Editing Needleman–Wunsch algorithm (section)

===Similarity matrix===
More complicated scoring systems attribute values not only for the type of alteration, but also for the letters that are involved. For example, a match between A and A may be given 1, but a match between T and T may be given 4. Here (assuming the first scoring system) more importance is given to the Ts matching than the As, i.e. the Ts matching is  assumed to be more significant to the alignment. This weighting based on letters also applies to mismatches.

In order to represent all the possible combinations of letters and their resulting scores  a similarity matrix is used. The similarity matrix for the most basic system is represented as:

{| class="wikitable"
! scope="col" |
! scope="col" | A
! scope="col" | G
! scope="col" | C
! scope="col" | T
|- style="text-align: right;"
! scope="row" | A
| 1 ||  −1|| −1 || −1
|- style="text-align: right;"
! scope="row" | G
| −1 || 1 || −1 || −1
|- style="text-align: right;"
! scope="row" | C
| −1 || −1 || 1 || −1
|- style="text-align: right;"
! scope="row" | T
| −1 || −1 || −1 ||  1
|}
Each score represents a switch from one of the letters the cell matches to the other. Hence this represents all possible matches and mismatches (for an alphabet of ACGT). Note all the matches go along the diagonal, also not all the table needs to be filled, only this triangle because the scores are reciprocal.= (Score for A → C = Score for C → A). If implementing the T-T = 4 rule from above the following similarity matrix is produced:

{| class="wikitable"
! scope="col" |
! scope="col" | A
! scope="col" | G
! scope="col" | C
! scope="col" | T
|- style="text-align: right;"
! scope="row" | A
| 1 || −1 || −1 || −1
|- style="text-align: right;"
! scope="row" | G
| −1 || 1 || −1 || −1
|- style="text-align: right;"
! scope="row" | C
| −1 || −1 || 1 || −1
|- style="text-align: right;"
! scope="row" | T
| −1 || −1 || −1 ||  4
|}

Different scoring matrices have been statistically constructed which give weight to different actions appropriate to a particular scenario. Having weighted scoring matrices is particularly important in protein sequence alignment due to the varying frequency of the different amino acids. There are two broad families of scoring matrices, each with further alterations for specific scenarios:
* [[Point accepted mutation|PAM]]
* [[BLOSUM]]