.

Class 5:Multiple Sequence

Alignment

Multiple sequence alignment

VTISCTGSSSNIGAG-NHVKWYQQLPG

VTISCTGTSSNIGS--ITVNWYQQLPG

LRLSCSSSGFIFSS--YAMYWVRQAPG

LSLTCTVSGTSFDD--YYSTWVRQPPG

PEVTCVVVDVSHEDPQVKFNWYVDG--

ATLVCLISDFYPGA--VTVAWKADS--

AALGCLVKDYFPEP--VTVSWNSG---

VSLTCLVKGFYPSD--IAVEWESNG--

Homologous residues are aligned together in columns Homologous - in the structural and evolutionary sense

Ideally, a column of aligned residues occupy similar 3d structural positions

Multiple alignment – why?

Identify sequence that belongs to a family Family – a collection of homologous, with similar

sequence, 3d structure, function or evolutionary history

Find features that are conserved in the whole family Highly conserved regions, core structural elements

The relation between the divergence of sequence and

structure

[Durbin p. 137, redrawn from data in Chothia and Lesk (1986)]

Scoring a multiple alignment (1)

Important features of multiple alignment: Some positions are more conserved than others Position specific scoring

Sequences are not independent (related by phylogenetic tree)

Ideally, specify a complete model of molecular sequence evolution

Scoring a multiple alignment (2)

Unfortunately, not enough data …

Assumption (1)Columns of alignment are statistically independent.

( ) ( )ii

S m G S m 1 2( , ,..., ) Column of alignment m

( ) Score for column

Gap scoring function

Ni i i i

i

m m m m i

S m i

G

Minimum entropy

Assumption (2)Symbols within columns are independent

Observed counts of ( )

symbol in column

The probability of

symbol in column

jia i

j

ia

c m aa i

Pa i

( )

( ) log

iaci ia

a

i ia iaa

P m P

S m c P

Entropy measure

Sum of pairs (SP)

Columns are scored by a “sum of pairs” function, using a substitution scoring matrix

Note:

( ) ( , )k li i i

k l

S m m m

log( ) log( ) log( ) log( )abc ab ac bc

a b c a b a c b c

P P P P

q q q q q q q q q

Multidimensional DP

( ) ( )ii

S m S m

Multidimensional DP

1 2 1 2

1 2 2

1 2 1

1 2 1 2 1 2

1 2 3

1 2 3

1 21, 1, , 1

2, 1, , 1

11, , , 1

1 2, , , 1, 1, ,

, , 1 , 1

, 1, 1 ,

( , , , )

( , , , )

( , , , )

max ( , , , )

( , , , )

N N

N N

N N

N N

N N

N

Ni i i i i i

Ni i i i i

Ni i i i i

i i i i i i i i

Ni i i i i

i i i i

x x x

x x

x x

x x

x

2

2( , , , )ix

Multidimensional DP

: 1

: 0i

ii

xx

1 2 1 1 2 2 1 2

1

1 2, , , , , , 1 2

0max ( , , , )

N N N NN

Ni i i i i i i i N ix x x

Complexity

Space: Time: 1

N

ii

O L

1

2N

Ni

i

O L

Pairwise projections of MA

MSA (i)

[Carrillo and Lipman, 1988]

pairwise alignment between sequences ,

optimal pairwise alignment of ,

( ) ( )

lower bound on the optimal ( )

multiple alignment score

( ) ( )

kl

kl

klkl

a k l

a k l

S a S a

l a

l a S a

MSA (ii)

' '

' '

' '

' '

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( , ) s.t. the best alignment of

, through ( , ) scores

kl k lkl

k l

kl k lkl kl

k l

k lkl

k l klk l

l a S a S a S a

S a l a S a S a

i iB

x x i i

MSA (iii)

Algorithm sketch

1 2

( ) , ,

( , , , )

( , )

kl

kl

N

klk l

l a a

B

i i i

i i B

kl1. Calculate

2. Find

3. Use multidimensional

DP to evaluate only

cells for

which

Progressive alignment methods (i)

Basic idea: construct a succession of PW alignments

Variatoins: PW alignment order One growing alignment or subfamilies Alignment and scoring procedure

Progressive alignment methods (ii)

Most important heuristic – align the most similar pairs first.

Many algorithms build a “guide tree”: Leaves – sequence Interior nodes – alignments Root – complete multiple alignment

Feng-Doolittle (1987)

Calculate all pairwise distances using alignment scores:

Construct a guide tree using hierarchical clustering

Highest scoring pairwise alignment determines sequence to group alignment

log log obs randeff

max rand

S SD S

S S

Profile alignment

Use profiles for group to sequence and group to group alignments

CLUSTALW (Thompson et al., 1994): Similar to Feng-Doolittle, but uses profile alignment

methods Numerous heuristics

Iterative Refinement

Addresses “frozen” sub-alignment problem

Iteratively realign sequences or groups to a profile of the rest

Barton and Sternberg (1987) Align two most similar sequences Align current profile to most similar sequence Remove each sequence and align it to profile