robust alignment of drosophila genomes lior pachter eecs joint colloquium, october 5th 2005

Robust Alignment of Drosophila Genomes

Lior PachterEECS Joint Colloquium, October 5th 2005

GGGCTGGGCGAGTATCTCTTCGAAAGGCTCACTCTCAAGCACGACTAAGAGCCTTCTGAGC. . . . . . . . . . . .

What is genomics?. . .

GGGCTGGGCGAGTATCTCTTCGAAAGGCTCACTCTCAAGCACGACTAAGAGCCTTCTGAGC. . . . . . . . . . . .

What is genomics?

GLGEYLFERLTLKHD*. . . .

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are needed to see this picture.

. . .

What is genomics?

TTCCTTAGACTCTTAGAAAGTACCTCAAAAACGAAATGCGAACAC . . . . . . . . .

What is genomics?

TTCCTTAGACTCTTAGAAAGTACCTCAAAAACGAAATGCGAACAC . . . . . . .

What is genomics?

TTCCTTAGACTCTTAGAAAGTACCTCAAAAACGAAATGCGAACAC . . . . . . . ATGGAGT

....

. . .. microRNA

What is comparative genomics?

TTCCCTAG--------CAAGTACCTCA------------------TTCCCTAG--------CAAGTACCTCA------------------TTCCCTAG--------CAAGTACCTCA------------------TTCCTTAGACTCTTAGCAAGTACCTCA------------------TTCCTTAGACTCTTAGAAAGTACCTCAAAAACGAAATGCGAACACGACTCT----TTTTAGCAAGTACCTCAAAATATTTAATTAAA-AC ACTCTT----TTTTAGCAAGTACCTCAAGAATTACAATTAAATAT

TTCCTTAGACTCTTAGAAAGTACCTCAAAAACGAAATGCGAACAC

Grun et al. microRNA target predictions across seven Drosophila species and comparison to mammalian targets, PloS Computational Biology, June 2005Lall et al. A genome wide map of conserved microRNA targets in C. Elegans, submitted to Cell, 2005.

ATGGAGT.

...

. . .. let-7

The Drosophila Genome Project

• 1911 Genetic Mapping in Drosophila• Sturtevant and Morgan

• • •

• 2000 Drosophila melanogaster genome sequenced• Celera and LBNL publish Drosophila genome in Science

• 2003 Proposal for Drosophila as a model system for comparative genomics• Clark, Gibson, Kaufman, McAllister, Myers, O’Grady

• 2005 Twelve Drosophila genomes sequenced• Consortium involving Agencourt, Broad Institute, Baylor College Medicine, Washington University St. Louis and the Venter Institute.

Sequencing & Assembly Status Sequencing Center~3-fold WGS of w501 strain & 1-foldcoverage of 6 other strains complete(2 assemblies currently available; deepercoverage of w501 strain expected Fall ‘05)

Washington Univ.(WUGSC)

~3-fold WGS complete (assembly to bereleased by Sept 1)

Broad Institute

Release 4.2: 118.4 Mb with 23 gapsremaining (Release 5 in Fall 2005)

Celera/BDGP

~6-fold WGS complete (assembly inGenBank)(additional coverage - automated sequenceimprovement expected Fall ‘05)

Washington Univ(WUGSC).

~12-fold WGS complete & assembled Agencourt

~8-fold WGS complete & assembled Agencourt~9-fold WGS complete & assembled Baylor College of

Medicine (BCM)~4-fold WGS complete & assembled Broad Institute

~6-fold WGS (BAC paired ends currentlybeing sequenced; assembly to be released bySept 15)

Venter Institute(JCVI)

~8-fold WGS complete & assembled Agencourt~9-fold WGS complete & assembled Agencourt~8-fold WGS complete (assembly to bereleased by Sept 15)

Agencourt

Drosophila Projects

• Transposable Element Annotation• A. Caspi and L. Pachter, Identification of transposable elements using multiple alignments of related genomes, Genome Research, in press.

• Multiple Sequence Alignment• C. Dewey and L. Pachter, Whole Genome Mapping, in preparation.

• A.S. Schwartz, E.W. Myers and L. Pachter, Alignment metric accuracy, submitted.

• N. Bray and L. Pachter, MAVID: Constrained ancestral alignment of multiple sequences, Genome Research 14 (2004), p 693--699.

• Gene Finding• S. Chatterji and L. Pachter, Multiple organism gene finding by collapsed Gibbs sampling, Journal of Computational Biology, 12 (2005), p 599--608.

• S. Chatterji and L. Pachter, GeneMapper: Evidence based multiple organism gene finding, in preparation.

Drosophila Projects

• Transposable Element Annotation• A. Caspi and L. Pachter, Identification of transposable elements using multiple alignments of related genomes, Genome Research, in press.

• Multiple Sequence Alignment• C. Dewey and L. Pachter, Whole Genome Mapping, in preparation.

• A.S. Schwartz, E.W. Myers and L. Pachter, Alignment metric accuracy, submitted.

• N. Bray and L. Pachter, MAVID: Constrained ancestral alignment of multiple sequences, Genome Research 14 (2004), p 693--699.

• Parametric alignment• Gene Finding

• S. Chatterji and L. Pachter, Multiple organism gene finding by collapsed Gibbs sampling, Journal of Computational Biology, 12 (2005), p 599--608.

• S. Chatterji and L. Pachter, GeneMapper: Evidence based multiple organism gene finding, in preparation.

Available Drosophila whole genome multiple alignments

• MAVID• http://hanuman.math.berkeley.edu/kbrowser

• MULTIZ• http://genome.ucsc.edu/ (currently no D. erecta)

DroAna_20041206_ GTCGCTCAACCAGCATTTGCAAAAGTCGCAGAACTTGCGCTCATTGGATTTCCAGTACTCDroMel_4_ GTCGCTCAGCCAGCATTTGCAGAAGTCGCAGAACTTGCGCTCGTTTGATTTCCAGTACTCDroMoj_20041206_ GTCGCTTAACCAGCATTTACAGAAATCGCAATACTTGCGTTCATTGGATTTCCAGTACTCDroPse_1_ GTCGCTCAGCCAGCACTTGCAGAAGTCGCAGTACTTGCGCTCGTTTGATTTCCAGAATTCDroSim_20040829_ GTCGCTCAGCCAGCATTTGCAGAAGTCGCAGAACTTGCGCTCGTTTGATTTCCAGTACTCDroVir_20041029_ GTCGCTCAACCAGCATTTGCAGAAGTCGCAATACTTGCGTTCATTCGACTTCCAGTACTCDroYak_1_ GTCGCTCAGCCAGCATTTGCAGAAGTCGCAGAACTTCCGCTCGTTTGACTTCCAGTACTC ****** * ****** ** ** ** ***** **** ** ** ** ** ****** * **

Alignment of an exon

DroAna_20041206_ CTGAAGGAAT-------TCTATATT---------AAAGAAGATTTCTCATCATTGGTTGDroMel_4_ CTGCGGGATTAGGGGTCATTAGAGT---------GCCGAAAAGCGA---------GTTTDroMoj_20041206_ CTGGAATAGTTAATTTCATTGTAACACATAAACGTTTTAAATTCTATTGAAA-------DroPse_1_ CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCG----DroSim_20040829_ CTGCGGGATTAGGAGTCATTAGAGT---------GCGGAAAAGCGG---------GTT-DroVir_20041029_ CTGCAGCAGTTAAATA-ATTGTAATAAACAATTCTCT--AATTTGGTCCAAA-------DroYak_1_ CTGCGGGATTAGCGGTCATTGGTGT---------GAAGAATAGATC---------CTTT *** * * * DroAna_20041206_ AATC-----ACTTACDroMel_4_ ATTCTATGGACTCACDroMoj_20041206_ ----TATTTACTCACDroPse_1_ ------TGTACTTACDroSim_20040829_ ATTCTATGGACTCACDroVir_20041029_ ----TATTTACTCACDroYak_1_ ATTTCATAAACTCAC

*** **

Alignment of an intron

DroAna_20041206_ GTCGCTCAACCAGCATTTGCAAAAGTCGCAGAACTTGCGCTCATTGGATTTCCAGTACTCDroMel_4_ GTCGCTCAGCCAGCATTTGCAGAAGTCGCAGAACTTGCGCTCGTTTGATTTCCAGTACTCDroMoj_20041206_ GTCGCTTAACCAGCATTTACAGAAATCGCAATACTTGCGTTCATTGGATTTCCAGTACTCDroPse_1_ GTCGCTCAGCCAGCACTTGCAGAAGTCGCAGTACTTGCGCTCGTTTGATTTCCAGAATTCDroSim_20040829_ GTCGCTCAGCCAGCATTTGCAGAAGTCGCAGAACTTGCGCTCGTTTGATTTCCAGTACTCDroVir_20041029_ GTCGCTCAACCAGCATTTGCAGAAGTCGCAATACTTGCGTTCATTCGACTTCCAGTACTCDroYak_1_ GTCGCTCAGCCAGCATTTGCAGAAGTCGCAGAACTTCCGCTCGTTTGACTTCCAGTACTC ****** * ****** ** ** ** ***** **** ** ** ** ** ****** * **

Alignment of an exon

Alignment of an introndroAna1.2448876 CTGAAGGAATTCTA--TATTAAAG-----------------------------------dm2.chr2L CTGCGGGATTAGGGGTCATTAGAG---------TGCCGAAA----AGCGAGT-TTATTCdroMoj1.contig_2959 CTGGAATAGTTAATTTCATTGTAA---------CACATAAA------CGTTTTAAATTCdp3.chr4_group3 CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGG----AGAGGCCATCATCGdroSim1.chr2L CTGCGGGATTAGGAGTCATTAGAG---------TGCGGAAA----AGCGGG--TTATTCdroVir1.scaffold_6 CTGCAGCAGTTAA-ATAATTGTAA---------TAAACAA--------TTCTCTAATTTdroYak1.chr2L CTGCGGGATTAGCGGTCATTGGTG---------TGAAGAAT----AGATCCT-TTATTT *** * * * *

droAna1.2448876 AAGATTTCTCATCATTGGTTGAATC---------------------ACTTAC dm2.chr2L -----------------------------------------TATGGACTCACdroMoj1.contig_2959 -------------------------AAATATTT--------TATTGACTCACdp3.chr4_group3 -----------------------------------------TGT--ACTTACdroSim1.chr2L -----------------------------------------TATGGACTCACdroVir1.scaffold_6 ---------------------------------AAATATTTGGTCCACTCACdroYak1.chr2L -----------------------------------------CATAAACTCAC *** **

dm2.chr2L CTGCGGGATTAGGGGTCATTAGAG---------TGCCGAAAAGCGAGT-TTATTCdp3.chr4_group3 CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCG

dm2.chr2L TATGGACTCACdp3.chr4_group3 TGT--ACTTAC

How is an alignment made from the sequences?

>dm2.chr2L CTGCGGGATTAGGGGTCATTAGAGTGCCGAAAAGCGAGTTTATTCTATGGACTCAC>dp3.chr4_group3CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCGTGTACTTAC

?

Given two sequences of lengths n,m:

Note that the length of an alignment is at least max(n,m) and at most n+m.

n=50

m=62



DroMel_4_ CTGCGGGATTAGGGGTCATTAGAGT---------GCCGAAAAGCGA---------GTTTDroPse_1_ CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCG---- DroMel_4_ ATTCTATGGACTCACDroPse_1_ ------TGTACTTAC

Each alignment can be summarized by counting the number of matches (#M), mismatches (#X), gaps (#G), and spaces (#S).



DroMel_4_ CTGCGGGATTAGGGGTCATTAGAGT---------GCCGAAAAGCGA---------GTTTDroPse_1_ CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCG---- DroMel_4_ ATTCTATGGACTCACDroPse_1_ ------TGTACTTAC

Each alignment can be summarized by counting the number of matches (#M), mismatches (#X), gaps (#G), and spaces (#S).

#M=31, #X=22, #G=3, #S=12

#M=27, #X=18, #G=3, #S=28

2(#M+#X)+#S=112 so #X,#G and #S suffice to specify a summary.

This notation follows Chapter 7 (Parametric Sequence Alignment) by Colin Dewey and Kevin Woods in the book Algebraic Statistics for Computational Biology.

The summary of an alignment is a point in 3 dimensional space. For example, the two alignments just shown correspond to the points:

(22,3,12) (18,3,28)

In the example of our two sequences there are 379522884096444556699773447791552717765633different alignments, but only53890 different summaries. So we don’t need to plot that many points.

But 53890 is still quite a large number. Fortunately, there are only 69 vertices on the convex hull of the 53890 points.

That is something we can draw…

>melCTGCGGGATTAGGGGTCATTAGAGTGCCGAAAAGCGAGTTTATTCTATGGAC>pseCTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCGTGTAC

For the sequences:

49 #x=24, #S=10, #G=2

There are eight alignments that have this summary.

the alignment polytope is:

mel CTGCGGGATTAGGGGTCATTAGAGT---------GCCGAAAAGCGAGTTTATTCTATGGACpse CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATC-GTGTAC

mel CTGCGGGATTAGGGGTCATTAGAGT---------GCCGAAAAGCGAGTTTATTCTATGGACpse CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCG-TGTAC

mel CTGCGGGATTAGGGGTCATTAGAG---------TGCCGAAAAGCGAGTTTATTCTATGGACpse CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATC-GTGTAC

mel CTGCGGGATTAGGGGTCATTAGAG---------TGCCGAAAAGCGAGTTTATTCTATGGACpse CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCG-TGTAC

mel CTGCGGGATTAGGGGTCATTAGA---------GTGCCGAAAAGCGAGTTTATTCTATGGACpse CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATC-GTGTAC

mel CTGCGGGATTAGGGGTCATTAGA---------GTGCCGAAAAGCGAGTTTATTCTATGGACpse CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCG-TGTAC

mel CTGCGGGATTAGGGGTCATTAG---------AGTGCCGAAAAGCGAGTTTATTCTATGGACpse CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATC-GTGTAC

mel CTGCGGGATTAGGGGTCATTAG---------AGTGCCGAAAAGCGAGTTTATTCTATGGACpse CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCG-TGTAC

mel CTGCGGGATTAGGGGTCATTAGAGT===------===GCCGAAAAGCGAGTTTATTCTA=TGGACpse CTGGAAGAGTTTTGATTAGTAG===GGGATCCATGGGGGCGAGGAGAGGCCATCATC==GTGTAC

Consensus at a vertex

The vertices of the polytope have special significance.

Given parameters for a model, e.g. the default parameters for MULTIZ:

M = 100, X = -100, S = -30, G = -400

the summary is the result of maximizing the linear form

-200*(#X)-400*(#G)-80*(#S)

over the polytope.

Thus, the vertices of the polytope correspond to optimal alignments.

49 #x=24, #S=10, #G=2

What is usually done, is that a single set of parameters is specified (M = 100, X = -100, S = -30, G = -400 is a standard default) and then the optimal vertex is identified using dynamic programming. An alignment optimal for the vertex is then selected. The running time of the algorithm is O(nm) [Needleman-Wunsch, 1970, Smith-Waterman, 1981] and it requires O(n+m) space [Hirschberg 1975] .

Standard scoring schemes are:

Parameters Model

M,X,S Jukes-Cantor with linear gap penalty

M,X,S,G Jukes-Cantor with affine gap penalty M,XTS,XTV,S,G Kimura-2 parameter with affine gap

penalty

Needleman-Wunsch Alignment

Available Drosophila whole genome multiple alignments

• MAVID• http://hanuman.math.berkeley.edu/kbrowser

• MULTIZ• http://genome.ucsc.edu/ (currently no D. erecta)


*** **

N. Bray and L. Pachter, MAVID: Constrained ancestral alignment of multiple sequences, Genome Research 14 (2004) p 693--699

MAVID

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Needleman-Wunsch

droAna1.2448876 CTGAAGGAATTCTA--TATTAAAG-----------------------------------dm2.chr2L CTGCGGGATTAGGGGTCATTAGAG---------TGCCGAAA----AGCGAGT-TTATTCdroMoj1.contig_2959 CTGGAATAGTTAATTTCATTGTAA---------CACATAAA------CGTTTTAAATTCdp3.chr4_group3 CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGG----AGAGGCCATCATCGdroSim1.chr2L CTGCGGGATTAGGAGTCATTAGAG---------TGCGGAAA----AGCGGG--TTATTCdroVir1.scaffold_6 CTGCAGCAGTTAA-ATAATTGTAA---------TAAACAA--------TTCTCTAATTTdroYak1.chr2L CTGCGGGATTAGCGGTCATTGGTG---------TGAAGAAT----AGATCCT-TTATTT *** * * * *


Blanchette et al., Aligning multiple sequences with the threaded blockset aligner, Genome Research 14 (2004) p 708--715

MULTIZ



Needleman-Wunsch


droAna1.2448876 -----ACTTAC dm2.chr2L TATGGACTCACdroMoj1.contig_2959 TATTGACTCACdp3.chr4_group3 TGT--ACTTACdroSim1.chr2L TATGGACTCACdroVir1.scaffold_6 GGTCCACTCACdroYak1.chr2L CATAAACTCAC *** **


*** **

One (possibly wrong) alignment is not enough: the history of parametric

inference• 1992: Waterman, M., Eggert, M. & Lander, E. • Parametric sequence comparisons, Proc. Natl. Acad. Sci. USA 89, 6090-6093

• 1994: Gusfield, D., Balasubramanian, K. & Naor, D. • Parametric optimization of sequence alignment, Algorithmica 12, 312-326.

• 2003: Wang, L., Zhao, J. • Parametric alignment of ordered trees, Bioinformatics, 19 2237-2245.

• 2004: Fernández-Baca, D., Seppäläinen, T. & Slutzki, G. • Parametric Multiple Sequence Alignment and Phylogeny Construction, Journal of Discrete Algorithms, 2 271-287.



XPARAL by Kristian Stevens and Dan Gusfield

Whole Genome Parametric AlignmentColin Dewey, Peter Huggins, Lior Pachter, Bernd Sturmfels and

Kevin Woods

Mathematics and Computer Science

• Parametric alignment in higher dimensions.• Faster new algorithms.• Deeper understanding of alignment polytopes.

Biology

• Whole genome parametric alignment.• Biological implications of alignment parameters.• Alignment with biology rather than for biology.

Whole Genome Parametric AlignmentColin Dewey, Peter Huggins, Lior Pachter, Bernd Sturmfels and

Kevin Woods

Mathematics and Computer Science

• Parametric alignment in higher dimensions.• Faster new algorithms.• Deeper understanding of alignment polytopes.

Biology

• Whole genome parametric alignment.• Biological implications of alignment parameters.•

CTGAAGGAAT-------TCTATATT---------AAAGAAGATTTCTCATCATTGGTTGCTGCGGGATTAGGGGTCATTAGAGT---------GCCGAAAAGCGA---------GTTTCTGGAATAGTTAATTTCATTGTAACACATAAACGTTTTAAATTCTATTGAAA-------CTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCG----CTGCGGGATTAGGAGTCATTAGAGT---------GCGGAAAAGCGG---------GTT-CTGCAGCAGTTAAATA-ATTGTAATAAACAATTCTCT--AATTTGGTCCAAA-------CTGCGGGATTAGCGGTCATTGGTGT---------GAAGAATAGATC---------CTTT

analysis



computational geometry

(#X #S #G)[#alignments]40 (15,16,16)[1080]41 (17,30,2)[4] 42 (18,14,5)[4]43 (18,16,4)[56]44 (20,10,6)[16]45 (20,10,7)[24]46 (23,8,6)[6]47 (23,8,8)[165]48 (24,8,3)[38]49 (24,10,2)[8]50 (25,8,2)[24]51 (25,62,3)[2]52 (28,48,2)[1]53 (29,8,1)[6]

Finding the polytope is called parametric inference.This polytope took 3 seconds to compute using the beneath-beyond method [Grünbaum, Convex Polytopes, 1967].

>melCTGCGGGATTAGGGGTCATTAGAGTGCCGAAAAGCGAGTTTATTCTATGGAC>pseCTGGAAGAGTTTTGATTAGTAGGGGATCCATGGGGGCGAGGAGAGGCCATCATCGTGTAC

Associated to every pair of sequences is a polynomial built from the “summaries” of the alignments.

49 #x=24, #S=10, #G=2

corresponds to the monomial 8X24S10G2

For example:

How do we build the polytope for ?

NPi,j = S*NPi-1,j+S*NPi,j-1+(X or M)*NPi-1,j-1

A

A

C

A

T

T

A

G

AA G A T T A C C A C A

Newton polytope forpositions [1,i] and [1,j]

in each sequence

Convex hull of union Minkowski sum

Polytope propagation

Complexity of polytope propagation

Theorem: The number of vertices of an alignment polytope for two sequences of length n and m is O((n+m)d(d-1)/(d+1)) where d is the number of free parameters in the scoring scheme.

Examples: Parameters Model Vertices M,X,S Jukes-Cantor with linear gap penaltyO(n+m)2/3

M,X,S,G Jukes-Cantor with affine gap penaltyO(n+m)3/2

M,XTS,XTV,S,G K2P with affine gap penalty O(n+m)12/5

L. Pachter and B. Sturmfels, Parametric inference for biological sequence analysis, Proceedings of the National Academy of Sciences, Volume 101, Number 46 (2004), p 16138--16143.L. Pachter and B. Sturmfels, Tropical geometry of statistical models, Proceedings of the National Academy of Sciences, Volume 101, Number 46 (2004), p 16132--16137.

Inference functions

Definition: Given two integers n and m and a scoring scheme for sequence alignment, an inference function assigns to every pair of sequences of lengths n and m respectively, an (optimal) alignment.

Remark: The number of inference functions could, in principle, be

doubly exponential in n+m. This is because the number of alignments is the Delannoy number D(n,m), which is

exponentialin n+m, and the number of sequence pairs is 4n+m.

Few inference functions theorem

Theorem (S. Elizalde 2005): The number of inference functions for two parameter alignment model with two sequences of length n is (n2).

Proof (outline):

1. The number of inference functions is the number of vertices of the Minkowski sum of the Newton polytopes of the observations.

2. The Newton polytopes are all lattice polytopes, and therefore have few non-parallel edges.

3. The number of vertices of the Minkowski sum is at most

where m is the number of non-parallel edges and d is the dimension of the polytopes.

Algebraic Statistics -- A language for unifying and developing many of the algorithms for biological

sequence analysis --

• The few inference functions theorem

• Polytope propagation

• Phylogenetic tree reconstruction

• Evolutionary models

• Maximum likelihood estimation

• Mutagenic tree models



QuickTime™ and aYUV420 codec decompressor




ATCCAGAAGTCTAGTATACATCTCAAAATTCATGCATCTGGCCGGGCACAGTGGCTCACACCTGCAATCCCAGCACTTTGGGAGGCCGAGGTGGGTGGATTACCTGAGGTCAGGAGTTTAAGACCAGCCTGGCCAACATGGTAAAACCCCATCTCTACTAAAAATACAAGTATTAGCCAGGCATTGTGGCAGGTGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAAAATCACTTGAACCGGGAGGCGGAGGTTGGAGTGAGCTGAGATCGTGCTACCGCACTCCATGCACTCTAGCCTGGGCAACAGAACGAGATGCTGTCACAACAACAACAACAACAACAACAACAACAACAACAACAACAACAAATTCTCACATCTAAAACAGAGTTCCTGGTTCCATTCCTGCTTCCTGCCTTTCCCACTCCCCCATATTCCCTACCATGCCTTCTTCATCTAATTTAATATTACTAACAAGATCTATTGTTCAAGCCAAAACCCAAGTGTCACTCCTTCAATTTCTCTTTACCTTATCCTCCAAATTTAATCCATTAGCAAGTCCTCTCTTCAAACCCATCCCAAACCAACCTTGTTTTTAACCATCTCCACACCACCAATTACCACAAGGATAAAATCTGAATTCCTTACCACCAAATACTATGTGATCTGGCCCTCATCTATGACCTTCTCCCATTCCTTGTGTAATCTCTGCCTCCACACATAATTTGCAAATTACTCCAGCTACACTGGCCTATTATTATTATTATTATTATTTTTGAGACGGAGTCTTGCTCTTTCGCCCAGCCTGGAGTGCAGTGGCGCAATCTCAGCTCACTGCAATCTCCGCCTCCTGGGTTCAAGCGATTCTCCTGCCCCAGCCTCCCAAGTAGCTGTGATTACAGGCACATGCCACCATTCCCAGCTAATTTTTTTTTGTTTTTGAGATGGAGTTTCACTCTTGTTGCCCAGGCTGGAGTGCAATGGTGCGATCTCAGCTCACCACAACCTCCACCTCCCGGGTTGATGAAGTGATTCTCTTGTCTCAGCCTCCCGTGTAGCTGGGATTAGAGGCACGCGCCACCACGCTGGGCAAATTTTTGTATTTTTAGTAGAGACAGGGTTTCTACCTCAGTGATCTGTCCGCCTTGACCTCCCAAAGTGCTGGGATTACAGGAATGAGCCACCACACCCAGCCGTGCCCAGCTAATTTTTGCATTTTTTAGTAGAGATGGGGTTTTGCCACGTTGGCCAGGCTGGTCTCAAACTCCTGACCTCAGGGGATCTGCCTGCCTCGGCCTCCTAGAGTGCTGGAATTACAGGTGTGAGCCACTGTGCCCGAACCTTTTATCATTATTATTTCTTGAGACAGGAGTCTTGCTCTGTCGTTCAGGCTGGAGTGCAGTGATGCGATCTTGGCTCACTGTAACTCCTACCTTTCGGTTCAAGTGATTCTCCTGCCTCAGCCTCTGGAGTAGCTGGGATTACAGGCACTGGGATTACAGGCACACACCACCACACCATGCTAGTTTTTTGTATTTTTAGTAGAGATGGGGTTTCACCATGTTGGCCAGGCTGGTCTCGAACTCCTGACCTCAAGTGATTTGCCTGCCTTGGCTTCCCAAAGTGCTGGGATTATAGGCACGAGCCACCACACACGACCAACATTGGCCTATCTTTTAAAAAATAAACCAAGCTCTGGCCGGGCACAGTGGCTCACACCTGTGATCCCAGCACTTTGGGAGGTTGAGGTGGTTGGATCACTTGAGTTCAGGAGTTTGAGACCAGCCTGACCAACGTGGTAAAACCCCATCTCTACTAAAAATAAAAACTAGTCGGGTGTGGTAGCACGCGTGCCTGTAATACCAGCTACTCAGGAGGCCAAGGCAGGAGAATTGCTTGAACCCAGGAGACAGAGTTTGCAGTGAGCCAAGATTGTGCCACTGCACTCCAGCCTGGGGGATAGAGGGAGACACCATCTCAAAAAAACCAAAATACAGAAATCAAAAAACCACACTCATTATTACCTCAAGACCTTTATGTTTGCTATTCCTCTGCCTATAAGATGCATTCCCTTCATTTTTCAAGGACAATTATTTCTTGTTATTTAGGTCTCAGCTCAATTTTTTCAGAAAGGCTTTCCCTGGCCTCCTTAAACGAAAGTAATCAACAACCTTTGACAGCTAATACTATTCCACTGTTCTGTATATTTCTCCATAGCATTTATTGTTATCTTAAATTCATCTTTATTGTGTATCTCCCCTCGACAGAACCTGAATCCTACCAGGGACTTAGTTAGTCTTATTTACTGTTGCATTCCTAGTGCCCAGAACACAGTAGGCTCCCAATAAATAGCCACTGAATAAAAGTTAAAACCAACAAAAATAATCATTTAATTAATTATGAATACATCGAATTGTGCACAATAGTTTATAAAATTACTTTTTTTTTTTTTTTAAGACAGGGTCTCATTCTGTCTCACAGGCTGGAGTGCAGTGGTGCAATCTAGGCTCACTGCAACCTCCGCCTCCCGGGTTCAAGTGATTCTCCTGCCTCAGCCTCCCCAGCAGCTAGGATTACAGGCACATGCCACCACGCTCGACTAATTTTTTTGTGTTTTTAGTAGAGACAAGGTTTCACCATGTTGACCAGGCTGGTCTCGAACTCCTGACCTCAAGTGATCCACCTGCCTTGGCCACTCAAAGTGCTGGGATTATAGGCATGAGCCACCACGCCTGGCCTATAAAATTACTTTCACATTTCATTTTGCCTGATCTGTTGTCACAGAAGTTCTCAGATGGCTGTTCTGAAATTATTCCTCCTCCTACACTCTATCTTATTTACTTCTCACTGTTCTCAGTATCATAAAGTGCAACATCTTTTTGAAGCAATCTGAATTATAAACAGATACATTTGCATGTATATATATGTATATATGCATATGCACACACACACTTTTTTTTTTTTAAGAGACAGGGTCTTGCTCTGTGCAAGTGCAAGAGTGCAATGGTATGATCATAGCTCACTGCAGCCTTGAACTCCTGGGCTCAAGTGATTCTTCTGGCTTAGCTTCCTCAGTAGCTAAGACTACAGAAGCACACTGCCATGCCCGGCTAATTAAAAAAAAATTTTGTGGAGACAGAGTCTCACTATGTTGCCCAGGCTGGTTTCAAACTCCTGGCCTCAAGTAATCTTCCTGTCTCAGCCTCCCAAAGGGCTGAGATTATAAGTGTGAGCCACTGCATCTGGACTGCATATTAATATGAAGAGCTTTTCTTCAACAACAGTGAACAGTTTTCTACAAAGGTATATGCAAGTGGGCCCACTTCTTGTTCTTATGAATCTTTTCTTTCCTTTTATAAAACTCCTTTTCCTTTCTCTTTTCCCCAAAGAAAGGACTGTTTCTTTTGAAATCTAGAACAAATGAGAACAGAGGATATCCTGGTTTGCGCTGCAAAATTTTTTTTTTTTTTAAGACGGAGTCTCGCTCTGTTGCCAGGTTGGAGTGCAGTGGCACGATCTTGGCTCATTGCAACCTCCACCTCCCGGGTTCAAGAGATTCTCCTGCCTCAGCCTCCTGAGTAGCTGGAACTAAAGGCGCATGCCACCACGCTGAGTAATTTTTTGTATTTTAGTAGAGACAGGGTTTCACCATGTTGCCCAGGCTGATCTCGAACTCCTGAGCTCAGGCAATCTGCCTGTCTTGGCCTCCCACAGTGTTAGGATTACAGGCATGAGCCACTGCACCCGATTTTTTTTTTCTTTTGATGGAGTTTTGCTCTTGTTGCCCAGGTTAGAGTGCAATGATGCGATCTCAGCTCACTGCAACCCCCGCCTCCCAGGTTCAAGTGATTCTCCTGCCTCAGCCTCCCGAGTAGCTGGAATTACAGGCAAGTGCCACCAAGCCCGGCTAATTTTGTATTTTTAGTAGAAACGGGGTTTCTCCATGTTGGTCAGGCTGGTCTTGAACTCCCGACATCAGGTGATCCAAGCGCCTCAGCCTCCCAAAGCGCTGGGATTATAGGTATGAGCCACAGTGCAGGCCTGCATAATTCTTGATGATCCTCATTATCATGGAAAATTTGTGCATTGTTAAGGAAAGTGGTGCATTGATGGAAGGAAGCAAATACATTTTTAACTATATGACTGAATGAATATCTCTGGTTAGTTTGTAACATCAAGTACTTACCTCATTCAGCATTTTTCTTTCTTTAATAGACTGGGTCACCCCTAAAGAGATCATAGAAAAGACAGGTTACATACAGCAGAAGAACGTGCTCTTTTCACGGAGATAGAGAGGTCAGCGATTCACAAAAGAGCACAGGAAGAATGACAGAGGAGAGGTCCTTCCCTCTAAAGCCACAGCCCTTTAATAAGGCTTGTAGCAGCAGTTTCCTTCTGGAGACAGAGTTGATGTTTAATTTAAACATTATAAGTTTGCCTGCTGCACATGGATTCCTGCCGACTATTAAATAAATCCCTAGCTCATATGCTAACATTGCTAGGAGCAGATTAGGTCCTATTAGTTATAAAAGAGACCCATTTTCCCAGCATCACCAGCTTATCTGAACAAAGTGATATTAAAGATAAAAGTAGTTTAGTATTACAATTAAAGACCTTTTGGTAACTCAGACTCAGCATCAGCAAAAACCTTAGGTGTTAAACGTTAGGTGTAAAAATGCAATTCTGAGGTGTTAAAGGGAGGAGGGGAGAAATAGTATTATACTTACAGAAATAGCTAACTACCCATTTTCCTCCCGCAATTCCTAGAAAATATTTCAGTGTCCGTTCACACACAAACTCAGCATCTGCAGAATGAAAAACACTCAAAGGATTAGAAGTTGAAAACAAAATCAGGAAGTGCTGTCCTAAGAAGCTAAAGAGCCTCAGTTTTTTACACTCCCAAGATCAATCTGGATTTATGATTCTAAAACCCCTGGTGACAGAATCAGAGGCTGAAAACACCACTAATTATAACCAGCAGGTATGGATATTTGGAAGTCTAGGGGAGGCTGATATGAAGTTAAGACCAGAGGAAATATCTGTCCACTCCCTCTTCTCAACACCCATCTTCTAGACGCCAAGGCTAGCTATAGATCTCCATTATAGTGTTCAAGGAATTAGGAATTATCCATGTCAATAGTTTTGATTAATGTGGACGGAGAACATCTATATTACTAGATGGCAATATGTGAAAGAAGAAAACAGTATTGTTGAAAACCTAAATCTGAAATGTCAATGTAATGACAAATTTTCACCCCTAGAATGTCTACCTGGGGAGTCCTAACCCTCTAATATTCCCCTGAGAGGGATGGGAGAATACAGTGCAGAGCTTTTATATAAGTATTTCAGAAAGCAGTAGCTAAAGAATCACTTGTTTATTTCCCAGTGTTTCAAAGGCCCTTCTGAAGAACTAAGCAAACTAAGGAAAGACCATTTAGTTTTAAACAGGAGAAATGTATTTAACTAAATCCTAAACACAGCAGGCTATCTGCAAGCAGCAGCAGCAGCAGCAGCCATGCTCCCTCACAGAATCCTTACAATTTTTGAAGTTTTTTGTTTAACTGCTACAAAAGCCGATTTAGTAACATTTATTACACTTAAAAACTTCAGTTCATTTGTAGTTCAAAGCAAATGTATTGGCTTTGAGTTTAAAGACTGAACTACTTTAGATTTGATTTGCATTTTTTTTTTTTTTTTTTTTTGAGATGCAGTCTTGCTCTGTCAGCCAGGCTGGAGTGCAGTGGCTGGATCTCAGCTCACGGCAAGCTCTGCCTCCTGGGTTCATGCCATTCTCCTGCCTCAGCCTCCTGAGTAGCTGGGACTACAGATGCCCGCCACCATGCCCGGCTAATTTTTTGTATTTTTACTAGAGATGGGGTTTCACCGTGTTAGCCAGGATGGTCTCGATCTCCTGACCTCGTGATCTGCCCGCCTTGGCCCCCCAAAGCGCTGGGATTACAGGCCTGAGCCACCACGCTTGGCATCTTTTTACCTTTCATTAACTTTGATGCAAACCTATAGCTTAAGGTATCTTAAACTTTAATGACATTTTTCTCTAAAATAGTAGTTTGTAATAACTTGTTCTGGCACCTGGCTCCAATGAACACTACCCTCTGACCCTGTGGTATAATTTTCATGAGTAAGTGGAAACCTAAGATCTTAGAAGTTCAACGGCAATGTGTCCAAGGGGTTTAGATCCTCTCCTTAAGTGCCTGTATCTCTGTGAAAAGAATCATCATAGGCTAGGCGCGATGGCTCACACCTGTAATCCCAGCACTTTGGGAGGCCGAGGTAGGTGGATCACCTGAGGTCGGGAGTCCAAGACCAGCCTGACTGACATGGAAAAACCCTGTCTCTACTAAAAATACAAAATTAGGTATGGTGGTGCATTCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGGGGAGGTTGCAGCAAGCCAAGATCGTGCCATTGCACTCCAGCAGCCTGGGCAACAAGAGTGAAAAACTACACCTCAAAAACAAAAACAAAAACAAAAGAATCATCATCAAGTGAACTGGAACACATCCAGAGAACTAATTTTGTTAGAAAGATTTTAGAGTTGAGCCACACAATCTGCATCTTCTGCGTCCTCCATGCACTCGTCTGCTTTCTGGAGCCCCATGAGTGAGTCTTAATCCTGTTCCAGATAACAGTTCTCTTCCGGGTAACGGTTCTTCAGATACTTGAAGACAGTGTCTTATTTCCTTAAATCTTCTCATTTCTTCTTCAAAAGACAGTATTTCAAGTTACTTTTATGTATCTTTACCATCTACCTCTGGATAAACACTCTCCAATTTGTCAGTGACCATGTTAAAAACCAAGCACGGTGCTTAAAACTGACATCATCTTTCAGGCAATCACTCCATTGGAGAATACAGTGGGGCTCTGGATCTGTACTTCACTTGCTCCAGAGCCTCTGCTTGTGTTAATACGGCCCAGTTTCAAATAAGCATTTTTAGCAGCCCTGAAATGTGTACTCAGATTTAGTTTATAGTCAACTAAAAACACCCAGAGGTCTCCTGTATTACACAAGTTATAATTAAAACCTTAAAAGAGAAAGGTATAGGACAAATGATCTGTCTCCTCCCTTTTTTGCTTTTTCATATGTTAAGACTATCTCGGAGCTGTTATCAGACTT

robust alignment of drosophila genomes lior pachter eecs joint colloquium, october 5th 2005

Documents

drosophila genome project

genome research

microrna slide

genome mapping

multiple sequence alignment

multiple organism gene

drosophila sturtevant

drosophila species