Dynamic Programming (DP)

• Three Steps: Initialization Matrix fill (scoring) Traceback (alignment)

• Global Alignment: Needleman-Wunsch

• Local Alignment: Smith-Waterman

• G A A T T C A G T T A (sequence #1)

• G G A T C G A (sequence #2)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Initialization)

• Create N+1 by M+1 Matrix

• M = Seq1 length = 11

• N = Seq2 length = 7

• Assuming no gap opening penalty, 0’s fill the first row and column

G A A T T C A G T T A (Seq1) G G A T C G A (Seq2)http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Scoring)

Simple Scoring Scheme

• Si,j = 1 (Match)

• Si,j = 0 (Mismatch)

• w = 0 (Gap)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Scoring)

Si,j = 1 (Match), Si,j = 0 (Mismatch), w = 0 (Gap)

F(i,j) = maxF(i-1, j-1) + s(xi, yi)F(i-1, j) - wF(i, j-1) - w

F(i,j)F(i-1, j)

F(i, j-1)F(i-1, j-1)

- w

- w

s(xi, yi)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Scoring)

Si,j = 1 (Match), Si,j = 0 (Mismatch), w = 0 (Gap)

F(i,j) = maxF(i-1, j-1) + s(xi, yi)F(i-1, j) - wF(i, j-1) - w

F(i,j)F(i-1, j)

F(i, j-1)F(i-1, j-1)

- w

- w

s(xi, yi)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Scoring)

Si,j = 1 (Match), Si,j = 0 (Mismatch), w = 0 (Gap)

F(i,j) = maxF(i-1, j-1) + s(xi, yi)F(i-1, j) - wF(i, j-1) - w

F(i,j)F(i-1, j)

F(i, j-1)F(i-1, j-1)

- w

- w

s(xi, yi)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Scoring)

Si,j = 1 (Match), Si,j = 0 (Mismatch), w = 0 (Gap)

F(i,j) = maxF(i-1, j-1) + s(xi, yi)F(i-1, j) - wF(i, j-1) - w

F(i,j)F(i-1, j)

F(i, j-1)F(i-1, j-1)

- w

- w

s(xi, yi)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Scoring)

Completed Matrix

F(i,j) = maxF(i-1, j-1) + s(xi, yi)F(i-1, j) - wF(i, j-1) - w

F(i,j)F(i-1, j)

F(i, j-1)F(i-1, j-1)

- w

- w

s(xi, yi)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Traceback)

G A A T T C A G T T A (Seq1) G G A T C G A (Seq2)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Traceback)

G A A T T C A G T T A (Seq1) G G A T C G A (Seq2)

Seq1 A |Seq2 A

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Traceback)

Seq1 T A |Seq2 _ A

G A A T T C A G T T A (Seq1) G G A T C G A (Seq2)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Traceback)

Seq1 T T A |Seq2 _ _ A

G A A T T C A G T T A (Seq1) G G A T C G A (Seq2)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Traceback)

Seq1 G A A T T C A G T T A | | | | | | Seq2 G G A _ T C _ G _ _ A

G A A T T C A G T T A (Seq1) G G A T C G A (Seq2)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

DP (Traceback)

Alternative:

Seq1 G _ A A T T C A G T T A | | | | | | Seq2 G G _ A _ T C _ G _ _ A

G A A T T C A G T T A (Seq1) G G A T C G A (Seq2)

http://www.avatar.se/molbioinfo2001/dynprog/dynamic.html

Basic Local Alignment Search Tool (BLAST)

Heuristic Method

BLAST

BLAST

BLAST

BLAST

What can we search and compare?

DNA vs DNA

Protein vs Protein

DNA vs Protein

Protein vs DNA

Reading Frames

The best BLAST program