1. Introduction to bioinformatics 2007E N T R F O I G A V B M S U
Introduction to bioinformatics 2007
Lecture 7
Pair-wise Sequence Alignment (III)

2. What can sequence alignment tell us about structure
HSSP Sander & Schneider, 1991
≥30% sequence identity

3. Global dynamic programming PAM250, Gap =6 (linear)S P E A R 2 1 H -1 -2 K 3 4 S P E A R -6
-12
-18
-24
-30
-36 2 -4
-10
-16
-22
-28 H -3 -9
-14
-20 -1 -7
-13 K 1
-15 -5 -2 6
These values are copied from the PAM250 matrix (see earlier slide)
Start in left upper cell before either sequence (circled in red). Path will end in lower right cell (circled in blue)
SPEARE
S-HAKE
The easy algorithm is only for linear gap penalties
Higgs & Attwood, p. 124 – Note: There are errors in the matrices!!

4. DP is a two-step process
Forward step: calculate scores
Trace back: start at highest score and reconstruct the path leading to the highest score
These two steps lead to the highest scoring alignment (the optimal alignment)
This is guaranteed when you use DP!

5. Time and memory complexity of DP
The time complexity is O(n2): if you would align two sequences of n residues, you would need to perform n2 algorithmic steps (square search matrix has n2 cells that need to be filled)
The memory (space) complexity is also O(n2): if you would align two sequences of n residues, you would need a square search matrix of n by n containing n2 cells

6. Global dynamic programming
j-1 j
i-1 i
H(i-1,j-1) + S(i,j)
H(i-1,j) - g
H(i,j-1) - g
diagonal
vertical
horizontal
H(i,j) = Max
Problem with simple DP approach:
Can only do linear gap penalties
Not suitable for affine and concave penalties

7. Global dynamic programming using affine penalties
j-2 j-1 j
Looking back from cell (i, j) we can adapt the algorithm for affine gap penalties by looking back to four more cells (magenta)
i-2
i-1 i
If you came from here, gap was already open, so apply gap-extension penalty
If you came from here, gap was opened so apply gap-open penalty

8. Global dynamic programming all three types of gap penalties
j-1
i-1
Gap opening penalty
Max{S0<x<i-1, j-1 - Pi - (i-x-1)Px}
Si-1,j-1
Max{Si-1, 0<y<j-1 - Pi - (j-y-1)Px}
Si,j = si,j + Max
Gap extension penalty

9. Global dynamic programming Gapo=10, Gape=2W V T A L K 8 3 11 9 12 1 6 4 25 2 5 10 14 7 13 D W V T A L K
-12
-14
-16
-18
-20
-22
-24 8 -9 -6 -5
-11 9 2 3 -3
-34
-13 25 11 5 4
-21
-10 -4 37 21 19 15 -2 23 46 31 26 1 17 33 53 39 50 14
-29 -1 27
These values are copied from the PAM250 matrix (see earlier slide), after being made non-negative by adding 8 to each PAM250 matrix cell (-8 is the lowest number in the PAM250 matrix)
The extra bottom row and rightmost column give the final global alignment scores

10. Easy DP recipe for using affine gap penalties
j-1
i-1
M[i,j] is optimal alignment (highest scoring alignment until [i,j])
Check
preceding row until j-2: apply appropriate gap penalties
preceding row until i-2: apply appropriate gap penalties
and cell[i-1, j-1]: apply score for cell[i-1, j-1]

11. DP is a two-step process
Forward step: calculate scores
Trace back: start at highest score and reconstruct the path leading to the highest score
These two steps lead to the highest scoring alignment (the optimal alignment)
This is guaranteed when you use DP!

12. Global dynamic programming

13. There are three kinds of alignments
Global alignment
Semi-global alignment
Local alignment

14. Semi-global pairwise alignment
Global alignment: all gaps are penalised
Semi-global alignment: N- and C-terminal gaps (end-gaps) are not penalised
MSTGAVLIY--TS-----
---GGILLFHRTSGTSNS
End-gaps
End-gaps

15. Semi-global dynamic programming PAM250, Gap =6 (linear)1 H -1 -2 K 3 4 S P E A R 2 1 H -1 3 4 -2 K 7 11
These values are copied from the PAM250 matrix (see earlier slide)
Start in left upper cell before either sequence (circled in red). Path will end in cell anywhere in the bottom row or rightmost columns with the highest score
SPEARE
-SHAKE
The easy algorithm is only for linear gap penalties
Higgs & Attwood, p. 124 – Note: There are errors in the matrices!!

16. Semi-global dynamic programming - two examples with different gap penalties -
These values are copied from the PAM250 matrix (see earlier slide), after being made non-negative by adding 8 to each PAM250 matrix cell (-8 is the lowest number in the PAM250 matrix)
Global score would have been 65 –10 – 1*2 –10 – 2*2 (because of the two end gaps)

17. Semi-global pairwise alignment
Applications of semi-global:
– Finding a gene in genome
– Placing marker onto a chromosome
– Generally: if one sequence is much longer than the other
Danger: if gap penalties high -- really bad alignments for divergent sequences

18. Local dynamic programming (Smith & Waterman, 1981)
LCFVMLAGSTVIVGTR E D A S T I L C G
Negative
numbers
Amino Acid
Exchange Matrix
Search matrix
Gap penalties
(open, extension)
AGSTVIVG
A-STILCG

19. Local dynamic programming (Smith and Waterman, 1981) basic algorithm
j-1 j
i-1 i
H(i-1,j-1) + S(i,j)
H(i-1,j) - g
H(i,j-1) - g
diagonal
vertical
horizontal
H(i,j) = Max

20. Local dynamic programming Match/mismatch = 1/-1, Gap =21 2 3
Fill the matrix (forward pass), then do trace back from highest cell anywhere in the matrix till you reach 0 or the beginning of a sequence

21. Local dynamic programming Match/mismatch = 1/-1, Gap =21 2 3
GAC
Fill the matrix (forward pass), then do trace back from highest cell anywhere in the matrix till you reach 0 or the beginning of a sequence

22. Local dynamic programming (Smith & Waterman, 1981)
j-1
This is the general DP algorithm, which is suitable for linear, affine and concave penalties, although for the examples here affine penalties are used
i-1
Gap opening penalty
Si,j + Max{S0<x<i-1,j-1 - Pi - (i-x-1)Px}
Si,j + Si-1,j-1
Si,j + Max {Si-1,0<y<j-1 - Pi - (j-y-1)Px}
Si,j = Max
Gap extension penalty

23. Local dynamic programming

24. Global and local alignment

25. Global or Local Pairwise alignment

26. Globin fold  protein myoglobin PDB: 1MBN
Alpha-helices are labelled ‘A’ (blue) to ‘H’ (red). The D helix can be missing in some globins:
What happens with the alignment if D-helix containing globin sequences are aligned with ‘D-less’ ones?

27.  sandwich  protein immunoglobulin PDB: 7FAB
Immunoglobulinstructures have variable regions where numbers of amino acids can vary substantially

28. TIM barrel  /  protein Triose phosphate IsoMerase PDB: 1TIM
The evolutionary history of this protein family has been the subject of rigorous debate. Arguments have been made in favor of both convergent and divergent evolution. Because of the general lack of sequence homology, the ancestry of this molecule is still a mystery.

29. Pyruvate kinase b barrel regulatory domain
Phosphotransferase
b barrel regulatory domain
a/b barrel catalytic substrate binding domain
a/b nucleotide binding domain

30. What does all this mean for alignments?
Alignments need to be able to skip secondary structural elements to complete domains (i.e. putting gaps opposite these motifs in the shorter sequence).
Depending on gap penalties chosen, the algorithm might have difficulty with making such long gaps (for example when using high affine gap penalties), resulting in incorrect alignment.
Alignments are only meaningful for homologous sequences (with a common ancestor)

31. There are three kinds of pairwise alignments
Global alignment – align all residues in both sequences; all gaps are penalised
Semi-global alignment – align all residues in both sequences; end gaps are not penalised (zero end gap penalties)
Local alignment – align one part of each sequence; end gaps are not applicable

32. Penalty = Pi + gap_length*Pe
Easy global DP recipe for using affine gap penalties (after Gotoh)
j-1
Penalty = Pi + gap_length*Pe
Max{S0<x<i-1, j-1 - Pi - (i-x-1)Px}
Si-1,j-1
Max{Si-1, 0<y<j-1 - Pi - (j-y-1)Px}
Si,j = si,j + Max
i-1
M[i,j] is optimal alignment (highest scoring alignment until [i, j])
At each cell [i, j] in search matrix, check Max coming from:
any cell in preceding row until j-2: add score for cell[i, j] minus appropriate gap penalties;
any cell in preceding column until i-2: add score for cell[i, j] minus appropriate gap penalties;
or cell[i-1, j-1]: add score for cell[i, j]
Select highest scoring cell in bottom row and rightmost column and do trace-back

33. Let’s do an example: global alignment Gotoh’s DP algorithm with affine gap penalties (PAM250, Pi=10, Pe=2) D W V T A L K -5 3 1 4 -7 -2 -4 17 -6 -3 2 6 -1 5 D W V T A L K
-12
-14
-16
-18
-20
-22
-24
-17
-13
-19 -8 -7
-42
-21 9 13 -3 -1 14
-41
PAM250
Cell (D2, T4) can alternatively come from two cells (same score): ‘high-road’ or ‘low-road’
Row and column ‘0’ are filled with 0, -12, -14, -16, … if global alignment is used (for N-terminal end-gaps); also extra row and column at the end to calculate the score including C-terminal end-gap penalties. Note that only ‘non-diagonal’ arrows are indicated for clarity (no arrow means that you go back to earlier diagonal cell).

34. Let’s do another example: semi-global alignment Gotoh’s DP algorithm with affine gap penalties (PAM250, Pi=10, Pe=2) D W V T A L K -5 3 1 4 -7 -2 -4 17 -6 -3 2 6 -1 5 D W V T A L K -5 3 4 -7 21
-13 -2 25 9
PAM250
Starting row and column ‘0’, and extra column at right or extra row at bottom is not necessary when using semi global alignment (zero end-gaps). Rest works as under global alignment.

35. Penalty = Pi + gap_length*Pe
Easy local DP recipe for using affine gap penalties (after Gotoh)
j-1
Penalty = Pi + gap_length*Pe
Si,j + Max{S0<x<i-1,j-1 - Pi - (i-x-1)Px}
Si,j + Si-1,j-1
Si,j + Max {Si-1,0<y<j-1 - Pi - (j-y-1)Px}
Si,j = Max
i-1
M[i,j] is optimal alignment (highest scoring alignment until [i, j])
At each cell [i, j] in search matrix, check Max coming from:
any cell in preceding row until j-2: add score for cell[i, j] minus appropriate gap penalties;
any cell in preceding column until i-2: add score for cell[i, j] minus appropriate gap penalties;
or cell[i-1, j-1]: add score for cell[i, j]
Select highest scoring cell anywhere in matrix and do trace-back until zero-valued cell or start of sequence(s)

36. Let’s do yet another example: local alignment Gotoh’s DP algorithm with affine gap penalties (PAM250, Pi=10, Pe=2) D W V T A L K -5 3 1 4 -7 -2 -4 17 -6 -3 2 6 -1 5 D W V T A L K 3 4 21 25 9 11
PAM250
Extra start/end columns/rows not necessary (no end-gaps). Each negative scoring cell is set to zero. Highest scoring cell may be found anywhere in search matrix after calculating it. Trace highest scoring cell back to first cell with zero value (or the beginning of one or both sequences)

37. For your first exam D1: Make sure you understand and can carry out 1
For your first exam D1: Make sure you understand and can carry out 1. the ‘simple’ DP algorithm for global, semi-global and local alignment (using linear gap penalties but make sure you know the extension of the basic algorithm for affine gap penalties) and 2. The general DP algorithm for global, semi-global and local alignment (using linear, affine and concave gap penalties)!

38. Dot plots
Way of representing (visualising) sequence similarity without doing dynamic programming (DP)
Make same matrix, but locally represent sequence similarity by averaging using a window

39. Comparing two sequences
We want to be able to choose the best alignment between two sequences.
A simple method of visualising similarities between two sequences is to use dot plots. The first sequence to be compared is assigned to the horizontal axis and the second is assigned to the vertical axis.

40. Dot plots can be filtered by window approaches (to calculate running averages) and applying a threshold
They can identify insertions, deletions, inversions

41. Introduction to Bioinformatics
Deriving Amino Acid Substitution matrices (I)

42. Sequence Analysis
Finding relationships between genes and gene products of different species, including those at large evolutionary distances

43. Archaea
Domain Archaea is mostly composed of cells that live in extreme environments. While they are able to live elsewhere, they are usually not found there because outside of extreme environments they are competitively excluded by other organisms. Species of the domain Archaea are not inhibited by antibiotics, lack peptidoglycan in their cell wall (unlike bacteria, which have this sugar/polypeptide compound), and can have branched carbon chains in their membrane lipids of the phospholipid bilayer.
It is believed that Archaea are very similar to prokaryotes (e.g. bacteria) that inhabited the earth billions of years ago. It is also believed that eukaryotes evolved from Archaea, because they share many mRNA sequences, have similar RNA polymerases, and have introns. Therefore, it is believed that the domains Archaea and Bacteria branched from each other very early in history, and membrane infolding* produced eukaryotic cells in the archaean branch approximately 1.7 billion years ago.
There are three main groups of Archaea: extreme halophiles (salt), methanogens (methane producing anaerobes), and hyperthermophiles (e.g. living at temperatures >100º C!).
*Membrane infolding is believed to have led to the nucleus of eukaryotic cells, which is a membrane-enveloped cell organelle that holds the cellular DNA. Prokaryotic cells are more primitive and do not have a nucleus.

44. The 20 common
amino acids

45. Example of sequence database entry for Genbank
LOCUS DRODPPC 4001 bp INV 15-MAR-1990
DEFINITION D.melanogaster decapentaplegic gene complex (DPP-C), complete cds.
ACCESSION M30116
KEYWORDS .
SOURCE D.melanogaster, cDNA to mRNA.
ORGANISM Drosophila melanogaster
Eurkaryote; mitochondrial eukaryotes; Metazoa; Arthropoda;
Tracheata; Insecta; Pterygota; Diptera; Brachycera; Muscomorpha;
Ephydroidea; Drosophilidae; Drosophilia.
REFERENCE 1 (bases 1 to 4001)
AUTHORS Padgett, R.W., St Johnston, R.D. and Gelbart, W.M.
TITLE A transcript from a Drosophila pattern gene predicts a protein
homologous to the transforming growth factor-beta family
JOURNAL Nature 325, (1987)
MEDLINE
COMMENT The initiation codon could be at either or
FEATURES Location/Qualifiers
source
/organism=“Drosophila melanogaster”
/db_xref=“taxon:7227”
mRNA <
/gene=“dpp”
/note=“decapentaplegic protein mRNA”
/db_xref=“FlyBase:FBgn ”
gene
/note=“decapentaplegic”
/allele=“”
CDS
/note=“decapentaplegic protein (1188 could be 1587)”
/codon_start=1
/db_xref=“PID:g157292”
/translation=“MRAWLLLLAVLATFQTIVRVASTEDISQRFIAAIAPVAAHIPLA
SASGSGSGRSGSRSVGASTSTALAKAFNPFSEPASFSDSDKSHRSKTNKKPSKSDANR
……………………
LGYDAYYCHGKCPFPLADHFNSTNAVVQTLVNNMNPGKVPKACCVPTQLDSVAMLYL
NDQSTBVVLKNYQEMTBBGCGCR”
BASE COUNT 1170 a 1078 c 956 g 797 t
ORIGIN
1 gtcgttcaac agcgctgatc gagtttaaat ctataccgaa atgagcggcg gaaagtgagc
61 cacttggcgt gaacccaaag ctttcgagga aaattctcgg acccccatat acaaatatcg
121 gaaaaagtat cgaacagttt cgcgacgcga agcgttaaga tcgcccaaag atctccgtgc
181 ggaaacaaag aaattgaggc actattaaga gattgttgtt gtgcgcgagt gtgtgtcttc
241 agctgggtgt gtggaatgtc aactgacggg ttgtaaaggg aaaccctgaa atccgaacgg
301 ccagccaaag caaataaagc tgtgaatacg aattaagtac aacaaacagt tactgaaaca
361 gatacagatt cggattcgaa tagagaaaca gatactggag atgcccccag aaacaattca
421 attgcaaata tagtgcgttg cgcgagtgcc agtggaaaaa tatgtggatt acctgcgaac
481 cgtccgccca aggagccgcc gggtgacagg tgtatccccc aggataccaa cccgagccca
541 gaccgagatc cacatccaga tcccgaccgc agggtgccag tgtgtcatgt gccgcggcat
601 accgaccgca gccacatcta ccgaccaggt gcgcctcgaa tgcggcaaca caattttcaa
………………………….
3841 aactgtataa acaaaacgta tgccctataa atatatgaat aactatctac atcgttatgc
3901 gttctaagct aagctcgaat aaatccgtac acgttaatta atctagaatc gtaagaccta
3961 acgcgtaagc tcagcatgtt ggataaatta atagaaacga g //

46. Example of sequence database entry for SWISS-PROT (now UNIPROT)
ID DECA_DROME STANDARD; PRT; 588AA.
AC P07713;
DT 01-APR-1988 (REL. 07, CREATED)
DT 01-APR-1988 (REL. 07, LAST SEQUENCE UPDATE)
DT 01-FEB-1995 (REL. 31, LAST ANNOTATION UPDATE)
DE DECAPENTAPLEGIC PROTEIN PRECURSOR (DPP-C PROTEIN).
GN DPP.
OS DROSOPHILA MELANOGASTER (FRUIT FLY).
OC EUKARYOTA; METAZOA; ARTHROPODA; INSECTA; DIPTERA.
RN [1]
RP SEQUENCE FROM N.A. RM
RA PADGETT R.W., ST JOHNSTON R.D., GELBART W.M.;
RL NATURE 325:81-84 (1987)
RN [2]
RP CHARACTERIZATION, AND SEQUENCE OF RM
RA PANGANIBAN G.E.F., RASHKA K.E., NEITZEL M.D., HOFFMANN F.M.;
RL MOL. CELL. BIOL. 10: (1990).
CC -!- FUNCTION: DPP IS REQUIRED FOR THE PROPER DEVELOPMENT OF THE
CC EMBRYONIC DOORSAL HYPODERM, FOR VIABILITY OF LARVAE AND FOR CELL
CC VIABILITY OF THE EPITHELIAL CELLS IN THE IMAGINAL DISKS.
CC -!- SUBUNIT: HOMODIMER, DISULFIDE-LINKED.
CC -!- SIMILARITY: TO OTHER GROWTH FACTORS OF THE TGF-BETA FAMILY.
DR EMBL; M30116; DMDPPC.
DR PIR; A26158; A26158.
DR HSSP; P08112; 1TFG.
DR FLYBASE; FBGN ; DPP.
DR PROSITE; PS00250; TGF_BETA.
KW GROWTH FACTOR; DIFFERENTIATION; SIGNAL.
FT SIGNAL 1 ? POTENTIAL.
FT PROPEP ? 456
FT CHAIN DECAPENTAPLEGIC PROTEIN.
FT DISULFID BY SIMILARITY.
FT DISULFID BY SIMILARITY.
FT DISULFID BY SIMILARITY.
FT DISULFID INTERCHAIN (BY SIMILARITY).
FT CARBOHYD POTENTIAL.
FT CARBOHYD POTENTIAL.
FT CARBOHYD POTENTIAL.
FT CARBOHYD POTENTIAL.
SQ SEQUENCE AA; MW; CN;
MRAWLLLLAV LATFQTIVRV ASTEDISQRF IAAIAPVAAH IPLASASGSG SGRSGSRSVG
ASTSTAGAKA FNRFSEPASF SDSDKSHRSK TNKKPSKSDA NRQFNEVHKP RTDQLENSKN
KSKQLVNKPN HNKMAVKEQR SHHKKSHHHR SHQPKQASAS TESHQSSSIE SIFVEEPTLV
LDREVASINV PANAKAIIAE QGPSTYSKEA LIKDKLKPDP STYLVEIKSL LSLFNMKRPP
KIDRSKIIIP EPMKKLYAEI MGHELDSVNI PKPGLLTKSA NTVRSFTHKD SKIDDRFPHH
HRFRLHFDVK SIPADEKLKA AELQLTRDAL SQQVVASRSS ANRTRYQBLV YDITRVGVRG
QREPSYLLLD TKTBRLNSTD TVSLDVQPAV DRWLASPQRN YGLLVEVRTV RSLKPAPHHH
VRLRRSADEA HERWQHKQPL LFTYTDDGRH DARSIRDVSG GEGGGKGGRN KRHARRPTRR
KNHDDTCRRH SLYVDFSDVG WDDWIVAPLG YDAYYCHGKC PFPLADHRNS TNHAVVQTLV
NNMNPGKBPK ACCBPTQLDS VAMLYLNDQS TVVLKNYQEM TVVGCGCR

47. What to align, nucleotide or amino acid sequences?
If you think you have an Open Reading Frame (ORF) then align at protein level
(i) Many mutations within DNA are synonymous, leading to overestimation of sequence divergence if compared at the DNA level.
(ii) Evolutionary relationships can be more finely expressed using a 20×20 amino acid exchange table than using nucleotide exchanges.
(iii) DNA sequences contain non-coding regions which should be avoided in homology searches. Still an issue when translating into (six) protein sequences through a codon table.
(iv) Searching at protein level: frameshifts can occur, leading to stretches of incorrect amino acids and possibly elongation of sequences due to missed stop codons. But frameshifts normally result in stretches of highly unlikely amino acids: can be used as a signal to trace.

48. How to get an amino acid exchange matrix?

57. PAM250 matrix WR exchange is too large (due to paucity of data) A 2Q E G H I L K M F P S T W Y V B Z
A R N D C Q E G H I L K M F P S T W Y V B Z
PAM250 matrix
WR exchange is too large (due to paucity of data)

58. PAM model
The scores derived through the PAM model are an accurate description of the information content (or the relative entropy) of an alignment (Altschul, 1991).
PAM-1 corresponds to about 1 million years of evolution
PAM-120 has the largest information content of the PAM matrix series
PAM-250 is the traditionally most popular matrix

59. PAM / MDM / Dayhoff -- summary
The late Margaret Dayhoff was a pioneer in protein databasing and comparison. She and her coworkers developed a model of protein evolution which resulted in the development of a set of widely used substitution matrices. These are frequently called Dayhoff, MDM (Mutation Data Matrix), or PAM (Percent Accepted Mutation) matrices:
Derived from global alignments of closely related sequences.
Matrices for greater evolutionary distances are extrapolated from those for lesser ones.
The number associated with the matrix (PAM40, PAM100) refers to the evolutionary distance; greater numbers correspond to greater distances.
Several later groups have attempted to extend Dayhoff's methodology or re-apply her analysis using later databases with more examples.
Extensions:
Jones, Thornton and coworkers used the same methodology as Dayhoff but with modern databases (CABIOS 8: )
Gonnett and coworkers (Science 256: ) used a slightly different (but theoretically equivalent) methodology
Henikoff & Henikoff (Proteins 17: ) compared these two newer versions of the PAM matrices with Dayhoff's originals.