1. Affine gaps for sequence alignment
Usman Roshan

2. Affine gaps A gap model that captures long insertions and deletions
Useful when aligning transcribed proteins to gene sequences (to account for introns)
Gives more accurate alignment than single gap model

3. Affine gaps In the standard model we score a series of k gaps as k*g
We could assign a different cost to k gaps with a function w(k). This results in a cubic algorithm (slower than quadratic Needleman-Wunsch)
If we score k gaps as g + e(k-1) we get the affine model and it still has quadratic time.
However, it uses three scoring matrices instead of one as in Needleman-Wunsch.

4. Affine gaps
In NW we defined V[i][j] to be the score of the optimal alignment of X1…i and Y1...j where X and Y are input DNA sequences
Here we define three matrices:
M[i][j] = optimal alignment score of X1…i and Y1...j such that Xi is aligned to Yj
E[i][j] = optimal alignment score of of X1…i and Y1...j such that gap is aligned to Yj
F[i][j] = optimal alignment score of of X1…i and Y1...j such that Xiis aligned to gap.
We derive the recurrence like we did for Needleman-Wunsch