g A n(a, g) n(a, ḡ) = n(a) n(a, g) n(a) B n(b, g) n(a, ḡ) = n(b) n(b, g) n(b) g A,B A, B 2 RNA-seq (D) RNA mrna [3] RNA 2. 2 NGS 2 A, B NGS n(

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1 ,a) RNA-seq RNA-seq Cuffdiff, edger, DESeq Sese Jun,a) Abstract: Frequently used biological experiment technique for observing comprehensive gene expression has been changed from microarray using cdna hybridization to RNA-seq using high-throughput sequencers so called NGS, which allow us to use statistical model to analyze the changes of gene expression levels of each gene. For example, while microarrays use the brightness of the spots, RNA-seqs measure the number of fragments on each gene, giving us more quantitative values. It is also important that biological replicates are generally required, but the number of really performed experiments is limited because of reducing the experimental cost. To handle these data, several statistical methods to find genes whose expression levels are statistically changed between two different conditions have been introduced, such as Cuffdiff, edger and DESeq. We here introduce the statistical methods.. RNA-seq DNA Highthroughput sequencer Next-generation sequencer NGS [], [2] RNA-seq CBRC CBRC, AIST, Koto, Tokyo , Japan a) RNA-seq RNA-seq RNA NGS RNA, * RNA RNA RNA * HiSeq MiSeq Pacific Biosciences

2 g A n(a, g) n(a, ḡ) = n(a) n(a, g) n(a) B n(b, g) n(a, ḡ) = n(b) n(b, g) n(b) g A,B A, B 2 RNA-seq (D) RNA mrna [3] RNA 2. 2 NGS 2 A, B NGS n(a), n(b) * 2 g n(a, g), n(b, g) n(a, g) n(b, g) *2 NGS 2. n(a) g n(a, g)/n(a) n(b) n(b, g) g y = n(b, g) Y y P (Y = y) ( ) n(b) P (Y = y) = p y ( p) n(b) y y p = n(a, g)/n(a) α α 2 y = n(b, g) g P (Y = y) = λy e λ y! λ = p n(b) λ NGS g p 2.2 NGS 3 A B χ 2 = (n(i, j) E(i, j)) 2 /E(i, j) i {A,B},j {g,ḡ} 2

3 E(i, j) = (n(a, j) + n(b, j)) n(i)/(n(a) + n(b)) RNA-seq t 2 t t t 2 2 A a RNA-seq A, A 2,..., A a B b RNA-seq B, B 2,..., B b 2 t n(i, g) i g T T = Ā B ( a ). b UAB Ā = a n(a i, g), a i= B = b n(b i, g), b i= a i= U AB = (n(a i, g) Ā)2 + b i= (n(b i, g) B) 2 m + n 2 t RNA-seq RNA-seq 2 λ λ λ ([4] Figure [2] Supplemnetal Text Figure 2.) P 4 Y p r ( ) y + r P (Y = y) = p y ( p) r r Γ(x) = 0 e t t x dt x Γ(x) = (x )! P (Y = y) = Γ(y + r) Γ(r)Γ(y + ) py ( p) r pr/( p) pr/( p) 2 r λ = pr p p = λ r+λ f(y; k, r) = P (Y = y) Γ(y + r) = Γ(r)Γ(y + ) py ( p) r = λy y! Γ(y + r) Γ(r)(r + λ) r ( + λ r r r 2 3 λy lim f(y; k, r) = r y! e λ ) r 3

4 λ m g µ(g), σ(g) 2 µ(g) = pr/( p) σ(g) 2 = pr/( p) 2 p r g i s(i, g) = n(i, g)/n(i) 3.3 µ(g) σ(g) 2 f(µ(g)) edger [5], [6] DESeq [4] Cuffdiff [2] edger edger µ ϕ P (Y = y µ, ϕ) = Γ(y + ϕ ) Γ(ϕ )Γ(y + ) ( ) ϕ ( + µϕ µ ϕ + µ µ µ + ϕµ 2 ϕ DESeq DESeq i, g σ(i, g) 2 σ(i, g) 2 = µ(i, g) + t(i) 2 ν(j) µ(i, g) i g i t(i) t(i) 2 ν(j) ν(j) µ(i, g) ) y (Genelarized linear model; GLM) R limma ν(j) edger 2 Cuffdiff(Cuffdiff2) Cuffdiff DESeq GLM LOCFIT 3.4 P (Y = y) 2 DESeq Cuffdiff P ( ) P ( 2 ) ( 3 ) P ( 4 ) 2,3 ( 5 ) P α P α α 0 α ( α) 0 α ( α) 0 α = % (Family-wise error rate; FWER) α 4

5 (q-value ) α (False discovery rate; FDR) 2 FDR FWER, FDR P FWER FDR α δ P δ 4.2 RNA-seq RNA-seq [7] MA 4.3 RNA-seq RNA-seq RNA-seq RNA-seq [8] RNA-seq 5. RNA-seq [9] [] Anders, S., McCarthy, D. J., Chen, Y., Okoniewski, M., Smyth, G. K., Huber, W. and Robinson, M. D.: Count based differential expression analysis of RNA sequencing data using R and Bioconductor, Nature Protocols, Vol. 8, No. 9, pp (203). [2] Trapnell, C., Hendrickson, D. G., Sauvageau, M., Goff, L., Rinn, J. L. and Pachter, L.: Differential analysis of gene regulation at transcript resolution with RNA-seq., Nature Biotechnology, Vol. 3, No., pp (203). [3] Schwanhäusser, B., Busse, D., Li, N., Dittmar, G., Schuchhardt, J., Wolf, J., Chen, W. and Selbach, M.: Global quantification of mammalian gene expression control., Nature, Vol. 473, No. 7347, pp (20). [4] Anders, S. and Huber, W.: Differential expression analysis for sequence count data, Genome Biology, Vol., No. 0, p. R06 (200). [5] Robinson, M. D. and Smyth, G. K.: Small-sample estimation of negative binomial dispersion, with applications to SAGE data, Biostatistics, Vol. 9, No. 2, pp (2007). [6] Robinson, M. D., McCarthy, D. J. and Smyth, G. K.: edger: a Bioconductor package for differential expression analysis of digital gene expression data, Bioinformatics, Vol. 26, No., pp (2009). [7] Sun, J., Nishiyama, T., Shimizu, K. and Kadota, K.: TCC: an R package for comparing tag count data with robust normalization strategies, BMC Bioinformatics, Vol. 4, No., p. 29 (203). [8] Kharchenko, P. V., Silberstein, L. and Scadden, D. T.: Bayesian approach to single-cell differential expression analysis, Nature Methods, Vol., No. 7, pp (204). [9] Soneson, C. and Delorenzi, M.: A comparison of methods for differential expression analysis of RNA-seq data., BMC Bioinformatics, Vol. 4, No., p. 9 (203). 4.4 RNA-seq 5