1. Multiple Sequence Composition Alignment
Name: Yip Chi Kin
Date:

2. Studied Papers [B03] Composition Alignment
[S98] Divide-and-conquer Alignment
[M99] DIALIGN Algorithm
[SMS03] DCA + Segment-based

3. Main Aspects ․Dynamic Programming ․Composition Alignment
․Meta-code MSA
․Simultaneous MSA
Pairwise Library (Global & Local)
Consistency & Ungapped
Divide-and-conquer
Segment-based (Optimal scores)

4. Dynamic Programming • -d -d Dot Matrix Edit Graph DP Matrix C T G A
matches
deletions
insertions
DP Matrix
C T G A C T G A •
s(ai,bi) -d -d

5. Needleman-Wunsch Algorithm
Global Alignment
Needleman-Wunsch Algorithm
Scoring
- C T T C T - G C A T -2 -3 -4 -7
-10 -1 -5 -8 -6 -9
GA Results
G C A T C -
- C T T C T

6. Smith-Waterman Algorithm
Local Alignment 1 3 5 4 2 6
- T T T A C A G G C A G - G A C T
Smith-Waterman Algorithm
Scoring
GA Results
- G A A C – G G T - -
T T T A C A G G C A G

7. MSA Methods ․Consistency-based ․Exact method ․Progressive method
․Iterative method
․Stochastic method
․Hidden Markov method

8. Consistency-based method
MSA Concepts
Consistency-based method
PSAs C - G T C - T G A C G - T A
Trace formulation C T G T G A C T A C G
Latter formulation C T G T G A C T G A C

9. MSA Results Results of MSA Aligned regions C T G A G T C - A T C G A
Unrealized
Realized
Consistent

10. Divide-and-conquer Prefix Suffix Divide Divide Divide Align optimally
S1C1
S2C2
S3C3
C1S1
C2S2
C3S3
Divide
Divide
Align optimally
Concatenate

11. DP Distance Wopt (prefix) Wopt (suffix)
Sequence: GTTCATGCCAGGTGTAAATC
Suffix
Prefix
Wopt (prefix)
- C T A T A C - G T A C
C T A T A C - G T A C -
Wopt (suffix)
CS1,S2[C1,C2] = Wopt (prefix) + Wopt (suffix) – Wopt (total)

12. Additional-cost CS1,S2[1,1] = 0 CS1,S2[2,2] = 0 CS1,S2[3,3] = 0
C T A T A C G T A C
Cost of Diagonal
CS1,S2[1,1] = 0
CS1,S2[2,2] = 0
CS1,S2[3,3] = 0
CS1,S2[4,4] = 0
CS1,S2[5,4] = 0
CS1,S2[6,5] = 0
CS1,S2[2,2] = – 3 = 0
= Wopt [CT,GT] + Wopt [ATAC,ATAC] – Wopt [CTATC,GTATAC]
CS1,S2[4,3] = – 3 = 1
= Wopt [CTAT,GTA] + Wopt [AC,TAC] – Wopt [CTATC,GTATAC]

13. Space & Time
‘Chain’ of boxes along Diagonal in order to reduce searching time
Full sequence searching

14. DIALIGN Non-Consistent (Simultaneous) Non-Consistent (Cross over) I AF E D C G S P W T Y I A V L F E D C G S P W T Y
Consistent diagonals
GA Results I A V L F E D C G S P W T Y y I A - V L F E d c G s p w T

15. Diagonals D1 , D4 and D5 Score = 1.9 + 2.6 + 0.2 = 4.7
Weighting
Diagonal Weights
where SD is sum of similarity values of same diagonal lD
lD is length of diagonal D
w(D) = – log P(lD, SD)
Overlap weighting
Y I A V L F A Y D D
L A C V I F G S
S W D D V M F Y A E
w(D1) = 1.9
w(D3) = 1.5
w(D2) = 1.7
w(D4) = 2.6
w(D5) = 0.2
Diagonals D1 , D4 and D5 Score = = 4.7
Diagonals D1 , D2 , D3 and D5
Score = = 5.3
Y I A V L F A Y D D
Y I A V L F A Y D D
L A C V I F G S
L A C V I F G S
S W D D V M F Y A E
S W D D V M F Y A E

16. Transitivity frontier [1,9]
Consistency check
Overlap weights S1 S2 S3
Fragments checking f2 f1 f3 S1 S2 S3
Transitivity frontier [1,9]

17. Greedy Approach Tandem duplications Greedy Strategy
Consistency conflicts
M1 (2)
M1 (1) M2 M3
M1 (2)
M1 (1) M2 M3 S1 S2 S3 S1 S2 S3

18. Composition Alignment
Composition matches
Single
character
match A C G T -
CM of Prefix Length
Sequence #1 1 + – 2 -1 -2 -3
Sequence #2
Matching
Prefix length

19. Match Length 111010001 001101110 Replaced by 7 7 1110100 01 0011011 10
Composition
Matching 3 2 2 2
Prefix length 1 4 9 15 –1 2 2 –2
Replaced by 2 –3

20. Composition Matching CM of Prefix Length (Total=9) 1 1 1 1 1 1 CM = 2
Sequence #1 1 1 1 1 1 1
CM = 2
Sequence #2 1 1 1 1 1 1 1 1 1
CM = -1
Sequence #1 1 1 1 1 1 1
CM = 1
Sequence #2 1 1 1 1 1 1 1 1 1
CM of Prefix Length (Total=9)
Sequence #1 1 1 1 1 1 1
CM = 0
Sequence #2 1 1 1 1 1 1 1 1 1

21. Meta-Code Code about code Mismatch code Input code Code Reservoir
Code for
Testing
Mismatch code
Original Code
Control Rule
Meta-Code

22. Reservoir Codes Code ‘A’ in S1 Code ‘G’ Store code in Reservoir S1
Code ‘CT’
Store code in Reservoir S2
Code from S1
Code from S2
Store code in Reservoir S1
If both Codes founded from Reservoir S1 and Reservoir S2 delete this two codes
Reservoir Code
(e.g. AGRCT)
Code ‘G’
Code ‘C’
Code ‘AG’
Code ‘A’ in S1
Code ‘T’ in S2

23. Meta-Code Rule If reservoir code = r, then stop the looping
Looping for creating
meta-code
If CM length is valid,
reservoir code = r,
Position = p.
Value of r
Values of
r and p
Copy the codes from
S1 and S2, p = p –1,
output meta-code.
Meta-code (e.g. AMT)
Codes from S1 and S2

24. Composition Matching of S1 and S2 in prefix length
CM (Lengths & Codes)
Composition Matching of S1 and S2 in prefix length
S1:
S2:
Meta
Code
Length T A C G 1 2 R
ART
AGRCT
GRC
GARTC
AGRTT
AGRCC
ARC
Reservoir codes in S1 A G
Reservoir codes in S2 T C

25. CM of Metacode 2 4 Invalid length Composition Matching AGRTT GARTC
ARC 2 1
Prefix length 2 6 10 12 2 4 –1
ART
ART
AGRCT
GARTC

26. Composition MSA Composition matching Meta-code MSA | T C G A S1 T A CT C G A
Meta-code MSA S1 T A C G
TMG
GMT
CMT
GMC
AMG
TMA S2
New S2

27. Fixed Segment A = Currency / Cards B = Stock / Structured P.
C = Unit Trusts / Bonds
D = Insurance / Finance
Code catalogue
E = Mortgages / Loans
․Semi-global alignment
․Least overlap problem
․Simple segmentation
․Composition alignment
․Weekly behaviour
Segment Length LS = 5
Week #1
Week #2
Branch bank #1 …
Branch bank #2
Branch bank #3 A C B E D
Time Granularities
1t1
1t2
1t3
1t4
1t5
2t1
2t2
2t3
2t4
2t5
3t1
3t2

28. Family Classifications
Meta-Code Branch bank #1
Branch bank #2
Meta-Code Branch bank #3 C B A D
PSA
Branch bank #1
Branch bank #2
Branch bank #3 C B A D
Composition
alignment
Family
Group
Fixed-Segment Composition MSA
Family
Group

29. Meta-Code Composition MSA
Further Problems
Meta-Code Composition MSA
․Fixed-segment length
․Prior sequence choice
․Speed-up PSAs
․Nos. of Segments/Codes

30. Conclusions ․Fixed-segment Composition ․Meta-code Approach
(Least Overlap Problems)
․Meta-code Approach
(Easier Transform Applications)
․Widespread use of MSA
(Simultaneous Multiple Sequences)