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1 Expression Quantification (I) Mario Fasold, LIFE, IZBI

2 Sequencing Technology One Illumina HiSeq 2000 run produces 2 times (paired-end) ca. 1,2 Billion reads ca. 120 GB FASTQ file

3 RNA-seq protocol

4 Task Obtain some value (estimate) representing the true abundance of transcripts in vivo

5 Overview 1. Basic Expression Measures 2. Statistical Poisson Model 1. Single Isoform 2. Multiple Isoform 3. Statistical Inference 4. Results 3. Paired-End Sequencing 4. Negative-Binomial

6 Expression Quantification What properties should the expression values have? Values should be comparable Between transcripts Between samples (-> differential expression)

7 Problems in Expression Quantification Differences in transcript length

8 Problems in Expression Quantification Fluctuations in sequencing depth

9 Basic Measure: RPKM RPKM/FPKM = Reads/Fragments per kilobase of exon model per million mapped reads FPKM 10 9 x wl x = the number of reads mapped onto the gene's exons w = total number of reads in the experiment l = the sum of the exons in base pairs.

10

11 However, there are isoforms...

12 Typical number of isoforms 7%

13

14 Notation fg,1 fg,2 ng=2

15 kf kf lf lf

16 f2 f1 f1 f2 f1 f1 f1 f2 Set of all isoforms in sample Total length of isoforms f1 f1 f1 f1 f1 f1 f1 f2 f2 f2

17 f2 f1 f1 f2 f1 f1 f1 f2 f1 f1 f1 f1 f1 f1 f1 f2 f2 f2 Expression value Probablity of a read coming from isoform f

18 Model Assumptions Reads sampled independently (-> unique reads) Read sampling probability uniform over all sequences (uniform coverage) Each transcript processed independently and then sequenced

19 Model (1) Let w be total number of reads Given isoform f and region of length l in f Let X be a random variable representing the number of reads falling in that region Then X~bin(w, Θfl)

20 Coin Toss gives Binomial Dist n

21

22 Poisson Model Each gene g handled separately Exons only shared as a whole isoforms either share an exon, or they don t Let X~Poisson( ) be a random variable representing the number of reads falling in some region of interest in g

23 Poisson Model Each gene g handled separately Exons only shared as a whole isoforms either share an exon, or they don t Let X~Poisson( ) be a random variable representing the number of reads falling in some region of interest in g Then for some exon j: λ= cij is 1 if isoform i contains exon j, 0 otherwise ai is the sampling rate

24 Estimation of expression

25 Single isoform case

26 Multiple isoform case No closed-form solution available for ML if n>1 Likelihood function is concave any local maximum is also a global one Use numerical methods to find maximum Here: coordinate-wise hill climbing

27 Fisher information matrix We now have a point estimate for the expression index according to some Poisson model How reliable is the estimate? We need some confidence interval to test for DE The distribution of the estimate can be approximated with a normal distribution with mean (true parameter) and covariance (inverse Fisher information matrix)

28 Results Use RNA-seq dataset from Mortavazi et al.(2008): three mouse tissue samples with 2 replicates M reads each Mapped with SeqMap tool from the same authors to mm9 mrna annotations from mm9 RefSeq mrna database

29 Differentially expressed isoforms

30 From isoforms to gene expression: which reads to count?

31 From isoforms to gene expression Exon intersection similar to microarrays, but they can reduce statistical power as reads are not considered Exon union underestimated expression for alternatively spliced genes This paper used sum of all reads = exon union

32

33 Statistical inference Problem: Fisher information matrix is degenerated especially for isoforms with low expression Need to regularize covariance matrix Use Importance Sampling method to simulate from posterior distribution

34

35 Summary: isoform expression Isoform expression inference in RNA-seq possible using Poisson model Inferences agree with detailed inspection Exon junction reads reduce confidence interval

36 Paired-end sequencing P5 grafting forward read primer DNA insert index read primer P7 grafting index reverse read primer

39 Incorporation in the Poisson Model Model insert size using sampling rate ai

40 Overdispersion and Negative Binomial Poisson distribution (one parameter) cannot account for (high) biological variability across samples Most RNA-seq studies have not enough replicates to estimate variability using a permutation-derived approach Model variance using e.g.negative binomial distribution

41

42 Summary and Challenges Straightforward statistical model for isoform expression available However, reads are not truly random and uniform High peaks and 3 bias in read distributions Positive correlations in read distributions between tissues Isoform-level annotations not complete Most studies comprise few biological replicates

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