Lecture 2: Sequence Alignment

BMI/IBGP 705 Kun Huang

Department of Biomedical InformaticsOhio State University

Major issues in genomics • Homology

Alignment as an optimization problem

Dynamical programming

BLAST

Tools and examples (in the lab session)

“I think …”

Charles Darwin(1809-1882)

Homology

A Working Definition:

Sequences or structures which share a common ancestor

"The same organ in different animals under a variety of form and function."

Sir Richard Owen, Lectures on the Comparative Anatomy and Physiology of the Invertebrate Animals, 1843.

"The mechanism of homology is heredity." Allan Boyden, Homology and Analogy: A century after the

definitions of "homologue" and "analogue" of Richard Owen, 1943.

"Homology is a relation bearing on recency of common ancestry.“

Olivier Rieppel, Homology and logical fallacy, 1993.

Homology Defined

Sequence Homology

Genes in separate species derived from the same ancestral genes in the last common ancestor of those two species are orthologs.

Related genes resulted from a gene duplication event within a single genome--and are likely to have diverged in their function--are paralogs.

Both orthologs and paralogs are homologs, a general term to cover both types of relationships

Recognizing Sequence Homology• Relies primarily on understanding random sequence

similarity

• Only by knowing what random similarity looks like can we tell when two sequences are significantly similar

• Understanding mutational regularity and sequence evolution increases the significance 1. Closely-related: Transitions/transversions

2. Distantly-related: PAM mutation probabilities

• Even distantly-related sequences can be recognized

• "Significant Similarity" is not a definition of homology.

Databases

• GenBank• EMBL• DDBJ• SWISSPROT• …

Major issues in genomics • Homology• Format• Search

Alignment as an optimization problem

Dynamical programming

BLAST

Tools and examples

Aligning Text Strings

T C A T GC A T T G

2 matches, 0 gapsT C A T G | |C A T T G

3 matches, 2 end gapsT C A T G

| | | C A T T G

4 matches, 1 inserted gapsT C A - T G | | | | C A T T G

4 matches, 1 inserted gapsT C A T - G | | | | C A T T G

Optimal solution: with respect to what criteria / cost function?

Alignment as An Optimization Problem

• Optimization criteria / cost function

• Parameters to be adjusted

• Search algorithm / process• Exhaustive testing• Suboptimal solutions• Computational cost / complexity

• Statistical significance

Alignment as An Optimization Problem

Optimization criteria / cost function

• What sort of alignment should be considered• Scoring system (maximize the score)

• Additive model• Based on probability compared with random

sequence (PAM, BLOSUM)• Assumption of independence• More complicated cases

Gap penalty – linear (s = -gd) affine (s = -d – (g-1)e)

Alignment as An Optimization Problem

Optimization criteria / cost function

• What sort of alignment should be considered• Scoring system

• Additive model• Based on probability compared with random

sequence (PAM, BLOSUM)• Assumption of independence• More complicated cases

Gap penalty – linear (s = -gd) affine (s = -d – (g-1)e)

Alignment as An Optimization Problem

Parameters to be adjusted

• Shift• Number of gaps• Position of gaps

3 matches, 2 end gapsT C A T G

| | | C A T T G

4 matches, 1 inserted gapsT C A - T G | | | | C A T T G

Alignment as An Optimization Problem

Search algorithm / process

• Exhaustive testingTry all possible configuration of parameters.E.g., sequence a with length m, sequence b with length n. Try all m+n shifts (if we use the O(.) annotation, then the running time is O(m+n)).

2 matches, 0 gapsT C A T G | |C A T T G

3 matches, 2 end gapsT C A T G

| | | C A T T G

0 matches, 0 gaps T C A T G

C A T T G

Alignment as An Optimization Problem

Search algorithm / process

• Computational cost / complexity

What if we allow gaps?

2 matches, 0 gapsT C A T G | |C A T T G

3 matches, 2 end gapsT C A T G

| | | C A T T G

0 matches, 0 gaps T C A T G

C A T T G

Many possible alignments to consider

• Without gaps, there are are n+m possible alignments between sequences of length n and m

• Once we start allowing gaps, there are many possible arrangements to consider: abcbcd abcbcd abcbcd | | | | | | | | || || abc--d a--bcd ab--cd

• This becomes a very large number when we allow mismatches, since we then need to look at every possible pairing between elements: there are roughly nm possible alignments.

Exponential computations get big fast

• If n=m=100, there are 100100 = 10200 = 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 different alignments.

• And 100 amino acids is a small protein!

Alignment as An Optimization ProblemStatistical significance

• Not only are there many possible gapped alignments, but introducing too many gaps makes nonsense alignments possible: s--e-----qu---en--ce sometimesquipsentice

• Need to distinguish between alignments that occur due to homology, and those that could be expected to be seen just by chance.

• Define a score function that accounts for statistical significance (logarithmic scale – multiplication of odds becomes addition of scores).

Major issues in genomics • Homology

Alignment as an optimization problem

Dynamical programming

BLAST

Tools and examples

Dot matrix sequence comparison • Write one sequence across top of matrix, the other across left side,

then put a dot where character on line i equals one in column j• Examples below: DNA and amino acid sequences of the phage

cI (vertical axis) and phage P22 c2 (horizontal axis) repressors

Dynamic programming

• The name comes from an operations research task, and has nothing to do with writing programs. Programming – use tabular structure for computing.

• The key idea is to start aligning the sequences left to right; once a prefix is optimally aligned, nothing about the remainder of the alignment changes the alignment of the prefix.

• We construct a matrix of possible alignment scores (nxm2 calculations worst case) and then "traceback" to find the optimal alignment.

• Called Needleman-Wunch (for global matching) or Smith-Waterman (for local matching)

Dynamic programming

• The name comes from an operations research task, and has nothing to do with writing programs. Programming – use tabular structure for computing.

A B

520

2 25

11 17

183

Dynamic programming matrix

• Each cell has the score for the best aligned sequence prefix up to that position.

• Example:

ATGCT vs. ACCGCT

Match: +2, mismatch: 0, gap: -1

Gap A T G C T

Gap 0 -1 -1 -1 -1 -1

A -1 2 0 0 0 0

C -1 0 0 0 2 0

C -1 0 0 0 2 0

G -1 0 0 2 0 0

C -1 0 0 0 2 0

T -1 0 2 0 0 2

Matching matrix, NOT the dynamical programming matrix!

Dynamic programming matrix

Gap A T G C T

Gap 0 -1 -2 -3 -4 -5

A -1 2 (2) 1(0) 0 0 0

C -2 1 (0) 2 (0) 1 2 1

C -3 0 1 (0) 2 3 2

G -4 0 0 3 (2) 2 3

C -5 0 0 2 5 (2) 4

T -6 0 2 1 4 7 (2)

0 1 2 3 4 5 6

0

1

2

3

4

5

6

7

A TA C

A TA C

A T _A _ C

A _ TA C _

Optimal alignment by traceback• We “traceback” a path that gets us the highest score.

If we don't have “end gap” penalties, then takeany path from thelast row or columnto the first.

• Otherwise we needto include the top and bottom corners

Gap A T G C T

Gap 0 -1 -2 -3 -4 -5

A -1 2 (2) 1(0) 0 -1 -2

C -2 1 (0) 2 (0) 1 2 1

C -3 0 1 (0) 2 3 2

G -4 -1 0 3 (2) 2 3

C -5 -2 -1 2 5 (2) 4

T -6 -3 0 1 4 7 (2)

0 1 2 3 4 5 6

0

1

2

3

4

5

6

7

AT - GCT ACCGCT

A - TGCT ACCGCT

Dynamic programming

• Global alignment – an alignment of two or more sequences that matches as many characters as possible in all of the sequences. Needleman-Wunch algorithm

• Local alignment – an alignment that includes only the best matching, highest-scoring regions in two or more sequences. Smith-Waterman algorithm

• Difference – all the scores are kept in the dynamical programming matrix for global alignment; only the positive scores are kept in the dynamical programming matrix for local alignment, the negative ones are converted to zero.

Major issues in genomics • Homology

Alignment as an optimization problem

Dynamical programming

BLAST

Tools and examples

Sequence alignment (BLAST)

The Basic Local Alignment Search Tool (BLAST) finds regions of local similarity between sequences. The program compares nucleotide or protein sequences to sequence databases and calculates the statistical significance of matches. BLAST can be used to infer functional and evolutionary relationships between sequences as well as help identify members of gene families.

http://www.ncbi.nlm.nih.gov/blast/

BLAST – Algorithm IntuitionThe BLAST algorithm.The BLAST algorithm is a heuristic search method that seeks words of length W (default = 3 in blastp) that score at least T when aligned with the query and scored with a substitution matrix. Words in the database that score T or greater are extended in both directions in an attempt to find a locally optimal ungapped alignment or HSP (high scoring pair) with a score of at least S or an E value lower than the specified threshold. HSPs that meet these criteria will be reported by BLAST, provided they do not exceed the cutoff value specified for number of descriptions and/or alignments to report.

BLAST – Algorithm Intuition

http://www.compbio.dundee.ac.uk/ftp/preprints/review93/Figure10.pdf

Databases are pre-indexed by the words.

Without gaps:Altschul, S. F., Gish, W., Miller, W., Myers, E. W., Lipman, D. J., J. Mol. Biol. (1990) 215:403-410

With gaps:Altschul, S. F., Madden, T. L., Schaffer, A. A., Zhang, J., Zhang, Z., Miller, W., Lipman, D. J., Nucleic Acids Research (1997) 25(17):3389-3402

BLAST – Scoring MatricesDNA scoring matrix (substitution matrix)

A T G CA 5 -4 -4 -4T -4 5 -4 -4G -4 -4 5 -4C -4 -4 -4 5

http://www.ncbi.nlm.nih.gov/BLAST/matrix_info.html#matrix

ATTTAGCCGACTTGGCCT5 55 555

Score = 5X6+(-4)X3=18

BLAST – Scoring Matrices

• DNA is relatively easy to choose and protein is harder.• PAM (Percent Accepted Mutation) matrices: predicted

matrices, most sensitive for alignments of sequences with evolutionary related homologs. The greater the number in the matrix name, the greater the expected evolutionary (mutational) distance, i.e. PAM30 would be used for alignments expected to be more closely related in evolution than an alignment performed using the PAM250 matrix.

• BLOSUM (Blocks Substitution Matrix): calculated matrices, most sensitive for local alignment of related sequences, ideal when trying to identify an unknown nucleotide sequence. BLOSUM62 is the default matrix set be the BLAST search tool.

BLAST – Parameters

• Word size – for MegaBlast, can work between w=16 and 64.

• Expected – statistical based notion, compare the matched sequence with random sequence (the likelihood). The larger the score, the smaller the expected value, the more significant the result.

• Percent Identity, match/mismatch scores.

BLAST – Program SelectionNucleotide• Quickly search for highly similar sequences

(megablast)

• Quickly search for divergent sequences (discontiguous megablast)

• Nucleotide-nucleotide BLAST (blastn) • Search for short, nearly exact matches • Search trace archives with megablast or

discontiguous megablast

Protein• Protein-protein BLAST (blastp) • Position-specific iterated and pattern-hit

initiated BLAST (PSI- and PHI-BLAST) • Search for short, nearly exact matches • Search the conserved domain database

(rpsblast) • Protein homology by domain architecture

(cdart)