Title: The Basic Local Alignment Search Tool (BLAST)
1The Basic Local Alignment Search Tool(BLAST)
- Rapid data base search tool (1990)
- Idea
- (1) Search for high scoring segment pairs
-
2The Basic Local Alignment Search Tool(BLAST)
- A Y W T Y I V A L T Q V R Q Y E A T
- S I L C I V M I Y S R A - Q Y R Y W R Y
- Most local alignments contain highly conserved
sections without gaps
3The Basic Local Alignment Search Tool(BLAST)
- A Y W T Y I V A L T Q V R Q Y E A T
- S I L C I V M I Y S R A - Q Y R Y W R Y
- -gt search for high scoring segment pairs
- (HSP), i.e. gap-free local alignments
4The Basic Local Alignment Search Tool(BLAST)
5The Basic Local Alignment Search Tool(BLAST)
- A Y W T Y I V A L T Q V R Q Y E A T
- S I L C I V M I Y S R A - Q Y R Y W R Y
- Advantages
- (a) speed
- (b) statistical theory about HSP exists.
6The Basic Local Alignment Search Tool(BLAST)
- Rapid data base search tool (1990)
- Idea
- (1) Search for high scoring segment pairs
- (2) Use word pairs as seeds
-
7Pair-wise sequence alignment
- T W L M H C A Q Y I
-
- C
- I
- M X
- H X
- C X
- T
- H
- Y
- (1) Search word pairs of length 3 with score gt T,
- Use them as seeds.
8Pair-wise sequence alignment
- Naïve algorithm would have a complexity of O(l1
l2) - Solution
- Preprocess query sequence
- Compile a list of all words that have a
- Score gt T when aligned to a word in the
- Query.
9Pair-wise sequence alignment
- Naïve algorithm would have a complexity of O(l1
l2) - Solution
- Preprocess query sequence
- Compile a list of all words that have a
- Score gt T when aligned to a word in the
- Query. Complexity O(l1)
- Organize words in efficient data structure (tree)
for fast look-up
10The Basic Local Alignment Search Tool(BLAST)
- Rapid data base search tool (1990)
- Idea
- (1) Search for high scoring segment pairs
- (2) Use word pairs as seeds
- (3) Extend seed alignments until score drops
below threshold value
11Pair-wise sequence alignment
- T W L M H C A Q Y I
-
- C
- I
- M X
- H X
- C X
- T
- H
- Y
- Extend seeds until score drops by X.
12Pair-wise sequence alignment
- T W L M H C A Q Y I
-
- C
- I X
- M X
- H X
- C X
- T X
- H X
- Y
- Extend seeds until score drops by X.
13Pair-wise sequence alignment
- Algorithm not guaranteed to find best
- segment pair
-
- (Heuristic)
- But works well in practice!
14The Basic Local Alignment Search Tool(BLAST)
- New BLAST version (1997)
- Two-hit strategy
15Pair-wise sequence alignment
- W L M H C A Q Y A R V
-
- I
- M X
- H X
- C X
- T
- H
- W
- A X
- R X
- v X
- Search two word pairs of at the same diagonal,
use lower threshold T
16The Basic Local Alignment Search Tool(BLAST)
- New BLAST version (1997)
- Two-hit strategy
- Gapped BLAST
- Position-Specific Iterative BLAST
- (PSI BLAST)
17The Basic Local Alignment Search Tool(BLAST)
18Multiple sequence alignment
- 1aboA 1 .NLFVALYDfvasgdntlsitkGEKLRVLgynhn
..............gE - 1ycsB 1 kGVIYALWDyepqnddelpmkeGDCMTIIhrede
............deiE - 1pht 1 gYQYRALYDykkereedidlhlGDILTVNkgslv
algfsdgqearpeeiG - 1ihvA 1 .NFRVYYRDsrd......pvwkGPAKLLWkg...
..............eG - 1vie 1 .drvrkksga.........awqGQIVGWYctnlt
.............peG - 1aboA 36 WCEAQt..kngqGWVPSNYITPVN......
- 1ycsB 39 WWWARl..ndkeGYVPRNLLGLYP......
- 1pht 51 WLNGYnettgerGDFPGTYVEYIGrkkisp
- 1ihvA 27 AVVIQd..nsdiKVVPRRKAKIIRd.....
- 1vie 28 YAVESeahpgsvQIYPVAALERIN......
-
19Multiple sequence alignment
- First question how to score multiple
alignments? - Possible scoring scheme
- Sum-of-pairs score
-
20Multiple sequence alignment
- Multiple alignment implies pairwise alignments
- 1aboA 36 WCEAQt..kngqGWVPSNYITPVN......
- 1ycsB 39 WWWARl..ndkeGYVPRNLLGLYP......
- 1pht 51 WLNGYnettgerGDFPGTYVEYIGrkkisp
- 1ihvA 27 AVVIQd..nsdiKVVPRRKAKIIRd.....
- 1vie 28 YAVESeahpgsvQIYPVAALERIN......
21Multiple sequence alignment
- Multiple alignment implies pairwise alignments
- 1aboA 36 WCEAQt..kngqGWVPSNYITPVN......
- 1ycsB 39 WWWARl..ndkeGYVPRNLLGLYP......
- 1pht 51 WLNGYnettgerGDFPGTYVEYIGrkkisp
- 1ihvA 27 AVVIQd..nsdiKVVPRRKAKIIRd.....
- 1vie 28 YAVESeahpgsvQIYPVAALERIN......
22Multiple sequence alignment
- Multiple alignment implies pairwise alignments
- 1aboA 36 WCEAQt..kngqGWVPSNYITPVN......
- 1ycsB 39 WWWARl..ndkeGYVPRNLLGLYP......
23Multiple sequence alignment
- Multiple alignment implies pairwise alignments
- 1aboA 36 WCEAQtkngqGWVPSNYITPVN
- 1ycsB 39 WWWARlndkeGYVPRNLLGLYP
24Multiple sequence alignment
- Multiple alignment implies pairwise alignments
- 1aboA 36 WCEAQt..kngqGWVPSNYITPVN......
- 1ycsB 39 WWWARl..ndkeGYVPRNLLGLYP......
- 1pht 51 WLNGYnettgerGDFPGTYVEYIGrkkisp
- 1ihvA 27 AVVIQd..nsdiKVVPRRKAKIIRd.....
- 1vie 28 YAVESeahpgsvQIYPVAALERIN......
25Multiple sequence alignment
- Multiple alignment implies pairwise alignments
- 1aboA 36 WCEAQt..kngqGWVPSNYITPVN......
- 1ycsB 39 WWWARl..ndkeGYVPRNLLGLYP......
- 1pht 51 WLNGYnettgerGDFPGTYVEYIGrkkisp
- 1ihvA 27 AVVIQd..nsdiKVVPRRKAKIIRd.....
- 1vie 28 YAVESeahpgsvQIYPVAALERIN......
26Multiple sequence alignment
- Multiple alignment implies pairwise alignments
- 1aboA 36 WCEAQt..kngqGWVPSNYITPVN......
- 1pht 51 WLNGYnettgerGDFPGTYVEYIGrkkisp
-
27Multiple sequence alignment
- Multiple alignment implies pairwise alignments
- 1aboA 36 WCEAQt..kngqGWVPSNYITPVN......
- 1pht 51 WLNGYnettgerGDFPGTYVEYIGrkkisp
-
28Multiple sequence alignment
- Multiple alignment implies pairwise alignments
- 1aboA 36 WCEAQt..kngqGWVPSNYITPVN......
- 1ycsB 39 WWWARl..ndkeGYVPRNLLGLYP......
- 1pht 51 WLNGYnettgerGDFPGTYVEYIGrkkisp
- 1ihvA 27 AVVIQd..nsdiKVVPRRKAKIIRd.....
- 1vie 28 YAVESeahpgsvQIYPVAALERIN......
29Multiple sequence alignment
- Multiple alignment implies pairwise alignments
- Use sum of scores of these p.a.
- 1aboA 36 WCEAQt..kngqGWVPSNYITPVN......
- 1ycsB 39 WWWARl..ndkeGYVPRNLLGLYP......
- 1pht 51 WLNGYnettgerGDFPGTYVEYIGrkkisp
- 1ihvA 27 AVVIQd..nsdiKVVPRRKAKIIRd.....
- 1vie 28 YAVESeahpgsvQIYPVAALERIN......
30Multiple sequence alignment
- Goal
- Find multi-alignment with maximum score !
31Multiple sequence alignment
- Needleman-Wunsch coring scheme can be generalized
from pair-wise to multiple alignment - Multidimensional search space instead of
two-dimensional matrix! -
32Multiple sequence alignment
33Multiple sequence alignment
- Complexity
- For sequences of length l1 l2 l3
- O( l1 l2 l3 )
- For n sequences ( average length l )
- O( ln )
- Exponential complexity!
34Multiple sequence alignment
- Needleman-Wunsch coring scheme can be generalized
from pair-wise to multiple alignment - Optimal solution not feasible
-
-
35Multiple sequence alignment
- Needleman-Wunsch coring scheme can be generalized
from pair-wise to multiple alignment - Optimal solution not feasible
- -gt Heuristics necessary
-
-
36Multiple sequence alignment
- (A) Carillo and Lipman (MSA)
- Find sub-space in dynamic-programming
- Matrix where optimal path can be found
-
37Multiple sequence alignment
- (B) Stoye, Dress (DCA)
- Divide search space into small
- Calculate optimal alignment for sub-spaces
- Concatenate sub-alignments
38Multiple sequence alignment
39Multiple sequence alignment
40Multiple sequence alignment
- Progressive alignment.
- Carry out a series of pair-wise alignment
41Multiple sequence alignment
- Most popular way of constructing multiple
alignments - Progressive alignment.
- Carry out a series of pair-wise alignment
42 Multiple sequence alignment
- WCEAQTKNGQGWVPSNYITPVN
- WWRLNDKEGYVPRNLLGLYP
- AVVIQDNSDIKVVPKAKIIRD
- YAVESEAHPGSFQPVAALERIN
- WLNYNETTGERGDFPGTYVEYIGRKKISP
-
-
43Multiple sequence alignment
- WCEAQTKNGQGWVPSNYITPVN
- WWRLNDKEGYVPRNLLGLYP
- AVVIQDNSDIKVVPKAKIIRD
- YAVESEAHPGSFQPVAALERIN
- WLNYNETTGERGDFPGTYVEYIGRKKISP
- Align most similar sequences
44Multiple sequence alignment
- WCEAQTKNGQGWVPSNYITPVN
- WW--RLNDKEGYVPRNLLGLYP-
- AVVIQDNSDIKVVP--KAKIIRD
- YAVESEASFQPVAALERIN
- WLNYNEERGDFPGTYVEYIGRKKISP
-
45Multiple sequence alignment
- WCEAQTKNGQGWVPSNYITPVN
- WW--RLNDKEGYVPRNLLGLYP-
- AVVIQDNSDIKVVP--KAKIIRD
- YAVESEASVQ--PVAALERIN------
- WLN-YNEERGDFPGTYVEYIGRKKISP
-
46Multiple sequence alignment
- WCEAQTKNGQGWVPSNYITPVN
- WW--RLNDKEGYVPRNLLGLYP-
- AVVIQDNSDIKVVP--KAKIIRD
- YAVESEASVQ--PVAALERIN------
- WLN-YNEERGDFPGTYVEYIGRKKISP
- Align sequence to alignment
47 Multiple sequence alignment
- WCEAQTKNGQGWVPSNYITPVN-
- WW--RLNDKEGYVPRNLLGLYP-
- AVVIQDNSDIKVVP--KAKIIRD
- YAVESEASVQ--PVAALERIN------
- WLN-YNEERGDFPGTYVEYIGRKKISP
- Align alignment to alignment
48 Multiple sequence alignment
- WCEAQTKNGQGWVPSNYITPVN--------
- WW--RLNDKEGYVPRNLLGLYP--------
- AVVIQDNSDIKVVP--KAKIIRD-------
- YAVESEA---SVQ--PVAALERIN------
- WLN-YNE---ERGDFPGTYVEYIGRKKISP
-
49 Multiple sequence alignment
- WCEAQTKNGQGWVPSNYITPVN--------
- WW--RLNDKEGYVPRNLLGLYP--------
- AVVIQDNSDIKVVP--KAKIIRD-------
- YAVESEA---SVQ--PVAALERIN------
- WLN-YNE---ERGDFPGTYVEYIGRKKISP
- Rule once a gap - always a gap
50 Multiple sequence alignment
- Order of pair-wise profile alignments determined
- by phylogenetic tree based on pair-wise
similarity - values (guide tree)
51Multiple sequence alignment
- WCEAQTKNGQGWVPSNYITPVN
- WWRLNDKEGYVPRNLLGLYP
- AVVIQDNSDIKVVPKAKIIRD
- YAVESEAHPGSFQPVAALERIN
- WLNYNETTGERGDFPGTYVEYIGRKKISP
52Multiple sequence alignment
- WCEAQTKNGQGWVPSNYITPVN
- WWRLNDKEGYVPRNLLGLYP
- AVVIQDNSDIKVVPKAKIIRD
- YAVESEAHPGSFQPVAALERIN
- WLNYNETTGERGDFPGTYVEYIGRKKISP
53 Multiple sequence alignment
- Problem simple guide tree determines multiple
alignment multiple alignment determines
phyolgeneitc analysis -
54Multiple sequence alignment
- Implementations
- Clustal W, PileUp, MultAlin
55Local multiple alignment
M
M
56Local multiple alignment
M
M
M
57Local multiple alignment
M
M
M
M
M
M
58Local multiple alignment
- Find motifs contained in all sequences in data
set - Problem
- motifs often present in only sub-families
-
59 Neither local nor global methods appliccable
60 Alignment possible if order conserved
61The DIALIGN approach
62The DIALIGN approach
- Combination of local and global methods.
63The DIALIGN approach
-
- Combination of local and global methods.
- Find local pair-wise similarities between input
sequences
- (fragments)
64The DIALIGN approach
-
- Combination of local and global methods.
- Find local pair-wise similarities between input
sequences
- (fragments)
- Compose alignments from fragments
65The DIALIGN approach
-
- Combination of local and global methods.
- Find local pair-wise similarities between input
sequences
- (fragments)
- Compose alignments from fragments
- Ignore non-related parts of the sequences
66The DIALIGN approach
-
- atctaatagttaaactcccccgtgcttagagatccaaac
- cagtgcgtgtattactaacggttcaatcgcgcacatccgc
-
-
67The DIALIGN approach
-
- atctaatagttaaactcccccgtgcttagagatccaaac
- cagtgcgtgtattactaacggttcaatcgcgcacatccgc
-
-
68The DIALIGN approach
-
- atctaatagttaaactcccccgtgcttagagatccaaac
- cagtgcgtgtattactaacggttcaatcgcgcacatccgc
-
-
69The DIALIGN approach
-
- atctaatagttaaactcccccgtgcttagagatccaaac
- cagtgcgtgtattactaacggttcaatcgcgcacatccgc
-
70The DIALIGN approach
-
- atctaatagttaaactcccccgtgcttagagatccaaac
- cagtgcgtgtattactaacggttcaatcgcgcacatccgc
- ------atctaatagttaaaccccctcgtgcttag-------agatccaa
ac - cagtgcgtgtattactaac----------ggttcaatcgcgcacatccgc
-- -
-
71The DIALIGN approach
-
- atctaatagttaaactcccccgtgcttagagatccaaac
- cagtgcgtgtattactaacggttcaatcgcgcacatccgc
- ------atctaatagttaaaccccctcgtgcttag-------agatccaa
ac - cagtgcgtgtattactaac----------ggttcaatcgcgcacatccgc
-- - ------atcTAATAGTTAaaccccctcgtGCTTag-------AGATCCaa
ac - cagtgcgtgTATTACTAAc----------GGTTcaatcgcgcACATCCgc
-- -
72The DIALIGN approach
- Score of an alignment
- Define score of fragment f
- l(f) length of f
- s(f) sum of matches (similarity values)
- P(f) probability to find a fragment with length
l(f) and - at least s(f) matches in random
sequences that have - the same length as the input sequences.
- Score w(f) -ln P(f)
73The DIALIGN approach
- Score of an alignment
- Define score of alignment as
-
- sum of scores w(f) of its fragments
- No gap penalty is used!
- Optimization problem for pair-wise alignment
- Find chain of fragments with maximal total
score
74The DIALIGN approach
-
- ------atctaatagttaaaccccctcgtgcttag-------agatccaa
ac - cagtgcgtgtattactaac----------ggttcaatcgcgcacatccgc
-- - Fragment-chaining algorithm finds optimal chain
of - fragments.
-
75The DIALIGN approach
- Multiple fragment alignment
- atctaatagttaaactcccccgtgcttag
- cagtgcgtgtattactaacggttcaatcgcg
- caaagagtatcacccctgaattgaataa
-
76The DIALIGN approach
- Multiple fragment alignment
- atctaatagttaaactcccccgtgcttag
- cagtgcgtgtattactaacggttcaatcgcg
- caaagagtatcacccctgaattgaataa
-
77The DIALIGN approach
- Multiple fragment alignment
- atctaatagttaaactcccccgtgcttag
- cagtgcgtgtattactaacggttcaatcgcg
- caaagagtatcacccctgaattgaataa
-
78The DIALIGN approach
- Multiple fragment alignment
- atctaatagttaaactcccccgtgcttag
- cagtgcgtgtattactaacggttcaatcgcg
- caaagagtatcacccctgaattgaataa
-
79The DIALIGN approach
- Multiple fragment alignment
- atctaatagttaaactcccccgtgcttag
- cagtgcgtgtattactaacggttcaatcgcg
- caaagagtatcacccctgaattgaataa
-
80The DIALIGN approach
- Multiple fragment alignment
- atctaatagttaaactcccccgtgcttag
- cagtgcgtgtattactaacggttcaatcgcg
- caaagagtatcacccctgaattgaataa
-
81The DIALIGN approach
- Multiple fragment alignment
- atc------taatagttaaactcccccgtgcttag
- cagtgcgtgtattactaacggttcaatcgcg
- caaagagtatcacccctgaattgaataa
-
82The DIALIGN approach
- Multiple fragment alignment
- atc------taatagttaaactcccccgtgcttag
- cagtgcgtgtattactaacggttcaatcgcg
- caaa--gagtatcacccctgaattgaataa
-
83The DIALIGN approach
- Multiple fragment alignment
- atc------taatagttaaactcccccgtgcttag
- cagtgcgtgtattactaac----------ggttcaatcgcg
- caaa--gagtatcacc----------cctgaattgaataa
-
84The DIALIGN approach
- Multiple fragment alignment
- atc------taatagttaaactcccccgtgc-ttag
- cagtgcgtgtattactaac----------gg-ttcaatcgcg
- caaa--gagtatcacc----------cctgaattgaataa
-
85The DIALIGN approach
- Multiple fragment alignment
- atc------taatagttaaactcccccgtgc-ttag
- cagtgcgtgtattactaac----------gg-ttcaatcgcg
- caaa--gagtatcacc----------cctgaattgaataa
- Consistency it is possible to introduce gaps
such that all segment pairs are aligned.
86The DIALIGN approach
- Multiple fragment alignment
- atc------TAATAGTTAaactccccCGTGC-TTag
- cagtgcGTGTATTACTAAc----------GG-TTCAATcgcg
- caaa--GAGTATCAcc----------CCTGaaTTGAATaa
-
87Program evaluation
- Use biologically verified alignments
- (known 3D structure of proteins)
- Compare alignments produced by
- computer programs to biologically correct
- alignments.
88Program evaluation
- (1) First evaluation of multiple alignment
programs (McClure, Vasi, Fitch,1994) - 4 protein families used
- Globin, kinase, protease, ribonuclease H,
- all globally related -gt global programs
- performed best
89Program evaluation
- (2) The BAliBASE (Thompson et al., 1999)
- 100 protein families with known 3D structure,
- some with large insertions/deletions.
90Program evaluation
1aboA 1 .NLFVALYDfvasgdntlsitkGEKLRVLgynhn
..............gE 1ycsB 1
kGVIYALWDyepqnddelpmkeGDCMTIIhrede............deiE
1pht 1 gYQYRALYDykkereedidlhlGDILTVNkgs
lvalgfsdgqearpeeiG 1ihvA 1
.NFRVYYRDsrd......pvwkGPAKLLWkg.................eG
1vie 1 .drvrkksga.........awqGQIVGWYctn
lt.............peG 1aboA 36
WCEAQt..kngqGWVPSNYITPVN...... 1ycsB 39
WWWARl..ndkeGYVPRNLLGLYP...... 1pht 51
WLNGYnettgerGDFPGTYVEYIGrkkisp 1ihvA 27
AVVIQd..nsdiKVVPRRKAKIIRd..... 1vie 28
YAVESeahpgsvQIYPVAALERIN...... Key alpha
helix RED beta strand GREEN core blocks
UNDERSCORE
91Program evaluation
Results Four programs performed best, but no
method was best in all test examples. ClustalW,
SAGA and RPPR best for global alignment, DIALIGN
best for sequences with large insertions
or deletions.
92Program evaluation
(3) Lassmann and Sonnhammer (2002) Used BAliBASE
plus artificial sequences for local
alignment Results T-COFFEE best for closely
related sequences, DIALIGN best for distal
sequences.
93Program evaluation
94Alignment of large genomic sequences
- Important tool for identifying functional
- sites (e.g. genes or regulatory elements)
95Alignment of large genomic sequences
- Phylogenetic Footprinting
- Functional sites more conserved during evolution
- gt Sequence similarity indicates biological
function
96Alignment of large genomic sequences
- DIALIGN performs well in identifying local
homologies, but is slow
97Quadratic program running time
98Quadratic program running time
99Quadratic program running time
100Quadratic program running time
101Quadratic program running time
102Quadratic program running time
103Quadratic program running time
104Solution Anchored alignments
105Solution Anchored alignments
106Solution Anchored alignments
107Solution Anchored alignments
108Solution Anchored alignments
109Solution Anchored alignments
110Solution Anchored alignments
111Solution Anchored alignments
Find anchor points to reduce search space
112Solution Anchored alignments
- Use fast heuristic method to find anchor points
- CHAOS developed together with Mike Brudno
- Brudno et al. (2003), BMC Bioinformatics 466
113Solution Anchored alignments
114(3) Anchored alignments
115(3) Anchored alignments
116First step to gene predictionExon discovery by
genomic alignment
117First step to gene predictionExon discovery by
genomic alignment
-
- Evaluation of different alignment programs
- Compare local sequence similarity identified by
alignment programs to known exons - Morgenstern et al. (2002), Bioinformatics
18777-787
118DIALIGN alignment of human and murine genomic
sequences
119DIALIGN alignment of tomato and Thaliana genomic
sequences
120- Evaluation of DIALIGN, PipMaker, WABA, BLASTN and
TBLASTX on a set of 42 human and murine genomic
sequences. - Compare similarities to annotated exons
- Apply cut-off parameter to resulting alignments
- Measure sensitivity and specificity
121Performance of long-range alignment programs for
exon discovery (human - mouse comparison)
122Performance of long-range alignment programs for
exon discovery (thaliana - tomato comparison)
123AGenDA Alignment-based Gene Detection Algorithm
- Bridge small gaps between DIALIGN fragments
- -gt cluster of fragments
- Search conserved splice sites and start/stop
codons at cluster boundaries to Identify
candidate exons - Recursive algorithm finds biologically consistent
chain of potential exons
124Identification of candidate exons
Fragments in DIALIGN alignment
125Identification of candidate exons
Build cluster of fragments
126Identification of candidate exons
Identify conserved splice sites
127Identification of candidate exons
Candidate exons bounded by conserved splice sites
128Construct gene models using candidate exons
- Score of candidate exon (E) based on DIALIGN
scores for fragments, score of splice junctions
and penalty for shortening / extending - Find biologically consistent chain of candidate
exons (starting with start codon, ending with
stop codon, no internal stop codons ) with
maximal total score -
129Find optimal consistent chain of candidate exons
130Find optimal consistent chain of candidate exons
131Find optimal consistent chain of candidate exons
132Find optimal consistent chain of candidate exons
133Find optimal consistent chain of candidate exons
atg
gt
ag
gt
ag
tga
atg
tga
134Find optimal consistent chain of candidate exons
atg
gt
ag
gt
ag
tga
atg
tga
G1
G2
135Find optimal consistent chain of candidate exons
Recursive algorithm calculates optimal chain of
candidate exons in N log N time
136DIALIGN fragments
137Candidate exons
138Complete model
139Results105 pairs of genomic sequences from
human and mouse (Batzoglou et al., 2000)
140Results105 pairs of genomic sequences from
human and mouse (Batzoglou et al., 2000)
141Results
- Quality of AGenDA-based gene models comparable to
results from GenScan - Exons identified that have not been identified by
GenScan - No statistical models derived from known genes
(no training data necessary!) - Method generally appliccable
142AGenDA Alignment-based Gene Detection Algorithm
- WWW server
- http//bibiserv/TechFak.Uni-Bielefeld.DE/agenda
- Rinner, Taher, Goel, Sczyrba, Brudno, Batzoglou,
Morgenstern, submitted
143(No Transcript)