CS177 Lecture 4 Sequence Alignment

Tom Madej 10.03.05

Overview

• The alignment problem.• Homology, divergence, convergence.• Dynamic programming overview.• Amino acid substitution matrices.• Fast sequence database searching: BLAST.• Multiple sequence alignment.• PSI-BLAST, position specific score matrices.• Databases of multiple sequence alignments.

What is a sequence alignment?

• A linear, one-to-one correspondence between some of the symbols in one sequence with some of the symbols in another sequence.

• May be DNA or protein sequences.

• A (sequence) alignment can also be derived from a superposition of two protein structures, it is then sometimes called a structure alignment.

Classwork

• In Exercise 1 we will see DNA-DNA alignments produced by the program Basic Local Alignment Search Tool (BLAST)

• In Exercise 2 we will see alignments of protein structures produced by Vector Alignment Search Tool (VAST)

Exercise 1: BLAST this DNA sequence against the Human Genome

> CCR5ATGGATTATCAAGTGTCAAGTCCAATCTATGACATCAATTATTATACATCGGAGCCCTGCCAAAAAATCA ATGTGAAGCAAATCGCAGCCCGCCTCCTGCCTCCGCTCTACTCACTGGTGTTCATCTTTGGTTTTGTGGG CAACATGCTGGTCATCCTCATCCTGATAAACTGCAAAAGGCTGAAGAGCATGACTGACATCTACCTGCTC AACCTGGCCATCTCTGACCTGTTTTTCCTTCTTACTGTCCCCTTCTGGGCTCACTATGCTGCCGCCCAGT GGGACTTTGGAAATACAATGTGTCAACTCTTGACAGGGCTCTATTTTATAGGCTTCTTCTCTGGAATCTT CTTCATCATCCTCCTGACAATCGATAGGTACCTGGCTGTCGTCCATGCTGTGTTTGCTTTAAAAGCCAGG ACGGTCACCTTTGGGGTGGTGACAAGTGTGATCACTTGGGTGGTGGCTGTGTTTGCGTCTCTCCCAGGAA TCATCTTTACCAGATCTCAAAAAGAAGGTCTTCATTACACCTGCAGCTCTCATTTTCCATACAGTCAGTA TCAATTCTGGAAGAATTTCCAGACATTAAAGATAGTCATCTTGGGGCTGGTCCTGCCGCTGCTTGTCATG GTCATCTGCTACTCGGGAATCCTAAAAACTCTGCTTCGGTGTCGAAATGAGAAGAAGAGGCACAGGGCTG TGAGGCTTATCTTCACCATCATGATTGTTTATTTTCTCTTCTGGGCTCCCTACAACATTGTCCTTCTCCT GAACACCTTCCAGGAATTCTTTGGCCTGAATAATTGCAGTAGCTCTAACAGGTTGGACCAAGCTATGCAG GTGACAGAGACTCTTGGGATGACGCACTGCTGCATCAACCCCATCATCTATGCCTTTGTCGGGGAGAAGT TCAGAAACTACCTCTTAGTCTTCTTCCAAAAGCACATTGCCAAACGCTTCTGCAAATGCTGTTCTATTTT CCAGCAAGAGGCTCCCGAGCGAGCAAGCTCAGTTTACACCCGATCCACTGGGGAGCAGGAAATATCTGTG GGCTTGTGA

Exercise 1: cont.

• From NCBI home page follow the “BLAST” link• Then from “Genomes” select “Human”• Paste the sequence from the previous slide into the box

(note that it is in FASTA format)• Click on “Begin Search”• Wait for a short while then try “Format”

Alignment format examples

• Aligned (similar) regions are in rectangles.

Exercise 2

• From http://www.ncbi.nlm.nih.gov/Structure/ go to the MMDB summary page for 1nqp.

• Click on the colored bar for chain “A”.

• Scroll down and select the VAST neighbor 1KR7 A.

• Click on “View 3D Structure” at the top to view the structural superposition using Cn3D.

• The sequence alignment will be shown in a separate window.

Divergence and Convergence

• Two proteins may be similar because of divergence from a common ancestor (i.e. they are homologous).

• … or, perhaps two proteins may be similar because they perform similar functions and are thereby constrained, even though they arose independently (functional convergence hypothesis, they are then called analogous).

Divergence vs. Convergence

• Convergence can occur; e.g. there exist enzymes with different overall structures but remarkably similar arrangements of active site residues to carry out a similar function.

• So how can one establish homology?

Homology

“… whenever statistically significant sequence or structural similarity between proteins or protein domains is observed, this is an indication of their divergent evolution from a common ancestor or, in other words, evidence of homology.”

E.V. Koonin and M.Y. Galperin, Sequence – Evolution – Function, Kluwer 2003

Two arguments…

• We see a continuous range of sequence similarity. Convergence is extremely unlikely for highly similar protein families. It then appears implausible to invoke it for less similar families.

• The same or very similar functions may be carried out by proteins with very different structures (folds). Therefore, functional constraints cannot force convergence of the sequence or structure between proteins.

Alignments of hemoglobins: human-wolf (83%); human-chicken (59%)

Alignments of hemoglobins: human-hagfish (24%); human-worm (17%)

Sequence identity for VAST neighbors of 1NQP A (a globin)

Issues in sequence alignment…

• How do you quantify amino acid similarity?

• How can you handle gaps in the alignment?

• How do you define the overall similarity score?

• Can you compute an optimal alignment?

• Can you compute an alignment efficiently?

• Can you calculate statistical significance?

Global and local alignment

• Alignment programs may be modified, e.g. by scoring parameters, to produce global or local alignments.

• Local alignments tend to be more useful, as it is highly possible that a significant similarity may encompass only a portion of one or both sequences being compared.

Dynamic Programming overview

• Computational algorithmic method devised in the 1940’s.

• An efficient method to find optimal solutions for certain classes of problems.

• Particularly useful in bioinformatics for protein sequence comparison, etc.

Characteristics of problems that can be solved by DP…

• Optimal substructure: The optimal solution may be constructed from optimal solutions to subproblems.

• Overlapping subproblems: To compute the optimal solution we only need to consider a “small” number of subproblems.

Example: Longest Common Subsequence (LCS)

• Given two sequences of symbols, find a longest subsequence that occurs in both sequences.

• seq1: abcabddcbaabb • seq2: bdacbaabcbaa

• abcabddcbaabb• bdacbaabcbaa• Here is another subsequence of length 8: bcabcbaa

Optimal substructure of an LCS

• X = x1…xm, Y = y1…yn input sequences; let Z = z1…zk be any LCS of X and Y

• If xm = yn then zk = xm = yn and Zk-1 is an LCS for Xm-1 and Yn-1

• If xm yn and zk xm then Z is an LCS for Xm-1 and Y

• If xm yn and zk yn then Z is an LCS for X and Yn-1

• (Note: Xm-1 = x1…xm-1, etc.)

Computing the length of an LCS

• sij = length of an LCS for Xi and Yj

• If xi = yj then sij = si-1,j-1 + 1

• Otherwise sij = max(si,j-1, si-1,j)

• This leads to a bookkeeping scheme where we calculate the scores by filling in an mxn table. The score at position (i, j) depends on the score at (i-1, j-1) if the symbols xi and yj match, otherwise it depends on the scores at positions (i-1, j) and (i, j-1).

• An LCS can be computed by “traceback”.

DP table initializations: fill in first row and first column

DP computation: fill in the rest of the tables row by row (or column by column)

Traceback to find an LCS: bab

Complexity of the DP algorithm

• Time O(nm); space O(nm) where n, m are the lengths of the two sequences.

• Space complexity can be reduced to O(n) by not storing the entries of dynamic programming table that are no longer needed for the computation (keep current row and the previous row only).

Using DP for protein sequence alignment

• In protein sequence alignments there are blocks of similarity and dissimilarity (gaps). E.g. look back at the globin alignments earlier in the lecture.

• The scoring is more complicated because there are “degrees of similarity” among the 20 amino acids.

• To enforce the block structure “gap penalties” have to be introduced.

DNA and proteins

• Much more sensitive comparison is possible between protein sequences than DNA sequences.

• One reason is that the third codon in the genetic code is highly redundant, and introduces noise into DNA comparisons.

• Another reason is that the physico-chemical properties of the amino acid residues provide information that is highly relevant to comparison.

Note the genetic code is degenerate.

Molecular Cell Biology, Lodish et al.Fig. 3-2.

Molecular Cell Biology, Lodish et. alFig. 3-2.

Amino acid substitution matrices

• Ab initio approaches; e.g. assign scores based on number of mutations needed to transform one codon to another, or on other physico-chemical measures of a.a. similarity.

• Empirical, i.e. derive statistics about a.a. substitutions from collections of alignments. (These work the best).

Computation of scores, empirical approach

sij = ln(qij/(pipj))/λ

• sij is the score for substituting amino acid type i by type j.

• qij is the observed frequency of substitutions of a.a. type i by a.a. type j (in the training set).

• pi is the background frequency for a.a. type i in the training set.

• λ is a positive constant.

Example (numbers are fictional)

• N = total number of a.a.’s in training set = 1000• F occurs 15 times• Y occurs 25 times• (F, Y) substitutions occur 200 times

• Np = total number of subst. pairs = 10000

• Then: pF = 0.015, pY = 0.025, qFY = 0.02

• ln(qFY/(pFpY)) ln(53) 4

Substitution matrices

• There are many different matrices available.

• The most commonly used are the BLOSUM or PAM series.

• BLAST defaults to the BLOSUM62 matrix. The BLOSUM matrices have been shown to be more sensitive than the PAM matrices for database searches.

Gap penalties

• There is no suitable theory for gap penalties.• The most common type of gap penalty is the affine gap

penalty: g = a + bx, where a is the gap opening penalty, b is the gap extension penalty, and x is the number of gapped-out residues.

• Typical values, e.g. a = 10 and b = 1 for BLAST.• If the gap penalty has different opening and extension

costs, then the DP algorithm becomes a little more complicated (cf. Chapter 3 in Mount).

Dynamic programming algorithm for computing the score of the optimal alignment

For a sequence S = a1, a2, …, an let Sj = a1, a2, …, aj

Align(Si,S’j) = the score of the highest scoring alignment between S1

i,S2j

S(ai, a’j)= similarity score between amino acids ai and a’j given by a scoring matrix like PAM, BLOSUM

g – gap penalty

Align(Si,S’j)= max

Align(Si-1,S’j-1)+ S(ai, a’j)

Align(Si,S’j-1) - g

Align(Si-1,S’j) - g

{

Organizing the computation – dynamic programming table

Align(Si-1,S’j-1)+ s(ai, a’j)

Align(Si-1,S’j) - g

Align(Si,S’j-1) - g

Align(Si,S’j) = max

{

j

i

Align[i, j] =

Align

+s(ai,aj)

max

Example of DP computation with g = 0; match = 1; mismatch = 0

Maximal Common Subsequence

A T T G C G C G C A T

ATGCTTAACCA

+1

max

0 0 0 0 0 0 0 0 0 0 0 0

0 1 1 1 1 1 1 1 1 1 1 1

0 1 2 2 2 2 2 2 2

0 1 2 2 3

0 1

0 1

0 1

0 1

0 1

0 1

0 1

0 1

initialization

Example of DP computation with g = 2; match = 2; mismatch = -1

A T T G C G C G C A T

ATGCTTAACCA

+2

max-2

-2

Initialization (penalty for starting with a gap)

0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22

-2 2 0 -2 -4

-4 0 4 2

-6 -2 2 3

-8 -4

-10

-12

-14

-16

-18

-20

-22

The iterative algorithm

m = |S|; n = |S’| for i 0 to m do A[i,0]- i * g for j 0 to n do A[0,j] - j * g for i 0 to m do for j 0 to n A[i,j]max ( A[i-1,j] – g A[i-1,j-1] + s(i,j) A[i,j-1] – g )return(A[m,n])

Exercise 3

• Copy and paste the sequences for 1nqpA and 1kr7A into a notepad.

• Go to the web site: http://pir.georgetown.edu/pirwww/search/textpsd.shtml

• Follow the “Search and Retrieval” link, then “Pairwise alignment”.

• Copy in your sequences (use FASTA format and remove numbers) and then run SSEARCH (Smith-Waterman algorithm, a DP alignment method).

SSEARCH (pir.georgetown.edu)

BLAST (Basic Local Alignment Search Tool)

• Extremely fast, can be on the order of 50-100 times faster than Smith-Waterman.

• Method of choice for database searches.

• Statistical theory for significance of results.

• Heuristic; does not guarantee optimal results.

• Many variants, e.g. PHI-, PSI-, RPS-BLAST.

Why database searches?

• Gene finding.

• Assigning likely function to a gene.

• Identifying regulatory elements.

• Understanding genome evolution.

• Assisting in sequence assembly.

• Finding relations between genes.

Issues in database searches

• Speed.

• Relevance of the search results (selectivity).

• Recovering all information of interest (sensitivity).– The results depend on the search parameters, e.g. gap

penalty, scoring matrix.– Sometimes searches with more than one matrix should be

performed.

Main idea of BLAST

• Homologous sequences are likely to contain a short high scoring similarity region, a hit. Each hit gives a seed that BLAST tries to extend on both sides.

Some BLAST terminology…

word – substring of a sequence

word pair – pair of words of the same length

score of a word pair – score of the gapless alignment of the two words:

V A L M R

V A K N S score = 4 + 4 – 2 – 2 - 1 = 3 (BLOSUM62)

HSP – high scoring word pair

Main steps of BLAST

• Parameters: w = length of a hit; T = min. score of a hit (for proteins: w = 3, T = 13 (BLOSUM62)).

• Step 1: Given query sequence Q, compile the list of possible words which form with words in Q high scoring word pairs.

• Step 2: Scan database for exact matching with the list of words compiled in step 1.

• Step 3: Extend the hits from step 2.

• Step 4: Evaluate significance of extended hits from step 3.

Step 1: Find high scoring words

• For every word x of length w in Q make a list of words that when aligned to x score at least T.

• Example: Let x = AIV then the score for AIA is 4+4+0 (dropped) and for AII 4+4+3 (taken).

• The number of words in the list depends on w and T, and is usually much less than 203 (typically about 50).

Step 2 – Finding hits

• Scan database for exact matching with the list of words compiled in step1 :

• Two techniques.– Hash table.– Keyword tree (there is a finite-automaton based method for

exact matching with a set of patterns represented as a tree).

Step 3: Extending hits

• Parameter: X (controlled by a user).

• Extend the hits in both ways along diagonal (ungapped alignment) until score drops more than X relative to the best score yet attained.

• Return the score of the highest scoring segment pair (HSP).

extensions

E-values, P-values

• E-value, Expectation value; this is the expected number of hits of at least the given score, that you would expect by random chance for the search database.

• P-value, Probability value; this is the probability that a hit would attain at least the given score, by random chance for the search database.

• E-values are easier to interpret than P-values.

• If the E-value is small enough, e.g. no more than 0.10, then it is essentially a P-value.

Karlin-Altschul statistics

• Expected number of HSPs with score ≥ S is:

E = KmNe –λS

• m = length of query sequence

• N = database size in residues

• K scales the search space size

• λ a scale for the scoring system

The bit score

• This formula “normalizes” a raw score:

S’ = (λS – ln K)/ln 2

• The E-value is then given by:

E = mN 2 –S’

• Allows direct comparison of E-values, even with differing scoring matrices.

Karlin and Altschul provided a theory for computing statistical significance

• Assumptions:

– The scoring matrix M must be such that the score for a random alignment is negative.

– n, m (lengths of the aligned sequences) are large.

– The amino acid distribution p(x) is in the query sequence and the data base is the same.

– Positive score is possible (i.e. M has at least one positive entry).

P(S<x) = exp (-e –(x-) ) thus:P(S>=x) =1- exp (-e –(x-) )

Score of high scoring sequence pairs follows extreme value distribution

normal

Extreme values

– decay constant u – value of the peak

Refinement of the basic algorithm-the two hit method

• Observation: HSPs of interest are long and can contain multiple hits a relatively short distance apart.

• Central idea: Look for non-overlapping pairs of hits that are of distance at most d on the same diagonal.

• Benefits: – Can reduce word size w from 3 two 2 without losing

sensitivity (actually sensitivity of two-hit BLAST is higher).

– Since extending a hit requires a diagonal partner, many fewer hits are extended, resulting in increased speed.

Gapped BLAST

• Find two non-overlapping hits of score at least T and distance at most d from one another.

• Invoke ungapped extension.

• If the HSP generated has normalized score at least Sg bits then start gapped extension.

• Report resulting alignment if it has sufficiently significant (very small) E-value.

Gapped BLAST statistics

• Theory does not work.• Simulations indicate that for the best hits scores for local

alignments follow an extreme value distribution.• Method approximates and to match experimental distribution

- and can be computed from the median and variation of the experimental distribution.

• BLAST approach – simulate the distribution for set of scoring matrices and a number of gap penalties. BLAST offers a choice of parameters from this pre-computed set.

Motivation for multiple alignments

• Look at a multiple alignment of several of the VAST structure neighbors of 1h1b chain A.

Multiple Sequence Alignment

• A multiple alignment of sequences from a protein family makes the conserved features much more apparent.

• Much more difficult to compute than pairwise alignments.

• The most commonly used and newer programs use the “progressive alignment strategy”.

• There are also important databases of multiple alignments for protein families.

Progressive alignment

• Determine an (approximate) phylogenetic tree for the sequences.

• Construct the multiple alignment by merging pairwise alignments based on the phylogenetic tree, the most closely related sequences first, etc.

• The idea is, if you are careless about the order and merge distantly related sequences too soon in the process, then errors in the alignment may occur and propagate.

Multiple sequence alignment programs

• CLUSTALW, Thompson et al. NAR 1994.

• T-Coffee (Tree-based Consistency Objective Function for alignment Evaluation), C. Notredame et al. JMB 2000.

• MUSCLE (Multiple sequence comparison by log expectation), R. Edgar NAR 2004.

PSI-BLAST

• Position Specific Iterated BLAST

• As a first step runs a (regular) BLAST.

• Hits that cross the threshold are used to construct a position specific score matrix (PSSM).

• A new search is done using the PSSM to find more remotely related sequences.

• The last two steps are iterated until convergence.

PSSM (Position Specific Score Matrix)

• One column per residue in the query sequence.

• Per-column residue frequencies are computed so that log-odds scores may be assigned to each residue type in each column.

• There are difficulties; e.g. pseudo-counts are needed if there are not a lot of sequences, the sequences must be weighted to compensate for redundancy.

Two key advantages of PSSMs

• More sensitive scoring because of improved estimates of probabilities for a.a.’s at specific positions.

• Describes the important motifs that occur in the protein family and therefore enhances the selectivity.

Position Specific Substitution Rates

Active site serineWeakly conserved serine

Position Specific Score Matrix (PSSM)

A R N D C Q E G H I L K M F P S T W Y V 206 D 0 -2 0 2 -4 2 4 -4 -3 -5 -4 0 -2 -6 1 0 -1 -6 -4 -1 207 G -2 -1 0 -2 -4 -3 -3 6 -4 -5 -5 0 -2 -3 -2 -2 -1 0 -6 -5 208 V -1 1 -3 -3 -5 -1 -2 6 -1 -4 -5 1 -5 -6 -4 0 -2 -6 -4 -2 209 I -3 3 -3 -4 -6 0 -1 -4 -1 2 -4 6 -2 -5 -5 -3 0 -1 -4 0 210 D -2 -5 0 8 -5 -3 -2 -1 -4 -7 -6 -4 -6 -7 -5 1 -3 -7 -5 -6 211 S 4 -4 -4 -4 -4 -1 -4 -2 -3 -3 -5 -4 -4 -5 -1 4 3 -6 -5 -3 212 C -4 -7 -6 -7 12 -7 -7 -5 -6 -5 -5 -7 -5 0 -7 -4 -4 -5 0 -4 213 N -2 0 2 -1 -6 7 0 -2 0 -6 -4 2 0 -2 -5 -1 -3 -3 -4 -3 214 G -2 -3 -3 -4 -4 -4 -5 7 -4 -7 -7 -5 -4 -4 -6 -3 -5 -6 -6 -6 215 D -5 -5 -2 9 -7 -4 -1 -5 -5 -7 -7 -4 -7 -7 -5 -4 -4 -8 -7 -7 216 S -2 -4 -2 -4 -4 -3 -3 -3 -4 -6 -6 -3 -5 -6 -4 7 -2 -6 -5 -5 217 G -3 -6 -4 -5 -6 -5 -6 8 -6 -8 -7 -5 -6 -7 -6 -4 -5 -6 -7 -7 218 G -3 -6 -4 -5 -6 -5 -6 8 -6 -7 -7 -5 -6 -7 -6 -2 -4 -6 -7 -7 219 P -2 -6 -6 -5 -6 -5 -5 -6 -6 -6 -7 -4 -6 -7 9 -4 -4 -7 -7 -6 220 L -4 -6 -7 -7 -5 -5 -6 -7 0 -1 6 -6 1 0 -6 -6 -5 -5 -4 0 221 N -1 -6 0 -6 -4 -4 -6 -6 -1 3 0 -5 4 -3 -6 -2 -1 -6 -1 6 222 C 0 -4 -5 -5 10 -2 -5 -5 1 -1 -1 -5 0 -1 -4 -1 0 -5 0 0 223 Q 0 1 4 2 -5 2 0 0 0 -4 -2 1 0 0 0 -1 -1 -3 -3 -4 224 A -1 -1 1 3 -4 -1 1 4 -3 -4 -3 -1 -2 -2 -3 0 -2 -2 -2 -3

Active site nucleophile

Serine scored differently in these two positions

Exercise: using PSI-BLAST

• Go to the NCBI BLAST web site.

• Click on the link to PHI- and PSI- BLAST.

• Choose the search database to be “pdb”.

• Enter the sequence for 1h1bA, Human Neutrophil Elastase.

• How many iterations does it take before 1dleB (Factor B Serine Protease domain) shows up as a significant hit?

Modifying thresholds…

• On occasion, it can prove useful to modify (increase) the inclusion threshold parameter.

• The user can also manually select hits to include in the PSSM that do not meet the threshold, e.g. if one is certain they are homologs to the query.

• Of course, one must always be extremely careful when doing so!

HMMs

• Hidden Markov Models, a type of statistical model.

• Have numerous applications (including outside of bioinformatics).

• HMMs were used to construct Pfam, a database of multiple alignments for protein families (HMMer).

CDD Search

• Conserved Domain Database (CDD) at NCBI.

• Contains alignments from Smart, Pfam, COG, KOG, and LOAD databases.

• Many multiple alignments are manually curated.

• PSSMs derived from multiple alignments may be searched with RPS-BLAST (Reverse Position Specific BLAST).

Multiple alignment of globins from CDD

Thank you to Dr. Teresa Przytycka for slides about dynamic programming and BLAST.