he forward propagation

ate rule of the Smith-Waterman algorithm for the forward

on is shown below, where D stands for the diagonal move, V is

ertical move and H represents the horizontal move:

ܯ௜௝ൌmax

ە^ۖ۔

ۖ^ۓ

0, ൞

ܯ௜ିଵ,௝ିଵ൅ݏ௜௝

D

max൛ܯ௜ି௑,௝൅ܩ௫ൟ

V

max൛ܯ௜,௝ି௑൅ܩ௫ൟ

H

ൢ

ۙ^ۖۘ

ۖ^ۗ

(7.13)

sidue from sequence y matched the first residue G of sequence x.

e all the cells of this row were filled by zeros. Their moving

s were not of interest. The cell (2, 3) was for the second residue

uence x and the third residue C of sequence y. This was the first

entical residues from two sequences from the top-left corner cell.

ment score for this cell was calculated as below,

ܯଶ,ଷൌmax ൞0, ൝

0 ൅1

D

maxሼ0 ൅ሺെ1 െܮ/3ሻሽ

V

maxሼ0 ൅ሺെ1 െܮ/3ሻሽ

H

ൡൢൌ1

iagonal move led to a score one shown below,

ܯଵ,ଶ൅ݏଶ,ଷൌ0 ൅1 ൌ1

the horizontal move and the vertical move ended up with a zero

r instance, the score of the horizontal move from the cell (2, 2)

ell (2, 1) was calculated as below,

maxሼ0 ൅ሺെ1 െ1 3

⁄ ሻ, 0 ൅ሺെ1 െ2 3

⁄ ሻሽൌെ4 3

⁄

−4/3 was capped to zero. Maximising three scores resulted in the

of the diagonal move for this cell, shown in Table 7.13.