Serghei Mangul Department of Computer Science Georgia State University Joint work with Irina Astrovskaya, Marius Nicolae, Bassam Tork, Ion Mandoiu and Alex Zelikovsky Maximum Likelihood Estimation of Incomplete Genomic Spectrum from HTS Data

Outline Introduction ML Model EM Algorithm VSEM Algorithm Experimental Results RNA-Seq 454 Conclusions and future work WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Outline Introduction ML Model EM Algorithm VSEM Algorithm Experimental Results RNA-Seq 454 Conclusions and future work WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Advances in High-Throughput Sequencing (HTS) 4 Roche/454 FLX Titanium million reads/run 400bp avg. length Illumina HiSeq 2000 Up to 6 billion PE reads/run bp read length SOLiD 4/ billion PE reads/run 35-50bp read length WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

5 Outline Introduction ML Model EM Algorithm VSEM Algorithm Experimental Results RNA-Seq 454 Conclusions and future work

ML Model Panel : bipartite graph —LEFT: genomic sequences (strings) >unknown frequencies —RIGHT: reads >observed frequencies —EDGES: probability of the read to be emitted by the string >weights are calculated based on the mapping of the reads to the strings strings S1 S2 S3 R1 R2 R4 reads R3 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Outline Introduction ML Model EM Algorithm VSEM Algorithm Experimental Results RNA-Seq 454 Conclusions and future work WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

ML estimates of string frequencies Probability that a read is sampled from string is proportional with its frequency f(j) ML estimates for f(j) is given by n(j)/(n(1) n(N)) —n(j) - number of reads sampled from string j WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

EM algorithm Initialization E-step: Compute the expected number n(j) of reads that come from string j under the assumption that string frequencies f(j) are correct M-step: For each string j, set the new value of f(j) equal to the portion of reads being originated by string j among all reads in the sample WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Outline Introduction ML Model EM Algorithm VSEM Algorithm Experimental Results RNA-Seq 454 Conclusions and future work WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

ML Model Quality How well the maximum likelihood model explain the reads Measured by deviation between expected and observed read frequencies —expected read frequency: WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

VSEM : Virtual String EM ML estimates of string frequencies ML estimates of string frequencies Compute expected read frequencies Compute expected read frequencies Update weights of reads in virtual string Update weights of reads in virtual string EM (Incomplete) Panel + Virtual String with 0-weights in virtual string (Incomplete) Panel + Virtual String with 0-weights in virtual string Virtual String frequency change>ε? Output string frequencies and weights Output string frequencies and weights EM YES NO WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Example : 1 st iteration 13 strings S1 S2 S3 R1 R2 R4 reads R3 strings S1 S2 R1 R2 R4 reads R3 Full Panel Incomplete Panel O 0.25 O WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

14 Example : 1 st iteration 14 strings S1 S2 S3 R1 R2 R4 reads R3 strings S1 S2 R1 R2 R4 reads R3 Full Panel Incomplete Panel O 0.25 O VS WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Example : 1 st iteration 15 strings S1 S2 S3 R1 R2 R4 reads R3 strings S1 S2 R1 R2 R4 reads R3 Full Panel Incomplete Panel OE.25 OE ML ML VS WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Example : 1 st iteration 16 strings S1 S2 S3 R1 R2 R4 reads R3 strings S1 S2 R1 R2 R4 reads R3 Full Panel Incomplete Panel OE.25 OE ML ML VS WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Example : last iteration 17 strings S1 S2 S3 R1 R2 R4 reads R3 strings S1 S2 R1 R2 R4 reads R3 Full Panel Incomplete Panel OE.25 OE ML ML VS WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

VSEM : Virtual String EM Decide if the panel is likely to be incomplete Estimate total frequency of missing strings Identify read spectrum emitted by missing strings WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

VSEM : Applications RNA-Seq —inferring isoform expressions from RNA-Seq Viral Quasispecies Sequencing by 454 pyrosequencing —inferring viral quasispecies spectrum from pyrosequencing shotgun reads 19 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Outline Introduction ML Model EM Algorithm VSEM Algorithm Experimental Results RNA-Seq 454 Conclusions and future work WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

21 RNA-Seq ABCDE Make cDNA & shatter into fragments Sequence fragment ends Map reads Gene Expression (GE) ABC AC DE Isoform Discovery (ID) Isoform Expression (IE) WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Previous Approach IsoEM [Nicolae et al. 2011] – novel expectation- maximization algorithm for inference of alternative splicing isoform frequencies from RNA-Seq data —Single and/or paired reads —Fragment length distribution —Strand information —Base quality scores —Insert sizes (library preparation) 22 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Simulation Setup Human genome UCSC/CCDS known isoforms —UCSC : isoforms, genes — CCDS : isoforms, genes GNFAtlas2 gene expression levels —geometric expression of gene isoforms Normally distributed fragment lengths — Mean 250, std. dev WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

EXP1 : Reduced transcriptome data Comparison between IsoEM and IsoVSEM on reduced transcriptome data —in every gene 25% of isoforms is missing —isoforms inside the gene - geometric distribution(p=0.5) —select genes with number of isoforms inside the gene is less or equal to 3. —removed isoforms with frequency WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

EXP2 : CCDS panel UCSC database represents the full panel CCDS represents the incomplete panel —reads were generated from UCSC library of isoforms —only frequencies of known isoforms(CCDS) were estimated 25 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Error Fraction Curves EXP1, 30M reads of length WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Outline Introduction ML Model EM Algorithm VSEM Algorithm Experimental Results RNA-Seq 454 Conclusions and future work WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

454 Pyrosequencing Pyrosequencing =Sequencing by Synthesis. GS FLX Titanium : — Divides the source genetic material into reads ( bp) 28 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Previous Approach ViSpA [Astrovskaya et al. 2011] – viral spectrum assembling tool for inferring viral quasispecies sequences and their frequencies from pyroseqencing shotgun reads —align reads —built a read graph : >V – reads >E – overlap between reads >each path – candidate sequence —filter based on ML frequencies 29 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

ViSpA-VSEM 30 ViSPA Weighted assembler assembled Qsps Qsps Library VSEM Virtual String EM reads, weights Viral Spectrum +Statistics reads ViSpA ML estimator removing duplicated & rare qsps Stopping condition YES NO WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Simulation Setup Real quasispecies sequences data from [von Hahn et al. 2006] —44 sequences (1739 bp long) from the E1E2 region of Hepatitis C virus —populations sizes: 10, 20, 30, and 40 sequences —population distributions: geometric, skewed normal, uniform 31 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Experimental Validation of VSEM Detection of panel incompleteness —VSEM can detect >1% of missing strings Improving quasispecies frequencies estimations Detection of reads emitted by missing string —Correlation between predicted reads and reads emitted by missing strings >65% 32 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

VSEM improving frequencies estimates 33 % of missing strings r.l./n.r<10%10%-20%20%-30%30%-40%40%-50%>50% rerrr r r r r ViSpA-EM100/20K ViSpA-VSEM100/20K ViSpA-EM300/20K ViSpA-VSEM300/20K ViSpA-EM100/100K ViSpA-VSEM100/100K ViSpA-EM300/100K ViSpA-VSEM300/100K WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany r - Correlation between real and predicted frequencies; err - average prediction error

ViSpA vs ViSpA-VSEM 34 ViSpAViSpA-VSEM DistributionPPVSensitivityrerrPPVSensitivityrerrGain Geometric Skewed Uniform K reads from 10 QSPS average length 300 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany r - Correlation between real and predicted frequencies; err - average prediction error

Outline Introduction ML Model EM Algorithm VSEM Algorithm Experimental Results RNA-Seq 454 Conclusions and future work WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Conclusions We propose VSEM, a novel modification of EM algorithm —improves the ML frequency estimations of multiple genomic sequences —identifies reads that belong to unassembled(missing) sequences We applied VSEM to improve two tools: —IsoEM —ViSpA 36 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Future work Assemble strings from the set of reads emitted by missing strings Improve other metagenomics tools 37 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Acknowledgments NSF awards IIS IIS , and DBI NSF award IIS Agriculture and Food Research Initiative Competitive Grant no from the USDA National Institute of Food and Agriculture. 38 WABI 2011, Max-Planck-Institute für Informatics, Saarbrücken, Germany

Thanks 39