an introduction to bioinformatics comparing biological sequences (3): database searching and...
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An Introduction to Bioinformatics
Comparing biological sequences (3): Database searching and Multiple alignment
An Introduction to Bioinformatics
• Goal: find similar (homologous) sequences of a query sequence in a sequence of database
• Input: query sequence & database
• Output: hits (pairwise alignments)
Database searching
An Introduction to Bioinformatics
Database searching
• Core: pair-wise alignment algorithm• Speed (fast sequence comparison)• Relevance of the search results (statistical
tests)• Recovering all information of interest
• The results depend of the search parameters like gap penalty, scoring matrix.
• Sometimes searches with more than one matrix should be preformed
An Introduction to Bioinformatics
What program to use for searching?
1) BLAST is fastest and easily accessed on the Web• limited sets of databases• nice translation tools (BLASTX, TBLASTN)
2) FASTA• precise choice of databases• more sensitive for DNA-DNA comparisons• FASTX and TFASTX can find similarities in sequences with
frameshifts
3) Smith-Waterman is slower, but more sensitive • known as a “rigorous” or “exhaustive” search• SSEARCH in GCG and standalone FASTA
An Introduction to Bioinformatics
FASTA1) Derived from logic of the dot plot
• compute best diagonals from all frames of alignment
2) Word method looks for exact matches between words in query and test sequence• hash tables (fast computer technique)• DNA words are usually 6 bases• protein words are 1 or 2 amino acids• only searches for diagonals in region of word
matches = faster searching
An Introduction to Bioinformatics
FASTA Algorithm
An Introduction to Bioinformatics
Makes Longest Diagonal
3) after all diagonals found, tries to join diagonals by adding gaps
4) computes alignments in regions of best diagonals
An Introduction to Bioinformatics
FASTA Alignments
An Introduction to BioinformaticsFASTA Results - Histogram !!SEQUENCE_LIST 1.0(Nucleotide) FASTA of: b2.seq from: 1 to: 693 December 9, 2002 14:02TO: /u/browns02/Victor/Search-set/*.seq Sequences: 2,050 Symbols: 913,285 Word Size: 6 Searching with both strands of the query. Scoring matrix: GenRunData:fastadna.cmp Constant pamfactor used Gap creation penalty: 16 Gap extension penalty: 4
Histogram Key: Each histogram symbol represents 4 search set sequences Each inset symbol represents 1 search set sequences z-scores computed from opt scoresz-score obs exp (=) (*)< 20 0 0: 22 0 0: 24 3 0:= 26 2 0:= 28 5 0:== 30 11 3:*== 32 19 11:==*== 34 38 30:=======*== 36 58 61:===============* 38 79 100:==================== * 40 134 140:==================================* 42 167 171:==========================================* 44 205 189:===============================================*==== 46 209 192:===============================================*===== 48 177 184:=============================================*
An Introduction to Bioinformatics
FASTA Results - List
The best scores are: init1 initn opt z-sc E(1018780)..
SW:PPI1_HUMAN Begin: 1 End: 269
! Q00169 homo sapiens (human). phosph... 1854 1854 1854 2249.3 1.8e-117
SW:PPI1_RABIT Begin: 1 End: 269
! P48738 oryctolagus cuniculus (rabbi... 1840 1840 1840 2232.4 1.6e-116
SW:PPI1_RAT Begin: 1 End: 270
! P16446 rattus norvegicus (rat). pho... 1543 1543 1837 2228.7 2.5e-116
SW:PPI1_MOUSE Begin: 1 End: 270
! P53810 mus musculus (mouse). phosph... 1542 1542 1836 2227.5 2.9e-116
SW:PPI2_HUMAN Begin: 1 End: 270
! P48739 homo sapiens (human). phosph... 1533 1533 1533 1861.0 7.7e-96
SPTREMBL_NEW:BAC25830 Begin: 1 End: 270
! Bac25830 mus musculus (mouse). 10, ... 1488 1488 1522 1847.6 4.2e-95
SP_TREMBL:Q8N5W1 Begin: 1 End: 268
! Q8n5w1 homo sapiens (human). simila... 1477 1477 1522 1847.6 4.3e-95
SW:PPI2_RAT Begin: 1 End: 269
! P53812 rattus norvegicus (rat). pho... 1482 1482 1516 1840.4 1.1e-94
An Introduction to Bioinformatics
FASTA Results - AlignmentSCORES Init1: 1515 Initn: 1565 Opt: 1687 z-score: 1158.1 E(): 2.3e-58
>>GB_IN3:DMU09374 (2038 nt) initn: 1565 init1: 1515 opt: 1687 Z-score: 1158.1 expect(): 2.3e-58 66.2% identity in 875 nt overlap (83-957:151-1022)
60 70 80 90 100 110 u39412.gb_pr CCCTTTGTGGCCGCCATGGACAATTCCGGGAAGGAAGCGGAGGCGATGGCGCTGTTGGCC || ||| | ||||| | ||| |||||DMU09374 AGGCGGACATAAATCCTCGACATGGGTGACAACGAACAGAAGGCGCTCCAACTGATGGCC 130 140 150 160 170 180
120 130 140 150 160 170 u39412.gb_pr GAGGCGGAGCGCAAAGTGAAGAACTCGCAGTCCTTCTTCTCTGGCCTCTTTGGAGGCTCA ||||||||| || ||| | | || ||| | || || ||||| || DMU09374 GAGGCGGAGAAGAAGTTGACCCAGCAGAAGGGCTTTCTGGGATCGCTGTTCGGAGGGTCC 190 200 210 220 230 240
180 190 200 210 220 230 u39412.gb_pr TCCAAAATAGAGGAAGCATGCGAAATCTACGCCAGAGCAGCAAACATGTTCAAAATGGCC ||| | ||||| || ||| |||| | || | |||||||| || ||| ||DMU09374 AACAAGGTGGAGGACGCCATCGAGTGCTACCAGCGGGCGGGCAACATGTTTAAGATGTCC 250 260 270 280 290 300
240 250 260 270 280 290 u39412.gb_pr AAAAACTGGAGTGCTGCTGGAAACGCGTTCTGCCAGGCTGCACAGCTGCACCTGCAGCTC |||||||||| ||||| | |||||| |||| ||| || ||| || | DMU09374 AAAAACTGGACAAAGGCTGGGGAGTGCTTCTGCGAGGCGGCAACTCTACACGCGCGGGCT 310 320 330 340 350 360
An Introduction to Bioinformatics
FASTA on the Web
Many websites offer FASTA searches• Various databases and various other services• Be sure to use FASTA 3
• Each server has its limits• Be aware that you are depending on the
kindness of strangers.
An Introduction to Bioinformatics
Institut de Génétique Humaine, Montpellier France, GeneStream server
http://www2.igh.cnrs.fr/bin/fasta-guess.cgiOak Ridge National Laboratory GenQuest server
http://avalon.epm.ornl.gov/European Bioinformatics Institute, Cambridge, UK
http://www.ebi.ac.uk/htbin/fasta.py?requestEMBL, Heidelberg, Germany
http://www.embl-heidelberg.de/cgi/fasta-wrapper-freeMunich Information Center for Protein Sequences (MIPS)at Max-Planck-Institut, Germany
http://speedy.mips.biochem.mpg.de/mips/programs/fasta.htmlInstitute of Biology and Chemistry of Proteins Lyon, France
http://www.ibcp.fr/serv_main.htmlInstitute Pasteur, France
http://central.pasteur.fr/seqanal/interfaces/fasta.htmlGenQuest at The Johns Hopkins University
http://www.bis.med.jhmi.edu/Dan/gq/gq.form.htmlNational Cancer Center of Japan
http://bioinfo.ncc.go.jp
An Introduction to Bioinformatics
BLAST Searches GenBank[BLAST= Basic Local Alignment Search Tool]
The NCBI BLAST web server lets you compare your query sequence to various sections of GenBank:
• nr = non-redundant (main sections)• month = new sequences from the past few weeks• ESTs• human, drososphila, yeast, or E.coli genomes• proteins (by automatic translation)
• This is a VERY fast and powerful computer.
An Introduction to Bioinformatics
BLAST• Uses word matching like FASTA• Similarity matching of words (3 aa’s, 11 bases)
• does not require identical words.
• If no words are similar, then no alignment• won’t find matches for very short sequences
• Does not handle gaps well• New “gapped BLAST” (BLAST 2) is better
An Introduction to Bioinformatics
BLAST Algorithm
An Introduction to Bioinformatics
BLAST Word MatchingMEAAVKEEISVEDEAVDKNI
MEA EAA AAV AVK VKE KEE EEI EIS ISV
...
Break query into words:
Break database sequences
into words:
An Introduction to Bioinformatics
Database Sequence Word Lists RTT AAQ
SDG KSSSRW LLNQEL RWYVKI GKGDKI NISLFC WDVAAV KVRPFR DEI… …
Compare Word Lists
Query Word List:
MEAEAAAAVAVKVKLKEEEEIEISISV
?
Compare word lists by Hashing
(allow near matches)
An Introduction to Bioinformatics
ELEPRRPRYRVPDVLVADPPIARLSVSGRDENSVELTMEAT
TDVRWMSETGIIDVFLLLGPSISDVFRQYASLTGTQALPPLFSLGYHQSRWNY
IWLDIEEIHADGKRYFTWDPSRFPQPRTMLERLASKRRVKLVAIVDPH
MEAEAAAAVAVKKLVKEEEEIEISISV
Find locations of matching words in database sequences
An Introduction to Bioinformatics
Extend hits one base at a time
An Introduction to Bioinformatics
HVTGRSAF_FSYYGYGCYCGLGTGKGLPVDATDRCCWA
QSVFDYIYYGCYCGWGLG_GK__PRDA
•Use two word matches as anchors to build an alignment between the query and a database sequence.
•Then score the alignment.
Query:
Seq_XYZ:
E-val=10-13
An Introduction to Bioinformatics
HSPs are Aligned Regions
• The results of the word matching and attempts to extend the alignment are segments
- called HSPs (High-scoring Segment Pairs) • BLAST often produces several short HSPs
rather than a single aligned region
An Introduction to Bioinformatics
BLAST 2 algorithm• The NCBI’s BLAST website now both use
BLAST 2 (also known as “gapped BLAST”)
• This algorithm is more complex than the original BLAST
• It requires two word matches close to each other on a pair of sequences (i.e. with a gap) before it creates an alignment
An Introduction to Bioinformatics
Statistical tests
• Evaluate the probability of an event taking place by chance (at random).
• P-value• Randomized data• Distribution under the same setup
• Z-score• Chebyshev Inequality
An Introduction to Bioinformatics
BLAST Statistics• E value is equivalent to standard P value
(based on Karlin-Altschul theorem)
• Significant if E < 0.05 (smaller numbers are more significant) • The E-value represents the likelihood that the
observed alignment is due to chance alone. A value of 1 indicates that an alignment this good would happen by chance with any random sequence searched against this database.
An Introduction to Bioinformatics
Program Query Database Comparison Common use
blastn DNA DNA DNA level Seek identical DNAsequences andsplicing patterns
blastp Protein Protein Protein level Find homologousproteins
blastx DNA Protein Protein level Analyze new DNAto find genes andseek homologousproteins
tblastn Protein DNA Protein level Search for genes inunannotated DNA
tblastx DNA DNA Protein level Discover genestructure
BLAST variants for different searchesa
(after S. Brenner, Trends Guide to Bioinformatics, 1998)
An Introduction to Bioinformatics
BLAST is Approximate• BLAST makes similarity searches very
quickly because it takes shortcuts.• looks for short, nearly identical “words” (11 bases)
• It also makes errors • misses some important similarities• makes many incorrect matches
• easily fooled by repeats or skewed composition
An Introduction to Bioinformatics
Interpretation of output• very low E values (e-100) are homologs or
identical genes
• moderate E values are related genes
• long list of gradually declining of E values indicates a large gene family
• long regions of moderate similarity are more significant than short regions of high identity
An Introduction to Bioinformatics
Biological Relevance• It is up to you, the biologist to scrutinize these
alignments and determine if they are significant.
• Were you looking for a short region of nearly identical sequence or a larger region of general similarity?
• Are the mismatches conservative ones?
• Are the matching regions important structural components of the genes or just introns and flanking regions?
An Introduction to Bioinformatics
Borderline similarity• What to do with matches with E() values in
the 0.5 -1.0 range?
• this is the “Twilight Zone”
• retest these sequences and look for related hits (not just your original query sequence)
• similarity is transitive:
if A~B and B~C, then A~C
An Introduction to Bioinformatics
Position Specific Iterated BLAST• Collect all database sequence segments that
have been aligned with query sequence with E-value below set threshold (default 0.01)
• Construct position specific scoring matrix for collected sequences. Rough idea:• Align all sequences to the query sequence as the
template.• Assign weights to the sequences • Construct position specific scoring matrix
• Iterate
An Introduction to Bioinformatics
Motif finding• Observation : Some regions have been better
conserved than others during evolution
• Idea: By analyzing the constant and variable properties of such groups of similar sequences, it is possible to derive a signature for a protein family or domain (motifs)
An Introduction to Bioinformatics
PROSITE patterns
• PROSITE fingerprints are described by regular grammars• There is a number of programs that allow to search databases
for PROSITE patterns (example GCG package)
• Example [EDQH]-x-K-x-[DN]-G-x-R-[GACV]• Rules:
• Each position is separated by a hyphen• One character denotes residuum at a given position• […] denoted a set of allowed residues• (n) denotes repeat of n• (n,m) denoted repeat between n and m inclusive
Ex. ATP/GTP binding motive [SG]=X(4)-G-K-[DT]
An Introduction to Bioinformatics
Multiple sequence alignment
An Introduction to Bioinformatics
Generalizing the Notion of Pairwise Alignment
• Alignment of 2 sequences is represented as a 2-row matrix• In a similar way, we represent alignment of 3
sequences as a 3-row matrix
A T _ G C G _ A _ C G T _ A A T C A C _ A
• Score: more conserved columns, better alignment
An Introduction to Bioinformatics
Alignments = Paths• Align 3 sequences: ATGC, AATC,ATGC
A A T -- C
A -- T G C
-- A T G C
An Introduction to Bioinformatics
Alignment Paths
0 1 1 2 3 4
A A T -- C
A -- T G C
-- A T G C
x coordinate
An Introduction to Bioinformatics
Alignment Paths• Align the 3 sequences: ATGC, AATC,ATGC
0 1 1 2 3 4
0 1 2 3 3 4
A A T -- C
A -- T G C
-- A T G C
•
x coordinate
y coordinate
An Introduction to Bioinformatics
Alignment Paths
0 1 1 2 3 4
0 1 2 3 3 4
A A T -- C
A -- T G C
0 0 1 2 3 4
-- A T G C
• Resulting path in (x,y,z) space:
(0,0,0)(1,1,0)(1,2,1) (2,3,2) (3,3,3) (4,4,4)
x coordinate
y coordinate
z coordinate
An Introduction to Bioinformatics
Aligning Three Sequences• Same strategy as
aligning two sequences• Use a 3-D “Manhattan
Cube”, with each axis representing a sequence to align
• For global alignments, go from source to sink
source
sink
An Introduction to Bioinformatics
2-D vs 3-D Alignment Grid
V
W
2-D edit graph
3-D edit graph
An Introduction to Bioinformatics
2-D cell versus 2-D Alignment Cell
In 3-D, 7 edges in each unit cube
In 2-D, 3 edges in each unit square
An Introduction to Bioinformatics
Architecture of 3-D Alignment Cell(i-1,j-1,k-1)
(i,j-1,k-1)
(i,j-1,k)
(i-1,j-1,k) (i-1,j,k)
(i,j,k)
(i-1,j,k-1)
(i,j,k-1)
An Introduction to Bioinformatics
Multiple Alignment: Dynamic Programming
• si,j,k = max
(x, y, z) is an entry in the 3-D scoring matrix
si-1,j-1,k-1 + (vi, wj, uk)
si-1,j-1,k + (vi, wj, _ )
si-1,j,k-1 + (vi, _, uk)
si,j-1,k-1 + (_, wj, uk)
si-1,j,k + (vi, _ , _)
si,j-1,k + (_, wj, _)
si,j,k-1 + (_, _, uk)
cube diagonal: no indels
face diagonal: one indel
edge diagonal: two indels
An Introduction to Bioinformatics
Multiple Alignment: Running Time
• For 3 sequences of length n, the run time is 7n3; O(n3)
• For k sequences, build a k-dimensional Manhattan, with run time (2k-1)(nk); O(2knk)
• Conclusion: dynamic programming approach for alignment between two sequences is easily extended to k sequences but it is impractical due to exponential running time.
An Introduction to Bioinformatics
Profile Representation of Multiple Alignment
- A G G C T A T C A C C T G T A G – C T A C C A - - - G C A G – C T A C C A - - - G C A G – C T A T C A C – G G C A G – C T A T C G C – G G
A 1 1 .8 C .6 1 .4 1 .6 .2G 1 .2 .2 .4 1T .2 1 .6 .2- .2 .8 .4 .8 .4
An Introduction to Bioinformatics
Profile Representation of Multiple Alignment
In the past we were aligning a sequence against a sequence
Can we align a sequence against a profile?
Can we align a profile against a profile?
- A G G C T A T C A C C T G T A G – C T A C C A - - - G C A G – C T A C C A - - - G C A G – C T A T C A C – G G C A G – C T A T C G C – G G
A 1 1 .8 C .6 1 .4 1 .6 .2G 1 .2 .2 .4 1T .2 1 .6 .2- .2 .8 .4 .8 .4
An Introduction to Bioinformatics
Aligning alignments
• Given two alignments, can we align them?
x GGGCACTGCATy GGTTACGTC-- Alignment 1 z GGGAACTGCAG
w GGACGTACC-- Alignment 2v GGACCT-----
An Introduction to Bioinformatics
Aligning alignments• Given two alignments, can we align them? • Hint: use alignment of corresponding profiles
x GGGCACTGCATy GGTTACGTC-- Combined Alignment z GGGAACTGCAG
w GGACGTACC-- v GGACCT-----
An Introduction to Bioinformatics
Multiple Alignment: Greedy Approach• Choose most similar pair of strings and combine into a
profile , thereby reducing alignment of k sequences to an alignment of of k-1 sequences/profiles. Repeat
• This is a heuristic greedy method
u1= ACGTACGTACGT…
u2 = TTAATTAATTAA…
u3 = ACTACTACTACT…
…
uk = CCGGCCGGCCGG
u1= ACg/tTACg/tTACg/cT…
u2 = TTAATTAATTAA…
…
uk = CCGGCCGGCCGG…
k
k-1
An Introduction to Bioinformatics
Greedy Approach: Example
• Consider these 4 sequences
s1 GATTCAs2 GTCTGAs3 GATATTs4 GTCAGC
An Introduction to Bioinformatics
Greedy Approach: Example (cont’d)• There are = 6 possible alignments
2
4
s2 GTCTGAs4 GTCAGC (score = 2)
s1 GAT-TCAs2 G-TCTGA (score = 1)
s1 GAT-TCAs3 GATAT-T (score = 1)
s1 GATTCA--s4 G—T-CAGC(score = 0)
s2 G-TCTGAs3 GATAT-T (score = -1)
s3 GAT-ATTs4 G-TCAGC (score = -1)
An Introduction to Bioinformatics
Greedy Approach: Example (cont’d)
s2 and s4 are closest; combine:
s2 GTCTGAs4 GTCAGC
s2,4 GTCt/aGa/cA (profile)
s1 GATTCAs3 GATATTs2,4 GTCt/aGa/c
new set of 3 sequences:
An Introduction to Bioinformatics
Progressive Alignment
• Progressive alignment is a variation of greedy algorithm with a somewhat more intelligent strategy for choosing the order of alignments.
• Progressive alignment works well for close sequences, but deteriorates for distant sequences• Gaps in consensus string are permanent• Use profiles to compare sequences
An Introduction to Bioinformatics
ClustalW
• Popular multiple alignment tool today• ‘W’ stands for ‘weighted’ (different parts of
alignment are weighted differently).• Three-step process
1.) Construct pairwise alignments
2.) Build Guide Tree
3.) Progressive Alignment guided by the tree
An Introduction to Bioinformatics
Step 1: Pairwise Alignment
• Aligns each sequence again each other giving a similarity matrix
• Similarity = exact matches / sequence length (percent identity)
v1 v2 v3 v4
v1 -v2 .17 -v3 .87 .28 -v4 .59 .33 .62 -
(.17 means 17 % identical)
An Introduction to Bioinformatics
Step 2: Guide Tree
•Create Guide Tree using the similarity matrix
•ClustalW uses the neighbor-joining method
•Guide tree roughly reflects evolutionary relations
An Introduction to Bioinformatics
Step 2: Guide Tree (cont’d)
v1
v3
v4 v2
Calculate:v1,3 = alignment (v1, v3)v1,3,4 = alignment((v1,3),v4)v1,2,3,4 = alignment((v1,3,4),v2)
v1 v2 v3 v4
v1 -v2 .17 -v3 .87 .28 -v4 .59 .33 .62 -
An Introduction to Bioinformatics
Step 3: Progressive Alignment• Start by aligning the two most similar sequences
• Following the guide tree, add in the next sequences, aligning to the existing alignment
• Insert gaps as necessary
FOS_RAT PEEMSVTS-LDLTGGLPEATTPESEEAFTLPLLNDPEPK-PSLEPVKNISNMELKAEPFDFOS_MOUSE PEEMSVAS-LDLTGGLPEASTPESEEAFTLPLLNDPEPK-PSLEPVKSISNVELKAEPFDFOS_CHICK SEELAAATALDLG----APSPAAAEEAFALPLMTEAPPAVPPKEPSG--SGLELKAEPFDFOSB_MOUSE PGPGPLAEVRDLPG-----STSAKEDGFGWLLPPPPPPP-----------------LPFQFOSB_HUMAN PGPGPLAEVRDLPG-----SAPAKEDGFSWLLPPPPPPP-----------------LPFQ . . : ** . :.. *:.* * . * **:
Dots and stars show how well-conserved a column is.
An Introduction to Bioinformatics
Multiple Alignments: Scoring
• Number of matches (multiple longest common subsequence score)
• Entropy score
• Sum of pairs (SP-Score)
An Introduction to Bioinformatics
Multiple LCS Score
• A column is a “match” if all the letters in the column are the same
• Only good for very similar sequences
AAAAAAAATATC
An Introduction to Bioinformatics
Entropy
• Define frequencies for the occurrence of each letter in each column of multiple alignment• pA = 1, pT=pG=pC=0 (1st column)
• pA = 0.75, pT = 0.25, pG=pC=0 (2nd column)
• pA = 0.50, pT = 0.25, pC=0.25 pG=0 (3rd column)
• Compute entropy of each column
CGTAX
XX pp,,,
log
AAAAAAAATATC
An Introduction to Bioinformatics
Entropy: Example
0
A
A
A
A
entropy
2)24
1(4
4
1log
4
1
C
G
T
A
entropy
Best case
Worst case
An Introduction to Bioinformatics
Multiple Alignment: Entropy Score
Entropy for a multiple alignment is the sum of entropies of its columns:
over all columns X=A,T,G,C pX logpX
An Introduction to Bioinformatics
Entropy of an Alignment: Example
column entropy: -( pAlogpA + pClogpC + pGlogpG + pTlogpT)
•Column 1 = -[1*log(1) + 0*log0 + 0*log0 +0*log0] = 0
•Column 2 = -[(1/4)*log(1/4) + (3/4)*log(3/4) + 0*log0 + 0*log0] = -[ (1/4)*(-2) + (3/4)*(-.415) ] = +0.811
•Column 3 = -[(1/4)*log(1/4)+(1/4)*log(1/4)+(1/4)*log(1/4) +(1/4)*log(1/4)] = 4* -[(1/4)*(-2)] = +2.0
•Alignment Entropy = 0 + 0.811 + 2.0 = +2.811
A A A
A C C
A C G
A C T
An Introduction to Bioinformatics
Multiple Alignment Induces Pairwise Alignments
Every multiple alignment induces pairwise alignments
x: AC-GCGG-C y: AC-GC-GAG z: GCCGC-GAG
Induces:
x: ACGCGG-C; x: AC-GCGG-C; y: AC-GCGAGy: ACGC-GAC; z: GCCGC-GAG; z: GCCGCGAG
An Introduction to Bioinformatics
Sum of Pairs Score(SP-Score)
• Consider pairwise alignment of sequences
ai and aj
imposed by a multiple alignment of k sequences
• Denote the score of this suboptimal (not necessarily optimal) pairwise alignment as
s*(ai, aj)
• Sum up the pairwise scores for a multiple alignment:
s(a1,…,ak) = Σi,j s*(ai, aj)
An Introduction to Bioinformatics
Computing SP-Score
Aligning 4 sequences: 6 pairwise alignments
Given a1,a2,a3,a4:
s(a1…a4) = s*(ai,aj) = s*(a1,a2) + s*(a1,a3) + s*(a1,a4) + s*(a2,a3) + s*(a2,a4) + s*(a3,a4)
An Introduction to Bioinformatics
SP-Score: Examplea1
.ak
ATG-C-AATA-G-CATATATCCCATTT
ji
jik aaSaaS,
*1 ),()...(
2
nPairs of Sequences
A
A A
11
1
G
C G
1
Score=3 Score = 1 –
Column 1 Column 3
s s*(
To calculate each column:
An Introduction to Bioinformatics
Multiple Alignment: History
1975 SankoffFormulated multiple alignment problem and gave dynamic programming solution
1988 Carrillo-LipmanBranch and Bound approach for MSA
1990 Feng-DoolittleProgressive alignment
1994 Thompson-Higgins-Gibson-ClustalWMost popular multiple alignment program
1998 Morgenstern et al.-DIALIGNSegment-based multiple alignment
2000 Notredame-Higgins-Heringa-T-coffeeUsing the library of pairwise alignments
2004 MUSCLE