bioinformatics phd. course 1. biological introduction exact extended approximate 6. projects: promo,...

Bioinformatics PhD. Course

1. Biological introduction

Exact Extended Approximate

6. Projects: PROMO, MREPATT, …

5. Sequence assembly

2. Comparison of short sequences ( up to 10.000bps) Dot Matrix Pairwise align. Multiple align. Hash alg.

3. Comparison of large sequences ( more that 10.000bps) Data structures Suffix trees MUMs

4. String matching

Comparison of large sequences

First part:

Alignment of large sequences

Dynamic programming

What about genomes?

• Quadratic cost of space and time.

accaccacaccacaacgagcata … acctgagcgatat

acc..t

• Short sequences (up to 10.000 bps) can be aligned using dynamic programming

• Quadratic cost of space and time.

acc.................................agt | | |.................................|xxacc.................................a--

Genomic sequences

In which case Dynamic Programming can be applied?

•The length of sequences is 1000 times longer.

• Genomic sequences have millions of base pairs.

•The running time is 1.000.000 times higher !

(1 second becomes 11 days)(1 minute becomes 2 years)

First assumption

……………………………………………………………….

………………………….………………...…………...….

Genome B

Genome A

……………………………………Genome B

……

……

……

……

……

….

Gen

ome

A

Realistic assumption?

Unrealistic assumption!

More realistic

assumption

……………………………………………………………….

………………………….………………...…………...….

Genome B

Genome A

………………………………………………………………….

………………………………………………...…………...….Genome A

Genome B

………………………

……

……G

enom

e A

Genome B

Realistic assumptions?

But, now is it a

real case?

Unrealistic assumption!

More realistic

assumption

……………………………………………………………….

………………………….………………...…………...….

Genome B

Genome A

…………………………………………………………………

………………………………………………...…………...….Genome A

Genome B

………………………

……

……G

enom

e A

Genome B

Preview in a real caseChlamidia muridarum: 1.084.689bps Chlamidia Thrachomatis:1057413bps

Preview in a real case

Pyrococcus abyssis: 1.790.334 bpsPyrococcus horikoshu: 1.763.341 bps

Methodology of an alignment

1st:

2nd:

3th: (Linear cost)

Identify the portions that can be aligned.

Make a preview: ……………………..….

…………………...….

Make the alignment:

…..…

……

………………….

(Linear cost)


(Linear cost)


…………………...….1st:

2nd:

3th:


Make the alignment:

…..…

……

………………….

?

Preview-Revisited

… a a t g….c t g...

… c g t g….c c c ...

MatchingUniqueMaximal

MUMConnect to MALGEN

http://alggen.lsi.upc.es/


1st:

2nd:

3th:



…………………...….

Make the alignment:

…..…

……

………………….

How can MUMs be found?

With CLUSTALW, TCOFFEE,…

How can these portions be determined?

Linear costwith

Suffix trees

Comparison of large sequences

M-GCAT

Todd Treangen

Homework

1. Javier 14. Alexis2. Dmitry 15. Ramon3. Ana Iris4. David5. Patricia6. Rogeli7. Atif8. Aina9. Isaac10. Maria Merce11. Romina12. Guillem13. Raul


Second part:

Introducing Suffix trees

Suffix trees

Given string ababaas:

1: ababaas

2: babaas

3: abaas

4: baas

5: aas

6: as7: s

as,3

s,6

as,5

s,7

as,4ba

baas,2

a

babaas,1

a

babaas,1

ba

baas,2

as,3

as,4

s,6

as,5

s,7

Suffixes:

What kind of queries?

Applications of Suffix trees

a

babaas,1as,3

ba

baas,2

as,4

s,6

as,5

s,7

1. Exact string matching

…………………………

• Does the sequence ababaas contain any ocurrence of patterns abab, aab, and ab?

Quadratic insertion algorithm

Given the string …………………………......

P1: the leaves of suffixes from have been inserted

and the suffix-tree

…...

Invariant Properties:


Given the string ababaabbs

ababaabbs,1



babaabbs,2

ababaabbs,1



babaabbs,2

ababaabbs,1ababaabbs,1



babaabbs,2

ababaabbs,1

abbs,3



babaabbs,2

ababaabbs,1

abbs,3

ba

baabbs,2



ababaabbs,1

abbs,3

ba

baabbs,2

abbs,4



ababaabbs,1

abbs,3

abbs,4ba

baabbs,2

abbs,4

abbs,3ba

a

baabbs,1



abbs,4ba

baabbs,2

abbs,4

abbs,3ba

a

baabbs,1

abbs,5



abbs,4

ba

ba

baabbs,2

abbs,4

a abbs,5

ba abbs,3

baabbs,1



abbs,4ba

baabbs,2

abbs,4

a abbs,5

ba abbs,3

baabbs,1

bs,6



a abbs,5

ba abbs,3

baabbs,1

bs,6

a

baabbs,2

b

abbs,4

bs,7



a abbs,5

ba abbs,3

baabbs,1

bs,6

a

baabbs,2

b

abbs,4

bs,7

s,8



a abbs,5

ba abbs,3

baabbs,1

bs,6

a

baabbs,2

b

abbs,4

bs,7

s,7

s,9

Generalizad suffix tree

The suffix tree of many strings …

and it is the suffix tree of the concatenation of strings.

the generalized suffix tree of ababaabb and aabaat …

is the suffix tree of ababaabαaabaatβ, :

is called the generalized suffix tree …

For instance,


a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

Given the suffix tree of ababaabα :

Construction of the suffix tree of ababaabbαaabaaβ :


a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9




a bα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

abaaβ,1


a bα,5

ba bbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

abaaβ,1

aβ,2




a bα,5

ba bbα,3

baabbα,1

bα,6

a

baabbα,2

b

bbα,4

bα,7

α,8

α,9

abaaβ,1

aβ,2

a β,3


a bα,5

ba bbα,3

baabbα,1

bα,6

a

baabbα,2

b

bbα,4

bα,7

α,8

α,9

baaβ,1

aβ,2

a β,3

aβ,4



a bα,5

ba bbα,3

baabbα,1

bα,6

a

baabbα,2

b

bbα,4

bα,7

α,8

α,9

baaβ,1

aβ,2

a β,3

aβ,4β,5



a bα,5

ba bbα,3

baabbα,1

bα,6

a

baabbα,2

b

bbα,4

bα,7

α,8

α,9

baaβ,1

aβ,2

a β,3

aβ,4β,5

β,6



a bα,5b

a bbα,3baabbα,1

bα,6

a

baabbα,2

b

bbα,4

bα,7

α,8

α,9

baaβ,1

aβ,2

a β,3

aβ,4β,5

β,6

Generalized suffix tree of ababaabbαaabaaβ :


a

babaas,1as,3

ba

baas,2

as,4

s,6

as,5

s,7

1. Exact string matching

…………………………

• Does the sequence ababaas contain any ocurrence of patterns abab, aab, and ab?


2. The substring problem for a database of strings DB• Does the DB contain any ocurrence of patterns abab, aab, and ab?

a bα,5b

a bbα,3baabbα,1

bα,6

a

baabbα,2

b

bbα,4

bα,7

α,8

α,9

baaβ,1

aβ,2

a β,3

aβ,4β,5

β,6


3. The longest common substring of two strings

a bα,5b

a bbα,3baabbα,1

bα,6

a

baabbα,2

b

bbα,4

bα,7

α,8

α,9

baaβ,1

aβ,2

a β,3

aβ,4β,5

β,6


5. Finding MUMs.

a bα,5b

a bbα,3baabbα,1

bα,6

a

baabbα,2

b

bbα,4

bα,7

α,8

α,9

baaβ,1

aβ,2

a β,3

aβ,4β,5

β,6


Third part:

Suffix links

Suffix links

a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

a

Suffix links

a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

a

?

Suffix links

a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

a

Traversal using Suffix links

a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

Given S2 = a a b a a


a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

Given S2 = a a b a a aa in S2 [1] Unique matchings


a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

Given S2 = a a b a a aa in S2 [1] Unique matchings

aab in S2 [1] =

S1[5..6-7] in S2 [1]


a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

Given S2 = a a b a a Unique matchings S1[5..6-7] in S2 [1]


a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

Given S2 = a a b a a b b a Unique matchings S1[5..6-7] in S2 [1] S1[3..6-…] in S2 [2]


a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

Given S2 = a a b a a b b a Unique matchings S1[5..6-7] in S2 [1] S1[3..6-8] in S2 [2]

S1[4..6-8] in S2 [3]


a abbα,5

ba abbα,3

baabbα,1

bα,6

a

baabbα,2

b

abbα,4

bα,7

α,8

α,9

Given S2 = a a b a a b b a Unique matchings S1[5..8] in S2 [4] S1[3..6-8] in S2 [2] S1[4..6-8] in S2 [3] S1[6..8] in S2 [5] S1[7..8] in S2 [6]

From UMs to MUMs

Given S2 = a a b a a b b a Unique matchings S1[5..8] in S2 [4] S1[3..6-8] in S2 [2] S1[4..6-8] in S2 [3] S1[6..8] in S2 [5] S1[7..8] in S2 [6]

Array of UMs123 6-84 6-85 86 87 889

and S1 = a b a b a a b b α

MUM: S1[3..6-8] in S2[2]


Third part:

Linear insertion algorithm




and the suffix-tree

…...


Linear insertion algorithm


P2: the string is the longest string that can be spelt through the tree.


and the suffix-tree

…...


Linear insertion algorithm: example

Given the string ababaababb...

ba

baababb...,2

a ababb...,5

ba ababb...,3

baababb...,1ababb...,4

a



ba

baababb...,2

a ababb...,5

ba ababb...,3


6 7 8


ba

baababb...,2

a ababb...,5

ba ababb...,3


6 7 8Given the string ababaababb...


ba

baababb...,2

a ababb...,5

ba ababb...,3


6 7 89Given the string ababaababb...


a ababb...,5

ba ababb...,3

baababb...,1ba

baababb...,2

ababb...,4


6 7 89

baababb...,1b

b...,6

aababb...,1


a ababb...,5

ba ababb...,3

ba

baababb...,2

ababb...,4


7 89

b

b...,6

aababb...,1


a ababb...,5

ba ababb...,3

ba

baababb...,2

ababb...,4


7 89

b

b...,6

aababb...,1

baababb...,2b aababb...,2


a ababb...,5

ba ababb...,3

ba

baababb...,2

ababb...,4


7 8…

b

b...,6

aababb...,1

baababb...,2b

b...,7

aababb...,2


a ababb...,5

ba ababb...,3

ba ababb...,4


89

b

b...,6

aababb...,1

b

b...,7

aababb...,2


a ababb...,5

b

ba ababb...,4


89

ababb...,3

b

b...,6

aababb...,1

b

b...,7

aababb...,2

a


a ababb...,5

b

ba ababb...,4


89

ababb...,3

b

b...,6

aababb...,1

b

b...,7

aababb...,2

a

b...,8


a ababb...,5

b

ba ababb...,4


9

ababb...,3

b

b...,6

aababb...,1

b

b...,7

aababb...,2

a

b...,8


a ababb...,5

b

b ababb...,4

Given the string ababaababb... 9

ababb...,3

b

b...,6

aababb...,1

b

b...,7

aababb...,2

a

b...,8a


a ababb...,5

b

b ababb...,4


ababb...,3

b

b...,6

aababb...,1

b

b...,7

aababb...,2

a

b...,8a

b...,9


a ababb...,5

b

b ababb...,4


ababb...,3

b

b...,6

ababb...,1

b

b...,7

aababb...,2

a

b...,8a

b...,9


a ababb...,5

b

b ababb...,4


9

ababb...,3

b

b...,6

ababb...,1

b

b...,7

aababb...,2

a

b...,8a

b...,9

Index

Suffix arrays Suffix-arrays: a new method for on-line

string searches, G. Myers, U. Manber

Suffix arrays

Given string ababaa#:

1: ababaa#2: babaa#

3: abaa#

4: baa#

5: aa#

6: a#

7: #

Suffixes: … but lexicographically sorted

1: ababaa#

2: babaa#

3: abaa#

4: baa#

5: aa#6: a#1: #1

234567

Which is the cost? O(n log(n))

Applications of suffix arrays

1. Exact string matching• Does the sequence ababaas contain any ocurrence of patterns abab, aab, and ab?

1: ababaa#

2: babaa#

3: abaa#

4: baa#

5: aa#6: a#1: #1

234567

Binary search

O(log(n) |P|)

… which is the cost?

O(log(n)+|P|) ?

Can it be improved to …

Fast search with cost O(log(n)+|P|) Query:


P1: α < query ≤ β α

β

12… …

n

Suffix array

P2: matches pref( query)

Fast search with cost O(log(n)+|P|) Query:


P1: α < query ≤ β α

β

γ Algorithm:

12… …

n

Suffix array

P2: matches pref( query)

If suff(γ)<suff(query) then α = γ else β = γ

bioinformatics phd. course 1. biological introduction exact extended approximate 6. projects: promo,...

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