optical mapping data: data generation and algorithmsthe burrows-wheeler transform (bwt) is a...
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OpticalMappingData:DataGenerationandAlgorithms
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SamplePreparation
Sequencing
Assembly
Analysis
Fragments
Reads
Contigs
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WhatisanOpticalMap?
GGCTTCCGACCACCACAACCGAATTATGAAGGATACCGAA
6,19,35
Opticalmapsareordered,genome-wide,high-resolutionrestrictionmaps.
- Muchlongerthanreads.Forexample,theaveragemapsizeforgoatcovers 360,000bp
- Nowcommerciallyavailable
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.
IsolatedDNA Microfludic device
DNAiselongatedandcleavedontheopticalmappingsurface
Epiflourescence microscopewithCCDcamera
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6 3 3 49
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6 3 3 49
6 3 9 4
Genomewideopticalmap
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“There is [..] a critical need for the continued development and public release of software tools for processing optical mapping data ..”
-GigaScience 2014
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Goal:tooltoalignthecontigtoa segmentofan
opticalmap
SamplePreparation
Sequencing
Assembly
Analysis
Genome-wideopticalmap
contigs
OpticalMapData
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• Previousapproachesusedynamicprogramming• Burrows-WheelerTransform(BWT)wouldimprovetimeefficiency
• ChallengesinapplyingBWT:(1)Sizingerrorand(2)alphabetsize
Challenges
6 3 9 4
5 4 9.5 6
ActualopticalmapvaluesOpticalmapobtainedfromexperiment
1 1 0.5 2SIZINGERROR
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• Previousapproachesusedynamicprogramming• Burrows-WheelerTransform(BWT)wouldimprovetimeefficiency
• ChallengesinapplyingBWT:(1)Sizingerror and(2)alphabetsize
Challenges
6 3 9 4
5 4 9.5 6
ActualopticalmapvaluesOpticalmapobtainedfromexperiment
1 1 0.5 2SIZINGERROR
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• Previousapproachesusedynamicprogramming• Burrows-WheelerTransform(BWT)wouldimprovetimeefficiency
• ChallengesinapplyingBWT:(1)Sizingerrorand(2)alphabetsize
Challenges
!𝑢𝑛𝑖𝑞𝑢𝑒𝑓𝑟𝑎𝑔𝑚𝑒𝑛𝑡𝑠𝑖𝑧𝑒𝑠 >�
�
16,000
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Twin
SamplePreparation
Sequencing
Assembly
Analysis
Contigs
OpticalMapData
Alignmentofcontigstoopticalmap
Genome-wideopticalmap
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Contig 1
Contig 2
Contig 3 Contig 5
Contig 4
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TwinAlgorithm
1. Insilico digestcontigs intoopticalmaps.
TTTCCGACCACTTTTCCGAATTATGACCGAA
4,13,24
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TwinAlgorithm
1. Insilico digestcontigs intoopticalmaps.2. BuildFM-index* andauxiliarydatastructures
onthegenome-wideopticalmap.
*adatastructurethatallowscompressionoftheinputtextwhilestillpermittingfastsubstringqueries
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BWTandFM-indexAsuffixarray(SA)ofstringSisanarrayofthesuffixesofSsortedintoalphabeticalorder.
1 acaaacgn2 caaacgn3 aaacgn4 aacgn5 acgn6 cgn7 gn8 n
3 aaacgn4 aacgn1 acaaacgn5 acgn2 caaacgn6 cgn7 gn8 n
acaaacgn
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BWTandFM-indexAsuffixarray(SA)ofstringSisanarrayofthesuffixesofSsortedintoalphabeticalorder.
The suffix array clusters all the occurrences of everypattern together into a contiguous range!
1 acaaacgn2 caaacgn3 aaacgn4 aacgn5 acgn6 cgn7 gn8 n
3 aaacgn4 aacgn1 acaaacgn5 acgn2 caaacgn6 cgn7 gn8 n
acaaacgn
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Asuffixarray(SA)ofstringSisanarrayofthesuffixesofSsortedintoalphabeticalorder.
The suffix array clusters all the occurrences of everypattern together into a contiguous range!
1 acaaacgn2 caaacgn3 aaacgn4 aacgn5 acgn6 cgn7 gn8 n
3 aaacgn4 aacgn1 acaaacgn5 acgn2 caaacgn6 cgn7 gn8 n
acaaacgn
BWTandFM-index
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1 acaaacgn2 caaacgn3 aaacgn4 aacgn5 acgn6 cgn7 gn8 n
3 aaacgn4 aacgn1 acaaacgn5 acgn2 caaacgn6 cgn7 gn8 n
acaaacgn
Asuffixarray(SA)ofstringSisanarrayofthesuffixesofSsortedintoalphabeticalorder.
The suffix array clusters all the occurrences of everypattern together into a contiguous range!
BWTandFM-index
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3 aaacgn4 aacgn1 acaaacgn5 acgn2 caaacgn6 cgn7 gn8 n
1 acaaacgn2 caaacgn3 aaacgn4 aacgn5 acgn6 cgn7 gn8 n
acaaacgn
Asuffixarray(SA)ofstringSisanarrayofthesuffixesofSsortedintoalphabeticalorder.
The suffix array clusters all the occurrences of everypattern together into a contiguous range!
BWTandFM-index
![Page 24: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/24.jpg)
TheBurrows-WheelerTransform(BWT)isapermutationofthestringsuchthatBWT[i] = S[SA[i] - 1].
3 aaacgnac4 aacgnaca1 acaaacgn5 acgnacaa2 caaacgna6 cgnacaaa7 gnacaaac8 nacaaacg
acaaacgn
BWTandFM-index
canaaacg
ExtractlastcolumnofSA
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TheBurrows-WheelerTransform(BWT)isapermutationofthestringsuchthatBWT[i] = S[SA[i] - 1].
rankK(i): returnthenumberofK’sinS[1,i]
3 aaacgnac4 aacgnaca1 acaaacgn5 acgnacaa2 caaacgna6 cgnacaaa7 gnacaaac8 nacaaacg
acaaacgn
BWTandFM-index
canaaacg
00012310
BWT rank
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TheBurrows-WheelerTransform(BWT)isapermutationofthestringsuchthatBWT[i] = S[SA[i] - 1].
rankK(i): returnthenumberofK’sinS[1,i]
3 aaacgnac4 aacgnaca1 acaaacgn5 acgnacaa2 caaacgna6 cgnacaaa7 gnacaaac8 nacaaacg
acaaacgn
BWTandFM-index
canaaacg
00012310
BWT rank
ranka[5] = 2
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TheBurrows-WheelerTransform(BWT)isapermutationofthestringsuchthatBWT[i] = S[SA[i] - 1].
FM-indexisthecompressedversionoftheBWT andrank.
3 aaacgnac4 aacgnaca1 acaaacgn5 acgnacaa2 caaacgna6 cgnacaaa7 gnacaaac8 nacaaacg
acaaacgn
BWTandFM-index
canaaacg
00012310
BWT rank
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TwinAlgorithm
1. Insilico digestcontigs intoopticalmaps.2. BuildFM-indexandauxiliarydatastructures
onthegenome-wideopticalmap.3. UsingtheFM-indexwefindallalignments
betweentheopticalmapandtheinsilicodigestedcontigs.- ModifiedFM-indexBackwardSearchAlgorithm
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FM-IndexBackwardSearchArecursivealgorithmforfindingsubstringsusingrank and BWT
rank[c]rank[a]
rank[a]
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ModifiedFM-IndexBackwardSearch
• Sizingerrorandalphabet sizearechallengestoovercome
• Wecannotaffordabruteforceenumerationofthealphabetateachstepinthebackwardsearch
• Noveltyforopticalmaps:WaveletTree
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WaveletTree
AWaveletTreeconvertsastringintoabalancedbinary-treeofbitvectors,wherea0replaceshalfofthesymbols,anda1replacestheotherhalf.Thisdefinitionisappliedrecursive
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{A,C,G,T} is encoded as {0,0,1,1}
ACGTATATAGGAAGA001101010110010
WaveletTree
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{A,C,G,T} is encoded as {0,0,1,1}
ACGTATATAGGAAGA001101010110010
WaveletTree
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Noambiguity!
WaveletTree
ACGTATATAGGAAGA001101010110010
ACAAAAAA01000000
0
{A,C} is encoded as {0,1}
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WaveletTree
ACGTATATAGGAAGA001101010110010
ACAAAAAA01000000
0
{G,T} is encoded as {0,1}
GTTTGGG0111000
1
Whichsymbolsin{A, G} existininputstring?
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Tomatchx weneedtofindallthesubstringswithintherangex +/- y, fortolerancey.
ModifiedFM-IndexBackwardSearch
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Tomatch9 weneedtofindallthesubstringswithintherange[6, 12] , fortolerance3.
ModifiedFM-IndexBackwardSearch
2,11,10,23,53,3,5,10,14,9,110, 1, 0, 1, 1,0,0, 0, 1,0, 1
Genomewideopticalmap
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ModifiedFM-IndexBackwardSearch
2,11,10,23,53,3,5,10,14,9,110, 1, 0, 1, 1,0,0, 0, 1,0, 1
Tomatch9 weneedtofindallthesubstringswithintherange[6, 12] , fortolerance3.
2,10,3,5,10,90, 1,0,0, 1,1
11,23,53,14,110, 1, 1, 0, 0
2,3,50,0,1
10,9,100,1, 0
2,30,1
51
11,14,110, 1, 0
23,530, 1
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ModifiedFM-IndexBackwardSearch
2,11,10,23,53,3,5,10,14,9,110, 1, 0, 1, 1,0,0, 0, 1,0, 1
Tomatch9 weneedtofindallthesubstringswithintherange[6, 12] , fortolerance3.
2,10,3,5,10,90, 1,0,0, 1,1
11,23,53,14,110, 1, 1, 0, 0
2,3,50,0,1
10,9,100,1, 0
2,30,1
51
11,14,110, 1, 0
23,530, 1
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Arecursivealgorithmforfindingsubstringsusingrank and BWT
rank[c] rank[a]
rank[a]
ModifiedFM-IndexBackwardSearch
WaveletTreeQuery
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TwinAlgorithm
1. Insilico digestcontigs intoopticalmaps.2. BuildFM-indexandauxiliarydatastructures
onthegenome-wideopticalmap.3. UsingtheFM-indexwefindallalignments
betweentheopticalmapandtheinsilicodigestedcontigs.
4. OutputthealignmentsinPSLformat.
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TWINTestDatasets
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TWINResults
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Twinisthefirstalignmentmethodthatiscapableofhandlinglargegenomesizes
• Theonlyindex-basedtoolandisordersofmagnitudefasterthanexistingapproaches(patentpending)
• Pinetree(20Gb)wouldtake~84machineyearswithSOMAbutacouplehourswithTwin
TWIN:Optical Map Aligner
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CORRECTINGERRORSINGENOMES
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Mis-assemblyinGenomesMis-assembly: Significantlylargeinsertion,deletion,inversion,orrearrangementthatistheresultofdecisionsmadebytheassemblyprogram
Correctassembly
Rearrangement
Deletion
Insertion
A R R B
A R RB
A R B
A R R BR
![Page 47: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/47.jpg)
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Extensivevs.LocalMis-assemblies
ExtensiveMis-assembly:1kbp insizeandregionsaligntodifferentstrandsordifferentchromosomes.
LocalMis-assembly:smallerinsizeandonthesamestrandandsamechromosome.
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DeBruijn GraphofaGenome
ExampleGenome:ABCDEFGHICDEFGKLExampleGenome:ABCDEFGHICDEFGKL
1 3
2
ABC BCD CDE DEF EFG FGK GKL
FGH
GHIHIC
ICD
![Page 50: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/50.jpg)
DeBruijn GraphofaGenome
ABC BCD CDE DEF EFG FGK GKL
ExampleGenome:ABCDEFGHICDEFGKLExampleGenome:ABCDEFGHICDEFGKL
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DeBruijn GraphofaGenome
ABC BCD CDE DEF EFG FGK GKL
ExampleGenome:ABCDEFGHICDEFGKLResultingErroneousGenome:ABCDEFGKL
1
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SamplePreparation
Sequencing
Assembly
Analysis
Fragments
Reads
Contigs
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misSEQuel*
RefinedContigs
Reads
Contigs
*(Muggli,Puglisi,Ronen,Boucher,ISMB2015)
SamplePreparation
Sequencing
Assembly
Analysis
Fragments
Reads
Contigs
OpticalMapData
![Page 54: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/54.jpg)
misSEQuel Algorithm
1. Alignsequencereadstocontigs usingastandardalignmenttool.GGCTTCCGACCACCACAAATGGATTATGAAGGATATATGGA
![Page 55: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/55.jpg)
misSEQuel Algorithm
1. Alignsequencereadstocontigs usingastandardalignmenttool.GGCTTCCGACCACCACAAATGGATATGAAGGATATATGGATTATGAAGGATATAGGCTTCCGACCACCACAAATGGATTATGAAGGATATATGGA
![Page 56: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/56.jpg)
misSEQuel Algorithm
1. Alignsequencereadstocontigs usingastandardalignmenttool.GGCTTCCGACCACCACAAATGGATTATGAAGGATATATGGA
![Page 57: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/57.jpg)
misSEQuel Algorithm
1. Alignsequencereadstocontigs usingastandardalignmenttool.GGCTTCCGACCACCACAAATGGATATGAAGGATATATGGATTATGAAGGATATAGGCTTCCGACCACCACAAATGGATTATGAAGGATATATGGA
1 9
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misSEQuel Algorithm
1. Alignsequencereadstocontigs usingastandardalignmenttool.
2. Buildthered-blackpositionaldeBruijn graphbasedonthealignment.
![Page 59: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/59.jpg)
SamplePreparation
Sequencing
ACGTAGAATCGACCATG
GGGACGTAGAATACGAC
ACGTAGAATACGTAGAA
Reads
Fragments
NextGenerationSequencing(NGS)
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ACGTAGAATCGACCATGGGGACGTAGAATACGA
Paired-EndReads/Mate-PairReads
SamplePreparation
Sequencing
Fragments
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ReadMatePairConcordance
A R R B
AR R B
A
R
R B
Correctassembly
Rearrangement
Inversion
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ReadDepth
A R R B
A R BR R
RA B
Correctassembly
Insertion
Deletion
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Red-BlackPositionalDeBruijn Graph
I. Chooseavalueof𝑘andΔ .II. Eachpositional𝑘-mer (sk)isanedgebetweentwo
positional𝑘–mers:prefix andsuffix ofsk.III. Positional𝑘–mers,sk-1 andsk-1’, aregluedifsk-1 andsk-1’
havethesamelabelandtheirdistancesdifferbyatmostΔ.IV. Ask-1 isredifthereaddepthistwostandarddeviationsfrom
themeanorthereisasignificantnumberofdisconcordinatereadalignments;otherwise,itisblack.
Apositional𝑘-mer isa𝑘-mer withanapproximateposition.
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PositionalRedBlackdeBruijn GraphReadsaligned tocontigs:
Positionalk-mers withreaddepth:
PositionalRedBlackdeBruijnGraph:
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misSEQuel Algorithm
1. Alignsequencereadstocontigs usingastandardalignmenttool.
2. Buildthered-blackpositionaldeBruijn graphbasedonthealignment.
3. Removeallbulgesandwhirlsforthered-blackpositionaldeBruijn graph.
![Page 66: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/66.jpg)
misSEQuel Algorithm
1. Alignsequencereadstocontigs usingastandardalignmenttool.
2. Buildthered-blackpositionaldeBruijn graphbasedonthealignment.
3. Removeallbulgesandwhirlsforthered-blackpositionaldeBruijn graph.
Correctassembledcontigs Mis-assembledcontigs
A R R B A R RBA R BA R R BRA R R B
…
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misSEQuel Algorithm
1. Alignsequencereadstocontigs usingastandardalignmenttool.
2. Buildthered-blackpositionaldeBruijn graphbasedonthealignment.
3. Removeallbulgesandwhirlsforthered-blackpositionaldeBruijn graph.
4. Contig refinementusingopticalmapalignment.
![Page 68: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/68.jpg)
OpticalMapAlignment
NheI=G^CTAGC
E.Coliopticalmapsegment
A R R B
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NheI=G^CTAGC
“GCTAGC”
OpticalMapAlignment
BA R R
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NheI=G^CTAGC
CorrectlyAssembledContigs Align
BA R R
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NheI=G^CTAGC
A R BR R
Mis-assembledContigs Don’tAlign
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NheI=G^CTAGC
A R BR R
Mis-assembledContigs Don’tAlign
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ResultsonTularensis
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ResultsonTularensis
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ResultsonTularensis
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ResultsonTularensis
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ResultsonTularensis
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ResultsonTularensis
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ResultsonTularensis
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ResultsonTularensis
![Page 81: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/81.jpg)
ResultsonTularensis
![Page 82: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/82.jpg)
![Page 83: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/83.jpg)
ResultsonPine
![Page 84: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/84.jpg)
B
BA R R
ImprovePrediction
A RR R
![Page 85: Optical Mapping Data: Data Generation and AlgorithmsThe Burrows-Wheeler Transform (BWT) is a permutation of the string such that BWT[i] = S[SA[i] -1]. 3 aaacgnac 4 aacgnaca 1 acaaacgn](https://reader035.vdocument.in/reader035/viewer/2022071010/5fc7ab45879b3669ff264acd/html5/thumbnails/85.jpg)
B
ImprovePrediction
A RR R
Deletionbetweentwoalignedregions