :
Seq#1 G A A T T C A G T TA
Seq#2 G A - T C – G - - A
So in this way we align the sequence using
dynamic programing.