A Table-Driven, Full-Sensitivity Similarity Search Algorithm

Gene Myers and Richard Durbin

Presented by Wang, Jia-Nan and Huang, Yu-Feng

Outline

Introduction Background Preliminary Method Experiment

Introduction

Given a Query and database . Do local alignment

Smith-Waterman : Guaranteed to find all local alignment . Expensive

BLAST FASTA

Improvement

Hardware: more investment on computer ,CPU

Software Phil Green’s SWAT appeal to sparsity and some machine-level coding tricks

60% of dynamic programming matrix has value 0

Avoiding computing most of these unproductive entries

Focus on improving protein similarity searches

This approach examines and compute only 4% of the underlying dynamic programming matrix

Recall

Sequence alignment Local sequence alignment Global sequence alignment

Goal – matching path with highest score

Table-based computation and dynamic programming

Dynamic Programming

Three basic components Recurrence relation Tabular computation Traceback

Smith-Waterman Method

Dynamic programming algorithm Find the most similar subsequences of

two sequences Problem

Lots of computation will be googol Programmer will be crazy and excite Why? how to accelerate

Background

Scoring System Simple scoring scheme Affine gap penalty scoring scheme PAM120 (PAMn) BLOSUM62 (BLOSUMn)

Simple Scoring Scheme

Match (e.g. +8) Mismatch (e.g. -5) Gap constant penalty (e.g. -20)

Affine Gap Penalty Scoring Scheme

Match (e.g. +8) Mismatch (e.g. -5) Gap symbol (e.g. -5) Gap open penalty (e.g. -10)

PAM

PAM – Percent Accepted Mutation Dayhoff et al. (1978)

PAM unit Evolutionary time corresponding to average of 1

mutation per 100 residues 1% accepted PAMn

Relates to mutation probabilities in evolutionary interval of n PAM units

Some information from: http://www.apl.jhu.edu/~przytyck/CAMS_2004_1b.pdf

PAM120

Source: http://eta.embl-heidelberg.de:8000/misc/mat/pam120.html

BLOSUM62

BLOSUM – BLOcks SUbstitution Matrix Steven and Jorga G. Henikoff (1992) Paper: Amino acid substitution matrices from pro

tein blocks [PubMed] BLOSUMn

Relates to mutation probabilities observed between pairs of related proteins that diverged so above n% identity

Some information from: http://www.apl.jhu.edu/~przytyck/CAMS_2004_1b.pdf

BLOSUM62C S T P A G N D E Q H R K M I L V F Y W

C 9 -1 -1 -3 0 -3 -3 -3 -4 -3 -3 -3 -3 -1 -1 -1 -1 -2 -2 -2

S -1 4 1 -1 1 0 1 0 0 0 -1 -1 0 -1 -2 -2 -2 -2 -2 -3

T -1 1 4 1 -1 1 0 1 0 0 0 -1 0 -1 -2 -2 -2 -2 -2 -3

P -3 -1 1 7 -1 -2 -1 -1 -1 -1 -2 -2 -1 -2 -3 -3 -2 -4 -3 -4

A 0 1 -1 -1 4 0 -1 -2 -1 -1 -2 -1 -1 -1 -1 -1 -2 -2 -2 -3

G -3 0 1 -2 0 6 -2 -1 -2 -2 -2 -2 -2 -3 -4 -4 0 -3 -3 -2

N -3 1 0 -2 -2 0 6 1 0 0 -1 0 0 -2 -3 -3 -3 -3 -2 -4

D -3 0 1 -1 -2 -1 1 6 2 0 -1 -2 -1 -3 -3 -4 -3 -3 -3 -4

E -4 0 0 -1 -1 -2 0 2 5 2 0 0 1 -2 -3 -3 -3 -3 -2 -3

Q -3 0 0 -1 -1 -2 0 0 2 5 0 1 1 0 -3 -2 -2 -3 -1 -2

H -3 -1 0 -2 -2 -2 1 1 0 0 8 0 -1 -2 -3 -3 -2 -1 2 -2

R -3 -1 -1 -2 -1 -2 0 -2 0 1 0 5 2 -1 -3 -2 -3 -3 -2 -3

K -3 0 0 -1 -1 -2 0 -1 1 1 -1 2 5 -1 -3 -2 -3 -3 -2 -3

M -1 -1 -1 -2 -1 -3 -2 -3 -2 0 -2 -1 -1 5 1 2 -2 0 -1 -1

I -1 -2 -2 -3 -1 -4 -3 -3 -3 -3 -3 -3 -3 1 4 2 1 0 -1 -3

L -1 -2 -2 -3 -1 -4 -3 -4 -3 -2 -3 -2 -2 2 2 4 3 0 -1 -2

V -1 -2 -2 -2 0 -3 -3 -3 -2 -2 -3 -3 -2 1 3 1 4 -1 -1 -3

F -2 -2 -2 -4 -2 -3 -3 -3 -3 -3 -1 -3 -3 0 0 0 -1 6 3 1

Y -2 -2 -2 -3 -2 -3 -2 -3 -2 -1 2 -2 -2 -1 -1 -1 -1 3 7 2

W -2 -3 -3 -4 -3 -2 -4 -4 -3 -2 -2 -3 -3 -1 -3 -2 -3 1 2 11

Preliminaries

Σ : sequences are composed |Σ| × |Σ| Substitution matrix S giving th

e score Uniform gap penalty g > 0 Query = q1q2 ． ． ． qp of P letters

Target = t1t2 ． ． ． tn of N letters Threshold T > 0

Score Table Edit Graph

Picture source: http://searchlauncher.bcm.tmc.edu/help/Pictures/S-Wexample.gif

Problem

Find a high score local alignment between Query and Target whose path score T≧

Edit-graph figure1 Limit our attention to prefix-positive paths If there is a path of score T or greater in

the edit graph then there is a prefix positive path of score T or greater

Definition A set P of index-value pairs { (i,v): i is [0,P]

The start and extension tables Consider a vertex x in row j of the edit

graph of Query vs. Target

Start Trimming

Limiting the dynamic programming to the startable vertices requires a table Start(w) where w = |Σ|ks

Start Trimming Worst case Let αbe the expected percentage of vertic

es that are seed

Extension Trimming

A table that eliminates vertices that are not extendable

(i,j) is extendable vertex iff C(i,j)>Extend(i,Target[j+1…j+ke])

Extension Trimming

A Table-Driven Scheme for DP

Goal: to restrict the SW computation to productive vertices

Jump table – captures the effect of Advance and Delete over kJ > 0 rows

space unmanageably large But only record those for which

} versus ofgraph edit in the

is ),( to),0( frompath maximal the:),{(),(

Queryw

ukkiukwiJump j

)( 2 Jk PO

),( uk )1( Tu

Jump table

Start table

Space-saving version for Jump and Start tables

Check for paths scoring T or more

jCand

jJ CandviTkjjetTiPeakv in ),(each for )])1(...1[arg,(

Recall – Affine Gap Penalty

Score Match Mismatch Gap symbol - gsp Gap open penalty - gop

Affine cost of gap of length k g + kh, g = gop, h = gsp

Diagram of Affine Gap Penalty

CI

D

CI

D

CI

D

CI

D

-h-g-h

-g-h

-h

δ(ai,bj)

Source: kmchao’s lecture note

Recurrence system - Gotoh

),(

),(

),()1,1(

max),(

)1,(

)1,(max),(

),1(

),1(max),(

jiI

jiD

bajiC

jiC

hgjiC

hjiIjiI

hgjiC

hjiDjiD

ji

The Case of Affine Gap Costs

Simple scoring scheme affine gap penalty scheme

Affine edit graph and vertex structure Question: how to modify the equations

defined above?

Recurrence System for Affine Gap Costs

Two observations To compute the jth row form the (j-1)st requires

knowing only the vectors of and values in row j-1, and not on the values in that row

If then the value at vertex need not be recorded as any maximal path through its will have score less than the maximal path passing through the corresponding

gjiCjiI ),(),(),( ji

I

vertexI

vertexC

C ID

Recurrence System

Results

Experiment

Method Edit graph based approach vs. SWAT

Scoring matrix PAM120

Affine gap cost 8+4n

Database (target) 3 million residue subset of the PIR database

Query A periodic clock protein of length 173 (pcp) A lactate dehydrogenase of length 319 (dehydro) A cGMP kinase of length 670 (kinase) A growth factor of length 1210 (g factor)

PAM120 & Gap Cost 8+4n

BLOSUM62 & Gap Cost 8+2n

Thanks for Your Attention

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