CS 581 Algorithmic Computational Genomicsweb.engr.illinois.edu/~warnow/CS581-Jan16-2018.pdf ·...

CS581AlgorithmicComputationalGenomics

TandyWarnowUniversityofIllinoisatUrbana-Champaign

Today

•  Explainthecourse•  Introducesomeoftheresearchinthisarea•  Describesomeopenproblems•  Talkaboutcourseprojects!

CS581

•  Algorithmdesignandanalysis(largelyinthecontextofstatisticalmodels)for– Multiplesequencealignment–  PhylogenyEstimation– Genomeassembly

•  Iassumemathematicalmaturityandfamiliaritywithgraphs,discretealgorithms,andbasicprobabilitytheory,equivalenttoCS374andCS361.Nobiologybackgroundisrequired!

Textbook

•  ComputationalPhylogenetics:AnintroductiontoDesigningMethodsforPhylogenyEstimation

•  ThismaybeavailableintheUniversityBookstore.Ifnot,youcangetitfromAmazon.

•  Thetextbookprovidesallthebackgroundyou’llneedfortheclass,andhomeworkassignmentswillbetakenfromthebook.

Grading

•  Homeworks:25%(worstgradedropped)•  Takehomemidterm:40%•  Finalproject:25%•  Courseparticipationandpaperpresentation:10%

CourseProject

•  Courseprojectisduethelastdayofclass,andcanbearesearchprojectorasurveypaper.

•  Ifyoudoaresearchproject,youcandoitwithsomeoneelse(includingsomeoneinmyresearchgroup);thegoalwillbetoproduceapublishablepaper.

•  Ifyoudoasurveypaper,youwilldoitbyyourself.

Orangutan Gorilla Chimpanzee Human

From the Tree of the Life Website, University of Arizona

Phylogeny (evolutionary tree)

Phylogeny+genomics=genome-scalephylogenyestimation.

Estimating the Tree of Life

BasicBiology:Howdidlifeevolve?

Applicationsofphylogeniesto:proteinstructureandfunctionpopulationgeneticshumanmigrationsmetagenomics

Figurefromhttps://en.wikipedia.org/wiki/Common_descent

Estimating the Tree of Life

Largedatasets!Millionsofspeciesthousandsofgenes

NP-hardoptimizationproblemsExactsolutionsinfeasibleApproximationalgorithmsHeuristicsMultipleoptima

HighPerformanceComputing:

necessarybutnotsufficient

Figurefromhttps://en.wikipedia.org/wiki/Common_descent

Background Results Conclusions References

Genomic data: challenges and opportunities

Muir et al. [2016]

Muir,2016

ComputerScienceSolvingProblemsinBiologyandLinguistics

•  Algorithmdesignusing–  Divide-and-conquer–  Iteration–  Heuristicsearch–  Graphtheory

•  Algorithmanalysisusing–  ProbabilityTheory–  GraphTheory

•  Simulationsandmodelling•  Collaborationswithbiologistsandlinguistsanddataanalysis•  Discoveriesabouthowlifeevolvedonearth(andhowlanguages

evolved,too)

ComputationalPhylogenetics(2005)

CourtesyoftheTreeofLifewebproject,tolweb.org

Current methods can use months to

estimate trees on 1000 DNA sequences

Our objective:

More accurate trees and alignments

on 500,000 sequences in under a week

ComputationalPhylogenetics(2018)

CourtesyoftheTreeofLifewebproject,tolweb.org

1997-2001: Distance-based phylogenetic tree estimation from polynomial length sequences

2012: Computing accurate trees (almost) without multiple sequence alignments

2009-2015: Co-estimation of multiple sequence alignments and gene trees, now on 1,000,000 sequences in under two weeks

2014-2015: Species tree estimation from whole genomes in the presence of massive gene tree heterogeneity

2016-2017: Scaling methods to very large heterogeneous datasets using novel machine learning and supertree methods.

Scientific challenges: •  Ultra-large multiple-sequence alignment •  Gene tree estimation •  Metagenomic classification •  Alignment-free phylogeny estimation •  Supertree estimation •  Estimating species trees from many gene trees •  Genome rearrangement phylogeny •  Reticulate evolution •  Visualization of large trees and alignments •  Data mining techniques to explore multiple optima •  Theoretical guarantees under Markov models of evolution

Techniques: applied probability theory, graph theory, supercomputing, and heuristics Testing: simulations and real data

The Tree of Life: Multiple Challenges

Thistalk

•  Divide-and-conquer:Basicalgorithmdesigntechnique

•  Applicationofdivide-and-conquerto:– Phylogenyestimation(andproofof“absolutefastconvergence”)

– Multiplesequencealignment– Almostalignment-freetreeestimation

•  Openproblems

Divide-and-Conquer

•  Divide-and-conquerisabasicalgorithmictrickforsolvingproblems!

•  Threesteps:– divideadatasetintotwoormoresets,– solvetheproblemoneachset,and– combinesolutions.

Sorting

10 3 54 23 75 5 1 25

Objective:sortthislistofintegersfromsmallesttolargest.10,3,54,23,75,5,1,25shouldbecome1,3,5,10,23,25,54,75

MergeSort

10 3 54 23 75 5 1 25

Step1:DivideintotwosublistsStep2:RecursivelysorteachsublistStep3:Mergethetwosortedsublists

Keytechnique:Divide-and-conquer!

•  Canbeusedtoproduceprovablycorrectalgorithms(asinMergeSort)

•  Butalso–inpractice,divide-and-conquerisusefulforscalingmethodstolargedatasets,becausesmalldatasetswithnottoomuch“heterogeneity”areeasytoanalyzewithgoodaccuracy.

Threedivide-and-conqueralgorithms

•  DCM1(2001):Improvingdistance-basedphylogenyestimation

•  SATé(2009,2012)andPASTA(2015):Co-estimationofmultiplesequencealignmentsandgenetrees(upto1,000,000sequences)

•  DACTAL(2012):Almostalignment-freetreeestimation

DNA Sequence Evolution

AAGACTT

TGGACTT AAGGCCT

-3 mil yrs

-2 mil yrs

-1 mil yrs

today

AGGGCAT TAGCCCT AGCACTT

AAGGCCT TGGACTT

TAGCCCA TAGACTT AGCGCTT AGCACAA AGGGCAT


AAGACTT

TGGACTT AAGGCCT


AAGGCCT TGGACTT

AGCGCTT AGCACAA TAGACTT TAGCCCA AGGGCAT

Gene Tree Estimation

TAGCCCA TAGACTT TGCACAA TGCGCTT AGGGCAT

U V W X Y

U

V W

X

Y

QuantifyingError

FN: false negative (missing edge) FP: false positive (incorrect edge)

FN

FP 50% error rate

MarkovModelofSiteEvolutionSimplest(Jukes-Cantor,1969):•  ThemodeltreeTisbinaryandhassubstitutionprobabilitiesp(e)on

eachedgee.•  Thestateattherootisrandomlydrawnfrom{A,C,T,G}(nucleotides)•  Ifasite(position)changesonanedge,itchangeswithequalprobability

toeachoftheremainingstates.•  TheevolutionaryprocessisMarkovian.Thedifferentsitesareassumedtoevolveindependentlyandidenticallydownthetree(withratesthataredrawnfromagammadistribution).

Morecomplexmodels(suchastheGeneralMarkovmodel)arealsoconsidered,oftenwithlittlechangetothetheory.

Sequencelengthrequirements

Thesequencelength(numberofsites)thataphylogenyreconstructionmethodMneedstoreconstructthetruetreewithprobabilityatleast1-εdependson

•  M(themethod)•  ε•  f=minp(e),•  g=maxp(e),and•  n,thenumberofleaves

Wefixeverythingbutn.

Statistical consistency, exponential convergence, and absolute fast convergence (afc)

Distance-basedestimation

Neighbor joining on large diameter trees

Simulation study based

upon fixed edge lengths, K2P model of evolution, sequence lengths fixed to 1000 nucleotides.

Error rates reflect proportion of incorrect edges in inferred trees.

[Nakhleh et al. Bioinf 17, Suppl

1 (2001) S190-S198]

NJ

0 400 800 1600 1200 No. Taxa

0

0.2

0.4

0.6

0.8

Erro

r Rat

e

DCMs: Divide-and-conquer for improving phylogeny reconstruction

DCM1Decompositions

DCM1 decomposition : Compute maximal cliques

Input: Set S of sequences, distance matrix d, threshold value

1. Compute threshold graph

}),(:),{(,),,( qjidjiESVEVGq ≤===2. Perform minimum weight triangulation (note: if d is an additive matrix, then the threshold graph is provably triangulated).

}{ ijdq∈

DCM1-boosting:Warnow,St.John,andMoret,

SODA2001

•  TheDCM1phaseproducesacollectionoftrees(oneforeachthreshold),andtheSQSphasepicksthe“best”tree.

•  Foragiventhreshold,thebasemethodisusedtoconstructtreesonsmallsubsets(definedbythethreshold)ofthetaxa.Thesesmalltreesarethencombinedintoatreeonthefullsetoftaxa.

DCM1 SQS

Exponentially converging (base) method

Absolute fast converging (DCM1-boosted) method

DCM1-boosting

• Theorem (Warnow, St. John, and Moret, SODA 2001): DCM1-NJ converges to the true tree from polynomial length sequences

NJ DCM1-NJ

0 400 800 1600 1200 No. Taxa

0

0.2

0.4

0.6

0.8

Erro

r Rat

e

[Nakhleh et al. Bioinf 17,

Suppl 1 (2001) S190-S198]

DNA Sequence Evolution

AAGACTT

TGGACTT AAGGCCT

-3 mil yrs

-2 mil yrs

-1 mil yrs

today


AAGGCCT TGGACTT

TAGCCCA TAGACTT AGCGCTT AGCACAA AGGGCAT


AAGACTT

TGGACTT AAGGCCT


AAGGCCT TGGACTT

AGCGCTT AGCACAA TAGACTT TAGCCCA AGGGCAT

…ACGGTGCAGTTACCA…

Mutation Deletion

…ACCAGTCACCA…

Indels (insertions and deletions)

…ACGGTGCAGTTACC-A…

…AC----CAGTCACCTA…

Thetruemultiplealignment–  Reflects historical substitution, insertion, and deletion

events –  Defined using transitive closure of pairwise alignments

computed on edges of the true tree

…ACGGTGCAGTTACCA…

Substitution Deletion

…ACCAGTCACCTA…

Insertion

Gene Tree Estimation

S1 = AGGCTATCACCTGACCTCCA S2 = TAGCTATCACGACCGC S3 = TAGCTGACCGC S4 = TCACGACCGACA

Input: unaligned sequences


Phase 1: Alignment

S1 = -AGGCTATCACCTGACCTCCA S2 = TAG-CTATCAC--GACCGC-- S3 = TAG-CT-------GACCGC-- S4 = -------TCAC--GACCGACA


Phase 2: Construct tree

S1 = -AGGCTATCACCTGACCTCCA S2 = TAG-CTATCAC--GACCGC-- S3 = TAG-CT-------GACCGC-- S4 = -------TCAC--GACCGACA


S1

S4

S2

S3

Two-phaseestimationAlignmentmethods•  Clustal•  POY(andPOY*)•  Probcons(andProbtree)•  Probalign•  MAFFT•  Muscle•  Di-align•  T-Coffee•  Prank(PNAS2005,Science2008)•  Opal(ISMBandBioinf.2007)•  FSA(PLoSComp.Bio.2009)•  Infernal(Bioinf.2009)•  Etc.

Phylogenymethods•  BayesianMCMC•  Maximumparsimony•  Maximumlikelihood•  Neighborjoining•  FastME•  UPGMA•  Quartetpuzzling•  Etc.

Two-phaseestimationAlignmentmethods•  Clustal•  POY(andPOY*)•  Probcons(andProbtree)•  Probalign•  MAFFT•  Muscle•  Di-align•  T-Coffee•  Prank(PNAS2005,Science2008)•  Opal(ISMBandBioinf.2007)•  FSA(PLoSComp.Bio.2009)•  Infernal(Bioinf.2009)•  Etc.

Phylogenymethods•  BayesianMCMC•  Maximumparsimony•  Maximumlikelihood•  Neighborjoining•  FastME•  UPGMA•  Quartetpuzzling•  Etc.

RAxML:heuristicforlarge-scaleMLoptimization

1000-taxonmodels,orderedbydifficulty(Liuetal.,Science19June2009)

Large-scaleCo-estimationofalignmentsandtrees

•  SATé:Liuetal.,Science2009(upto10,000sequences)andSystematicBiology2012(upto50,000sequences)

•  PASTA:Mirarabetal.,J.ComputationalBiology2015(upto1,000,000sequences)

Re-aligning on a tree A

B D

C

Merge sub-alignments

Estimate ML tree on merged

alignment

Decompose dataset

A B

C DAlign

subproblems

A B

C D

ABCD

SATé and PASTA Algorithms

Tree

Obtain initial alignment and estimated ML tree


Tree


Use tree to compute new alignment

Alignment


Estimate ML tree on new alignment

Tree



Alignment

SATéandPASTAAlgorithms

Estimate ML tree on new alignment

Tree



Alignment

Repeatuntilterminationcondition,and

returnthealignment/treepairwiththebestMLscore


24hourSATéanalysis,ondesktopmachines

(Similarimprovementsforbiologicaldatasets)

RNASim

0.00

0.05

0.10

0.15

0.20

10000 50000 100000 200000

Tree

Erro

r (FN

Rat

e) Clustal−OmegaMuscleMafftStarting TreeSATe2PASTAReference Alignment

•  SimulatedRNASimdatasetsfrom10Kto200Ktaxa•  Limitedto24hoursusing12CPUs•  Notallmethodscouldrun(missingbarscouldnotfinish)•  PASTA:JCompBiol22(5):377-386,Mirarabetal.,2015

PASTA

Multiple Sequence Alignment (MSA): a scientific grand challenge1

S1 = -AGGCTATCACCTGACCTCCA S2 = TAG-CTATCAC--GACCGC-- S3 = TAG-CT-------GACCGC-- … Sn = -------TCAC--GACCGACA

S1 = AGGCTATCACCTGACCTCCA S2 = TAGCTATCACGACCGC S3 = TAGCTGACCGC … Sn = TCACGACCGACA

Novel techniques needed for scalability and accuracy NP-hard problems and large datasets Current methods do not provide good accuracy Few methods can analyze even moderately large datasets Many important applications besides phylogenetic estimation

1 Frontiers in Massive Data Analysis, National Academies Press, 2013

DACTAL

•  Divide-And-ConquerTrees(Almost)withoutalignments

•  Nelesenetal.,ISMB2012andBioinformatics2012

•  Input:unalignedsequences•  Output:Tree(butnoalignment)

DACTAL

Superfine

RAxML(MAFFT)

Decompose into small local subsets in tree

BLAST-based

Overlapping subsets

A tree for each subset

Unaligned Sequences

A tree for the entire dataset

Resultsonthreebiologicaldatasets–6000to28,000sequences.Weshowresultswith5DACTALiterations

DACTAL

Any supertree method

Any tree estimation method!

Any decomposition strategy

Overlapping subsets

A tree for each subset

Arbitrary input

A tree for the entire dataset

Startwithanytreeestimatedonthedata,decomposetoanydesiredsize

“Boosters”, or “Meta-Methods”

•  Meta-methods use divide-and-conquer and iteration (or other techniques) to “boost” the performance of base methods (phylogeny reconstruction, alignment estimation, etc)

Meta-methodBase method M M*

Summary

•  Weshowedthreetechniquestoimproveaccuracyandscalability,thatuseddivide-and-conquer(andsometimesiteration):–  DCM1(improvesaccuracyandscalabilityfordistance-basedmethods)

–  SATeandPASTA(improvesaccuracyandscalabilityformultiplesequencealignmentmethods)

–  DACTAL(generaltechniqueforimprovingtreeestimation)

•  Innovativealgorithmdesigncanimproveaccuracyaswellasreducerunningtime.

Openproblems(andpossiblecourseprojects)

•  MultipleSequenceAlignment:–  Mergingtwoalignments–  Consensusalignments

•  Supertreeestimation–  Needtoscaleto100,000+specieswithhighaccuracy–  Approximationalgorithms

•  Speciestreeandphylogeneticnetworkestimation–  Addressgenetreeheterogeneityduetomultiplecauses–  Theoreticalguaranteesunderstochasticmodels–  Scalabilitytolargenumbersofspecieswithwholegenomes

•  StatisticalModelsofevolution–  Allmodelsareseriouslyunrealistic–  Weneedbetterstatisticalmodels–  Newtheory

•  Applicationstohistoricallinguistics,microbiomeanalysis,proteinstructureandfunctionprediction,tumorevolution,etc.

Somepriorcourseprojectsthatwerepublished

•  ASTRAL:genome-scalecoalescent-basedspeciestreeestimation,Mirarabetal.2014(ECCB2014andBioinformatics2014)

•  Phylogenomicspeciestreeestimationinthepresenceofincompletelineagesortingandhorizontalgenetransfer,Davidsonetal.2014(RECOMB-CG2014andBMCGenomics2014)

•  AcomparativestudyofSVDquartetsandothercoalescent-basedspeciestreeestimationmethods,Chouetal.(RECOMB-CGandBMCGenomics2014)

•  ASTRID:Accuratespeciestreesfrominternodedistances,VachaspatiandWarnow(RECOMB-CG2015andBMCGenomics2015)

•  Scalingstatisticalmultiplesequencealignmenttolargedatasets,NuteandWarnow(RECOMB-CG2016andBMCGenomics2016)

Scientific challenges: •  Ultra-large multiple-sequence alignment •  Gene tree estimation •  Metagenomic classification •  Alignment-free phylogeny estimation •  Supertree estimation •  Estimating species trees from many gene trees •  Genome rearrangement phylogeny •  Reticulate evolution •  Visualization of large trees and alignments •  Data mining techniques to explore multiple optima •  Theoretical guarantees under Markov models of evolution

Techniques: applied probability theory, graph theory, supercomputing, and heuristics Testing: simulations and real data

The Tree of Life: Multiple Challenges

OtherInformation

•  Tandy’sofficehours:Tuesdays3:15-4:15(andbyappointment).

•  Tandy’semail:[email protected]•  TA:SarahChristensen([email protected])•  HomeworkwillbesubmittedthroughMoodle.•  Coursewebpage:http://tandy.cs.illinois.edu/581-2018.html

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