Multiple Sequence Alignment

H.C.Huang @ 2005/9/29

2005 Autumn / YM / Bioinformatics

Outline

Pairwise alignment reviewScoring matrix

Substition matrices Gap penalties

Multiple sequence alignment

Reference

D.W. Mount / BioinformaticsCh.3 pp.94-112Ch.5 pp.163-189

Slides fromProf. C.H.ChangUW / Genomic Informatics / W.S. NobleWFU / Bioinformatics / J. Burg

PA Review

Scoring a pairwise alignment requires a substition matrix and gap penalties.

Dynamic programming is an efficient algorithm for finding the optimal alignment.

Entry (i,j) in the DP matrix stores the score of the best-scoring alignment up to those positions.

DP iteratively fills in the matrix using a simple mathematical rule.

PA Review

Local alignment finds the best match between subsequences.

Smith-Waterman local alignment algorithm:No score is negative.Trace back from the largest score in the matrix.

Global alignment algorithm: Needleman-Wunsch.

Local alignment algorithm: Smith-Waterman.

Dynamic Programming

A method for solving recursive problemBreak a problem into smaller

subproblemsSolve subproblems optimally,

recursivelyUse these optimal solutions to

construct an optimal solution for the original problem

Global alignment DP

• Align sequence x and y.

• F is the DP matrix; s is the substitution matrix; d is the linear gap penalty.

djiF

djiF

yxsjiF

jiF

F

ji

1,

,1

,1,1

max,

00,0

Local alignment DP

• Align sequence x and y.

• F is the DP matrix; s is the substitution matrix; d is the linear gap penalty.

0

1,,1

,1,1

max,

00,0

djiFdjiF

yxsjiF

jiF

F

ji

Local alignment

A C G T

A 2 -7 -5 -7

C -7 2 -7 -5

G -5 -7 2 -7

T -7 -5 -7 2

A A G

0 0 0 0

G 0 0 0 2

A 0 2 2 0

A 0 2 4 0

G 0 0 0 6

G 0 0 0 1

C 0 0 0 0

1,1 jiF

jiF , jiF ,1

1, jiF

d

d ji yxs ,

Find the optimal local alignment of AAG and GAAGGC.Use a gap penalty of d=-5.

0

Substitution matrices

A C G T

A 2 -7 -5 -7

C -7 2 -7 -5

G -5 -7 2 -7

T -7 -5 -7 2

A A G

0 0 0 0

G 0 0 0 2

A 0 2 2 0

A 0 2 4 0

G 0 0 0 6

G 0 0 0 1

C 0 0 0 0

1,1 jiF

jiF , jiF ,1

1, jiF

d

d ji yxs ,

Find the optimal local alignment of AAG and GAAGGC.Use a gap penalty of d=-5.

0

Where did this substitution matrix

come from?

Substitution Matrix

(scoring matrix)

Why Sequence Alignment?

To find sequence similarity

Origin of Sequence Similarity

Evolution

Similar sequences come from same ancestor sequence with mutations

Substitution Matrices for Scoring Functions Also called “symbol comparison tables” Used for scoring matches of amino acid

or nucleic acids Residues label the rows and columns of

the matrix; scores for aligning them are given in the matrix

Can be used in the dynamic programming method of pair-wise sequence alignment

Sub. Matrix: Basic idea

Probability of substitution (mutation)

Nucleic acid PAM matrices

• PAM = point accepted mutation• 1 PAM = 1% probability of mutation at each

sequence position.• A uniform PAM1 matrix:

A G T C

A 0.99 0.00333 0.00333 0.00333

G 0.00333 0.99 0.00333 0.00333

T 0.00333 0.00333 0.99 0.00333

C 0.00333 0.00333 0.00333 0.99

Transitions and transversions

• Transitions (A G or C T) are more likely than transversions (A T or G C)

• Assume that transitions are three times as likely:

A G T C

A 0.99 0.006 0.002 0.002

G 0.006 0.99 0.002 0.002

T 0.002 0.002 0.99 0.006

C 0.002 0.002 0.006 0.99

Distant relatives

• If the probability of a substitution is 2%, simply multiply the probabilities from 1% by themselves.

• A PAM N matrix is computed by raising PAM 1 to the Nth power.

A G T C

A 0.98014 0.011888 0.003984 0.003984

G 0.011888 0.98014 0.003984 0.003984

T 0.003984 0.003984 0.98014 0.011888

C 0.003984 0.003984 0.011888 0.98014

Most Commonly-Used Amino Acid Subtitution Matrices

PAM (Percent Accepted Mutation, also called Dayhoff Amino Acid Substitution Matrix)

BLOSUM (Blocks Amino Acid Substitution Matrix)

PAM Matrices

A family of matrices (PAM-N) Based upon an evolutionary model The score for a pairing of amino acids is

based on how much we expect that pairing to be observed after a certain length of evolutionary time

The scores are derived by a Markov model – i.e., the probability that one amino acid will change to another is not affected by changes that occurred at an earlier stage of evolutionary history

PAM-N Matrices

N is a measure of evolutionary distance PAM-1 is modeled on an estimate of how

long in evolutionary time it would take one amino acid out of 100 to change. That length of time is called 1 PAM unit, roughly 10 million years (abbreviated my).

Values in a PAM-1 matrix show the probability that an amino acid will change over 10 my.

To get the PAM-N matrix for any N, multiply PAM-(N-1) by PAM-1.

How did they get the values for PAM-1? Look at 71 groups of protein sequences

where the proteins in each group are at least 85% similar (Why these groups?)

Compute relative mutability of each amino acid – probability of change

From relative mutability, compute mutability probability for each amino acid pair X,Y– probability that X will change to Y over a certain evolutionary time

Normalize the mutability probability for each pair to a value between 0 and 1

Computing Relative Mutability – A Measure of the Likelihood that an Amino Acid Will Mutate For each amino acid changes = number of times the amino acid

changed into something else exposure to mutation =

(percentage occurrence of the amino acid in the group of sequences being analyzed) * (frequency of amino acids changes in the group – based on the phylogenetic tree)

relative mutability = (changes/exposure to mutation) / 100

Computing Mutability Probability Between Amino Acid PairsFor each pair of amino acids X and Y:

r = relative mutability of X

c = num times X becomes Y or vice versa

p = num changes involving X

mutability probability of X to Y =

(r * c) / p

Computing Relative Mutability of A:changes = # times A changes into something else = 4% occurrence of A in group = 10 / 63 = 0.159frequency of all amino acid changes in group = 6 * 2 = 12

(Note: Count changes backwards and forwards.)exposure to mutation = (% occurrence of A in group)

* (frequency of all amino acid changes in group) = 12 * 0.159

relative mutability = (changes / exposure to mutation) / 100 = (4 / (12 * 0.159)) = 2.09 / 100 = 0.0209Divide this value by 100 to give us PAM – 1, where we’re modeling 1 substitution per 100 residues. Example from Fundamental Concepts of Bioinformatics by Krane and Raymer.

How can we understand relative mutability intuitively?

relative mutability = changes / exposure to mutation =the number of times A changed in proportion to thethe probability that it COULD have changed

exposure to mutation – that were 6 times when somethingchanged in the tree. Each time, that change could have been A changing to something else, or something elsechanging to A – 12 chances for a change involving A. But Aappears in a sequence only .159 of the time.

Computing Mutability Probability that A will change to G:

r = relative mutability of A = .0209c = num times A becomes G or vice versa = 3p = num changes involving A = 4mutability probability of A to G =

(r * c) / p = (0.0209 * 3) / 4 = 0.0156

Normalizing Mutability Probability, X to Y

For each Y among all amino acids, compute mutability probability of X to Y as described above

Get a total of these 20 probabilities. Divide them by a normalizing factor such that the probability that X will NOT change is 99% and the sum of probabilities that it will change to any other amino acid is 1%

These are the numbers that go in the PAM-1 matrix!

See Table 3.2, p. 96 in Bioinformatics by Mount.

Converting Mutability Probabilities to Log Odds Score for X to Y

Compute the relative frequency of change for X to Y as follows: Get the X to Y mutability probability Divide by the % frequency of X in the sequence data Convert to log base 10, multiply by 10

In our example, we get log10(0.0156/0.1587) =

log10(.098) To compute log10(.098) solve for x:

10x = 0.098 x = -1.01 10-1.01 = 1/101.01 = 0.098 Compute log odds score for Y to X Take the average of these two values

Usefulness of Log Odds Scores

A score of 0 indicates that the change from one amino acid to another is what is expected by chance

A negative score means that the change is probably due to chance

A positive score means that the change is more than expected by chance

Because the scores are in log form, they can be added (i.e., the chance that X will change to Y and then Y to Z)

See Figure 3.14, page 98 of Bioinformatics by Mount.

Disadvantages of PAM Matrices A phylogenetic tree must be constructed

first, implying some circularity in the analysis

Disadvantage: The original PAM-1 matrix was based on a limited number of families, not necessarily representative of all protein families

The Markov model does not take into account that multi-step mutations should be treated differently from single-step ones

BLOSUM Scoring Matrices

Based on a larger set of protein families than PAM (about 500 families). The proteins in the families are known to be biochemically related.

Focuses on blocks of conserved amino acid patterns in these families

Designed to find conserved domains in protein families

BLOSUM matrices with lower numbers are more useful for scoring matches in pairs that are expected to be less closely related through evolution – e.g., BLOSUM50 is used for more distantly-related proteins than BLOSUM62. (This is the opposite of the PAM matrices.)

BLOSUM

BLOSUM (blocks amino acid substitution matrices)

Blocks: ungapped amino acid patterns

Block alignment: example

BLOSUM50

Gap Penalty

(Gap Scoring)

Better gap scoring>gi|729942|sp|P40601|LIP1_PHOLU Lipase 1 precursor (Triacylglycerol lipase) Length = 645

Score = 33.5 bits (75), Expect = 5.9 Identities = 32/180 (17%), Positives = 70/180 (38%), Gaps = 9/180 (5%)

Query: 2038 IYSLYGLYNVPYENLFVEAIASYSDNKIRSKSRRVIATTLETVGYQTANGKYKSESYTGQ 2097 +++ YGL+ Y+ ++ Y D K +R ++ + N + G+Sbjct: 441 VFTAYGLWRY-YDKGWISGDLHYLDMKYEDITRGIVLNDW----LRKENASTSGHQWGGR 495

Query: 2098 LMAGYTYMMPENINLTPLAGLRYSTIKDKGYKETGTTYQNLTVKGKNYNTFDGLLGAKVS 2157 + AG+ + + +P+ + KGY+E+G + + Y++ G LG ++Sbjct: 496 ITAGWDIPLTSAVTTSPIIQYAWDKSYVKGYRESGNNSTAMHFGEQRYDSQVGTLGWRLD 555

Query: 2158 SNINVNEIVLTPELYAMVDYAFKNKVSAIDARLQGMTAPLPTNSFKQSKTSFDVGVGVTA 2217 +N P ++ F +K I + + + S KQ + +G+ ASbjct: 556 TNFG----YFNPYAEVRFNHQFGDKRYQIRSAINSTQTSFVSESQKQDTHWREYTIGMNA 611

Real gaps are often more than one letter long.

Affine gap penaltyLETVGYW----L

-5 -1 -1 -1

Separate penalties for gap opening and gap extension.

This requires modifying the DP algorithm to store three values in each box.

Summary

Substitution matrices represent the probability of mutations.

PAM / BLOSUM(62)Affine gap penalties include a large

gap opening penalty and small gap extension penalty.

Multiple Sequence Alignment

MSA Introduction

Goal of protein sequence alignment:To discover “biological” (structural /

functional) similaritiesIf sequence similarity is weak,

pairwise alignment can fail to identify …

Simultaneous comparison of many sequences often find similarities that are invisible in PA.

Why do we care about sequence alignment? It can tell us something about the evolution of organisms. We can see which regions of a gene (or its derived protein)

are susceptible to mutation and which can have one residue replaced by another without changing function.

Homologous genes (genes with share evolutionary origin) have similar sequences.

Orthologs are genes that are evolutionarily related, have a similar function, but now appear in different species.

Paralogs are evolutionarily related (share an origin) but no longer have the same function.

You can uncover either orthologs or paralogs through sequence alignment.

Multiple Sequence Alignment

Often applied to proteins Proteins that are similar in sequence are

often similar in structure and function Sequence changes more rapidly in

evolution than does structure and function.

Work with proteins!Work with proteins!If at all possible —If at all possible —

Twenty match symbols versus four, plus similarity! Way better signal to noise.

Also guarantees no indels are placed within codons. So translate, then align.

Nucleotide sequences will only reliably align if they are very similar to each other. And they will require extensive hand editing and careful consideration.

Overview of Methods

Dynamic programming – too computationally expensive to do a complete search; uses heuristics

Progressive – starts with pair-wise alignment of most similar sequences; adds to that

Iterative – make an initial alignment of groups of sequences, adds to these (e.g. genetic algorithms)

Locally conserved patterns Statistical and probabilistic methods

Dynamic Programming

Computational complexity – even worse than for pair-wise alignment because we’re finding all the paths through an n-dimensional hyperspace (We can picture this in 2 or 3 dimensions.)

Can align about 7 relatively short (200-300) protein sequences in a reasonable amount of time; not much beyond that

A Heuristic for Reducing the Search Space in Dynamic Programming Let’s picture this in 3 dimensions (pp. 174-180 in

book). It generalizes to n. Consider the pair-wise alignments of each pair

of sequences. Create a phylogenetic tree from these scores. Consider a multiple sequence alignment built

from the phylogenetic tree. These alignments circumscribe a space in which

to search for a good (but not necessarily optimal) alignment of all n sequences.

Phylogenetic Tree

Dynamic programming uses a phylogenetic tree to build a “first-cut” msa

The tree shows how protein could have evolved from shared origins over evolutionary time.

See page 180 in Bioinformatics by Mount. Chapter 7 goes into detail on this.

Dynamic Programming -- MSA

Create a phylogenetic tree based on pair-wise alignments (Pairs of sequences that have the best scores are paired first in the tree.)

Do a “first-cut” msa by incrementally doing pair-wise alignments in the order of “alikeness” of sequences as indicated by the tree. Most alike sequences aligned first.

Use the pair-wise alignments and the “first-cut” msa to circumscribe a space within which to do a full msa that searches through this solution space.

The score for a given alignment of all the sequences is the sum of the scores for each pair, where each of the pair-wise scores is multiplied by a weight є indicating how far the pair-wise score differs from the first-cut msa alignment score.

Heuristic Dynamic Programming Method for MSA Does not guarantee an optimal alignment

of all the sequences in the group. Does get an optimal alignment within the

space chosen.

Progressive Methods Similar to dynamic programming method in that it uses

the first step (i.e., it creates a phylogenetic tree, aligns the most-alike pair, and incrementally adds sequences to the alignment in order of “alikeness” as indicated by the tree.)

Differs from dynamic programming method for MSA in that it doesn’t refine the “first-cut” MSA by doing a full search through the reduced search space. (This is the computationally expensive part of DP MSA in that, even though we’ve cut down the search space, it’s still big when we have many sequences to align.)

Progressive Method

Generally proceeds as follows: Choose a starting pair of sequences and align them Align each next sequence to those already aligned, one

at a time Heuristic method – doesn’t guarantee an optimal alignment Details vary in implementation:

How to choose the first sequence to align? Align all subsequence sequences cumulatively or in

subfamilies? How to score?

ClustalW

Based on phylogenetic analysis A phylogenetic tree is created using a pairwise distance

matrix and nearest-neighbor algorithm The most closely-related pairs of sequences are aligned

using dynamic programming Each of the alignments is analyzed and a profile of it is

created Alignment profiles are aligned progressively for a total

alignment W in ClustalW refers to a weighting of scores depending

on how far a sequence is from the root on the phylogenetic tree (See p. 180-182 of Bioinformatics by Mount.)

ClustalW Procedure

“Once a gap, always a

gap”

Basic Steps in Progressive Alignment

“Once a gap, always a gap”

Problems with Progressive Method

Highly sensitive to the choice of initial pair to align. If they aren’t very similar, it throws everything off.

It’s not trivial to come up with a suitable scoring matrix or gap penaties.

Summary

Global multiple sequence alignment

Progressive MethodUse pairwise alignment to iteratively

add one sequence to a growing MSAClustalWLocal MSA Sequence pattern

search