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MPI for Developmental Biology, Tubingen

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BLAST and FASTAHeuristics in pairwise sequence alignment

Christoph Dieterich

Department of Evolutionary BiologyMax Planck Institute for Developmental Biology

Christoph Dieterich Max Planck Institute for Developmental Biology

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Introduction BLAST Statistical analysis FASTA

Introduction

1 Pairwise alignment is used to detect homologies between

different protein or DNA sequences, e.g. as global or local

alignments.

2 Problem solved using dynamic programming inO(nm)time andO(n)space.

3 This istoo slowfor searching current databases.


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Heuristics for large-scale database searching

In practice algorithms are used that run much faster, at the

expense of possibly missing some significant hits due to the

heuristics employed.

Such algorithms are usually seed-and-extendapproaches in

which first small exact matches are found, which are then

extended to obtain long inexact ones.


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Basic idea: Preprocessing

After preprocessing, a large part of the computation is already

finished before we search for similarities.For biological sequences of lengthnthere are 4n (for the

DNA-alphabet ={A,G,C,T}) and/or 20n (for the amino acidalphabet) different strings.

For small||andn, it is possible to store all in a hash table.


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Basic idea: Preprocessing

1 A certain consistency of the database entries is assumed.

2 Large sequence databases are split into two parts: oneconsists of the constant part, containing all the sequences

that were used for hash table generation, and of a dynamic

part, containing all new entries.


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BLAST

BLAST, the Basic Local Alignment Search Tool (Altschul et al.,

1990), is perhaps the most widely used bioinformatics tool ever

written. It is an alignment heuristic that determines localalignments between aqueryand adatabase. It uses an

approximation of the Smith-Waterman algorithm.

BLAST consists of two components: a search algorithm and

computation of the statistical significance of solutions.


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BLAST terminology

Definition

Letqbe the query anddthe database. Asegmentis simply asubstringsofqord.

Asegment-pair(s, t)(or hit) consists of two segments, one inqand oned, of the same length.


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BLAST terminology

Example

V A L L A R

P A M M A R

We think ofsandtas being aligned without gaps andscore

this alignment using a substitution score matrix, e.g. BLOSUM

or PAM in the case of protein sequences.

The alignment score for(s, t)is denoted by(s, t).


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BLAST terminology

Alocally maximal segment pair (LMSP)is any segment

pair(s, t)whose score cannot be improved by shorteningor extending the segment pair.

Amaximum segment pair (MSP)is any segment pair(s, t)of maximal alignment score(s, t).

Given a cutoff scoreS, a segment pair(s, t)is called ahigh-scoring segment pair (HSP), if it is locally maximal

and(s, t) S.Finally, awordis simply a short substring of fixed length w.


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The BLAST algorithm

Goal: Find all HSPs for a given cut-off score.

Given three parameters, i.e. a word size w, a word similarity

thresholdTand a minimum cut-off score S. Then we are

looking fora segment pair with a score of at least S that

contains at least one word pair of length w with score at least T.


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The BLAST algorithm - Preprocessing

Preprocessing: Of the query sequenceqfirst all words of

lengthware generated. Then a list of all w-mers of lengthw

over the alphabetthat have similarity>Tto some word inthe query sequenceqis generated.


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The BLAST algorithm - Preprocessing

Example

For the query sequence RQCSAGWthe list of words of length

w=2 with a scoreT>8 using the BLOSUM62 matrix are:

word 2 merwith score> 8RQ RQQC QC, RC, EC, NC, DC, KC, MC, SCCS CS,CA,CN,CD,CQ,CE,CG,CK,CT

SA -AG AGGW GW,AW,RW,NW,DW,QW,EW,HW,KW,PW,SW,TW,WW


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The BLAST algorithm - Searching

1 Localization of the hits:The database sequenced is

scanned for all hitstofw-merssin the list, and the

position of the hit is saved.

2 Detection of hits: First all pairs of hits are searched that

have a distance of at most A (think of them lying on thesame diagonal in the matrix of the SW-algorithm).

3 Extension to HSPs:Each suchseed(s, t)is extended inboth directions until its score(s, t)cannot be enlarged

(LMSP). Then all best extensions are reported that havescore S, these are the HSPs. Originally the extensiondid not include gaps, the modern BLAST2 algorithm allows

insertion of gaps.


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The BLAST algorithm - Searching

The listLof all words of length wthat have similarity> Tto some word in the query sequence qcan be produced in

O(|L|)time.

These are placed in a keyword tree and then, for each

word in the tree, all exact locations of the word in the

databasedare detected in time linear to the length of d.

As an alternative to storing the words in a tree, a

finite-state machine can be used, which Altschul et al.found to have the faster implementation.


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The BLAST algorithm

Use of seeds of lengthwand the termination of extensions with

fading scores (score dropoff threshold X) are both steps that

speed up the algorithm.Recent improvements (BLAST 2.0):

Two word hits must be found within a window ofA residues.

Explicit treatment of gaps.

Position-specific iterative BLAST (PSI-BLAST).

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The BLAST algorithm - DNA

ForDNAsequences, BLAST operates as follows:

The list of all words of lengthwin the query sequence q is

generated. In practice,w=12 for DNA.The databasedis scanned for all hits of words in this list.

Blast uses a two-bit encoding for DNA. This saves space

and also search time, as four bases are encoded per byte.

Note that the T parameter dictates the speed and sensitivity ofthe search.


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All flavors of BLAST

BLASTN: compares a DNA query sequence to a DNA

sequence database; qDNAsDNA

BLASTP: compares a protein query sequence to a proteinsequence database; qproteinsprotein

TBLASTN: compares a protein query sequence to a DNA

sequence database (6 frames translation); qproteinst{+1

,

+2,

+3,

1,

2,

3}(DNA)


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All flavors of BLAST - continued

BLASTX: compares a DNA query sequence (6 frames

translation) to a protein sequence database.TBLASTX: compares a DNA query sequence (6 frames

translation) to a DNA sequence database (6 frames

translation).


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Statistical analysis

1 Thenull hypothesis H0 states that the two sequences (s, t)arenothomologous. Then thealternative hypothesis

states that the two sequences are homologous.

2 Choose an experiment to find the pair(s, t): use BLAST to

detect HSPs.3 Compute the probability of the result under the hypothesis

H0, P(Score(s, t)| H0)by generating a probabilitydistribution with random sequences.

4 Fix a rejection level forH0.5 Perform the experiment, compute the probability of

achieving the result or higher and compare with the

rejection level.


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Poisson and extreme value distributions

The Karlin and Altschul theory for local alignments (without

gaps) is based on Poisson and extreme value distributions. Thedetails of that theory are beyond the scope of this lecture, but

basics are sketched in the following.


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Poisson distribution

Definition

The Poisson distribution with parameterv is given by

P(X =x) =vx

x!

ev

Note thatv is theexpected valueas well as the variance. From

the equation we follow that the probability that a variable X will

have a value at least x is

P(X x) =1 x1

i=0

vi

i!ev


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Statistical significance of an HSP

Problem

Given an HSP(s, t)with score(s, t). How significant is thismatch(i.e., local alignment)?

Given the scoring matrixS(a, b), the expected score foraligning a random pair of amino acid is required to be negative:

E=

a,b

papbS(a,b)


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HSP scores are characterized by two parameters,K and.The parametersK and depend on the backgroundprobabilities of the symbols and on the employed scoring

matrix. is the unique value for ythat satisfies the equation

a,b

papbeS(a,b)y =1

K and are scaling-factors for the search space and for thescoring scheme, respectively.


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The number of random HSPs(s, t)with(s, t) Scan bedescribed by a Poisson distribution with parameter

v=KmneS

. The number of HSPs with score Sthat weexpectto see due to chance is then the parameter v, alsocalled theE-value:

E(HSPs with scoreS) =KmneS


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Hence, the probability of finding exactlyxHSPs with a score

Sis given by

P(X=x) =eEEx

x!,

whereE is theE-value forC.The probability of finding at least one HSP by chance is

P(S) =1 P(X =0) =1 eE.


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We would like to hide the parametersK and to make iteasier to compare results from different BLAST searches.

For a given HSP(s, t)we transform therawscoreSinto abit-score:

S := S ln Kln 2

.

Such bit-scores can be compared between different BLAST

searches, as the parameters of the given scoring systems are

subsumed in them.


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We would like to hide the parametersK and to make iteasier to compare results from different BLAST searches.

For a given HSP(s, t)we transform therawscoreSinto abit-score:

S := S ln Kln 2

.

Such bit-scores can be compared between different BLAST

searches, as the parameters of the given scoring systems are

subsumed in them.


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Significance of a bit-score

To determine the significance of a given bit-score S the only

additional value required is the size of the search space. Since

S= (S ln 2 + ln K)/, we can express theE-value in terms ofthe bit-score as follows:

E=KmneS =Kmne(S ln 2+ln K) =mn2S

.


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FASTA

FASTA (pronounced fast-ay) is a heuristic for finding significant

matches between a query string qand a database stringd. It is

the older of the two heuristics introduced in the lecture.

FASTAs general strategy is to find the most significant

diagonals in the dot-plot or dynamic programming matrix.

The algorithm consists of four phases: Hashing, 1st

scoring, 2nd scoring, alignment.


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FASTA

FASTA (pronounced fast-ay) is a heuristic for finding significant

matches between a query string qand a database stringd. It is

the older of the two heuristics introduced in the lecture.

FASTAs general strategy is to find the most significant

diagonals in the dot-plot or dynamic programming matrix.

The algorithm consists of four phases: Hashing, 1st

scoring, 2nd scoring, alignment.


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Phase 1: Hashing

The first step of the algorithm is to determine all exact

matches of lengthk(word-size) between the two

sequences, calledhot-spots.

Ahot-spotis given by(i,j), whereiandjare thelocations(i.e., start positions) of an exact match of length k in the

query and database sequence respectively.

Any such hot-spot(i,j)lies on the diagonal(ij)of the

dot-plot or dynamic programming matrix.


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Phase 1: Hashing

Using this scheme, the main diagonal has number 0 (i=j),whereas diagonals above the main one have positive

numbers (i


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Phase 2+3:

Each of the ten diagonal runs with highest score are further

processed. Within each of these scores an optimal local

alignment is computed using the match score substitution

matrix. These alignments are called initial regions.

The score of the best sub-alignment found in this phase is

reported asinit1.

The next step is to combine high scoring sub-alignments

into a single larger alignment, allowing the introduction of

gaps into the alignment. The score of this alignment isreported asinitn


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Phase 4:

Finally, abandedSmith-Waterman dynamic program is used toproduce an optimal local alignment along the best matched

regions. The center of the band is determined by the region

with the scoreinit1, and the band has width 8 for ktup=2. The

score of the resulting alignment is reported asopt.

In this way, FASTA determines a highest scoring region, not all

high scoring alignments between two sequences. Hence,

FASTA may miss instances of repeats or multiple domains

shared by two proteins.

After all sequences of the databases have thus been searched

a statistical significance similar to the BLAST statistics is

computed and reported.


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FASTA

Example

Two sequences ACTGACandTACCGA: The hot spots fork=2 are

marked as pairs of black bullets, a diagonal run is shaded in dark

grey. An optimal sub-alignment in this case coincides with the

diagonal run. The light grey shaded band of width 3 around thesub-alignment denotes the area in which the optimal local alignment

is searched.


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Comparing BLAST and FASTA

BLAST FASTA

Query

Data ase

Query

ata ase

Qu

ery

Data ase

Query

Data ase

(a) (b)


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BLAT- BLAST-Like Alignment Tool

BLAT (Kent et al. 2002), is supposedly more accurate and 500times faster than popular existing tools for mRNA/DNA

alignments and 50 times faster for protein alignments at

sensitivity settings typically used when comparing vertebrate

sequences.

BLATs speed stems from an index of all non-overlapping

K-mers in the genome. The program has several stages: It

uses the index to find regions in the genome that are possibly

homologous to the query sequence. It performs an alignment

between such regions. It stitches together the aligned regions

(often exons) into larger alignments (typically genes). Finally,

BLAT revisits small internal exons and adjusts large gap

boundaries that have canonical splice siteswherefeasible.Christoph Dieterich Max Planck Institute for Developmental Biology

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