Oxford

University

Press

Nucleic

Acids

Research

Vol

No.

Gapped

BLAST

and

PSI-BLAST

a

new

generation

of

protein

database

search

programs

Stephen

F.

Altschul

Thomas

L.

Madden

Alejandro

A.

Sch

Jinghui

Zhang

Zheng

Webb

and

David

J.

Lipman

National

Center

for

Biotechnology

Information

National

Library

of

Medicine

National

Institutes

of

Health

Bethesda

MD

USA

of

Genetic

Disease

Research

National

Human

Genome

Research

Institute

National

Institutes

of

Health

Bethesda

MD

USA

and

of

Computer

Science

and

Engineering

Pennsylvania

State

University

University

Park

PA

USA

Received

June

Revised

and

Accepted

July

ABSTRACT

The

BLAST

programs

are

widely

used

tools

for

searching

protein

and

DNA

databases

for

sequence

similarities

For

protein

comparisons

a

variety

of

definitional

algorithmic

and

statistical

refinements

described

here

permits

the

execution

time

of

the

BLAST

programs

to

be

decreased

substantially

while

enhancing

their

sensitivity

to

weak

similarities

A

new

criterion

for

triggering

the

extension

of

word

hits

combined

with

a

new

heuristic

for

generating

gapped

alignments

yields

a

gapped

BLAST

program

that

runs

at

approximately

three

times

the

speed

of

the

original

In

addition

a

method

is

introduced

for

automatically

combining

statistically

significant

alignments

produced

by

BLAST

into

a

position-specific

score

matrix

and

searching

the

database

using

this

matrix

The

resulting

Position-Specific

Iterated

BLAST

-LRB-

PSIBLAST

-RRB-

program

runs

at

approximately

the

same

speed

per

iteration

as

gapped

BLAST

but

in

many

cases

is

much

more

sensitive

to

weak

but

biologically

relevant

sequence

similarities

PSI-BLAST

is

used

to

uncover

several

new

and

interesting

members

of

the

BRCT

superfamily

INTRODUCTION

Variations

of

the

BLAST

algorithm

-LRB-

-RRB-

have

been

incorporated

into

several

popular

programs

for

searching

protein

and

DNA

databases

for

sequence

similarities

BLAST

programs

have

been

written

to

compare

protein

or

DNA

queries

with

protein

or

DNA

databases

in

any

combination

with

DNA

sequences

often

undergoing

conceptual

translation

before

any

comparison

is

performed

We

will

use

the

blastp

program

which

compares

protein

queries

to

protein

databases

as

a

prototype

for

BLAST

although

the

ideas

presented

extend

immediately

to

other

versions

that

involve

the

translation

of

a

DNA

query

or

database

Some

of

the

refinements

described

are

applicable

as

well

to

DNA

DNA

comparison

but

have

yet

to

be

implemented

BLAST

is

a

heuristic

that

attempts

to

optimize

a

specific

similarity

measure

It

permits

a

tradeoff

between

speed

and

sensitivity

with

the

setting

of

a

threshold

parameter

T

A

higher

value

of

T

yields

greater

speed

but

also

an

increased

probability

of

missing

weak

similarities

The

BLAST

program

requires

time

proportional

to

the

product

of

the

lengths

of

the

query

sequence

and

the

database

searched

Since

the

rate

of

change

in

database

sizes

currently

exceeds

that

of

processor

speeds

computers

running

BLAST

are

subjected

to

increasing

load

However

the

conjunction

of

several

new

algorithmic

ideas

allow

a

new

version

of

BLAST

to

achieve

improved

sensitivity

at

substantially

augmented

speed

This

paper

describes

three

major

refinements

to

BLAST

-LRB-

i

-RRB-

For

increased

speed

the

criterion

for

extending

word

pairs

has

been

modified

The

original

BLAST

program

seeks

short

word

pairs

whose

aligned

score

is

at

least

T.

Each

such

hit

is

then

extended

to

test

whether

it

is

contained

within

a

high-scoring

alignment

For

the

default

T

value

this

extension

step

consumes

most

of

the

processing

time

The

new

two-hit

method

requires

the

existence

of

two

non-overlapping

word

pairs

on

the

same

diagonal

and

within

a

distance

A

of

one

another

before

an

extension

is

invoked

To

achieve

comparable

sensitivity

the

threshold

parameter

T

must

be

lowered

yielding

more

hits

than

previously

However

because

only

a

small

fraction

of

these

hits

are

extended

the

average

amount

of

computation

required

decreases

-LRB-

ii

-RRB-

The

ability

to

generate

gapped

alignments

has

been

added

The

original

BLAST

program

often

finds

several

alignments

involving

a

single

database

sequence

which

when

considered

together

are

statistically

significant

Overlooking

any

one

of

these

alignments

can

compromise

the

combined

result

By

introducing

an

algorithm

for

generating

gapped

alignments

it

becomes

necessary

to

find

only

one

rather

than

all

the

ungapped

alignments

subsumed

in

a

significant

result

This

allows

the

T

parameter

to

be

raised

increasing

the

speed

of

the

initial

database

scan

The

new

gapped

alignment

algorithm

uses

dynamic

programming

to

extend

a

central

pair

of

aligned

residues

in

both

directions

For

speed

earlier

heuristic

methods

-LRB-

-RRB-

confined

the

alignments

produced

to

a

predefined

strip

of

the

dynamic

To

whom

correspondence

should

be

addressed

Tel

301 496 2475

Fax

301 480 9241

Email

altschul@ncbi.nlm.nih.gov

Nucleic

Acids

Research

Vol

No.

programming

path

graph

-LRB-

-RRB-

Our

approach

considers

only

alignments

that

drop

in

score

no

more

than

Xg

below

the

best

score

yet

seen

The

algorithm

is

able

thereby

to

adapt

the

region

of

the

path

graph

it

explores

to

the

data

-LRB-

iii

-RRB-

BLAST

searches

may

be

iterated

with

a

position-specific

score

matrix

generated

from

significant

alignments

found

in

round

i

used

for

round

i

Motif

or

profile

search

methods

frequently

are

much

more

sensitive

than

pairwise

comparison

methods

at

detecting

distant

relationships

However

creating

a

set

of

motifs

or

a

profile

that

describes

a

protein

family

and

searching

a

database

with

them

typically

has

involved

running

several

different

programs

with

substantial

user

intervention

at

various

stages

The

BLAST

algorithm

is

easily

generalized

to

use

an

arbitrary

position-specific

score

matrix

in

place

of

a

query

sequence

and

associated

substitution

matrix

Accordingly

we

have

automated

the

procedure

of

generating

such

a

matrix

from

the

output

produced

by

a

BLAST

search

and

adapted

the

BLAST

algorithm

to

take

this

matrix

as

input

The

resulting

PositionSpecific

Iterated

BLAST

or

PSI-BLAST

program

may

not

be

as

sensitive

as

the

best

available

motif

search

programs

but

its

speed

and

ease

of

operation

can

bring

the

power

of

these

methods

into

more

common

use

After

describing

these

refinements

to

BLAST

in

greater

detail

we

consider

several

biological

examples

for

which

the

sensitivity

and

speed

of

the

program

are

greatly

enhanced

STATISTICAL

PRELIMINARIES

To

analyze

the

BLAST

algorithm

and

its

refinements

we

need

first

to

review

the

statistics

of

high-scoring

local

alignments

BLAST

employs

a

substitution

matrix

which

specifies

a

score

sij

for

aligning

each

pair

of

amino

acids

i

and

j.

Given

two

sequences

to

compare

the

original

BLAST

program

seeks

equal-length

segments

within

each

that

when

aligned

to

one

another

without

gaps

have

maximal

aggregate

score

Not

only

the

single

best

segment

pair

may

be

found

but

also

other

locally

optimal

pairs

-LRB-

-RRB-

whose

scores

can

not

be

improved

by

extension

or

trimming

Such

locally

optimal

alignments

are

called

high-scoring

segment

pairs

or

HSPs

For

the

sake

of

the

statistical

theory

we

assume

a

simple

protein

model

in

which

the

amino

acids

occur

randomly

at

all

positions

with

background

probabilities

Pi

We

require

that

the

expected

score

for

two

random

amino

acids

i

j

where

N

mn

is

the

search

space

size

-LRB-

-RRB-

If

a

protein

is

compared

to

a

whole

database

rather

than

a

single

sequence

n

is

the

database

length

in

residues

Equation

may

be

inverted

to

yield

S

-LRB-

N/E

-RRB-

the

normalized

score

required

to

achieve

a

particular

E-value

In

a

typical

current

database

search

a

protein

of

length

might

be

compared

to

a

protein

database

of

50 000 000

total

residues

To

achieve

a

marginally

significant

E-value

of

a

normalized

score

of

bits

is

necessary

While

the

theory

just

outlined

has

not

been

proved

for

gapped

local

alignments

and

their

associated

scores

computational

experiments

strongly

suggest

that

it

remains

valid

-LRB-

-RRB-

The

statistical

parameters

and

K

however

are

no

longer

supplied

by

theory

but

must

be

estimated

using

comparisons

of

either

simulated

or

real

but

unrelated

sequences

To

distinguish

below

whether

a

given

set

of

parameters

and

K

refer

to

gapped

or

ungapped

alignments

we

use

the

subscripts

g

and

u

respectively

When

gaps

are

not

allowed

a

further

important

theorem

states

that

within

HSPs

the

aligned

pair

of

letters

-LRB-

i

j

-RRB-

tends

to

occur

with

the

target

frequency

q

ij

PiPjelusij

The

qij

of

equation

sum

to

indeed

u

is

calculated

to

be

the

unique

positive

number

for

which

this

is

the

case

-LRB-

-RRB-

The

scores

sij

are

optimal

for

detecting

alignments

with

these

particular

target

frequencies

-LRB-

-RRB-

and

by

inverting

equation

to

sij

-LSB-

ln

-LRB-

qij/PiPj

-RRB-

-RSB-

u

scores

may

be

chosen

with

arbitrary

scale

that

correspond

to

any

desired

set

of

qij

The

popular

PAM

-LRB-

-RRB-

and

BLOSUM

-LRB-

-RRB-

substitution

matrices

are

constructed

with

explicit

use

of

this

log-odds

formula

No

corresponding

result

has

been

established

for

gapped

alignment

scoring

systems

However

if

the

gap

costs

used

are

sufficiently

large

it

is

expected

that

the

target

frequencies

observed

in

high-scoring

local

alignments

of

random

sequences

will

not

differ

greatly

from

those

for

the

no-gap

case

REFINEMENT

OF

THE

BASIC

ALGORITHM

THE

TWO-HIT

METHOD

The

central

idea

of

the

BLAST

algorithm

is

that

a

statistically

significant

alignment

is

likely

to

contain

a

high-scoring

pair

of

aligned

words

BLAST

first

scans

the

database

for

words

-LRB-

typically

of

length

three

for

proteins

-RRB-

that

score

at

least

T

when

aligned

with

some

word

within

the

query

sequence

Any

aligned

word

pair

satisfying

this

condition

is

called

a

hit

The

second

step

of

the

algorithm

checks

whether

each

hit

lies

within

an

alignment

with

score

sufficient

to

be

reported

This

is

done

by

extending

a

hit

in

both

directions

until

the

running

alignment

's

score

has

dropped

more

than

X

below

the

maximum

score

yet

attained

This

extension

step

is

computationally

quite

costly

with

the

T

and

X

parameters

necessary

to

attain

reasonable

sensitivity

to

weak

alignments

the

extension

step

typically

accounts

for

of

BLAST

's

execution

time

It

is

therefore

desirable

to

reduce

the

number

of

extensions

performed

Our

refined

algorithm

is

based

upon

the

observation

that

an

HSP

of

interest

is

much

longer

than

a

single

word

pair

and

may

therefore

entail

multiple

hits

on

the

same

diagonal

and

within

a

relatively

short

distance

of

one

another

-LRB-

The

diagonal

of

a

hit

involving

words

starting

at

positions

-LRB-

-RRB-

of

the

database

and

query

sequences

may

be

defined

as

The

distance

between

two

hits

on

the

same

diagonal

is

the

difference

between

their

first

coordinates

-RRB-

This

signature

may

be

used

to

locate

HSPs

more

P

iP

js

ij

be

negative

Given

the

Pi

and

sij

the

basic

theory

-LRB-

-RRB-

yields

two

calculable

parameters

and

K

which

can

be

used

to

convert

nominal

HSP

scores

to

normalized

scores

thereby

rendering

all

scoring

systems

directly

comparable

from

a

statistical

perspective

The

normalized

score

S

for

an

HSP

is

given

by

the

equation

S

lS

ln

K

ln

In

this

paper

a

nominal

score

is

given

without

units

while

a

score

normalized

by

equation

is

said

to

be

expressed

in

bits

-LRB-

-RRB-

When

two

random

protein

sequences

of

sufficient

lengths

m

and

n

are

compared

the

number

E

of

distinct

HSPs

with

normalized

score

at

least

S

expected

to

occur

by

chance

is

well

approximated

by

E

N

Nucleic

Acids

Research

Vol

No

Nucleic

Acids

Research

Vol

No.

Figure

The

sensitivity

of

the

two-hit

and

one-hit

heuristics

as

a

function

of

HSP

score

Using

the

amino

acid

substitution

matrix

-LRB-

-RRB-

and

the

target

frequencies

qij

implied

by

equation

and

the

background

amino

acid

frequencies

Pi

of

Robinson

and

Robinson

-LRB-

-RRB-

model

HSPs

were

generated

for

each

of

the

nominal

scores

corresponding

to

normalized

scores

bits

It

was

determined

by

inspection

whether

each

HSP

failed

to

contain

two

non-overlapping

word

pairs

with

nominal

score

at

least

and

within

a

distance

of

one

another

or

a

single

word

pair

with

nominal

score

at

least

The

corresponding

probabilities

of

missing

an

HSP

using

the

two-hit

heuristic

with

T

and

the

one-hit

heuristic

with

T

are

plotted

as

a

function

of

normalized

HSP

score

The

two-hit

method

is

more

sensitive

for

HSPs

with

score

at

least

bits

Figure

The

BLAST

comparison

of

broad

bean

leghemoglobin

I

-LRB-

-RRB-

-LRB-

SWISS-PROT

accession

no

-RRB-

and

horse

globin

-LRB-

-RRB-

-LRB-

SWISS-PROT

accession

no

-RRB-

The

hits

with

score

at

least

are

indicated

by

plus

signs

An

additional

non-overlapping

hits

with

score

at

least

are

indicated

by

dots

Of

these

hits

only

the

two

indicated

pairs

are

on

the

same

diagonal

and

within

distance

of

one

another

Thus

the

two-hit

heuristic

with

T

triggers

two

extensions

in

place

of

the

extensions

invoked

by

the

one-hit

heuristic

with

T

Because

this

is

just

one

example

the

relative

numbers

of

hits

and

extensions

at

the

various

settings

of

T

correspond

only

roughly

to

the

ratios

found

in

a

full

database

search

An

ungapped

extension

of

the

leftward

of

the

two

hit

pairs

yields

an

HSP

with

nominal

score

or

bits

calculated

using

u

and

Ku

efficiently

Specifically

we

choose

a

window

length

A

and

invoke

an

extension

only

when

two

non-overlapping

hits

are

found

within

distance

A

of

one

another

on

the

same

diagonal

Any

hit

that

overlaps

the

most

recent

one

is

ignored

Efficient

execution

requires

an

array

to

record

for

each

diagonal

the

first

coordinate

of

the

most

recent

hit

found

Since

database

sequences

are

scanned

sequentially

this

coordinate

always

increases

for

successive

hits

The

idea

of

seeking

multiple

hits

on

the

same

diagonal

was

first

used

in

the

context

of

biological

database

searches

by

Wilbur

and

Lipman

-LRB-

-RRB-

Because

we

require

two

hits

rather

than

one

to

invoke

an

extension

the

threshold

parameter

T

must

be

lowered

to

retain

comparable

sensitivity

The

effect

is

that

many

more

single

hits

are

found

but

only

a

small

fraction

have

an

associated

second

hit

on

the

same

diagonal

that

triggers

an

extension

The

great

majority

of

hits

may

be

dismissed

after

the

minor

calculation

of

looking

up

for

the

appropriate

diagonal

the

coordinate

of

the

most

recent

hit

checking

whether

it

is

within

distance

A

of

the

current

hit

's

coordinate

and

finally

replacing

the

old

with

the

new

coordinate

Empirically

the

computation

saved

by

requiring

fewer

extensions

more

than

offsets

the

extra

computation

required

to

process

the

larger

number

of

hits

To

study

the

relative

abilities

of

the

one-hit

and

two-hit

methods

to

detect

HSPs

of

varying

score

we

model

proteins

using

the

background

amino

acid

frequencies

of

Robinson

and

Robinson

-LRB-

-RRB-

and

use

the

substitution

matrix

-LRB-

-RRB-

for

sequence

comparison

Given

these

Pi

and

sij

the

statistical

parameters

for

ungapped

local

alignments

are

calculated

to

be

u

and

Ku

Using

equation

above

we

may

calculate

the

qij

for

which

the

scoring

system

is

optimized

and

employ

these

target

frequencies

to

generate

model

HSPs

Finally

we

evaluate

the

sensitivity

of

the

one-hit

and

two-hit

BLAST

heuristics

using

these

HSPs

The

one-hit

method

will

detect

an

HSP

if

it

somewhere

contains

a

length-W

word

of

score

at

least

T.

For

W

and

T

Figure

shows

the

empirically

estimated

probability

that

an

HSP

is

missed

by

this

method

as

a

function

of

its

normalized

score

The

two-hit

method

will

detect

an

HSP

if

it

contains

two

nonoverlapping

length-W

words

of

score

at

least

T

with

starting

positions

that

differ

by

no

more

than

A

residues

For

W

T

and

A

Figure

shows

the

estimated

probability

that

an

HSP

is

missed

by

this

method

as

a

function

of

its

normalized

score

For

HSPs

with

score

at

least

bits

the

two-hit

heuristic

is

more

sensitive

To

analyze

the

relative

speeds

of

the

one-hit

and

two-hit

methods

using

the

parameters

studied

above

we

note

that

the

two-hit

method

generates

on

average

times

as

many

hits

but

only

times

as

many

hit

extensions

-LRB-

Fig.

-RRB-

Because

it

takes

approximately

one

ninth

as

long

to

decide

whether

a

hit

need

be

extended

as

actually

to

extend

it

the

hit-processing

component

of

the

two-hit

method

is

approximately

twice

as

rapid

as

the

same

component

of

the

one-hit

method

TRIGGERING

THE

GENERATION

OF

GAPPED

ALIGNMENTS

Figure

shows

that

even

when

using

the

original

one-hit

method

with

threshold

parameter

T

there

is

generally

no

greater

than

a

chance

of

missing

an

HSP

with

score

bits

While

this

would

appear

sufficient

for

most

purposes

the

one-hit

default

T

parameter

has

typically

been

set

as

low

as

yielding

an

execution

time

nearly

three

times

that

for

T

Why

pay

this

price

for

what

appears

at

best

marginal

gains

in

sensitivity

The

Nucleic

Acids

Research

Vol

No.

a

b

c

Figure

A

gapped

extension

generated

by

BLAST

for

the

comparison

of

broad

bean

leghemoglobin

I

-LRB-

-RRB-

and

horse

globin

-LRB-

-RRB-

-LRB-

a

-RRB-

The

region

of

the

path

graph

explored

when

seeded

by

the

alignment

of

alanine

residues

at

respective

positions

and

This

seed

derives

from

the

HSP

generated

by

the

leftward

of

the

two

ungapped

extensions

illustrated

in

Figure

The

Xg

dropoff

parameter

is

the

nominal

score

used

in

conjunction

with

substitution

scores

and

a

cost

of

k

for

gaps

of

length

k.

-LRB-

b

-RRB-

The

path

corresponding

to

the

optimal

local

alignment

generated

superimposed

on

the

hits

described

in

Figure

The

original

BLAST

program

using

the

one-hit

heuristic

with

T

is

able

to

locate

three

of

the

five

HSPs

included

in

this

alignment

but

only

the

first

and

last

achieve

a

score

sufficient

to

be

reported

-LRB-

c

-RRB-

The

optimal

local

alignment

with

nominal

score

and

normalized

score

bits

In

the

context

of

a

search

of

SWISS-PROT

-LRB-

-RRB-

release

-LRB-

21 219 450

residues

-RRB-

using

the

leghemoglobin

sequence

-LRB-

residues

-RRB-

as

query

the

E-value

is

if

no

edge-effect

correction

-LRB-

-RRB-

is

invoked

The

original

BLAST

program

locates

the

first

and

last

ungapped

segments

of

this

alignment

Using

sum-statistics

with

no

edge-effect

correction

this

combined

result

has

an

E-value

of

-LRB-

-RRB-

On

the

central

lines

of

the

alignment

identities

are

echoed

and

substitutions

to

which

the

matrix

-LRB-

-RRB-

gives

a

positive

score

are

indicated

by

a

symbol

reason

is

that

the

original

BLAST

program

treats

gapped

alignments

implicitly

by

locating

in

many

cases

several

distinct

HSPs

involving

the

same

database

sequence

and

calculating

a

statistical

assessment

of

the

combined

result

-LRB-

-RRB-

This

means

that

two

or

more

HSPs

with

scores

well

below

bits

can

in

combination

rise

to

statistical

significance

If

any

one

of

these

HSPs

is

missed

so

may

be

the

combined

result

The

approach

taken

here

allows

BLAST

to

simultaneously

produce

gapped

alignments

and

run

significantly

faster

than

previously

The

central

idea

is

to

trigger

a

gapped

extension

for

any

HSP

that

exceeds

a

moderate

score

Sg

chosen

so

that

no

more

than

about

one

extension

is

invoked

per

database

sequences

-LRB-

By

equation

for

a

typical-length

protein

query

Sg

should

be

set

at

bits

-RRB-

A

gapped

extension

takes

much

longer

to

execute

than

an

ungapped

extension

but

by

performing

very

few

of

them

the

fraction

of

the

total

running

time

they

consume

can

be

kept

relatively

low

By

seeking

a

single

gapped

alignment

rather

than

a

collection

of

ungapped

ones

only

one

of

the

constituent

HSPs

need

be

located

for

the

combined

result

to

be

generated

successfully

This

means

that

we

may

tolerate

a

much

higher

chance

of

missing

any

single

moderately

scoring

HSP

For

example

consider

a

result

involving

two

HSPs

each

with

the

same

probability

P

of

being

missed

at

the

hit-stage

of

the

BLAST

algorithm

and

suppose

that

we

desire

to

find

the

combined

result

with

probability

at

least

The

original

algorithm

needing

to

find

both

HSPs

requires

or

P

less

than

In

contrast

the

new

algorithm

requires

only

that

and

thus

can

tolerate

P

as

high

as

This

permits

the

T

parameter

for

the

hit-stage

of

the

algorithm

to

be

raised

substantially

while

retaining

comparable

sensitivity

from

T

to

T

for

the

one-hit

heuristic

-LRB-

The

two-hit

heuristic

described

above

lowers

T

back

to

-RRB-

As

will

be

discussed

below

the

resulting

increase

in

speed

more

than

compensates

for

the

extra

time

required

for

the

rare

gapped

extension

In

summary

the

new

gapped

BLAST

algorithm

requires

two

non-overlapping

hits

of

score

at

least

T

within

a

distance

A

of

one

another

to

invoke

an

ungapped

extension

of

the

second

hit

If

the

HSP

generated

has

normalized

score

at

least

Sg

bits

then

a

gapped

extension

is

triggered

The

resulting

gapped

alignment

is

reported

only

if

it

has

an

E-value

low

enough

to

be

of

interest

For

example

in

the

pairwise

comparison

of

Figure

the

ungapped

extension

invoked

by

the

hit

pair

on

the

left

produces

an

HSP

with

score

bits

-LRB-

calculated

using

u

and

Ku

-RRB-

This

is

sufficient

to

trigger

a

gapped

extension

which

generates

an

alignment

with

score

bits

-LRB-

calculated

using

g

and

Kg

-RRB-

and

E-value

of

-LRB-

Fig.

-RRB-

The

original

BLAST

program

locates

only

the

first

and

last

ungapped

segments

of

this

alignment

-LRB-

Fig.

-RRB-

and

assigns

them

a

combined

E-value

times

greater

Nucleic

Acids

Research

Vol

No

Nucleic

Acids

Research

Vol

No.

THE

CONSTRUCTION

AND

STATISTICAL

EVALUATION

OF

GAPPED

LOCAL

ALIGNMENTS

The

standard

dynamic

programming

algorithms

for

pairwise

sequence

alignment

perform

a

fixed

amount

of

computation

per

cell

of

a

path

graph

whose

dimensions

are

the

lengths

of

the

two

sequences

being

compared

-LRB-

-RRB-

In

order

to

gain

speed

database

search

algorithms

such

as

Fasta

-LRB-

-RRB-

and

an

earlier

gapped

version

of

BLAST

-LRB-

-RRB-

sacrifice

rigor

by

confining

the

dynamic

programming

to

a

banded

section

of

the

full

path

graph

-LRB-

-RRB-

chosen

to

include

a

region

of

already

identified

similarity

One

problem

with

this

approach

is

that

the

optimal

gapped

alignment

may

stray

beyond

the

confines

of

the

band

explored

As

the

width

of

the

band

is

increased

to

reduce

this

possibility

the

speed

advantage

of

the

algorithm

is

vitiated

We

have

accordingly

taken

a

different

heuristic

approach

to

constructing

gapped

local

alignments

which

is

a

simple

generalization

of

BLAST

's

method

for

constructing

HSPs

The

central

idea

is

to

consider

only

cells

for

which

the

optimal

local

alignment

score

falls

no

more

than

Xg

below

the

best

alignment

score

yet

found

Starting

from

a

single

aligned

pair

of

residues

called

the

seed

the

dynamic

programming

proceeds

both

forward

and

backward

through

the

path

graph

-LRB-

Zheng

Zhang

et

al.

manuscript

in

preparation

-RRB-

-LRB-

Figs

and

-RRB-

The

advantage

of

this

approach

is

that

the

region

of

the

path

graph

explored

adapts

to

the

alignment

being

constructed

The

alignment

can

wander

arbitrarily

many

diagonals

away

from

the

seed

but

the

number

of

cells

expanded

on

each

row

tends

to

remain

limited

and

may

even

shrink

to

zero

before

a

boundary

of

the

path

graph

is

encountered

-LRB-

Fig.

-RRB-

The

Xg

parameter

serves

a

similar

function

to

the

band-width

parameter

of

the

earlier

heuristic

but

the

region

of

the

path

graph

it

implicitly

specifies

be

explored

is

in

general

more

productively

chosen

An

important

element

for

this

heuristic

is

the

intelligent

choice

of

a

seed

Given

an

HSP

whose

score

is

sufficiently

high

that

it

triggers

a

gapped

extension

how

does

one

choose

a

residue

pair

to

force

into

alignment

While

more

sophisticated

approaches

are

possible

the

simple

procedure

we

have

implemented

is

to

locate

along

the

HSP

the

segment

with

highest

alignment

score

and

use

its

central

residue

pair

as

the

seed

If

the

HSP

itself

is

shorter

than

a

central

residue

pair

is

chosen

For

example

the

first

ungapped

region

in

the

alignment

of

Figure

constitutes

the

HSP

that

triggered

the

alignment

The

highest-scoring

segment

of

this

HSP

aligns

leghemoglobin

residues

with

globin

residues

Thus

the

alanine

residues

at

respective

positions

and

are

used

as

the

seed

for

the

gapped

extension

illustrated

in

Figure

As

discussed

in

the

performance

evaluation

section

below

this

procedure

is

extremely

good

at

selecting

seeds

that

in

fact

participate

in

an

optimal

alignment

Most

gapped

extensions

are

triggered

by

chance

similarities

and

are

therefore

likely

to

be

of

limited

extent

as

illustrated

in

Figure

The

reverse

extension

in

this

example

explores

Figure

The

path

graph

region

explored

by

BLAST

during

a

gapped

extension

for

the

comparison

of

broad

bean

leghemoglobin

I

and

the

protein

small

T-antigen

from

human

adenovirus

type

-LRB-

-RRB-

-LRB-

SWISS-PROT

accession

no

-RRB-

The

Xg

dropoff

parameter

is

the

nominal

score

used

in

conjunction

with

substitution

scores

and

k

gap

costs

The

bit

HSP

that

triggers

this

extension

involving

leghemoglobin

residues

and

adenovirus

residues

is

merely

a

random

similarity

and

not

part

of

a

larger

and

higher-scoring

alignment

The

gapped

extension

is

seeded

by

the

alignment

of

residues

and

The

optimal

alignment

score

through

points

in

the

path

graph

drops

steadily

as

one

moves

beyond

the

triggering

HSP

and

the

reverse

extension

terminates

before

the

beginning

of

either

protein

is

reached

A

total

of

path

graph

cells

are

explored

with

the

reverse

extension

accounting

for

of

these

cells

path

graph

cells

so

that

a

typical

two-way

gapped

extension

that

does

not

encounter

the

end

of

either

sequence

is

expected

to

involve

cells

Because

Sg

is

set

so

that

a

gapped

extension

is

invoked

less

than

once

per

database

sequences

fewer

than

cells

need

be

explored

per

database

sequence

The

execution

time

required

for

a

gapped

extension

is

times

that

for

an

ungapped

extension

However

by

triggering

gapped

extensions

in

the

manner

described

while

simultaneously

raising

T

for

the

single-hit

version

of

BLAST

from

to

approximately

one

gapped

extension

is

invoked

for

every

ungapped

extensions

avoided

Because

the

number

of

ungapped

extensions

is

reduced

by

about

two

thirds

the

total

time

spent

on

the

extension

stage

of

BLAST

is

cut

by

well

over

half

Of

course

the

two-hit

strategy

described

above

reduces

the

time

needed

for

the

ungapped

extensions

still

further

Once

program

overhead

is

accounted

for

the

net

speedup

is

a

factor

of

about

three

For

any

alignment

actually

reported

a

gapped

extension

that

records

traceback

information

-LRB-

-RRB-

needs

to

be

executed

To

increase

BLAST

's

accuracy

in

producing

optimal

local

alignments

these

gapped

extensions

use

by

default

a

substantially

larger

Xg

parameter

than

employed

during

the

program

's

search

stage

Table

Relative

times

spent

by

the

original

and

gapped

BLAST

programs

on

various

algorithmic

stages

Overhead

database

scanning

output

etc.

Original

BLAST

Gapped

BLAST

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

Calculating

whether

hits

qualify

for

ungapped

extension

Ungapped

extensions

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

Gapped

extensions

Nucleic

Acids

Research

Vol

No.

The

times

required

by

various

steps

of

the

BLAST

algorithm

vary

substantially

from

one

query

and

one

database

to

another

Table

shows

typical

relative

times

spent

by

the

original

and

the

gapped

BLAST

programs

on

various

algorithmic

stages

The

original

BLAST

program

is

represented

here

and

below

by

a

variant

form

of

blastp

version

modified

so

that

it

uses

the

same

edge-effect

correction

-LRB-

-RRB-

and

background

amino

acid

frequencies

as

the

gapped

BLAST

The

times

represent

the

average

for

three

different

queries

with

the

time

for

the

original

BLAST

program

normalized

in

each

instance

to

units

More

concretely

to

search

SWISS-PROT

-LRB-

-RRB-

release

-LRB-

sequences

21 219 450

residues

-RRB-

with

the

influenza

A

virus

hemagglutinin

precursor

-LRB-

-RRB-

as

query

the

original

BLAST

program

requires

s

and

the

gapped

BLAST

program

s

This

timing

experiment

and

others

referred

to

below

was

run

on

one

MHz

cpu

processor

of

a

lightly

loaded

SGI

Power

Challenge

XL

computer

with

Gbytes

of

RAM

This

machine

runs

the

operating

system

IRIX

version

which

is

an

implementation

of

UNIX

We

used

the

standard

SGI

C

compiler

with

the

O

flag

for

optimization

to

compile

all

versions

of

the

programs

The

times

reported

are

the

user

times

given

by

the

time

command

and

are

for

the

better

of

two

identical

runs

A

closely

related

type

of

gapped

extension

routine

to

that

used

here

was

developed

by

G.

Myers

during

the

evaluation

of

the

original

BLAST

algorithm

It

was

not

included

in

the

publicly

distributed

code

primarily

because

the

then

current

strategy

of

extending

every

hit

decreased

the

algorithm

's

speed

unduly

for

the

relatively

small

gain

in

sensitivity

realized

-LRB-

-RRB-

As

discussed

above

the

statistical

significance

of

gapped

alignments

may

be

evaluated

using

the

two

statistical

parameters

g

and

Kg

The

current

version

of

the

Fasta

program

-LRB-

-RRB-

estimates

these

parameters

on

each

run

by

analyzing

the

distribution

of

alignment

scores

produced

by

all

the

sequences

in

the

database

BLAST

gains

speed

by

producing

alignments

for

only

the

few

database

sequences

likely

to

be

related

to

the

query

and

therefore

does

not

have

the

option

of

estimating

g

and

Kg

on

the

fly

Instead

it

uses

estimates

of

these

parameters

produced

beforehand

by

random

simulation

-LRB-

-RRB-

A

drawback

of

this

approach

is

that

the

program

may

not

accept

an

arbitrary

scoring

system

for

which

no

simulation

has

been

performed

and

still

produce

accurate

estimates

of

statistical

significance

The

original

BLAST

programs

in

contrast

because

they

dealt

only

with

ungapped

local

alignments

could

derive

u

and

Ku

from

theory

for

any

scoring

matrix

-LRB-

-RRB-

ITERATED

APPLICATION

OF

BLAST

TO

POSITION-SPECIFIC

SCORE

MATRICES

Database

searches

using

position-specific

score

matrices

also

called

profiles

or

motifs

often

are

much

better

able

to

detect

weak

relationships

than

are

database

searches

that

use

a

simple

sequence

as

query

-LRB-

-RRB-

Employing

these

methods

however

frequently

has

involved

the

use

of

several

different

programs

and

a

fair

degree

of

expertise

Accordingly

to

render

the

power

of

motif

searches

more

readily

available

we

have

written

a

procedure

to

construct

a

position-specific

score

matrix

automatically

from

the

output

of

a

BLAST

run

and

modified

BLAST

to

operate

using

such

a

matrix

in

the

place

of

a

simple

query

The

resulting

PSI-BLAST

program

often

is

substantially

more

sensitive

than

the

corresponding

BLAST

program

but

for

each

iteration

takes

little

more

than

the

same

time

to

run

In

related

work

Henikoff

and

Henikoff

-LRB-

-RRB-

have

described

how

short

of

modifying

BLAST

so

that

it

may

operate

on

a

position-specific

score

matrix

a

single

artificial

sequence

that

approximates

such

a

matrix

may

be

used

as

a

query

with

the

original

BLAST

programs

The

construction

of

a

position-specific

score

matrix

is

a

multi-stage

process

and

at

each

stage

a

choice

must

be

made

among

a

number

of

alternative

routes

We

have

been

guided

by

the

goals

of

automatic

operation

speed

of

execution

and

general

simplicity

The

issues

discussed

below

are

-LRB-

i

-RRB-

general

architecture

of

the

score

matrix

-LRB-

ii

-RRB-

construction

of

the

multiple

alignment

from

which

the

matrix

is

derived

-LRB-

iii

-RRB-

weights

for

sequences

within

the

multiple

alignment

and

evaluation

of

the

effective

number

of

independent

observations

it

constitutes

-LRB-

iv

-RRB-

estimation

of

target

frequencies

and

the

construction

of

matrix

scores

-LRB-

v

-RRB-

applying

BLAST

to

a

position-specific

matrix

and

the

statistical

evaluation

of

search

results

We

do

not

claim

our

current

implementation

is

optimal

and

it

is

likely

that

over

time

some

of

its

details

will

change

Score

matrix

architecture

The

alignment

of

a

simple

sequence

with

a

pattern

embodied

by

a

position-specific

score

matrix

is

almost

completely

analogous

to

the

alignment

of

two

simple

sequences

The

only

real

difference

is

that

the

score

for

aligning

a

letter

with

a

pattern

position

is

given

by

the

matrix

itself

rather

than

with

reference

to

a

substitution

matrix

For

proteins

a

query

of

length

L

and

a

substitution

matrix

of

dimension

are

replaced

by

a

position-specific

matrix

of

dimension

L

Position-specific

gap

costs

may

be

defined

as

well

-LRB-

-RRB-

As

with

pairwise

sequence

comparison

one

may

choose

among

finding

the

best

global

alignment

of

the

matrix

and

the

simple

sequence

-LRB-

-RRB-

finding

the

best

alignment

of

the

complete

matrix

with

a

segment

of

the

sequence

-LRB-

-RRB-

and

finding

the

best

local

alignment

of

the

matrix

and

sequence

-LRB-

-RRB-

Position-specific

protein

score

matrices

draw

their

power

from

two

sources

The

first

is

improved

estimation

of

the

probabilities

with

which

amino

acids

occur

at

various

pattern

positions

leading

to

a

more

sensitive

scoring

system

The

second

is

relatively

precise

definition

of

the

boundaries

of

important

motifs

By

demanding

the

complete

alignment

of

one

or

more

motifs

rather

than

seeking

an

arbitrary

local

alignment

the

size

of

the

search

space

may

be

greatly

reduced

thereby

lowering

the

level

of

random

noise

Unfortunately

there

are

many

obstacles

to

automating

well

the

delineation

of

a

set

of

motifs

from

the

output

of

a

database

search

The

query

sequence

may

contain

a

variety

of

different

domains

and

share

different

subsets

of

them

with

different

proteins

in

the

database

Furthermore

defining

the

proper

extent

of

even

a

single

motif

may

be

challenging

-LRB-

-RRB-

Accordingly

we

have

chosen

to

forgo

the

potential

advantages

of

restricting

the

length

of

our

derived

matrices

and

then

demanding

that

they

be

completely

aligned

with

segments

of

database

sequences

-LRB-

-RRB-

Instead

each

matrix

we

construct

has

length

precisely

equal

to

that

of

the

original

query

sequence

When

searching

the

database

with

such

a

matrix

we

seek

local

alignments

in

full

analogy

to

those

sought

by

BLAST

when

used

for

straightforward

sequence

sequence

comparison

Finally

we

do

not

attempt

to

derive

position-specific

gap

scores

for

use

with

our

position-specific

substitution

scores

Instead

in

each

iteration

Nucleic

Acids

Research

Vol

No

Nucleic

Acids

Research

Vol

No.

a

b

c

Figure

-LRB-

a

-RRB-

The

multiple

alignment

generated

by

PSI-BLAST

when

the

human

fragile

histidine

triad

-LRB-

HIT

-RRB-

protein

-LRB-

-RRB-

-LRB-

SWISS-PROT

accession

no

-RRB-

is

compared

to

SWISS-PROT

All

pairwise

local

alignments

have

E-value

and

are

identified

in

SWISS-PROT

as

belonging

to

the

HIT

family

Thick

bars

within

the

six

database

sequences

represent

segments

that

align

with

various

segments

from

the

query

In

constructing

sequence

weights

for

the

indicated

multiple

alignment

column

corresponding

to

residue

of

the

query

only

the

shaded

portions

of

the

multiple

alignment

are

used

-LRB-

b

-RRB-

A

local

alignment

of

the

human

HIT

protein

and

H.influenzae

uridylyltransferase

-LRB-

-RRB-

-LRB-

SWISS-PROT

accession

no

-RRB-

In

its

first

position-specific

iteration

PSI-BLAST

gives

this

alignment

a

score

of

bits

corresponding

to

an

E-value

of

symbols

reflect

positive

matrix

scores

even

though

a

position-specific

matrix

is

used

to

construct

the

alignment

-LRB-

c

-RRB-

A

local

alignment

of

the

human

HIT

protein

and

yeast

phosphorylase

I

-LRB-

-RRB-

-LRB-

SWISS-PROT

accession

no

-RRB-

In

its

second

position-specific

iteration

PSI-BLAST

gives

this

alignment

a

score

of

bits

corresponding

to

an

E-value

of

of

PSI-BLAST

we

employ

the

same

gap

scores

that

are

used

in

the

first

simple

BLAST

run

Our

reasons

are

that

there

is

no

good

theory

for

deriving

gap

costs

from

a

multiple

alignment

and

that

as

will

be

discussed

below

by

eschewing

position-specific

gap

costs

we

can

make

a

reasonable

estimate

of

the

statistical

significance

of

the

resulting

local

alignments

Multiple

alignment

construction

To

produce

a

multiple

alignment

from

the

BLAST

output

we

simply

collect

all

database

sequence

segments

that

have

been

aligned

to

the

query

with

E-value

below

a

threshold

by

default

set

to

The

query

is

used

as

a

master

or

template

for

constructing

a

multiple

alignment

M.

Any

row

-LRB-

i.e.

database

sequence

segment

-RRB-

identical

to

the

query

segment

with

which

it

aligns

is

purged

and

only

one

copy

is

retained

of

any

rows

that

are

identical

to

one

another

Pairwise

alignment

columns

that

involve

gap

characters

inserted

into

the

query

are

simply

ignored

so

that

M

has

exactly

the

same

length

as

the

query

Because

we

are

dealing

with

local

alignments

the

columns

of

M

may

involve

varying

numbers

of

sequences

and

many

columns

may

include

nothing

but

the

query

We

make

no

attempt

to

improve

M

by

comparing

database

sequences

with

one

another

or

by

any

other

true

multiple

alignment

procedure

As

will

be

discussed

the

matrix

scores

constructed

for

a

given

alignment

column

should

depend

not

only

upon

the

residues

appearing

there

but

upon

those

in

other

columns

as

well

To

make

this

dependency

easy

to

formulate

however

we

need

to

prune

our

raw

multiple

alignment

M

to

a

simpler

reduced

one

This

pruning

is

done

independently

for

each

column

so

the

reduced

multiple

alignment

MC

will

in

general

vary

from

one

column

C

to

the

next

To

construct

MC

we

first

specify

the

set

R

of

sequences

it

includes

to

be

exactly

those

that

contribute

a

residue

to

column

C

We

then

define

the

columns

of

MC

to

be

just

those

columns

of

M

in

which

all

the

sequences

of

R

are

represented

By

construction

the

reduced

multiple

alignment

MC

has

residues

or

gap

characters

in

every

row

and

column

-LRB-

Fig.

-RRB-

and

is

therefore

amenable

to

the

various

manipulations

described

below

Sequence

weights

When

constructing

a

score

matrix

from

a

multiple

alignment

it

is

a

mistake

to

give

all

sequences

of

the

alignment

equal

weight

A

large

set

of

closely

related

sequences

carries

little

more

information

than

a

single

member

but

its

size

alone

may

allow

it

easily

to

outvote

a

small

number

of

more

divergent

sequences

One

way

past

this

difficulty

is

to

assign

weights

to

the

various

sequences

with

those

having

many

close

relatives

receiving

smaller

weight

The

many

sequence

weighting

methods

that

have

been

proposed

-LRB-

-RRB-

often

produce

roughly

equivalent

results

Because

of

its

speed

and

simplicity

we

have

implemented

a

modified

version

of

the

sequence

weighting

method

of

Henikoff

and

Henikoff

-LRB-

-RRB-

Gap

characters

are

treated

as

a

distinct

character

and

any

columns

consisting

of

identical

residues

are

ignored

in

calculating

weights

In

speaking

of

a

column

's

observed

residue

frequencies

fi

we

shall

henceforth

mean

its

weighted

rather

its

raw

frequencies

In

constructing

matrix

scores

not

only

a

column

's

observed

residue

frequencies

are

important

but

also

the

effective

number

of

independent

observations

it

constitutes

a

column

consisting

of

a

single

valine

and

a

single

isoleucine

carries

different

information

than

one

consisting

of

five

independently

occurring

instances

of

each

Accordingly

we

need

to

estimate

the

relative

number

NC

of

independent

observations

constituted

by

the

alignment

MC

A

simple

count

of

the

number

of

sequences

in

MC

is

a

poor

measure

for

identical

sequences

imply

fewer

independent

observations

than

do

divergent

ones

We

thus

propose

as

a

simple

first

estimate

for

NC

the

mean

number

of

different

residue

types

including

gap

characters

observed

in

the

various

columns

of

MC

This

estimate

is

clearly

not

ideal

as

it

saturates

at

no

matter

how

many

independent

sequences

are

contained

in

MC

However

for

the

data

we

are

likely

to

encounter

NC

is

typically

much

Nucleic

Acids

Research

Vol

No.

smaller

than

and

therefore

perhaps

a

good

enough

approximation

for

our

purposes

As

will

be

seen

it

is

not

the

absolute

value

of

NC

that

is

important

but

rather

its

relative

value

from

one

column

to

another

NC

is

essentially

the

same

measure

of

alignment

variability

as

that

proposed

by

Henikoff

and

Henikoff

-LRB-

-RRB-

for

use

in

a

different

manner

Target

frequency

estimation

Given

a

multiple

alignment

many

methods

for

generating

score

matrices

have

been

advanced

-LRB-

-RRB-

The

prescription

with

perhaps

the

best

theoretical

foundation

is

that

the

scores

for

a

specific

pattern

position

be

of

the

form

log

-LRB-

Qi/Pi

-RRB-

where

Qi

is

the

estimated

probability

for

residue

i

to

be

found

in

that

column

-LRB-

-RRB-

This

leaves

open

the

question

how

best

to

estimate

the

Qi

Given

a

multiple

alignment

involving

a

large

number

of

independent

sequences

the

estimate

of

Qi

for

a

specific

column

should

converge

simply

to

the

observed

frequency

of

residue

i

in

that

column

However

in

addition

to

the

sequence

weighting

issues

discussed

above

factors

that

complicate

estimating

the

Qi

include

small

sample

size

-LRB-

-RRB-

and

prior

knowledge

of

relationships

among

the

residues

-LRB-

-RRB-

Various

studies

suggest

that

the

best

currently

available

method

for

estimating

the

Qi

is

that

of

Dirichlet

mixtures

-LRB-

-RRB-

However

because

it

often

performs

nearly

as

well

-LRB-

-RRB-

and

due

to

its

relative

simplicity

we

have

implemented

the

data-dependent

pseudocount

method

introduced

by

Tatusov

et

al.

-LRB-

-RRB-

This

method

uses

the

prior

knowledge

of

amino

acid

relationships

embodied

in

the

substitution

matrix

sij

to

generate

residue

pseudocount

frequencies

gi

which

are

averaged

with

the

observed

frequencies

fi

to

estimate

the

Qi

Specifically

for

a

given

column

C

we

construct

pseudocount

frequencies

gi

using

the

formula

gi

j

fj

q

P

j

ij

where

the

qij

are

the

target

frequencies

implicit

in

the

substitution

matrix

and

given

by

equation

Intuitively

those

residues

favored

by

the

substitution

matrix

to

align

with

the

residues

actually

observed

receive

high

pseudocount

frequencies

We

then

estimate

Qi

by

Qi

af

i

-RRB-

bg

i

a

-RRB-

b

where

and

are

the

relative

weights

given

to

observed

and

pseudocount

residue

frequencies

So

that

the

scores

we

construct

will

reduce

to

sij

in

columns

where

nothing

has

been

aligned

to

the

query

sequence

we

let

NC

remains

an

arbitrary

pseudocount

parameter

the

larger

its

value

the

greater

the

emphasis

given

to

prior

knowledge

of

residue

relationships

vis

a

vis

observed

residue

frequencies

We

have

found

empirically

that

in

conjunction

with

our

method

for

calculating

a

reasonably

good

setting

for

is

BLAST

applied

to

position-specific

score

matrices

The

initial

step

of

the

BLAST

algorithm

is

the

construction

of

a

list

of

words

that

align

to

query

words

with

score

at

least

T.

Only

minor

modifications

to

the

code

are

necessary

for

this

step

to

be

performed

on

a

query

consisting

of

a

position-specific

matrix

rather

than

a

simple

sequence

The

same

holds

for

the

ungapped

and

gapped

extension

steps

of

BLAST

One

important

issue

is

whether

key

parameters

such

as

T

and

Xg

used

at

various

heuristic

stages

of

the

algorithm

and

tuned

to

simple

sequence

comparison

can

be

applied

unchanged

to

position-specific

matrices

without

degrading

unduly

either

the

speed

or

sensitivity

of

database

searches

We

approach

this

problem

by

ensuring

that

the

scale

u

of

the

matrix

scores

produced

internally

by

PSI-BLAST

corresponds

to

that

of

the

substitution

matrix

sij

In

other

words

we

calculate

the

scores

for

a

column

of

the

matrix

as

-LSB-

ln

-LRB-

Qi/Pi

-RRB-

-RSB-

u

There

is

no

analytic

theory

with

which

to

estimate

the

statistical

significance

of

a

gapped

alignment

of

a

position-specific

score

matrix

and

a

simple

sequence

However

one

may

hypothesize

that

for

a

score

matrix

constructed

to

the

same

scale

as

sij

a

given

set

of

gap

costs

should

produce

the

same

gapped

alignment

scale

parameter

g

as

for

sij

This

would

be

convenient

because

then

PSI-BLAST

could

estimate

statistical

significance

without

expending

after

each

iteration

the

substantial

time

required

to

estimate

g

and

Kg

by

random

simulation

To

test

this

hypothesis

we

performed

a

number

of

statistical

tests

on

PSI-BLAST

generated

score

matrices

scaled

to

have

u

the

value

applicable

to

previously

published

simulations

-LRB-

-RRB-

First

we

searched

SWISS-PROT

using

as

query

the

influenza

A

virus

hemagglutinin

precursor

-LRB-

-RRB-

and

captured

the

score

matrix

constructed

by

PSI-BLAST

from

the

local

alignments

with

E-value

We

then

compared

this

matrix

to

random

sequences

of

length

generated

using

the

background

amino

acid

frequencies

of

Robinson

and

Robinson

-LRB-

-RRB-

A

gap

of

length

k

was

charged

a

cost

of

k.

Counts

of

the

optimal

local

alignment

scores

calculated

using

an

appropriately

modified

version

of

the

Smith

Waterman

algorithm

-LRB-

-RRB-

are

plotted

in

Figure

Also

shown

is

the

best

fitting

extreme

value

distribution

-LRB-

-RRB-

which

using

the

edge-effect

correction

described

by

Altschul

and

Gish

-LRB-

-RRB-

has

statistical

parameters

g

and

Kg

It

is

apparent

that

the

distribution

fits

the

random

trial

reasonably

well

a

goodness-of-fit

test

with

degrees

of

freedom

has

value

which

is

lower

than

one

would

expect

of

the

time

even

were

the

theory

precisely

valid

This

supports

the

idea

that

the

statistical

theory

described

above

applies

to

local

alignments

of

position-specific

score

matrices

and

simple

sequences

Furthermore

the

estimate

g

agrees

to

within

experimental

error

with

the

value

previously

published

for

these

gap

costs

-LRB-

-RRB-

Similar

agreement

was

obtained

with

a

number

of

other

protein

sequences

as

initial

query

-LRB-

results

not

shown

-RRB-

and

in

all

cases

the

much

less

important

Kg

parameter

could

be

estimated

accurately

as

well

In

general

values

of

g

for

the

comparison

of

position-specific

score

matrices

with

simple

sequences

appear

to

differ

by

from

the

values

for

simple

pairwise

sequence

comparison

Using

these

precomputed

values

for

g

should

thus

entail

an

error

of

less

than

one

bit

for

PSI-BLAST

scores

bits

corresponding

to

a

factor

of

less

than

two

in

the

estimation

of

statistical

significance

PERFORMANCE

EVALUATION

To

test

more

directly

the

statistics

used

by

PSI-BLAST

we

compared

query

sequences

from

large

and

well

characterized

protein

families

to

the

SWISS-PROT

database

and

then

ran

the

position-specific

score

matrices

generated

against

a

shuffled

version

of

the

same

database

For

each

query

we

recorded

the

Nucleic

Acids

Research

Vol

No

Nucleic

Acids

Research

Vol

No.

Figure

The

distribution

of

optimal

local

alignment

scores

from

the

comparison

of

a

position-specific

score

matrix

with

random

protein

sequences

The

score

matrix

was

constructed

by

PSI-BLAST

from

the

local

alignments

with

E-value

found

in

a

search

of

SWISS-PROT

using

as

query

the

influenza

A

virus

hemagglutinin

precursor

-LRB-

-RRB-

-LRB-

SWISSPROT

accession

no

-RRB-

The

random

sequences

each

of

length

were

generated

using

the

amino

acid

frequencies

of

Robinson

and

Robinson

-LRB-

-RRB-

Optimal

local

alignment

scores

were

calculated

using

the

position-specific

matrix

in

conjunction

with

k

gap

costs

The

extreme

value

distribution

that

best

fits

the

data

-LRB-

-RRB-

is

plotted

A

goodness-of-fit

test

with

degrees

of

freedom

has

value

corresponding

to

a

P-value

of

lowest

E-value

found

as

well

as

the

number

of

shuffled

sequences

yielding

E-values

and

For

comparison

we

performed

the

identical

shuffled-database

test

on

the

gapped

and

original

versions

of

BLAST

To

reduce

the

probability

that

high-scoring

alignments

were

missed

due

to

the

heuristic

nature

of

the

algorithms

we

performed

these

tests

with

T

rather

than

the

default

value

of

The

results

are

given

in

Table

For

the

queries

the

median

of

the

low

PSI-BLAST

E-values

was

which

corresponds

to

a

median

P-value

of

-LRB-

-RRB-

The

mean

numbers

of

shuffled

database

sequences

with

E-values

and

were

and

respectively

within

of

the

expected

values

of

and

The

equivalent

tests

for

the

ungapped

and

gapped

versions

of

BLAST

also

yielded

results

that

diverged

from

theory

by

The

ability

to

estimate

with

reasonable

accuracy

the

significance

of

gapped

local

matrix-sequence

alignments

permits

us

to

automate

the

construction

of

position-specific

score

matrices

during

multiple

iterations

of

the

PSI-BLAST

program

After

each

iteration

we

generate

a

new

multiple

alignment

simply

by

collecting

those

alignments

with

E-value

lower

than

a

defined

threshold

An

interactive

version

of

PSI-BLAST

allows

the

user

to

override

either

the

inclusion

or

exclusion

of

specific

local

alignments

Once

a

given

database

sequence

has

been

used

in

the

generation

of

a

position-specific

score

matrix

low

E-values

for

this

sequence

are

virtually

guaranteed

in

future

iterations

for

the

sequence

is

to

a

certain

extent

being

compared

with

itself

The

biological

relevance

of

PSI-BLAST

output

thus

depends

critically

on

avoiding

the

inappropriate

inclusion

of

sequences

in

the

multiple

alignment

constructed

Specifically

the

utility

of

the

score

matrix

produced

is

immediately

vitiated

by

the

inclusion

of

any

alignment

involving

a

region

of

highly

biased

amino

acid

composition

-LRB-

-RRB-

Table

The

comparison

of

various

query

sequences

with

a

shuffled

version

of

SWISS-PROT

Protein

family

SWISS-PROT

accession

no

of

query

Original

BLAST

Low

No

of

seqs

E-value

with

E-value

Gapped

BLAST

Low

No

of

seqs

E-value

with

E-value

PSI-BLAST

Low

No

of

seqs

E-value

with

E-value

Serine

protease

Serine

protease

inhibitor

Ras

Globin

Hemagglutinin

Interferon

Alcohol

dehydrogenase

Histocompatibility

antigen

Cytochrome

Glutathione

transferase

H

transporting

ATP

synthase

Average

-LRB-

median

or

mean

-RRB-

The

original

and

gapped

BLAST

comparisons

use

substitution

scores

-LRB-

-RRB-

All

three

programs

use

threshold

T

parameter

set

to

but

the

gapped

BLAST

and

PSI-BLAST

programs

use

the

two-hit

method

to

trigger

ungapped

extensions

The

original

BLAST

program

has

the

X

dropoff

parameter

set

to

nominal

score

The

gapped

BLAST

and

PSI-BLAST

comparisons

charge

gaps

of

length

k

a

cost

of

k

They

have

Xu

set

to

and

Xg

set

to

for

the

database

search

stage

and

to

for

the

output

stage

of

the

algorithms

Gapped

alignments

are

triggered

by

a

score

corresponding

to

bits

For

PSI-BLAST

the

query

is

first

compared

to

the

SWISS-PROT

database

and

the

position-specific

score

matrix

generated

is

then

compared

to

a

shuffled

version

of

SWISS-PROT

The

median

is

used

for

the

average

of

the

low

E-values

and

the

mean

otherwise

Nucleic

Acids

Research

Vol

No.

Table

The

number

of

SWISS-PROT

sequences

yielding

alignments

with

E-value

and

relative

running

times

for

Smith

Waterman

and

various

versions

of

BLAST

Protein

family

Serine

protease

Serine

protease

inhibitor

Ras

Globin

Hemagglutinin

Interferon

Alcohol

dehydrogenase

Histocompatibility

antigen

Cytochrome

Glutathione

transferase

H

transporting

ATP

synthase

Normalized

running

time

Query

Smith

Waterman

275 108 255

128 53 138 262

Original

BLAST

273 105 249

114 53 128 241

Gapped

BLAST

275 108 252

128 53 137 261

PSI-BLAST

286 111 375 623

130 53 160 338

224 142 207

To

score

and

evaluate

the

significance

of

the

alignments

found

the

original

BLAST

program

uses

substitution

scores

-LRB-

-RRB-

and

sum-statistics

-LRB-

-RRB-

The

Smith

Waterman

and

gapped

BLAST

programs

use

substitution

scores

k

gap

costs

and

the

statistics

of

equations

and

in

conjunction

with

the

experimentally

determined

parameters

g

and

Kg

-LRB-

-RRB-

PSI-BLAST

uses

the

same

gap

costs

and

g

but

applied

to

the

position-specific

score

matrix

constructed

from

the

output

of

the

gapped

BLAST

run

Only

one

PSI-BLAST

iteration

is

executed

All

three

BLAST

programs

use

the

same

parameter

settings

as

in

Table

except

that

T

is

set

to

Normalized

running

times

are

the

mean

ratio

of

program

running

time

to

that

for

the

original

BLAST

The

time

for

PSI-BLAST

includes

the

time

for

the

initial

BLAST

search

To

compare

the

performance

of

the

new

gapped

version

of

BLAST

and

its

PSI-BLAST

extension

to

that

of

the

Smith

Waterman

algorithm

-LRB-

-RRB-

and

the

original

ungapped

BLAST

algorithm

we

employed

the

same

query

sequences

that

were

used

above

to

investigate

the

accuracy

of

PSI-BLAST

statistics

Because

as

shown

these

statistics

are

quite

accurate

we

may

use

the

number

of

statistically

significant

sequences

found

in

a

database

search

as

a

reasonable

measure

of

algorithm

sensitivity

We

employed

the

ssearch

program

version

from

the

Fasta

package

-LRB-

-RRB-

as

our

implementation

of

the

Smith

Waterman

algorithm

Using

each

of

the

queries

we

searched

SWISSPROT

with

each

of

the

four

programs

We

show

in

Table

the

numbers

of

sequences

found

with

E

value

as

well

as

the

average

ratio

of

running

time

to

that

for

the

original

BLAST

program

Based

upon

SWISS-PROT

annotation

all

sequences

recorded

in

Table

appear

to

be

true

family

members

with

the

exception

of

one

of

the

lowest-scoring

alignments

found

by

Smith

Waterman

when

applied

to

the

histocompatibility

antigen

query

and

the

lowest-scoring

alignment

found

by

the

original

BLAST

applied

to

the

hemagglutinin

query

While

some

alignments

involve

hypothetical

proteins

the

pattern

of

conserved

residues

in

all

such

cases

suggests

a

true

positive

As

can

be

seen

the

gapped

BLAST

program

runs

on

average

three

times

faster

then

the

original

and

in

all

but

one

case

examined

finds

a

greater

number

of

statistically

significant

alignments

It

runs

times

faster

than

Smith

Waterman

but

for

the

combined

queries

misses

only

eight

of

the

significant

similarities

found

by

the

rigorous

algorithm

Of

these

eight

only

one

has

an

E-value

and

another

appears

to

be

a

random

as

opposed

to

a

biologically

meaningful

similarity

The

scores

produced

by

gapped

BLAST

for

the

similarities

it

finds

differ

from

those

produced

by

the

Smith

Waterman

algorithm

in

only

two

instances

The

discrepancy

arises

in

both

cases

from

an

Xg

parameter

that

is

too

low

rather

than

from

an

incorrect

choice

of

seed

Thus

despite

its

simplicity

the

seed-selection

heuristic

is

extremely

accurate

A

search

that

includes

a

single

PSI-BLAST

iteration

still

runs

faster

than

the

original

BLAST

and

times

faster

than

Smith

Waterman

but

can

in

many

cases

be

much

more

sensitive

It

finds

every

true

positive

returned

by

Smith

Waterman

but

frequently

many

others

as

well

Here

only

a

single

PSI-BLAST

iteration

has

been

considered

but

as

will

be

seen

below

multiple

iterations

can

yield

even

better

results

Furthermore

we

have

found

PSI-BLAST

to

perform

better

on

searches

of

the

nonredundant

protein

sequence

database

maintained

by

the

NCBI

-LRB-

-RRB-

than

on

searches

of

SWISS-PROT

because

of

the

greater

number

of

significant

similarities

that

are

found

by

the

initial

BLAST

run

For

the

particular

examples

in

Table

the

PSI-BLAST

iteration

takes

noticeably

longer

than

the

gapped

BLAST

iteration

due

primarily

to

the

time

needed

to

construct

the

position-specific

score

matrix

from

the

large

number

of

significant

local

alignments

found

by

BLAST

For

queries

that

return

a

small

number

of

significant

alignments

each

PSI-BLAST

iteration

requires

more

nearly

the

same

time

as

BLAST

PSI-BLAST

EXAMPLES

In

many

instances

PSI-BLAST

is

able

automatically

to

uncover

biologically

interesting

similarities

that

elude

simple

database

searches

Multiple

iterations

of

PSI-BLAST

are

sometimes

required

to

recognize

the

more

distantly

related

protein

family

members

We

here

consider

two

representative

cases

in

greater

detail

HIT

proteins

Holm

and

Sander

-LRB-

-RRB-

describe

how

a

comparison

of

three-dimensional

structures

is

able

to

identify

significant

similarity

between

histidine

triad

-LRB-

HIT

-RRB-

proteins

and

uridylyltransferase

-LRB-

GalT

-RRB-

proteins

Indeed

using

the

human

HIT

protein

-LRB-

-RRB-

as

query

a

BLAST

search

of

SWISS-PROT

reveals

hits

with

E-value

only

to

other

HIT

proteins

-LRB-

Fig.

-RRB-

An

alignment

to

Nucleic

Acids

Research

Vol

No

Nucleic

Acids

Research

Vol

No.

the

rat

GalT

protein

-LRB-

-RRB-

has

the

only

marginally

significant

E-value

of

A

PSI-BLAST

search

using

the

score

matrix

generated

from

the

six

alignments

illustrated

in

Figure

can

immediately

cement

confidence

in

the

biological

relevance

of

this

similarity

The

E-value

of

the

similarity

with

rat

GalT

drops

to

and

an

alignment

to

Haemophilus

influenzae

GalT

-LRB-

-RRB-

-LRB-

Fig.

-RRB-

receives

the

even

more

significant

E-value

of

These

similarities

of

course

are

uncovered

using

no

structural

information

In

addition

on

the

next

iteration

PSI-BLAST

finds

a

strongly

significant

alignment

-LRB-

Fig.

E-value

-RRB-

to

yeast

phosphorylase

I

-LRB-

-RRB-

for

which

no

structure

is

available

BRCT

proteins

Proteins

containing

one

or

multiple

copies

of

the

BRCT

domain

form

a

superfamily

many

of

whose

members

are

involved

in

DNA

damage-responsive

cell

cycle

checkpoints

-LRB-

-RRB-

While

detailed

analysis

is

needed

to

delineate

completely

this

diverse

set

of

proteins

PSI-BLAST

is

able

to

automatically

identify

most

of

the

superfamily

We

used

the

C-terminal

residues

of

human

-LRB-

-RRB-

which

includes

two

BRCT

domains

-LRB-

-RRB-

as

the

initial

query

for

a

search

of

NCBI

's

non-redundant

protein

sequence

database

Using

the

default

cutoff

E-value

of

the

initial

BLAST

search

recognized

as

significant

only

alignments

to

other

sequences

and

the

previously

described

BRCT

protein

BARD

-LRB-

-RRB-

-LRB-

Table

-RRB-

Subsequent

PSI-BLAST

iterations

however

retrieved

all

the

proteins

recorded

in

Table

additional

close

homologs

are

omitted

from

the

table

Almost

all

the

BRCT

proteins

described

by

Bork

et

al.

-LRB-

-RRB-

were

recognized

Not

found

were

the

retinoblastoma

family

whose

putative

BRCT

domain

is

particularly

divergent

worm

which

was

not

in

the

database

searched

and

human

DNA-ligase

III

PSI-BLAST

did

report

yeast

and

the

Kluyveromyces

lactis

homolog

worm

and

various

terminal

deoxynucleotidyltransferases

and

poly

-LRB-

ADP-ribose

-RRB-

polymerases

but

all

with

E-values

-LRB-

Table

-RRB-

Detailed

examination

of

the

alignments

produced

suggests

that

the

only

likely

false

positives

involved

a

trypanosome

EST

-LRB-

-RRB-

and

the

Methanococcus

jannaschii

mutT

protein

-LRB-

-RRB-

the

latter

despite

its

involvement

in

DNA

repair

-LRB-

Table

-RRB-

Seven

recent

additions

to

the

protein

databases

are

reported

here

as

members

of

the

BRCT

superfamily

-LRB-

Table

-RRB-

-LRB-

i

-RRB-

Arabidopsis

-LRB-

-RRB-

is

the

first

plant

protein

observed

to

contain

BRCT

domains

-LRB-

ii

-RRB-

-LRB-

-RRB-

is

a

large

human

protein

of

unknown

function

with

eight

BRCT

domains

the

greatest

number

so

far

observed

within

a

single

protein

-LRB-

iii

-RRB-

-LRB-

-RRB-

is

a

worm

protein

with

a

low-complexity

-LRB-

-RRB-

N-terminus

-LRB-

iv

-RRB-

-LRB-

-RRB-

is

a

fission

yeast

protein

strongly

similar

to

the

previously

recognized

-LRB-

-RRB-

yeast

BRCT

protein

-LRB-

-RRB-

-LRB-

v

-RRB-

-LRB-

-RRB-

is

a

worm

protein

whose

C-terminus

contains

a

single

BRCT

domain

and

whose

N-terminus

containing

a

RING

finger

domain

is

strongly

similar

to

that

of

The

similar

organization

to

makes

this

protein

of

particular

interest

-LRB-

vi

-RRB-

Synechocystis

sp.

-LRB-

-RRB-

is

the

first

bacterial

BRCT

protein

that

is

not

a

bacterial

ligase

While

it

failed

to

pass

the

cutoff

E-value

of

its

C-terminal

BRCT

domain

is

very

similar

to

that

of

several

bacterial

ligases

which

presumably

led

to

its

incorrect

classification

as

such

in

the

databases

Most

of

the

protein

N-terminal

to

its

BRCT

domain

consists

of

a

coiled-coil

domain

The

actual

Synechocystis

sp.

DNA

ligase

-LRB-

-RRB-

is

found

by

PSI-BLAST

on

the

iteration

with

an

E-value

of

Figure

The

location

of

BRCT

domains

within

human

-LRB-

-RRB-

Arabidopsis

-LRB-

-RRB-

human

-LRB-

-RRB-

worm

-LRB-

-RRB-

fission

yeast

-LRB-

-RRB-

worm

-LRB-

-RRB-

Synechocystis

sp.

-LRB-

-RRB-

and

human

Pescadillo

-LRB-

-RRB-

and

each

have

in

addition

an

N-terminal

RING

finger

domain

The

near

identity

to

other

worm

sequences

of

a

short

region

directly

preceding

the

BRCT

domain

of

suggests

the

possibility

that

this

protein

has

been

misassembled

-LRB-

vii

-RRB-

Pescadillo

is

a

human

protein

whose

zebrafish

ortholog

is

essential

for

embryonic

development

-LRB-

-RRB-

and

whose

yeast

ortholog

-LRB-

-RRB-

has

been

previously

recognized

as

a

BRCT

protein

-LRB-

-RRB-

It

failed

to

pass

the

cutoff

E-value

of

but

appeared

with

near-significant

E-values

in

PSI-BLAST

output

from

the

iteration

onward

The

approximate

positions

of

the

BRCT

domains

within

and

the

seven

newly

identified

BRCT

proteins

are

illustrated

in

Figure

DISCUSSION

AND

CONCLUSION

In

addition

to

the

major

algorithmic

changes

described

above

we

have

modified

an

aspect

of

the

original

BLAST

program

's

output

routine

that

on

occasion

caused

important

similarities

to

be

overlooked

When

a

very

large

number

of

statistically

significant

alignments

was

found

BLAST

would

typically

report

only

the

top

scoring

These

alignments

however

might

all

involve

one

domain

of

the

query

that

occurred

frequently

within

the

database

Interesting

but

weaker

relationships

to

other

regions

of

the

query

might

simply

be

forced

off

the

bottom

of

the

list

Accordingly

following

the

general

idea

of

Sonnhammer

and

Durbin

-LRB-

-RRB-

we

have

limited

the

number

of

alignments

reported

that

involve

each

region

of

the

query

but

set

no

overall

upper

limit

The

BLAST

programs

are

unlikely

to

remain

static

and

there

are

many

possible

avenues

for

future

improvement

We

discuss

three

of

them

briefly

here

Gap

costs

Gapped

alignments

may

be

constructed

using

a

variety

of

different

types

of

gap

cost

Because

a

single

mutational

event

may

insert

or

delete

a

large

number

of

residues

it

has

been

argued

that

long

gaps

should

not

cost

much

more

than

short

ones

and

affine

gap

costs

which

assess

a

score

-LRB-

a

bk

-RRB-

for

a

gap

of

length

k

-LRB-

-RRB-

have

become

the

most

widely

used

A

generalization

of

these

costs

has

been

proposed

that

allows

a

gap

to

involve

residues

in

both

sequences

rather

than

just

one

-LRB-

-RRB-

Specifically

a

gap

in

which

k

residues

are

inserted

or

deleted

and

j

pairs

of

residues

are

left

unaligned

receives

the

score

-LRB-

a

bk

cj

-RRB-

The

algorithm

necessary

Nucleic

Acids

Research

Vol

No.

for

using

such

costs

is

only

a

minor

variant

on

that

for

traditional

affine

gap

costs

In

many

cases

the

new

gap

costs

generate

local

alignments

that

are

both

more

accurate

and

more

statistically

significant

-LRB-

-RRB-

These

costs

are

potentially

of

particular

value

for

use

with

PSI-BLAST

because

by

imposing

alignment

only

where

it

is

justified

they

may

lead

to

the

construction

of

more

sensitive

position-specific

score

matrices

Whether

it

is

desirable

to

use

generalized

affine

gap

costs

as

the

default

for

general

purpose

database

searches

awaits

detailed

empirical

study

Table

PSI-BLAST

protein

database

search

results

using

the

C-terminus

of

as

query

Protein

BARD

a

a

a

a

DNA

ligase

IV

DNA

ligase

mutTc

homolog

TDT

Pescadilloa

PPOL

Species

Homo

sapiens

Arabidopsis

thaliana

Caenorhabditis

elegans

H.sapiens

C.elegans

Schizosaccharomyces

pombe

H.sapiens

H.sapiens

C.elegans

C.elegans

C.elegans

S.pombe

Saccharomyces

cerevisiae

Mus

musculus

M.musculus

S.pombe

S.cerevisiae

Trypanosoma

cruzi

S.cerevisiae

S.cerevisiae

S.pombe

S.cerevisiae

S.cerevisiae

C.elegans

S.cerevisiae

H.sapiens

Candida

albicans

Thermus

scotoductus

Drosophila

melanogaster

M.jannaschii

S.cerevisiae

K.lactis

C.elegans

Synechocystis

sp.

Mus

domestica

S.cerevisiae

H.sapiens

Sarcophaga

peregrina

GenBank

ID

number

PSI-BLAST

iteration

E-value

Iteration

zero

refers

to

the

initial

BLAST

run

using

the

C-terminal

residues

of

-LRB-

-RRB-

-LRB-

SWISS-PROT

accession

no

-RRB-

as

query

Subsequent

PSI-BLAST

iterations

use

derived

position-specific

score

matrices

in

place

of

the

query

The

score

matrix

for

iteration

i

is

constructed

from

alignments

achieving

an

E-value

for

iteration

i.

For

each

protein

the

E-value

is

that

returned

during

the

PSI-BLAST

iteration

indicated

and

precedes

the

protein

's

use

for

score

matrix

construction

Only

one

representative

is

listed

for

families

of

closely

related

proteins

On

its

iteration

PSI-BLAST

uncovered

no

new

proteins

with

E-value

and

therefore

ceased

iteration

At

the

end

of

the

table

are

shown

BRCT

proteins

returned

by

PSI-BLAST

with

E-value

but

listed

for

the

iteration

in

which

they

achieved

their

lowest

E-value

aRecent

additions

to

the

database

first

identified

as

BRCT

proteins

here

bThe

C.elegans

protein

-LRB-

-RRB-

while

a

recent

addition

to

the

databases

is

a

close

homolog

of

the

previously

recognized

-LRB-

-RRB-

family

of

C.elegans

BRCT

proteins

containing

for

example

-LRB-

-RRB-

cThe

trypanosome

EST

-LRB-

-RRB-

and

the

M.jannaschii

mutT

protein

-LRB-

-RRB-

are

the

only

likely

false

positives

Nucleic

Acids

Research

Vol

No

Nucleic

Acids

Research

Vol

No.

Position-specific

score

matrices

as

input

to

PSI-BLAST

PSI-BLAST

performs

three

distinct

operations

it

constructs

a

multiple

alignment

from

BLAST

output

data

it

processes

this

alignment

into

a

position-specific

score

matrix

and

it

uses

this

matrix

to

search

the

database

A

researcher

may

wish

however

to

bypass

the

first

two

of

these

operations

and

provide

a

score

matrix

as

query

directly

to

PSI-BLAST

The

central

difficulty

is

retaining

the

ability

to

calculate

reliable

statistics

as

described

above

PSI-BLAST

imposes

strict

scaling

rules

on

the

matrices

it

generates

permitting

the

use

of

precomputed

g

to

assess

significance

Three

possible

routes

are

open

-LRB-

i

-RRB-

One

may

permit

the

specification

of

target

frequencies

Qi

for

each

position

rather

than

scores

These

can

then

be

converted

internally

to

log-odds

scores

with

the

appropriate

scale

for

precomputed

statistical

parameters

to

apply

-LRB-

ii

-RRB-

One

may

estimate

by

random

simulation

the

statistical

parameters

for

an

input

score

matrix

-LRB-

-RRB-

An

advantage

is

the

applicability

to

a

greater

range

of

scoring

systems

including

the

possible

use

of

position-specific

gap

costs

A

disadvantage

is

that

obtaining

reasonably

accurate

estimates

of

the

relevant

statistical

parameters

may

increase

the

program

's

execution

time

unduly

-LRB-

iii

-RRB-

One

may

abandon

the

statistical

assessment

of

the

alignments

produced

This

gives

the

greatest

scope

to

input

scoring

systems

but

precludes

any

reasonable

scheme

for

automatic

iteration

of

PSIBLAST

Much

experimentation

will

be

required

to

determine

which

of

these

approaches

is

the

most

fruitful

Realignment

After

the

initial

BLAST

run

or

a

later

PSI-BLAST

iteration

the

multiple

alignment

used

for

subsequent

iterations

can

be

constructed

in

a

more

sophisticated

manner

than

described

above

Rather

than

coalescing

all

the

pairwise

alignments

that

pass

the

threshold

immediately

into

a

multiple

alignment

the

most

significant

among

them

can

be

used

to

build

an

initial

multiple

alignment

and

associated

position-specific

score

matrix

which

can

then

be

used

to

rescore

and

realign

database

sequences

that

received

lower

scores

This

step

can

be

iterated

several

times

before

another

full-scale

database

search

is

executed

There

are

several

potential

advantages

to

this

procedure

-LRB-

i

-RRB-

Weaker

pairwise

alignments

that

may

be

somewhat

inaccurate

can

be

improved

and

perhaps

extended

before

they

are

incorporated

into

the

evolving

multiple

alignment

-LRB-

ii

-RRB-

Unrelated

sequences

that

received

chance

high

scores

can

have

their

scores

downgraded

by

an

improved

matrix

and

perhaps

be

rejected

before

they

are

included

in

the

alignment

-LRB-

iii

-RRB-

Related

sequences

that

received

relatively

high

alignment

scores

but

missed

the

threshold

for

inclusion

can

have

their

scores

increased

and

perhaps

be

included

in

the

multiple

alignment

In

short

the

realignment

procedure

can

prevent

inaccurate

pairwise

alignments

from

corrupting

the

evolving

multiple

alignment

and

can

accelerate

the

recognition

of

related

sequences

all

for

very

little

computational

cost

Preliminary

studies

suggest

this

line

of

development

to

be

a

fruitful

one

In

conclusion

the

new

gapped

version

of

BLAST

is

both

considerably

faster

than

the

original

one

and

able

to

produce

gapped

alignments

While

the

relevant

statistical

parameters

can

no

longer

be

calculated

from

theory

random

simulation

allows

them

to

be

estimated

beforehand

for

commonly

used

amino

acid

substitution

matrices

and

gap

costs

For

many

queries

the

PSI-BLAST

extension

can

greatly

increase

sensitivity

to

weak

but

biologically

relevant

sequence

relationships

PSI-BLAST

retains

the

ability

to

report

accurate

statistics

per

iteration

runs

in

times

not

much

greater

than

gapped

BLAST

and

can

be

used

both

iteratively

and

fully

automatically

These

developments

should

enhance

significantly

the

utility

of

database

search

methods

to

the

molecular

biologist

Note

Source

code

for

the

new

BLAST

programs

is

available

by

anonymous

ftp

from

the

machine

ncbi.nlm.nih.gov

within

the

directory

blast

and

the

programs

may

be

run

from

NCBI

's

web

site

at

ACKNOWLEDGEMENTS

W.M.

and

Z.Z.

are

supported

by

grant

from

the

National

Library

of

Medicine

We

thank

Dr

Warren

Gish

for

helpful

conversations

Dr

Eugene

Koonin

for

assistance

with

the

examples

and

Dr

Gregory

Schuler

for

producing

several

of

the

figures

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