using dynamic programming to align sequences
DESCRIPTION
Using Dynamic Programming To Align Sequences. Cédric Notredame. Our Scope. Understanding the DP concept. Coding a Global and a Local Algorithm. Aligning with Affine gap penalties. Saving memory. Sophisticated variants…. Outline. -Coding Dynamic Programming with Non-affine Penalties. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/1.jpg)
Cédric Notredame (19/04/23)
Using Dynamic Programming To Align Sequences
Cédric Notredame
![Page 2: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/2.jpg)
Cédric Notredame (19/04/23)
Our Scope
Coding a Global and a Local Algorithm
Understanding the DP concept
Aligning with Affine gap penalties
Sophisticated variants…
Saving memory
![Page 3: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/3.jpg)
Cédric Notredame (19/04/23)
Outline
-Coding Dynamic Programming with Non-affine Penalties
-Adding affine penalties
-Turning a global algorithm into a local Algorithm
-Using A Divide and conquer Strategy
-The repeated Matches Algorithm
-Double Dynamic Programming
-Tailoring DP to your needs:
![Page 4: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/4.jpg)
Cédric Notredame (19/04/23)
Global Alignments Without Affine Gap
penalties
Dynamic Programming
![Page 5: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/5.jpg)
Cédric Notredame (19/04/23)
How To align Two Sequences With a Gap Penalty, A Substitution
matrix and Not too Much Time
Dynamic Programming
![Page 6: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/6.jpg)
Cédric Notredame (19/04/23)
A bit of History…
-DP invented in the 50s by Bellman
-Programming Tabulation
-Re-invented in 1970 by Needlman and Wunsch
-It took 10 year to find out…
![Page 7: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/7.jpg)
Cédric Notredame (19/04/23)
The Foolish Assumption
The score of each column of the alignment is independent from the rest of the alignment
It is possible to model the relationship between two sequences with:
-A substitution matrix-A simple gap penalty
![Page 8: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/8.jpg)
Cédric Notredame (19/04/23)
The Principal of DP
If you extend optimally an optimal alignment of two sub-sequences, the result remains an optimal alignment
X-XXXXXX
X-
XX
-X
Deletion
Alignment
Insertion
??+
![Page 9: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/9.jpg)
Cédric Notredame (19/04/23)
Finding the score of i,j
-Sequence 1: [1-i]-Sequence 2: [1-j]
-The optimal alignment of [1-i] vs [1-j] can finish in three different manners:
X-
XX
-X
![Page 10: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/10.jpg)
Cédric Notredame (19/04/23)
Finding the score of i,j
i-
ij
-j
1…i1…j-1
1…i-11…j-1
1…i-11…j
+
+
+
Three ways to buildthe alignment
1…i1…j
![Page 11: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/11.jpg)
Cédric Notredame (19/04/23)
Finding the score of i,j
1…i-11…j-1
1…i1…j-1
1…i-11…j
In order to Compute the score of
1…i1…j
All we need are the scores of:
![Page 12: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/12.jpg)
Cédric Notredame (19/04/23)
Formalizing the algorithm
F(i,j)= best
F(i-1,j) + Gep
F(i-1,j-1) + Mat[i,j]
F(i,j-1) + Gep X-
XX
-X
1…i1…j-1
1…i-11…j-1
1…i-11…j
+
+
+
![Page 13: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/13.jpg)
Cédric Notredame (19/04/23)
Arranging Everything in a Table
- F A
-
F
A
S
T
T
1…I-11…J-1
1…I1…J-1
1…I-11…J
1…I 1…J
![Page 14: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/14.jpg)
Cédric Notredame (19/04/23)
Taking Care of the Limits
In a Dynamic Programming strategy, the most delicate part is to take care of the limits:
-what happens when you start-what happens when you finish
The DP strategy relies on the idea that ALL the cells in your table have the same environment…
This is NOT true of ALL the cells!!!!
![Page 15: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/15.jpg)
Cédric Notredame (19/04/23)
Taking Care of the Limits
- F A-FAS
T
T -4Match=2MisMatch=-1Gap=-1
-3
FAT---
-1
F-
-2
FA--
-1F-
-2FA--
-3FAS---
0
![Page 16: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/16.jpg)
Cédric Notredame (19/04/23)
Filing Up The Matrix
![Page 17: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/17.jpg)
Cédric Notredame (19/04/23)
- F A
-
F
A
S -3
-2
-1
-1 -2
T
-3
T -4
-2+2
-2 +2-3
-2
+1 +1-4
-3
0 0+1
-2
-3 +10
+4
0 +4-1
0
+3 +30
-3
-4 0+3
0
-1 +3+2
+3
+2 +3-1
-4
-5 -1+2
-1
-2 +2+2
+5
+1 +5
0
![Page 18: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/18.jpg)
Cédric Notredame (19/04/23)
Delivering the alignment: Trace-back
Score of 1…3 Vs 1…4
Optimal Aln Score
TT
S-
AAFF
![Page 19: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/19.jpg)
Cédric Notredame (19/04/23)
Trace-back: possible implementation
while (!($i==0 && $j==0)) { if ($tb[$i][$j]==$sub) #SUBSTITUTION
{ $alnI[$aln_len]=$seqI[--$i]; $alnJ[$aln_len]=$seqJ[--$j]; }
elsif ($tb[$i][$j]==$del) #DELETION{ $alnI[$aln_len]='-'; $alnJ[$aln_len]=$seqJ[--$j]; }
elsif ($tb[$i][$j]==$ins) #INSERTION{ $alnI[$aln_len]=$seqI[0][--$i]; $alnJ[$aln_len]='-'; }
$aln_len++; }
![Page 20: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/20.jpg)
Cédric Notredame (19/04/23)
Local Alignments Without Affine Gap
penalties
Smith and Waterman
![Page 21: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/21.jpg)
Cédric Notredame (19/04/23)
Getting rid of the pieces of Junk between the
interesting bits
Smith and Waterman
![Page 22: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/22.jpg)
Cédric Notredame (19/04/23)
![Page 23: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/23.jpg)
Cédric Notredame (19/04/23)
The Smith and Waterman Algorithm
F(i,j)= best
F(i-1,j) + Gep
F(i-1,j-1) + Mat[i,j]
F(i,j-1) + Gep X-
XX
-X
1…i1…j-1
1…i-11…j-1
1…i-11…j
+
+
+
0
![Page 24: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/24.jpg)
Cédric Notredame (19/04/23)
The Smith and Waterman Algorithm
0
Ignore The rest of the Matrix
Terminate a local Aln
![Page 25: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/25.jpg)
Cédric Notredame (19/04/23)
Filing Up a SW Matrix
0
![Page 26: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/26.jpg)
Cédric Notredame (19/04/23)
Filling up a SW matrix: borders
* - A N I C E C A T - 0 0 0 0 0 0 0 0 0C 0A 0T 0A 0N 0 D 0O 0G 0
Easy:Local alignments
NEVER start/end with a gap…
![Page 27: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/27.jpg)
Cédric Notredame (19/04/23)
Filling up a SW matrix
* - A N I C E C A T - 0 0 0 0 0 0 0 0 0C 0 0 0 0 2 0 2 0 0 A 0 2 0 0 0 0 0 4 0T 0 0 0 0 0 0 0 2 6A 0 2 0 0 0 0 0 0 4N 0 0 4 2 0 0 0 0 2D 0 0 2 2 0 0 0 0 0O 0 0 0 0 0 0 0 0 0G 0 0 0 0 0 0 0 0 0
Best Local score
Beginning of the trace-back
![Page 28: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/28.jpg)
Cédric Notredame (19/04/23)
for ($i=1; $i<=$len0; $i++) { for ($j=1; $j<=$len1; $j++)
{ if ($res0[0][$i-1] eq $res1[0][$j-1]){$s=2;}
else {$s=-1;} $sub=$mat[$i-1][$j-1]+$s; $del=$mat[$i ][$j-1]+$gep; $ins=$mat[$i-1][$j ]+$gep; if ($sub>$del && $sub>$ins && $sub>0)
{$smat[$i][$j]=$sub;$tb[$i][$j]=$subcode;} elsif($del>$ins && $del>0 )
{$smat[$i][$j]=$del;$tb[$i][$j]=$delcode;} elsif( $ins>0 )
{$smat[$i][$j]=$ins;$tb[$i][$j]=$inscode;} else {$smat[$i][$j]=$zero;$tb[$i][$j]=$stopcode;}
if ($smat[$i][$j]> $best_score) { $best_score=$smat[$i][$j]; $best_i=$i; $best_j=$j; }
} }
PrepareTraceback
Turning
NW
into
SW
![Page 29: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/29.jpg)
Cédric Notredame (19/04/23)
A few things to remember
SW only works if the substitution matrix has been normalized to give a Negative score to a random alignment.
Chance should not pay when it comes to local alignments !
![Page 30: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/30.jpg)
Cédric Notredame (19/04/23)
More than One match…
-SW delivers only the best scoring Match
-If you need more than one match:-SIM (Huang and Millers)Or-Waterman and Eggert (Durbin, p91)
![Page 31: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/31.jpg)
Cédric Notredame (19/04/23)
Waterman and Eggert
-Iterative algorithm:
-1-identify the best match-2-redo SW with used pairs forbidden
-Delivers a collection of non-overlapping local alignments
-Avoid trivial variations of the optimal.
-3-finish when the last interesting local extracted
![Page 32: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/32.jpg)
Cédric Notredame (19/04/23)
Adding Affine Gap Penalties
The Gotoh Algorithm
![Page 33: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/33.jpg)
Cédric Notredame (19/04/23)
Forcing a bit of Biology into your alignment
The Gotoh Formulation
![Page 34: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/34.jpg)
Cédric Notredame (19/04/23)
Why Affine gap Penalties are Biologically better
Cost
L
Afine Gap Penalty
GOP
GEP
GOP GOP
GOP
Parsimony: Evolution takes the simplest path
(So We Think…)
Cost=gop+L*gep
Or Cost=gop+(L-1)*gep
![Page 35: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/35.jpg)
Cédric Notredame (19/04/23)
But Harder To compute…
More Than 3 Ways to extend an Alignment
X-XXXXXX
X-
XX
-X
Deletion
Alignment
Insertion
??+
Opening
Extension
Opening
Extension
![Page 36: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/36.jpg)
Cédric Notredame (19/04/23)
More Questions Need to be asked
For instance, what is the cost of an insertion ?
1…I-1 ??X1…J-1 ??X
1…I ??- 1…J ??X
1…I ??-1…J-1 ??X
GOP GEP
![Page 37: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/37.jpg)
Cédric Notredame (19/04/23)
Solution:Maintain 3 Tables
Ix: Table that contains the score of every optimal alignment 1…i vs 1…j that
finishes with an Insertion in sequence X.
Iy: Table that contains the score of every optimal alignment 1…I vs 1…J that
finishes with an Insertion in sequence Y.
M: Table that contains the score of every optimal alignment 1…I vs 1…J that
finishes with an alignment between sequence X and Y
![Page 38: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/38.jpg)
Cédric Notredame (19/04/23)
The Algorithm
M(i,j)= best M(i-1,j-1) + Mat(i,j) X
X1…i-11…j-1 +Ix(i-1,j-1) + Mat(i,j)
Iy(i-1,j-1) + Mat(i,j)
X-
1…i-1 X1…j X
+
Ix(i,j)= best M(i-1,j) + gop
Ix(i-1,j) + gepX-
1…i-1 X1…j -
+
-X
1…i X1…j-1 X
+
Iy(i,j)= best M(i,j-1) + gop
Iy(i,j-1) + gep-X
1…i -1…j-1 X
+
![Page 39: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/39.jpg)
Cédric Notredame (19/04/23)
FAQ: Why isn’t One table Enough ?
In each Cell we could remember if the optimal sub-alignment finishes with a Match or a Gap?
if best (i,j)= Ix[i,j]
We have no guaranty that Ix[i,j] is a part of A[L,M]the complete optimal alignment.
The optimal alignment may go through Iy[i,j] instead
even if Ix[i,j]>Iy[i,j]
IT WOULD BE GREEDY !!!!!!
![Page 40: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/40.jpg)
Cédric Notredame (19/04/23)
Trace-back?
MIx Iy
Start From BEST M(i,j)Ix(i,j)Iy(i,j)
![Page 41: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/41.jpg)
Cédric Notredame (19/04/23)
Trace-back?
M Iy
Navigate from one table to the next, knowing that a gap always finishes with an aligned column…
Ix
![Page 42: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/42.jpg)
Cédric Notredame (19/04/23)
Going Further ?
With the affine gap penalties, we have increased the number of possibilities when building our alignment.
CS talk of states and represent this as a Finite State Automaton (FSA are HMM cousins)
![Page 43: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/43.jpg)
Cédric Notredame (19/04/23)
Going Further ?
![Page 44: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/44.jpg)
Cédric Notredame (19/04/23)
Going Further ?
In Theory, there is no Limit on the number of states one may consider when doing such a computation.
![Page 45: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/45.jpg)
Cédric Notredame (19/04/23)
![Page 46: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/46.jpg)
Cédric Notredame (19/04/23)
Going Further ?
Imagine a pairwise alignment algorithm where the gap penalty depends on the length of the gap.
Can you simplify it realistically so that it can be efficiently implemented?
![Page 47: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/47.jpg)
Cédric Notredame (19/04/23)
Ly
Lx
![Page 48: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/48.jpg)
Cédric Notredame (19/04/23)
A divide and Conquer Strategy
The Myers and Miller Strategy
![Page 49: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/49.jpg)
Cédric Notredame (19/04/23)
Remember Not To Run Out of Memory
The Myers and Miller Strategy
![Page 50: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/50.jpg)
Cédric Notredame (19/04/23)
A Score in Linear Space
You never Need More Than The Previous Row To Compute the optimal score
![Page 51: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/51.jpg)
Cédric Notredame (19/04/23)
A Score in Linear Space
For I For J
R2[i][j]=best
For J, R1[j]=R2[j]
R1R2 R2[j-1],
+gep
R1[j-1]+mat
R1[j]+gep
![Page 52: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/52.jpg)
Cédric Notredame (19/04/23)
A Score in Linear Space
![Page 53: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/53.jpg)
Cédric Notredame (19/04/23)
A Score in Linear Space
You never Need More Than The Previous Row To Compute the optimal score
You only need the matrix for the Trace-Back,
Or do you ????
![Page 54: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/54.jpg)
Cédric Notredame (19/04/23)
An Alignment in Linear Space
Forward Algorithm
F(i,j)=Optimal score of0…i Vs 0…j
Backward algorithm
B(i,j)=Optimal score ofM…i Vs N…j
B(i,j)+F(i,j)=Optimal score of the alignment that passes through pair i,j
![Page 55: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/55.jpg)
Cédric Notredame (19/04/23)
An Alignment in Linear Space
Backward algorithm
Forward Algorithm
Optimal B(i,j)+F(i,j)
Backward algorithm
Forward Algorithm
![Page 56: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/56.jpg)
Cédric Notredame (19/04/23)
![Page 57: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/57.jpg)
Cédric Notredame (19/04/23)
An Alignment in Linear Space
Backward algorithm
Forward Algorithm
Recursive divide and conquer strategy: Myers and Miller (Durbin p35)
![Page 58: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/58.jpg)
Cédric Notredame (19/04/23)
An Alignment in Linear Space
![Page 59: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/59.jpg)
Cédric Notredame (19/04/23)
A Forward-only Strategy(Durbin, p35)
Forward Algorithm
-Keep Row M in memory
-Keep track of which Cell in RowM lead to the optimal score
-Divide on this cell
M
![Page 60: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/60.jpg)
Cédric Notredame (19/04/23)
M
M
![Page 61: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/61.jpg)
Cédric Notredame (19/04/23)
An interesting application: finding sub-optimal alignments
Backward algorithm
Forward Algorithm
Backward algorithm
Forward Algorithm
Sum over the Forw/Bward and identify the score of the best aln going through cell i,j
![Page 62: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/62.jpg)
Cédric Notredame (19/04/23)
Application:Non-local models
Double Dynamic Programming
![Page 63: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/63.jpg)
Cédric Notredame (19/04/23)
Outline
The main limitation of DP: Context independent measure
![Page 64: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/64.jpg)
Cédric Notredame (19/04/23)
11
9
1213
8
1314
5
Double Dynamic Programming
High Level Smith and WatermanDynamic Programming
Score=MaxS(i-1, j-1)+RMSd scoreS(i, j-1)+gpS(i, j-1)+gp{
Rigid Body Superposition where i and j are forced together
RMSd Score
![Page 65: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/65.jpg)
Cédric Notredame (19/04/23)
Double Dynamic Programming
![Page 66: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/66.jpg)
Cédric Notredame (19/04/23)
Application:Repeats
The Durbin Algorithm
![Page 67: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/67.jpg)
Cédric Notredame (19/04/23)
![Page 68: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/68.jpg)
Cédric Notredame (19/04/23)
In The End:Wraping it Up
![Page 69: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/69.jpg)
Cédric Notredame (19/04/23)
Dynamic Programming
Needleman and Wunsch: Delivers the best scoring global alignment
Smith and Waterman: NW with an extra state 0
Affine Gap Penalties: Making DP more realistic
![Page 70: Using Dynamic Programming To Align Sequences](https://reader035.vdocuments.mx/reader035/viewer/2022062719/56813096550346895d967481/html5/thumbnails/70.jpg)
Cédric Notredame (19/04/23)
Dynamic Programming
Linear space: Using Divide and Conquer Strategies Not to run out of memory
Double Dynamic Programming, repeat extraction: DP can easily be adapted to a special need