1. LECTURE 2
Splicing graphs /
Annoteted transcript expression estimation

3. Transcriptomics Study of RNA biology gene genome
Transcription, alternative splicing
1203x
87x
How to measure these?
234x

4. RNA-seq split read alignment
gene
genome
More on this on Thursday
study group
align …

5. Splicing graph We’ll study this problem next week 220
Find paths that best explain the graph, e.g:
1203x
1511
1198
1303
1603
1508
1380
1597
87x
234x 95

6. Annotated transcript expression estimation
220
Assume we know the possible transcripts but their relative abundancies are unknown a b c ?x
1511
1198
1303
1603
1508
1380
1597 ?x ?x 95
(1603-(a+b+c))2+(95-b) 2 +(1511-(a+c)) 2 +
(1508-(a+c)) 2 +(220-c) 2 +(1198-a) 2 +(1380-(a+b)) 2 +
(1303-(a+b)) 2 +(1597-(a+b+c)) 2
f(a,b,c)=
Least squares problem:
Minimize

7. Least squares problem
f(a,b,c) receives minimum when all partial derivates of f are zero.
f’a(a,b,c) = 2(a+b+c-1603)+ 2(a+c-1511) +
2(a+c-1508) + 2(a-1198) + 2(a+b-1380) +
2(a+b-1303) + 2(a+b+c-1597)
f’b(a,b,c) = 2(a+b+c-1603)+ 2(b-95) +2(a+b-1380) +
2(a+b-1303) + 2(a+b+c-1597)
f’c(a,b,c) = 2(a+b+c-1603) + 2(a+c-1511) +
2(a+c-1508) + 2(c-220) + 2(a+b+c-1597)
Google: linear equations solver, click first link, copy-paste,
click ”solve the system”, copy-paste the result
7a+4b+4c=10100
4a+5b+2c=5978
4a+2b+5c=6439
This system has a unique solution, which is
{ a = 21032/17, b = 5260/51, c = 13097/51 }.

8. Solution
220 a
1237 x
1511
1198
1303
1603
1508
1380
1597 b
103 x c
257 x 95

9. Without annotation 2n possible transcripts for a gene with n exons
Solve least squares for each combination of possible transcripts and select the combination with best solution
22n combinations to consider
In the next week Thursday study group we study an algorithm solving the same problem in polynomial time!
Before that we study an easier problem, where the goal is just to predict transcripts, not their expression levels

10. Study group this Thursday
An algorithm for split-read alignment
Input: Maximal exact matches between genome and RNA- sequencing read
E.g. ACGATCATCGCT vs. ACGAGATCCGCTAGT
Such alignment anchors can be computed efficiently using methods from Biological Sequence Analysis course

11. Study group this Thursday
Output: Consistent split-read alignment covering maximally the initial local alignments
Exon 1
Exon 2
Exon 3