bio medical tics - sequence analysis- alignment- 2011

8/4/2019 Bio Medical tics - Sequence Analysis- Alignment- 2011

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D N A S E Q U E N C I N G

& S E Q U E N C E A L I G N M E N T

Sequence Analysis


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Sequence Alignment


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Study Goal

What is a sequence alignment?

The difference between a global and local alignment and what theuses of each are.

How to use the dot matrix methods to analyze genes andchromosomes

The steps performed by the Needleman-Wunsh and Smith-Waterman Algorithms to produce a sequence alignment

How to use scoring matrix values and gap penalties to produce asequence alignment


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Sequence Alignment

Definition: the comparison of two or more sequences bysearching for a series of individual characters or characterpatterns that are in the same order in the sequences

Sequence alignment score:

Sum of the individual log odds scores for each pair of alignedsequence characters in an alignment less a penalty for each gap ofone more position


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Pair-wise Sequence Alignment

-AGGCTATCACCTGACCTCCAGGCCGA--TGCCC---

TAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC

DefinitionGiven two strings x = x1x2...xM, y = y1y2yN,

an alignment is an assignment of gaps to positions0,, N in x, and 0,, N in y, so as to line up eachletter in one sequence with either a letter, or a gapin the other sequence

AGGCTATCACCTGACCTCCAGGCCGATGCCC

TAGCTATCACGACCGCGGTCGATTTGCCCGAC


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What is a good alignment?

AGGCTAGTT, AGCGAAGTTT

AGGCTAGTT- 6 matches, 3 m ismatches, 1 gap

AGCGAAGTTT

AGGCTA-GTT- 7 m atches, 1 m isma tch, 3 gaps

AG-CGAAGTTT

AGGC-TA-GTT- 7 m atches, 0 m isma tches, 5 gapsAG-CG-AAGTTT


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Evolution at the DNA level

SEQUENCE EDITSACGGTGCAGTTACCA

AC----CAGTCCACCA

MutationDeletion

REARRANGEMENTS

InversionTranslocationDuplication


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Evolutionary

Still OK?

OK

OK

OK

X

X

next generation


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Scor ing Function

Sequence edits: AGGCCTC

Mutations AGGACTC

Insertions AGGGCCTC Deletions AGG . CTC

Scor ing Function: Match: +m

Mismatch: -s

Gap: -d

Score F = (# matches) m - (# mismatches) s(#gaps) d

Alternative definition:

m in im a l ed i t d i st a n ce

Given two strings x, y,find minimum # of edits

(insertions, deletions, mutations)

to transform one string to theother


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Pair-wise Alignment

The alignment of two sequences (DNA or protein) is

a relatively straightforward computational problem. There are lots of possible alignments.

Two sequences can always be aligned.

Sequence alignments have to be scored. Often there is m ore than one solution with the

same score.


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How do we compute the best alignment?

AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA

AGTGACCTGGGAAGACC

CTGACCCTGGGTCACAAAACTC

Too many possible

alignments:

>> 2N


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Local alignment vs. Global Alignment

Use to align the entire sequence

Best for same length sequence


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Local alignment vs. Global Alignment

Use to align the similar sequence along certain length

Best for sequence sharing a conserved region or domain


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What do we want alignment for?

Xenologous transferred genes

Orthologous


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Matches to similar sequences

Sequence conservation Structure conservation

function conservation What is conserved in a gene [protein] family is functionally important

Due to purifying selection driven by functional constraints observable in abckground described by the theory of neutral evolution

Fast enough that pseudogenes rapidly deteriorate over evolutionarytimescale

In any prokaryotic genome, homologs from more than one distantly relatedspecies are detectable for 70 80 % of proteins

Application: Comparison of sequence/structures can identifyhomologous relationships, allowing inference of function based on thatrelationship


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Methods of Alignment

By hand - slide sequences on two lines of a word

processor Dot plot

with windows

Rigorous mathematical approach Dynamic programming (slow, optimal)

Heuristic methods (fast, approximate)

BLAST and FASTAWord matching and hash tables0


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Align by Hand

GATCGCCTA_TTACGTCCTGGAC AGGCATACGTA_GCCCTTTCGC

You still need some kind of scoring system to find thebest alignment


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Dotplot19

A

T

T

C

A C

A

T

A

T A C A T T A C G T A C

Sequence 1

Sequence 2

A dotplot gives an overview of all possible alignments


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Dotplot20

A

T

T

C

A

C A

T

A



A T A C A C T T A

Sequence 1

Sequence 2

One possible alignment:

In a dotplot each diagonal corresponds to a possible(ungapped) alignment


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21Insertions / Deletions in a DotplotT

A

CT

G

T

C

A

T

T A C T G T T C A TSequence 1

Sequence 2

T A C T G - T C A T| | | | | | | | |

T A C T G T T C A T


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Hemoglobin -chain

Hemoglobin

-chain

Dotplot(Window = 130 / Stringency = 9)


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23Word Size Algorithm

TA C G G T A T G

A C AG T A T C

T A C G G T A T G

A C A G T A T C

T A C G G T A T G

A CA G T A T C

T A C G G T AT G

A C A G T AT C

C

T

A

T G

A

C

A

T A C G G T A T G

Word Size = 3


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PTHPLASKTQILPEDLASEDLTI

PTHPLAGERAIGLARLAEEDFGM

Score = 7



Score = 11

Matrix: PAM250

Window = 12

Stringency = 9

Scoring Matrix Filtering



Score = 11

Window / Stringency

Typical window size for DNA sequences is 15 bases, and stringency or matchrequirement in this window is 10, meaning if there are 10-15 matches within thewindow, and a dot is printed at the first base in the windows


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25Dotplot(Window = 18 / Stringency = 10)

Hemoglobin

-chain

Hemoglobin -chain


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Considerations

The window/stringency method is more sensitive than thewordsize method (ambiguities are permitted).

The smaller the window, the larger the weight of statistical(unspecific) matches.

With large windows the sensitivity for short sequences isreduced.

Insertions/deletions are not treated explicitly.

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Dot Matrix

Unless two sequences are known to be very much alike, thedot matrix method should be considered as a first choice for

pair-wise sequence alignment Readily reveal the presence of insertions/deletions and

direct and inverted repeats

DNA sequence dot matrix comparison: long windows andhigh stringencies (7/11, 11/15)

Protein sequences: short windows, stringencies (1/1) exceptfor short domain of partial similaritity in not similar

sequences (15/5)


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Programs:

DOTTER -

http://www.cgb.ki.se/cgb/groups/sonnhammer/Dotter.html

DOTPLOT - http://helix.nih.gov/docs/gcg/dotplot.html

PLALIGN in FASTA EMBOSS http://emboss.sourceforge.net/download/

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Methods of Alignment

By hand - slide sequences on two lines of a wordprocessor

Dot plot

with windows

Rigor ous m athem atical appro ach Dynam ic progr am m ing (slow , optim al)

Heuristic methods (fast, approximate)

BLAST and FASTAWord matching and hash tables0


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Alignment is additive

Observation:

The score of aligning x1xMy1yN

is additive

Say that x1xi xi+1xMaligns to y1yj yj+1yN

The two scores add up:

F(x[1:M], y[1:N]) = F(x[1:i], y[1:j]) + F(x[i+1:M], y[j+1:N])


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Basic pr inciples of dynam ic program m ing32

- Creation of an alignment path matrix

- Stepwise calculation of score values

- Backtracking (evaluation of the optimal path)

It is applicable when a large search space can be structuredinto a succession of stages, such that the initial stage contains

trivial solutions to sub-problems, each partial solution in a later

stage can be calculated by recurring a fixed number of partial

solutions in an earlier stage, the final stage contains the overallsolution - Mount


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33Creation of an alignment path matrix

Idea:

Build up an optimal alignment using previous solutions foroptimal alignments of smaller subsequences

Construct matrix Findexed by iandj(one index for each sequence)

F(i,j) is the score of the best alignment between the initial

segment x1...iof xup to xi and the initial segment y1...j of yup to

yj

Build F(i,j) recursively beginning with F(0,0) = 0


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If F(i-1,j-1), F(i-1,j) and F(i,j-1) are known we can

calculate F(i,j) Three possibilities:

xi and yj are aligned, F(i,j) = F(i-1,j-1) + s(xi ,yj)

xi is aligned to a gap, F(i,j) = F(i-1,j) - d yj is aligned to a gap, F(i,j) = F(i,j-1) - d

The best score up to (i,j) will be the largest of the threeoptions

Creation of an alignment path matrix


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Dynam ic Program m ing

There are only a polynomial number of subproblems

Align x1

xi

to y1

yj

Original problem is one of the subproblems

Align x1xM to y1yN Each subproblem is easily solved from smaller

subproblems

???

Then, we can applyDynamic Programming!!!

Let F(i,j) = optimal score of aligning

x1xiy1yj


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Example of Dynamic programming algorithm

Sequences a1, a2, a3, a4 and b1, b2, b3, b4

Align sequences in a global alignment


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Types of Scores44


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Scoring Matr ix / Substitution Matr ix45


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Scoring Matrix: Example

A R N K

A 5 -2 -1 -1

R - 7 -1 3

N - - 7 0

K - - - 6

Notice that although R andK are different amino acids,

they have a positive score.

Why? They are bothpositively charged amino

acidswill not greatlychange function of protein.


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Conservation

Amino acid changes that tend to preserve thephysicochemical properties of the original residue

Polar to polar

aspartate glutamate

Nonpolar to nonpolaralanine valine

Similarly behaving residues

leucine to isoleucine

l


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Scoring Examples48

i i


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Dynam ic Program m ing


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Scoring systems

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DNA Scor ing System s -very sim ple


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DNA Scor ing System s -very sim ple60

actaccagttcatttgatacttctcaaataccattaccgtgttaactgaaaggacttaaagact

Sequence 1Sequence 2

A G C T

A 1 0 0 0

G 0 1 0 0

C 0 0 1 0

T 0 0 0 1

Match: 1Mismatch: 0

Score = 5

Protein Scoring System s


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Protein Scoring System s61



Sequence 1

Sequence 2

Scoringmatrix

T:G = -2T:T = 5Score = 48

C S T P A G N D . .

C 9

S -1 4

T -1 1 5

P -3 -1 -1 7

A 0 1 0 -1 4

G -3 0 -2 -2 0 6

N -3 1 0 -2 -2 0 5

D -3 0 -1 -1 -2 -1 1 6

.

.

C S T P A G N D . .

C 9

S -1 4

T -1 1 5

P -3 -1 -1 7

A 0 1 0 -1 4

G -3 0 -2 -2 0 6

N -3 1 0 -2 -2 0 5

D -3 0 -1 -1 -2 -1 1 6

.

.



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Protein Scoring System s62

Amino acids have different biochemical and physical propertiesthat influence their relative replaceability in evolution.

CP

GGA

VI

L

MF

Y

W H

K

R

EQ

DNS

TCSH

S+S

positive

charged

polar

aliphatic

aromatic

small

tiny

hydrophobic



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Scoring m atr ices r eflect:

# of mu tations to convert one to another

chem ical similarity

observed m utation frequen cies

the pr obability of occur rence of each am ino acid

W idely used scoring m atrices:

PAM

BLOSUM

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PAM 250


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A R N D C Q E G H I L K M F P S T W Y V B Z

A 2 -2 0 0 -2 0 0 1 -1 -1 -2 -1 -1 -3 1 1 1 -6 -3 0 2 1

R -2 6 0 -1 -4 1 -1 -3 2 -2 -3 3 0 -4 0 0 -1 2 -4 -2 1 2

N 0 0 2 2 -4 1 1 0 2 -2 -3 1 -2 -3 0 1 0 -4 -2 -2 4 3

D 0 -1 2 4 -5 2 3 1 1 -2 -4 0 -3 -6 -1 0 0 -7 -4 -2 5 4C -2 -4 -4 -5 12 -5 -5 -3 -3 -2 -6 -5 -5 -4 -3 0 -2 -8 0 -2 -3 -4

Q 0 1 1 2 -5 4 2 -1 3 -2 -2 1 -1 -5 0 -1 -1 -5 -4 -2 3 5

E 0 -1 1 3 -5 2 4 0 1 -2 -3 0 -2 -5 -1 0 0 -7 -4 -2 4 5

G 1 -3 0 1 -3 -1 0 5 -2 -3 -4 -2 -3 -5 0 1 0 -7 -5 -1 2 1

H -1 2 2 1 -3 3 1 -2 6 -2 -2 0 -2 -2 0 -1 -1 -3 0 -2 3 3

I -1 -2 -2 -2 -2 -2 -2 -3 -2 5 2 -2 2 1 -2 -1 0 -5 -1 4 -1 -1

L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6 -3 4 2 -3 -3 -2 -2 -1 2 -2 -1K -1 3 1 0 -5 1 0 -2 0 -2 -3 5 0 -5 -1 0 0 -3 -4 -2 2 2

M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 0 -2 -2 -1 -4 -2 2 -1 0

F -3 -4 -3 -6 -4 -5 -5 -5 -2 1 2 -5 0 9 -5 -3 -3 0 7 -1 -3 -4

P 1 0 0 -1 -3 0 -1 0 0 -2 -3 -1 -2 -5 6 1 0 -6 -5 -1 1 1

S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 2 1 -2 -3 -1 2 1

T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -3 0 1 3 -5 -3 0 2 1

W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17 0 -6 -4 -4

Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10 -2 -2 -3

V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4 0 0

B 2 1 4 5 -3 3 4 2 3 -1 -2 2 -1 -3 1 2 2 -4 -2 0 6 5

Z 1 2 3 4 -4 5 5 1 3 -1 -1 2 0 -4 1 1 1 -4 -3 0 5 6

PAM 250

C

-8 17

W

W

PAM


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Dayhoff Matr ix


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y66

Dayhoff Matr ix


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y67

Dayhoff Matr ix


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y68

BLOSUM Matrix


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BLOSUM Matrix


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AABCDA...BBCDA

DABCDA.A.BBCBB

BBBCDABA.BCCAA

AAACDAC.DCBCDB

CCBADAB.DBBDCC

AAACAA...BBCCC

Conserved blocks in alignments

BLOSUM Matrix


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AABCDA...BBCDA

DABCDA.A.BBCBB

BBBCDABA.BCCAA

AAACDAC.DCBCDB

CCBADAB.DBBDCC

AAACAA...BBCCC

Conserved blocks in alignments


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TIPS on choosing a scoring matrix


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S o c oos g a sco g at

Generally, BLOSUM matrices perform better than PAM matricesfor local similarity searches (Henikoff & Henikoff, 1993).

When comparing closely related proteins one should use lowerPAM or higher BLOSUM matrices, for distantly related proteinshigher PAM or lower BLOSUM matrices.

For database searching the commonly used matrix is BLOSUM62.

Significance of alignm ent


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Significance of alignm ent


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Database Sear ching


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Database Sear ching


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Local vs. Global Alignm ent


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Global Alignm ent

Local Alignm entbetter alignm ent to find

conserved segment

--T-CC-C-AGT-TATGT-CAGGGGACACGA-GCATGCAGA-GAC

| || | || | | | ||| || | | | | |||| |AATTGCCGCC-GTCGT-T-TTCAG----CA-GTTATGT-CAGAT--C

tccCAGTTATGTCAGgggacacgagcatgcagagac

||||||||||||

aattgccgccgtcgttttcagCAGTTATGTCAGatc

Global vs. Local Alignm ent


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Global Alignment Needleman and Wunsch (1970)

Local Alignment Smith and Waterman (1981a)

Global Alignment


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needle (Needleman & Wunsch) creates an end-to-end

alignment.

Two closely related sequences:

Global Alignment


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Two sequences sharing several regions of local similarity:

1 AGGATTGGAATGCTCAGAAGCAGCTAAAGCGTGTATGCAGGATTGGAATTAAAGAGGAGGTAGACCG.... 67

1 AGGATTGGAATGCTAGGCTTGATTGCCTACCTGTAGCCACATCAGAAGCACTAAAGCGTCAGCGAGACCG 70

|||||||||||||| | | | |||| || | | | ||

The Needlem an-W unsch Matr ix


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x1 xMy1

yN

Every non-decreasing

path

from (0,0) to (M, N)

corresponds toan alignment

of the two sequences

An optimal alignment is composed ofoptimal subalignments

The Needlem an-W unsch Algor ithm


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831. Initialization.

F(0, 0) = 0 , F(0, j) = - j d, F(i, 0)= - i d

2. Main Iteration. Filling-in partial alignmentsa. For each i = 1M

For each j = 1N

F(i-1,j-1) + s(xi, yj ) [case 1]

F(i, j) = max F(i-1, j) d [case 2]

F(i, j-1) d [case 3]

DIAG, if [case 1]

Ptr(i,j) = LEFT, if [case 2]

UP, if [case 3]

3. Termination. F(M, N) is the optimal score, and

from Ptr(M, N) can trace back optimal alignment


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Local Alignment (Smith-Waterman)


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Local alignment

Identify the most similar sub-region shared between two

sequences Smith-Waterman

The local alignm ent problem


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Given two strings x = x1xM,

y = y1yN

Find substrings x, ywhose similarity

(optimal global alignment value)

is maximum

x = aaaacccccggggtta

y = ttcccgggaaccaacc

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W hy local alignm ent examples


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Genes areshuffled between

genomes

Portions ofproteins(domains) areoften conserved

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Cross-species genom e sim ilar ity


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98% of genes are conserved between any two mammals

>70% average similarity in protein sequence

hum_a : GTTGACAATAGAGGGTCTGGCAGAGGCTC--------------------- @ 57331/400001

mus_a : GCTGACAATAGAGGGGCTGGCAGAGGCTC--------------------- @ 78560/400001

rat_a : GCTGACAATAGAGGGGCTGGCAGAGACTC--------------------- @ 112658/369938

fug_a : TTTGTTGATGGGGAGCGTGCATTAATTTCAGGCTATTGTTAACAGGCTCG @ 36008/68174

hum_a : CTGGCCGCGGTGCGGAGCGTCTGGAGCGGAGCACGCGCTGTCAGCTGGTG @ 57381/400001mus_a : CTGGCCCCGGTGCGGAGCGTCTGGAGCGGAGCACGCGCTGTCAGCTGGTG @ 78610/400001

rat_a : CTGGCCCCGGTGCGGAGCGTCTGGAGCGGAGCACGCGCTGTCAGCTGGTG @ 112708/369938

fug_a : TGGGCCGAGGTGTTGGATGGCCTGAGTGAAGCACGCGCTGTCAGCTGGCG @ 36058/68174

hum_a : AGCGCACTCTCCTTTCAGGCAGCTCCCCGGGGAGCTGTGCGGCCACATTT @ 57431/400001

mus_a : AGCGCACTCG-CTTTCAGGCCGCTCCCCGGGGAGCTGAGCGGCCACATTT @ 78659/400001

rat_a : AGCGCACTCG-CTTTCAGGCCGCTCCCCGGGGAGCTGCGCGGCCACATTT @ 112757/369938

fug_a : AGCGCTCGCG------------------------AGTCCCTGCCGTGTCC @ 36084/68174

hum_a : AACACCATCATCACCCCTCCCCGGCCTCCTCAACCTCGGCCTCCTCCTCG @ 57481/400001

mus_a : AACACCGTCGTCA-CCCTCCCCGGCCTCCTCAACCTCGGCCTCCTCCTCG @ 78708/400001

rat_a : AACACCGTCGTCA-CCCTCCCCGGCCTCCTCAACCTCGGCCTCCTCCTCG @ 112806/369938

fug_a : CCGAGGACCCTGA------------------------------------- @ 36097/68174

atoh enhancer inhuman, mouse, rat,fugu fish

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The Sm ith-W aterm an algor ithm


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Termination:

1. If we want the best local alignment

FOPT = maxi,j F(i, j)Find FOPT and trace back

2. If we want all local alignments scoring > t

For all i, j find F(i, j) > t, and trace backComplicated by overlapping local alignments

(WatermanEggert 87: find all non-overlapping local alignments with minimal

recalculation of the DP matrix)

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Sm ith-w aterm an algor ithm


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Basic Local Alignm ent Search Tool

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BLAST Algor ithm

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BLAST Algor ithm

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BLAST Algor ithm

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BLAST Algor ithm

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Basic BLAST Algorithms

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bio medical tics - sequence analysis- alignment- 2011

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