first generation sequencing and pairwise alignment · dna alignment rules: match = 2, mismatch =...

First generation sequencing and pairwise alignment

Analysis of Biological Sequences 140.638

where do sequences come from?

DNA is not hard to extract (getting DNA from a strawberry is a classic elementary school project).The trick is to get a lot of DNA that has exactly the same sequence.

where do sequences come from?

Molecular Cell Biology. 4th edition. 2000

Holland-Frei Cancer Medicine. 5th edition. 2000

sequence-specific cleavage enzymes (restriction enzymes)

and PCR (polymerase chain reaction)

dye-terminator sequencing (sequencing by synthesis)

TGCAGAATTC*TGCAGAATTCA*TGCAGAATTCAG*TGCAGAATTCAGT*TGCAGAATTCAGTG*

smaller products come through the substrate first

dye-terminator sequencing (sequencing by synthesis)when fluorophore intensities are low, the identity of the base is unclear; this is reflected in the quality of the base

so now we have our sequence!

what is it? what does it do?

Two approaches: analyze intrinsic properties of the sequence look for similarities to already known sequences

Goals of sequence alignment

determine the function of an uncharacterized sequence• look for matches to protein-coding or noncoding sequences• look for conserved domains

find the mutational distance between sequences (for species characterization, forensics etc)

Steps in sequence alignment

• Obtain sequences• Align sequences• Score alignment• Is it significant, mathematically? Biologically?

Example alignment

PLSQETFSDLWKLL---PENNVLSPLPSQAMD---------DLMLSPDDIEQWFTEPLSQETF+ LW L +N L+ + +Q +D DL + + IE PLSQETFNQLWTTLGDITDNGNLTQIVTQPLDFSFSETGVADLDIHENRIEMEVER

human TP53 vs acorn worm genome

is this a statistically significant similarity?is this biologically significant?

Dot matrix analysis

The simplest, most visual, most intuitive way to create an alignment

Reference: Gibbs AJ, McIntyre GA. The diagram, a method for comparing sequences. Its use with amino acid and nucleotide sequences. Eur J. Biochem 1970 16(1):1-11.

Dot matrix alignment

PKD protein against itself


PKD vs itself with better parameters


• Lots of variations—can align DNA vs DNA, protein vs protein, many scoring schemes

• Sequence repeats and inverse repeats readily apparent• Can be used to find self-complementary portions of sequences (e.g. RNA)

to help predict secondary structure• Still used today—you will see it occasionally even in major papers

Elements of an alignment

ACC--TAGCTAGCCGAT-ACCCCTAGG----CGAAA

• Matches• Mismatches• Gaps/indels

• aligned vs unaligned: the relationship between these two sequences would likely be stored in three sections (the aligned pieces)

Creating alignments from scratch

Example: ACCTAGCTAGCCGATAnd ACCCCTAGGCGAAA

Possible alignment:ACC--TAGCTAGCCGAT-ACCCCTAGG----CGAAA

Choosing the best alignment

ACC--TAGCTAGCCGAT-ACCCCTAG---G-CGAAA

ACCTAGCTAGCCGAT-ACCC--CTAG-CGAAA

ACC--TAGCTAGCCGAT-ACCCC----TAGGCGAAA

Need Scoring Rules

For example: score = (#matches) - (#mismatches) - (#gaps)x2




Score = 10 - 1 - 7x2 = -5

Score = 10 - 2 - 4x2 = 0

Score = 9 - 1 - 7x2 = -6

Need Scoring Rules

For example: score = 3x(#matches) - 4x(#mismatches) - (#gaps)




Score = 3x10 - 4x1 - 7 = 19

Score = 3x10 - 4x2 - 4 = 18

Score = 3x9 - 4x1 - 7 = 16

Global alignment: Needleman-Wunsch algorithm (Gotoh)

Dynamic programming: achieve optimal alignment by constructing optimal alignments of smaller subsequences

Assume that the optimal alignment is known up to a point, and then extend the alignment optimally to create a new optimal alignment

Global alignment: Needleman-Wunsch-Gotoh

Algorithm:

ACTTGAA CACA| ||| |AGTTGTA CTCA

ACTTGAAC ACA| ||| ||AGTTGTAC TCA

ACTTGAAC ACA| ||| |AGTTGTA- CTCA

ACTTGAA- CACA| ||| |AGTTGTAC TCA

Dynamic programming algorithm: example

DNA alignment rules: match = 2, mismatch = -1, gap = -2

Global alignment: start at the beginning of the sequences and progress to the end

Score of the alignment = score of the alignment up to the previous character + maximum score of aligning the next two symbols or adding a gap in either sequence.

Implementation: dynamic programming

- A C C T G

- 0 -2 -4 -6 -8 -10

A -2

C -4

T -6

T -8

G -10

rules: match +2

mismatch -1 gap -2

Cross vertical line = put gap in sequence B Cross horizontal line = put gap in sequence A

Cross at an intersection = align two residues


- A C C T G

- 0 -2 -4 -6 -8 -10

A -2 2

C -4

T -6

T -8

G -10

rules: match +2

mismatch -1 gap -2




- A C C T G

- 0 -2 -4 -6 -8 -10

A -2 2 0

C -4 0

T -6

T -8

G -10

rules: match +2

mismatch -1 gap -2



Implementation: dynamic programmingrules:

match +2 mismatch -1

gap -2A C

A 2 0

C 04 -2-2

- A C C T G

- 0 -2 -4 -6 -8 -10

A -2 2 0

C -4 0 4

T -6

G -8

G -10

Implementation: dynamic programming Backtracking step

- A C C T G

- 0 -2 -4 -6 -8 -10

A -2 2 0 -2 -4 -6

C -4 0 4 2 0 -2

T -6 -2 2 3 4 2

G -8 -4 0 1 2 6

G -10 -6 -2 -1 0 4

rules: match +2

mismatch -1 gap -2

Implementation: dynamic programming Backtracking step

GTCCAGGTCA

G-TCCAGGT-CA

G-TCCAGGTC-A

-GTCCAGGTC-A

-GTCCAGGT-CA

- A C C T G

- 0 -2 -4 -6 -8 -10

A -2 2 0 -2 -4 -6

C -4 0 4 2 0 -2

T -6 -2 2 3 4 2

G -8 -4 0 1 2 6

G -10 -6 -2 -1 0 4

Reference

Needleman and Wunsch, “A general method applicable to the search for similarities in the amino acid sequence of two proteins” J. Mol. Biol. (1970) 48:443-453

(available through PubMed)

Local alignment

A local alignment between two sequences is an alignment with maximum similarity between a substring of sequence a and a substring of sequence b

Smith and Waterman, “Identification of Common Molecular Subsequences,” J. Mol Biol. (1981) 147:195-197 (available through PubMed)

Local alignment: Smith-Waterman

• Exactly the same algorithm as NWG except that if the score drops below zero, the alignment is terminated.

• This means that subsequences can be aligned optimally, without incurring penalties from surrounding irrelevant sequence that aligns badly

• Can end up with more than one optimal alignment, and the same piece of sequence can have more than one alignment to the other sequence

Local alignment: Smith-Waterman

Algorithm:


ACTTGAAC ACA| ||| ||AGTTGTAC TCA

ACTTGAAC ACA| ||| |AGTTGTA- CTCA

ACTTGAA- CACA| ||| |AGTTGTAC TCA


Implementation: dynamic programming for local alignment

rules: match +2

mismatch -1 gap -2

A C

A 2 0

C 04 -2-2

- A C C T G

- 0 0 0 0 0 0

A 0 2

C 0

T 0

G 0

G 0 XX


- A C C T G

- 0 0 0 0 0 0

A 0 2 0 0 0 0

C 0 0 4 2 0 0

T 0 0 2 3 4 2

G 0 0 0 1 2 6

G 0 0 0 0 0 4

rules: match +2

mismatch -1 gap -2


- A C C T G

- 0 0 0 0 0 0

A 0 2 0 0 0 0

C 0 0 4 2 0 0

T 0 0 2 3 4 2

G 0 0 0 1 2 6

G 0 0 0 0 0 4

rules: match +2

mismatch -1 gap -2

GTCCAGT-CA

GTCCAGTC-A

Local vs global

• Scoring matrix or match/mismatch scores will determine whether a local alignment is obtained

• Needleman-Wunsch can return a local alignment depending on the weighting of end gaps and other scoring parameters

• Look at alignment: if there are long internal gaps, the alignment is local• The best way to tell what’s going on is to align random or unrelated

sequences under the same conditions (next lecture)

Local vs global

- A C T

-

A

C

0 -2 -4 -6

-2 2 0 -2

-4 0 4 2

rules: match +2 mismatch -1 gap -2

Local vs global

- A C T

-

A

C

0 0 0 0

0 2 0 0

0 0 4 2

rules: match +2 mismatch -1 gap -2

Scoring rules/matrices

Why are they important?• Choice of scoring rule can dramatically influence the sequence

alignments obtained and, therefore, the analysis being done• Different scoring matrices have been developed for different

situations; using the wrong one can make a big difference (choosing the wrong sequence as a potential functional ortholog, for example)

Scoring rules/matrices

What do they mean?• Your goal is to figure out whether the two sequences have a

common ancestor• Scoring matrices implicitly represent a particular theory of

evolution• Elements of the matrices reflect significance of co-occurence of

each pair of amino acid residues or nucleotides

Substitution Matrices

We need scoring terms for each aligned residue pairModels: Random model (R): letter a occurs with frequency qa

Substitution Matrices—random model

ACCTGCC|| | |ACGTCCA

p(A)= 0.2p(T)= 0.2p(C)= 0.3p(G)= 0.3

x = ACCTGCCy = ACGTCCA

Substitution Matrices—match model

Models: Match model (M): aligned pairs of residues have joint probability pabpab=probability that a and b came from common ancestor residue


Odds ratio:

=

=


Change to a sum by using logarithms . . .

Score =

Where s(a,b) is just the score of aligning a residue of type a to a residue of type b


s(a,b)

A G M Y

A 4 0 -1 -3

G 0 6 -3 -2

M -1 -3 5 -1

Y -3 -2 -1 11


s(a,b)

A G M Y

A 4 0 -1 -3

G 0 6 -3 -2

M -1 -3 5 -1

Y -3 -2 -1 11

=

=

MAGAMAGY score = 12

Two major scoring matrices

PAM = accepted point mutation• derived from 71 trees with 1572 accepted mutations,

sequences with >85% identity• “accepted” means new amino acid doesn’t disrupt the

protein’s function too severely

BLOSUM = Blocks substitution matrices• Based on BLOCKS database (Henikoff & Henikoff, 1992) of

over 2000 conserved amino acid patterns in over 500 proteins

PAM overview

based on well-accepted phylogenetic trees

STTWC

SSTWCSTTPC

STTPC

observations: one S/T change between close relatives, one P/W change over distant branches, no change from C

BLOSUM overview

based on alignments of known protein motifs, evolutionary relationship unknown

STTWCSSTWCSTTPCSTTWC

observations: three T/S mismatches, three P/W mismatches, no change from C

PAM matrices

• Each matrix describes changes expected for a given period of evolutionary time (measured by expected similarity of proteins)

• Count # of changes to each amino acid in the phylogenetic group and divide by the “exposure to mutation” of the residue

• Exposure to mutation = frequency of occurrence of amino acid * #amino acid changes in the group/100 sites

PAM matrices—assumptions

• P(X->Y) = P(Y->X)• P(X->Z->Y) is low in a single PAM period• changes are independent across time• neighboring amino acids have no influence on probability of

substitution• All sequences have similar amino acid composition

BLOSUM

Henikoff & Henikoff used PROTOMAT program to create BLOCKS database from Prosite catalog of aligned proteins

PROTOMAT looks for A1-d1-A2-d2-A3 where A1, A2, A3 are conserved residues and d1,d2 < 25 residue intervening sequence

BLOSUM construction1. Count mutations

VVAPV AAAPA PVAPV PAAAV

NAA = 0+1+6+0+0 = 7 NVV = 0+1+0+0+3 = 4 NPP = 1+0+0+3+0 = 4 NAV = 1+4+0+0+3 = 8 NAP = 2+0+0+3+0 = 5 NPV = 2+0+0+0+0 = 2

BLOSUM construction2. Tallying mutation frequencies

qij = # times amino acid j mutates to amino acid iSince we don’t know ancestry, each mutation gets entered twice


qij A V P

A 14 8 5

V 8 8 2

P 5 2 8

qAA = 14 qAV = qVA = 8

BLOSUM construction3. Matrix of mutation probabilities

• Create probabilities from mutation frequencies by dividing by total number of observations (60)

pij A V P

A 14/60 8/60 5/60

V 8/60 8/60 2/60

P 5/60 2/60 8/60

BLOSUM construction4. Calculate probability of observing each residue

pi is the marginal probability, meaning the expected probability of occurrence of amino acid i


pi

A 9/20

V 6/20

P 5/20

BLOSUM construction5. Obtaining a BLOSUM matrix

BLOSUM is a log-likelihood matrix: Sij = 2log2(pij/(pipj))

Sij A V P

A 0.41

V -0.04 1.13

P -0.87 -2.34 2.19

AAPVA APPVA

Choice of matrix

High PAM numbers (up to PAM250) are derived from multiplying lots of PAM1 matrices.Low BLOSUM numbers (down to BLOSUM 30) come from very similar sequence blocks

Long sequences and sequences from very distantly related organisms should be aligned with high PAM or low BLOSUM #s.

The best alignments between sequences with high similarity come from high BLOSUM or low PAM numbers.

BLOSUM vs PAM

BLOSUM: based on short conserved sequences (blocks)• Based on a range of evolutionary periods• Each matrix constructed separately• Indirectly accounts for interdependence of residues• Range of sequences, range of replacements• Overcounts related mutations

PAM: evolutionary model• Based on extrapolation from a short evolutionary period• Errors in PAM1 are magnified through PAM250• Assumes Markov process• Many sequences depart from average composition• Rare replacements too infrequent to be represented accurately

Issues

Both BLOSUM and PAM matrices are derived from small sets of sequences from biased databases

Both types of matrices require aligned sequences for their construction

Both types of matrices depend on global, ungapped alignments

first generation sequencing and pairwise alignment · dna alignment rules: match = 2, mismatch =...

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