irst incremental alignment type is to pick up the first remaining

of both sequences. This is to align ݔ௠ାଵ with ݕ௡ାଵ. If they are

in a new alignment, the current total alignment distance is

d based on the following formula,

ݔ௠|ݔ௠ାଵ,

⋯ݕ௡|ݕ௡ାଵሻൌ݀௠௡൅ߜሺݔ௠ାଵ, ݕ௡ାଵሻ

(7.7)

e bar | is used to separate the aligned residues from the remaining

d residues of two sequences. The residue just on the right side of

ands for a newly aligned residue. They are ݔ௠ାଵ and ݕ௡ାଵ in the

uation. ߜሺݔ௠ାଵ, ݕ௡ାଵሻ is the alignment distance between ݔ௠ାଵ

. It is calculated based on Table 7.1. ݀௠௡ is the alignment score

esidues from two sequences, which have been aligned in the

steps, i.e., ݔଵݔଶ⋯ݔ௠ and ݕଵݕଶ⋯ݕ௡. In a dynamic programming

s incremental alignment is called the diagonal move.

econd incremental alignment type is to align the first remaining

௡ାଵ ^{of sequence y with a gap. This implies that a gap is inserted}

ence x. The formula of calculating the alignment cost is shown

⋯ݔ௠|െ,

⋯ݕ௡|ݕ௡ାଵሻൌ݀௠௡൅ߜሺെ, ݕ௡ାଵሻ

(7.8)

e hyphen key stands for an insertion in sequence x and ߜሺെ, ݕ௡ାଵሻ

enalty applied in this new alignment. This incremental alignment

the horizontal move in the dynamic programming table.

hird incremental alignment aligns the first remaining residue

sequence x with a gap. A gap is therefore inserted into sequence

s alignment. The formula of calculating the alignment cost is

low

⋯ݔ௠|ݔ௠ାଵ,

⋯ݕ௡| െሻൌ݀௠௡൅ߜሺݔ௠ାଵ, െሻ

(7.9)

arly, ߜሺݔ௠ାଵ, െሻ is the gap penalty applied in this new

t. This is called the vertical move in the dynamic programming