Yaniv Erlich Hannon Lab

1. Compressed Genotyping YanivErlich Hannon Lab Cold Spring Harbor Laboratory erlich@cshl.edu

2. Poster in a nutshell • Genotyping is the process of determining the genetic variation for a certain trait in an individual. • It is one of the main diagnostic tools in medical genetics • - Finding carriers for rare genetic diseases such as Cystic Fibrosis • - Tissue matching in organ donation • - Forensic DNA analysis • Until now - only serial genotyping is possible. This is expensive and tedious. • Taking advantage on the ‘signal sparsity’, we developed and tested a compressed genotyping framework.

3. Abstract Significant volumes of knowledge have been accumulated in recent years linking subtle genetic variations to a wide variety of medical disorders from cystic fibrosis to mental retardation. Nevertheless, there are still great challenges in applying this knowledge routinely in the clinic, largely due to the relatively tedious and expensive process of DNA sequencing. Since the genetic polymorphisms that underlie these disorders are relatively rare in the human population, the presence or absence of a disease-linked polymorphism can be thought of as a sparse signal. Using methods and ideas from compressed sensing and group testing, we have developed a cost-effective reconstruction protocol, called "DNA Sudoku", to retrieve useful data. In particular, we have adapted our scheme to a recently developed class of high throughput DNA sequencing technologies, and assembled a mathematical framework that has some important distinctions from 'traditional' compressed sensing ideas in order to address different biological and technical constraints. erlich@cshl.edu

4. The genotyping problem Input: Thousands of specimens Output: Genotype of each specimen Genotype

5. Genotyping as a sparse graph reconstruction • An example of carrier screen for Cystic Fibrosis. There are two allele nodes, the Wild Type (WT) and the and the Cystic Fibrosis mutation. Samples 1, 2, 3, 5 are WT, while specimen 4 is a carrier. The specimen labeled with ’X’ is affected and does not enter to the screen. Genotyping is equivalent of finding the edges in the graph. • THE GRAPH IS SPARSE • Number of carriers is very low • No affected individuals • The degree of every sample node is always two (human genome is diploid) Genotyping is equivalent to reveal the edges of the bipartite graph Samples Alleles

6. The main idea – pooled processing One could reveal the graph edges by DNA sequence each sample - expensive, tedious, and slow Better: Pool the samples and then sequence the pools erlich@cshl.edu

7. Mathematically speaking Allele • 0 2 • 0 2 • 0 2 • 1 • 0 2 Specimen Allele 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 7 1 5 0 6 Specimen Pool Pool What the observer sees The pooling design A binary matrix (‘1’ – in the pool, ‘0’ – otherwise) The biadjacency matrix of the graph What the observer wants erlich@cshl.edu

8. What is a good pooling design Trivial compressed sensing demands Biological oriented requirements We need a light-weight d-disjunct matrix

9. Light Chinese Design • Inputs:N (number of specimens) • Column Weight (robotics efforts) • Algorithm: • 1. Find W numbers {x1,x2,…,xw} such that: • Bigger than • Pairwise coprime • 2. Generate W modular equations: • 3. Construct the pooling matrix upon the modular equations • Output: Pooling matrix The algorithm reaches the bound derived by Kautz & Singleton (1964)

10. Example of a pooling matrix

11. Decoding the genotyping results by Belief Propagation Specimens Pools A-priori biological information Genotyping results The pooled results can be decoded as using Belief Propagation

12. Example of Belief Propagation 2. I can’t be B 1.You can be either A, C, or D Specimens #1 Pools A B C D A C D #2 A B C D B C A #3 A B C D A B C D Possible genotypes: A B C D #4 A B C 3.Specimen #3, #6 and #7: One of you guys should be B #5 A B C D A B C D A B C D #6 B D C #7 A B C D Specimen is in a pool A B C D 03/06/09

13. Simulation results 1000 specimens W = 5 Total pools = 180 Number of carriers

14. Real results – biotechnology application 40,000 specimens W = 5 Total pools = 1900

15. Work in progress

16. References & Acknowledgments • Compressed Genotyping. Yaniv Erlich, Assaf Gordon, Michael Brand, Gregory J. Hannon & Partha P. Mitra. Submitted to IEEE Trans. Info. Theory. 2009. • DNA Sudoku - harnessing high-throughput sequencing for multiplexed specimen analysis. Yaniv Erlich, Kenneth Chang, Assaf Gordon, Roy Ronen, Oron Navon, Michelle Rooks & Gregory J. Hannon. Genome Research. 2009. Lindsay-Goldberg Fellowship