Lecture5,6Localsequencealignment

Chapter6inJonesandPevzner

Fall2019September12,17,2019

Evolutionasatoolforbiologicalinsight

•  “Nothinginbiologymakessenseexceptinthelightofevolution”-TheodosiusDobzhansky.

•  Thefunctionalityofmany

genesisvirtuallythesameamongmanyorganisms:Canunderstandbiologyinsimplerorganismsthanourselves(“modelorganisms”).

Localalignment:rationale

•  Proteinsareoftenmulti-functional,andarecomposedofregions(domains),eachofwhichcontributesaparticularfunction

•  Example:

² Homeoboxgeneshaveashortregioncalledthehomeodomainthatishighlyconservedbetweenspecies.

² AglobalalignmentmightnotfindthehomeodomainbecauseitwouldtrytoaligntheENTIREsequence

Drosophila homeodomain PDB: 1ZQ3

Localvs.GlobalAlignment(cont’d)

Global Alignment Local Alignment—better for finding a conserved segment

--T—-CC-C-AGT—-TATGT-CAGGGGACACG—A-GCATGCAGA-GAC | || | || | | | ||| || | | | | |||| | AATTGCCGCC-GTCGT-T-TTCAG----CA-GTTATG—T-CAGAT--C

tccCAGTTATGTCAGgggacacgagcatgcagagac ||||||||||||

aattgccgccgtcgttttcagCAGTTATGTCAGatc

TheLocalAlignmentProblem

•  Goal:Findthebestlocalalignmentbetweentwostrings

•  Input:Stringsv,wandscoringmatrixδ•  Output:Alignmentofsubstringsofvandwwhosealignmentscoreismaximumamongallpossiblealignmentofallpossiblesubstrings

Localvs.globalalignment

Global alignment

Local alignment

Compute a “mini” global alignment to get a local alignment

Localvs.GlobalAlignment

•  TheGlobalAlignmentProblemtriestofindthelongestpathbetweenvertices(0,0)and(n,m)intheeditgraph.

•  TheLocalAlignmentProblemtriestofindthelongestpathamongpathsbetweenarbitraryvertices(i,j)and(i’,j’)intheeditgraph.

•  Inaneditgraphwithnegatively-scorededges,alocalalignmentmayscorehigherthanaglobalalignment

TheProblemwiththisProblem

•  Naïvemethod(runtimeO(n4)):

-Inagridofsizenxntherearen2nodes(i,j)thatmayserveasasource.

-Foreachsuchnodecomputingalignmentsfrom(i,j)to(i’,j’)takesO(n2)time.

LocalAlignment:Example

LocalAlignment:Example

LocalAlignment:Example

LocalAlignment:Example

LocalAlignment:Example

LocalAlignment:FreeRides

(0,0)

The dashed edges represent the free rides from (0,0) to every other node.

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Yeah, a free ride!

LocalAlignment:Recurrence

0 si-1,j-1 + δ (vi, wj)

s i-1,j + δ (vi, -) s i,j-1 + δ (-, wj)

Power of ZERO: this is the only change from the original recurrence of a global alignment, representing the “free ride” edge

si,j = max

LocalAlignment:Backtrace

•  Scoreofbestlocalalignmentisthemaximumentryofsij

•  Thealignmentisfoundbyabacktracefromthemaximumnode,toanodeforwhichthescoreis0.

LocalAlignment:SW

•  Thislocalalignmentalgorithmisknownasthe“Smith-Waterman”algorithm1.

•  T.F.SmithandM.W.Waterman.Identificationofcommonmolecularsubsequences.J.Mol.Biol.147:195-197,1981.

1TheSmith-Watermanalgorithmconsidersamoresophisticatedgappenaltyscheme

ScoringIndels:NaiveApproach

•  Afixedpenaltyσisgiventoeveryindel:•  -σfor1indel,•  -2σfor2consecutiveindels•  -3σfor3consecutiveindels,etc.

Canbetooseverepenaltyforaseriesof100consecutiveindels

AffineGapPenalties

•  Innature,aseriesofkindelsoftencomesasasingleeventratherthanaseriesofksinglenucleotideevents:

Normal scoring would give the same score for both alignments

This is more likely.

This is less likely.

Affinegappenalty

•  Scoreforagapoflengthxis:-(ρ+σx)where:ρ>0isthegapopeningpenalty σ>0isthegapextensionpenalty

•  ρislargerelativetoσbecauseyoudonotwanttoadd

toomuchofapenaltyforextendingthegap.

AffineGapPenaltiesandEditGraph

Toreflectaffinegappenaltieswehavetoadd“long”horizontalandverticaledgestotheeditgraph.Eachsuchedgeoflengthxshouldhaveweight -ρ - x *σ

Adding“AffinePenalty”EdgestotheEditGraph

•  Therearemanysuchedges!

•  Addingthemtothegraphincreasestherunningtimeofthealignmentalgorithmbyafactorofn.

•  ThecomplexityincreasesfromO(n2)toO(n3)

The3-leveledManhattanGrid

gaps in w

matches/mismatches

gaps in v

Manhattanin3Layers

ρ

ρ

σ

σ δ δ

δ

δ δ

AffineGapPenaltiesand3LayerManhattanGrid

• We’llhavethreerecurrencesina3-layeredgraph.

•  Thetoplevelcreates/extendsgapsinthesequencew.

•  Thebottomlevelcreates/extendsgapsinsequencev.

•  Themiddlelevelextendsmatchesandmismatches.

SwitchingBetweentheLayers

•  Levels:•  Themainlevelisfordiagonaledges•  Thelowerlevelisforhorizontaledges•  Theupperlevelisforverticaledges

•  Ajumpingpenaltyisassignedtomovingfromthemainleveltoeithertheupperlevelorthelowerlevel(-ρ- σ)

•  Thereisagapextensionpenaltyforeachcontinuationonalevelotherthanthemainlevel(-σ)

AffineGapPenaltyRecurrences

si,j = s i-1,j - σ max s i-1,j - (ρ+σ) si,j = s i,j-1 - σ max s i,j-1 - (ρ+σ) si,j = si-1,j-1 + δ (vi, wj) max s i,j s i,j

Continue gap in w Start gap in w : from middle

Continue gap in v Start gap in v : from middle

Match or Mismatch End gap: from top End gap: from bottom

ShouldwecompareDNAorproteinsequences?

• DNAsequenceislessconservedthanproteinsequence

•  TheproteinsequencecontainsmoreinformationthantheDNAsequence

⇒Lesseffectivetocomparecodingregionsatthenucleotidelevel

ScoringMatrices

MakingaScoringMatrix

•  Scoringmatricesarecreatedbasedontheintuitionthatsomemutationshaveasmallereffectonthefunctionofaprotein⇒Suchmismatchpenaltiesshouldbelessharshthanothers.

ScoringMatrix:Example

A R N K

A 5 -2 -1 -1

R - 7 -1 3

N - - 7 0

K - - - 6

•  AlthoughRandKaredifferentaminoacids,theyhaveapositivescore.

•  Why?Theyarebothpositivelychargedaminoacids,thereforesubstitutionwillnotgreatlychangethefunctionoftheprotein.

SubstitutionsofAminoAcidsMutationratesbetweenaminoacidshavedramaticdifferences!

Conservation

•  Aminoacidchangesthatpreservethephysico-chemicalpropertiesoftheoriginalresidueshouldreceivehigherscores•  polartopolar•  aspartateàglutamate

•  hydrophobictohydrophobic•  alanineàvaline

PercentSequenceIdentity

•  Ameasureoftheextenttowhichtwonucleotideoraminoacidsequencesaresimilar

A C C T G A G – A G A C G T G – G C A G

70% identical mismatch

indel

BLOSUM

•  BlocksSubstitutionMatrix•  Scoresderivedfromobservationsofthefrequenciesofsubstitutionsinalignmentsofrelatedproteins

•  Matrixnameindicatesevolutionarydistance:•  BLOSUM62wascreatedusingsequencessharingnomorethan62%identity

Henikoff, S. and Henikoff, J. (1992) Amino acid substitution matrices from protein blocks. Proc. Natl. Acad. Sci. USA. 89(biochemistry): 10915 - 10919. 1992

AnentryfromtheBLOCKSdatabase

Block PR00851A ID XRODRMPGMNTB; BLOCK AC PR00851A; distance from previous block=(52,131) DE Xeroderma pigmentosum group B protein signature BL adapted; width=21; seqs=8; 99.5%=985; strength=1287 XPB_HUMAN|P19447 ( 74) RPLWVAPDGHIFLEAFSPVYK 54XPB_MOUSE|P49135 ( 74) RPLWVAPDGHIFLEAFSPVYK 54P91579 ( 80) RPLYLAPDGHIFLESFSPVYK 67XPB_DROME|Q02870 ( 84) RPLWVAPNGHVFLESFSPVYK 79RA25_YEAST|Q00578 ( 131) PLWISPSDGRIILESFSPLAE 100Q38861 ( 52) RPLWACADGRIFLETFSPLYK 71O13768 ( 90) PLWINPIDGRIILEAFSPLAE 100O00835 ( 79) RPIWVCPDGHIFLETFSAIYK 86//

The BLOCKS database is at: http://blocks.fhcrc.org/

TheBlosum50ScoringMatrix