smith waterman algorithm choose more than one alignment - python-2.7

Question

I want to align a small sequence S1 to another larger nucleotide sequence S2 for example:
S1: acgtgt
S2: ttcgtgacagt...
In this example s1 hit in 2 places in s2 : cgtg and acgt with gap in s2 the 2. I want to use smith waterman algorithm but my question is : in case the 2 alignments have 2 diffrent score i.e one 4 and another 3 how to get the2 alignments from the dynamic programimg matrix? Is there any tool or library that do this already? I tried paorwise2 from biopython and it only gives the alignments with high score in tje matrix

Answer 1

Pairwise alignment algorithms such as Smith-Waterman will only provide the one best alignment. A worse alignment will have a different traceback walk that will not be followed by the Dynamic Programming algorithm Smith-Waterman uses.
If there are multiple alignments with the same best score, S-W will choose only one of those alignments (which one is implementation specific since it doesn't really matter since they have the same score).
If you really really wanted to have multiple alignments returned AND use something like Smith-Waterman, you will have to re-align the sequences multiple times each time configuring the gap penalties differently. I do not recommend this since it will be very expensive.
Instead of using Smith-Waterman, you may want to try something like BLAST which will give you multiple hits

Answer 2

see section Repeated matches in the Durbin - Biological Sequence Analysis
Let us assume that we are only interested in matches scoring higher
than some threshold T . This will be true in general, because there
are always short local alignments with small positive scores even
between entirely unrelated sequences. Let y be the sequence containing
the domain or motif, and x be the sequence in which we are looking for
multiple matches.
An example of the repeat algorithm is given in Figure 2.7. We again
use the matrix F, but the recurrence is now different, as is the
meaning of F(i, j). In the final alignment, x will be partitioned into
regions that match parts of y in gapped alignments, and regions that
are unmatched. We will talk about the score
of a completed match region as being its standard gapped alignment
score minus the threshold T . All these match scores will be positive.
F(i, j) for j ≥ 1 is now the best sum of match scores to x1...i,
assuming that xi is in a matched region, and the corresponding match
ends in xi and yj (they may not actually be aligned, if this is a
gapped section of the match). F(i,0) is the best sum of completed
match scores to the subsequence x1...i, i.e. assuming that xi is in an
unmatched region.
To achieve the desired goal, we start by
initialising F(0,0) = 0 as usual, and then fill the matrix using the
following recurrence relations:
Equation (2.11) handles unmatched regions and ends of matches, only
allowing matches to end when they have score at least T . Equation
(2.12) handles starts of matches and extensions. The total score of
all the matches is obtained by adding an extra cell to the matrix, F(n
+ 1,0), using (2.11). This score will have T subtracted for each match; if there were no matches of score greater than T it will be 0,
obtained by repeated application of the first option in (2.11).
The
individual match alignments can be obtained by tracing back from cell
(n + 1,0) to (0,0), at each point going back to the cell that was the
source of the score in the current cell in the max() operation. This
traceback procedure is a global procedure, showing what each residue
in x will be aligned to. The resulting global alignment will contain
sections of more conventional gapped local alignments of subsequences
of x to subsequences of y.
Note that the algorithm obtains all the
local matches in one pass. It finds the maximal scoring set of
matches, in the sense of maximising the combined total of the excess
of each match score above the threshold T . Changing the value of T
changes what the algorithm finds. Increasing T may exclude matches.
Decreasing it may split them, as well as finding new weaker ones. A
locally optimal match in the sense of the preceding section will be
split into pieces if it contains internal subalignments scoring less
than −T . However, this may be what is wanted: given two similar high
scoring sections significant in their own right, separated by a
non-matching section with a strongly negative score, it is not clear
whether it is preferable to report one match or two.

Answer 3

All possible alignments that conform to the scoring in the substitution matrix are rerpresented in the trace back matrix T - its just that some implementations might not give you access to T.
To extract multiple alignments, you'll need first to look at the scoring matrix H and choose which scores you want to trace back - for example, you might look at the highest 10 scores. The values in the matrix T will tell you the route to trace back. Keep going until the corresponding score in H is zero.
Be careful though - the 10 highest scores might all be part of the same alignment, in which case you'd just get a result that are subsequences of another result. To avoid this, it's probably best to trace back the highest scoring alignment first, and then look for high values in cells that are not passed through by the first alignment.