1. Iterative resolution of multi-reads in multiple genomes
Main source for Background Material, slide backgrounds: Eran Halperin's Accurate Estimation of Expression Levels of Homologous Genes In RNA-Seq Experiments

2. 2
SeqEm – Eran Halperin
1/12/11

3. Microarrays: Known Issues3
Background hybridization
Genes with low expression levels
Different hybridization properties
Relative expression levels
Limited set of probes
SeqEm – Eran Halperin
1/12/11

4. RNA-Seq Procedure 4
Isolate Total RNA (e.g. by poly(A) binding), Sequence short reads (25-40bp)
Map to reference genome (Eland, MAQ, BWA, Bowtie, etc.)
QC, Splice Variants, etc.
Estimate concentration of mRNA in sample
Statistics/Analysis
SeqEm – Eran Halperin
1/12/11

5. 5
SeqEm – Eran Halperin
1/12/11

6. Homologous Genes 6
SeqEm – Eran Halperin
1/12/11

7. 7 SeqEm – Eran Halperin 1/12/11 7
SeqEm – Eran Halperin
1/12/11

8. MULTIREADS - Current Standard8
Discard
Uniformly distribute
Map according to unique read distribution (Erange)
SeqEm – Eran Halperin
1/12/11

9. Generative Model + Algorithm9
Notation:
G = (G1, G2, , Gn)
P = (P1, P2, , Pn); ΣPi = 1
R = (r1, r2, , rm)
Model for RNA-Seq:
Choose Gi from distribution P
Generate short reads: copy (with errors) a random substring of G
SeqEm – Eran Halperin
1/12/11

10. SeqEm 10 R G P1 P2 P3
SeqEm – Eran Halperin
1/12/11

11. SeqEm: Problem 1 11
SeqEm – Eran Halperin
1/12/11

12. SeqEm: Likelihood 12
SeqEm – Eran Halperin
1/12/11

13. 13 SeqEm – Eran Halperin 1/12/11
Problem shown to be concave – EM converges to global maximum 13
SeqEm – Eran Halperin
1/12/11

14. 1/12/11 14
SeqEm – Eran Halperin

15. MGMR motivation
Cartoon:

16. MGMR intution
-Assume same gene structures
-Most expression levels expected to be similar...

17. New Generative Model Notation: Model for RNA-Seq:
G = (G_1, G_2, , G_M) genes
S = (S_1, S_2, , S_N) samples (i.e., genomes)
P = (P_11, P_12, , P_MN); for each sample, Σ(genes)P = 1
For i-th sample, R = (r_1, r_2, , r_Ri)
Model for RNA-Seq:
Sample vector of Ps from Dirichlet distribution
Ps define probability of sampling each gene
Generate short reads: copy (with errors) a random substring of G

19. Why Dirichlet?
Distribution's parameters (alphas) define distributions of multinomials (e.g., P_iks you draw)
Conjugate prior of multinomial distribution – i.e., Mult(x|Θ)Dir(Θ|α)~Dir(x+α)

20. Dirichlet distribution
Spend time here because gives intuition and next comes math
-point out that each point is prob mass function – sums to one and all pos
-colors rep values of pdf
-explain gamma is factorial of n-1, explain where it should be high/low in each case and why
- right side is points drawn from this distribution in each case

23. Estimating alpha given P

24. Project status
Current status: math done (I hope!), coding...
Plans:
Simulation - small in silico genomes having known percent of homologs, differential expression
Compare results of method to discarding reads, uniform assignment, weighted assignment
Test on real data
Sanity check: multiple lanes of same subject
Population studies – e.g genomes project
Issue: do more mixed pools lead to less accuracy?
Deal with SNPs, transcripts instead of genes
Your suggestions...