Watson School of Biological Sciences Cold Spring Harbor Laboratory Watson School of Biological Sciences Cold Spring Harbor Laboratory Yaniv Erlich Compressed Sensing Approaches for High Throughput Carrier Screen Joint work with Noam Shental, Amnon Amir and Or Zuk

Outline What is a carrier screen? Our vision - compressed sensing carrier screen Unique features of our setting Bayesian reconstruction algorithm Simulations Intro - carrier screensCS visionUnique featuresBP solverSimulations Compressed sensing carrier screen

Rare recessive genetic diseases Normal Carrier Affected Healthy Healthy! Disease NameGenotypePhenotype Intro - carrier screens CS visionUnique featuresBP solverSimulations Compressed sensing carrier screen ~29/30 ~1/ % Cystic Fibrosis

Carrier breading may lead to devastating results AffectedCarrier 1:21:4 No Carrier 1:4 Intro - carrier screens CS visionUnique featuresBP solverSimulations Carrier couple Compressed sensing carrier screen

What can we do? Several countries employ nationwide programs - screen the bulk population - very limited set of genes Intro - carrier screens CS visionUnique featuresBP solverSimulations Compressed sensing carrier screen

Carrier screen - the current mechanism Input: Thousands of specimens. Output: Finding carriers for rare genetic diseases A needle in a haystack problem Intro - carrier screens CS visionUnique featuresBP solverSimulations Serial processing: - sequence: 1 region of 1 person per reaction - expensive and does not scale Compressed sensing carrier screen

Carrier screens - our vision Ultra-high throughput carrier screen Many specimens + many regions Adding more genes to the test panel while keeping the task in a tractable scale Increase the participation by reducing the cost Intro - carrier screens CS vision Unique featuresBP solverSimulations Compressed sensing carrier screen

BUT On pooled samples - only histogram of the DNA sequence type. How to multiplex many specimens with next generation sequencers? Next generation sequencers – parallel processing Sequence 100 million DNA molecules in a single batch (~1 week) Fraction of reads Example: When pooling 4 normal specimens and 1 carrier WT allele Mutant Intro - carrier screens CS vision Unique featuresBP solverSimulations Compressed sensing carrier screen

Multiplexing - the compressed sensing approach y = Φx CS principle: when x is sparse, very few measurements are sufficient for faithful reconstruction. X N carrier = Φ T pools y Pooling design 0-1 matrix The ratio of carrier reads Intro - carrier screens CS vision Unique featuresBP solverSimulations Compressed sensing carrier screen

Distinctions from traditional CS ‘On a budget’ compressed sensing Not all pools were born equal Signal domain Intro - carrier screensCS vision Unique features BP solverSimulations Compressed sensing carrier screen

Distinctions from traditional CS ‘On a budget’ compressed sensing Not all pools were born equal Signal domain Intro - carrier screensCS vision Unique features BP solverSimulations Compressed sensing carrier screen

On a budget compressed sensing Heavy weight design requires long pooling steps and higher material consumption Higher compression level is more prone to technical difficulties We want a very sparse sensing matrix Specimens (N) Pools (t) Φ=Φ= Weight (w) Compression level Random matrix with p=0.5 Intro - carrier screensCS vision Unique features BP solverSimulations Compressed sensing carrier screen

Inputs: N (number of specimens in the experiment) Weight (pooling efforts) Algorithm: 1. Find W numbers {x 1,x 2,…,x w } such that: (a)Bigger than (b)Pairwise coprime 2. Generate W modular equations: 3. Construct the pooling design upon the modular equations Output: Sparse pooling design with Light Chinese Design Advantages: (w-1)-disjunct matrix The weight does not explicitly depend on the number of specimens The compression level is Easy to debug mod 6 mod 7 Intro - carrier screensCS vision Unique features BP solverSimulations Compressed sensing carrier screen

Distinctions from traditional CS ‘On a budget’ compressed sensing Not all pools were born equal Signal domain Intro - carrier screensCS vision Unique features BP solverSimulations Compressed sensing carrier screen

Not all pools were born equal The sequencer does not report the absolute number of carriers in the pool Instead: # carrier reads ~ # total sequence reads Fraction of carriers in the pool / 2 Pools with ↑sequence reads and ↓carriers provide more reliable information. The noise is not additive but with correlation to the content of the pool. We need a reconstruction algorithm that takes into account the reliability of the data from each pool. Intro - carrier screensCS vision Unique features BP solverSimulations Compressed sensing carrier screen

Distinctions from traditional CS ‘On a budget’ compressed sensing Not all pools were born equal Signal domain Intro - carrier screensCS vision Unique features BP solverSimulations Compressed sensing carrier screen

Signal Domain In traditional CS: In compressed carrier screen: Traditional CS decoder solves: What are the implications of using traditional decoder and employing rounding procedure? Can we find reconstruction procedure that directly finds Intro - carrier screensCS vision Unique features BP solverSimulations Compressed sensing carrier screen

Bayesian reconstruction algorithm Biological expectations Pooling model and sequencing Biologically, the genotype of one specimen is not dependent on the genotype of other one (unless relatives) Only the specimens in the pool are affecting the pool results Biological data Pooling data Approximation by loopy Belief Propagation… Φ Intro - carrier screensCS visionUnique features BP solver Simulations Compressed sensing carrier screen

Advantages of Belief Propagation Bottom up approach – weighs the reliability of each individual pool Bayesian – everything speaks the same language. Can incorporate a-priori medical information and familial connections. Encoding advantage – Chinese pooling ensures that there are no short cycles Binary results directly – no rounding procedure at the end Biological data Pooling data Intro - carrier screensCS visionUnique features BP solver Simulations Compressed sensing carrier screen

Simulations of compressed carrier screen in Ashkenazi Jews Genetic DisorderCarrier rate Tay-Sachs1:25 Cystic Fibrosis1:30 Familial Dysautonomia1:30 Usher Syndrome1:40 Canavan 1:40 Glycogen Storage 1:71 Fanconi Anemia C 1:80 Niemann-Pick 1:80 Mucolipidosis type 4 1:100 Bloom1:102 Nemaline Myopathay1:108 Finding carriers for two Ashkenazi Jews diseases: Tay-Sachs and Bloom syndrome. Chinese pooling design Comparing GPSR (traditional solver) and BP Evaluating N max – the largest number of specimens for which at least 48 out of 50 runs give 100% accuracy. Intro - carrier screensCS visionUnique featuresBP solver Simulations Compressed sensing carrier screen

Results Bloom Tay-Sachs BP GPSR Pools/Specimen = 6.5% Pools/Specimens= 13% Intro - carrier screensCS visionUnique featuresBP solver Simulations Compressed sensing carrier screen

Conclusions CS framework can be utilized for ultra-high throughput carrier screens. Our setting shows several unique features not in traditional framework - We suggest tailored encoding (light Chinese) and decoding (BP) procedures At least in our settings: a tailor decoder, BP, has an advantage over reconstructing with off-the shelf CS solver CS carrier screen has the potential to reduce dramatically the cost of sequencing. Intro - carrier screensCS visionUnique featuresBP solver Simulations Compressed sensing carrier screen

An ongoing study… Introduct ion Naïve Solutions Chinese Pooling AnalysisResults Intro - carrier screensCS visionUnique featuresBP solver Simulations The real thing Compressed sensing carrier screen

Greg Hannon Acknowledgements For more information: hannonlab.cshl.edu/labmembers/erlich hannonlab.cshl.edu/labmembers/erlich Noam Shental Or Zuk & Amnon Amir Igor Carron (Nuit Blanche) Funding: Lindsay Goldberg PhD Fellowship ACM/IEEE-CS HPC PhD Fellowship Compressed sensing carrier screen

Loopy belief propagation is tricky Damping is the key DNA Sudoku

Pooling imperfections Background contamination Pooling failures (erasures) mod 377 Data from a real experiment  Pools not in use  Pools # Reads Intro - carrier screensCS vision Unique features BP solverSimulations

Distinctions from traditional CS ‘On a budget’ compressed sensing Not all pools were born equal Pooling imperfections Signal domain Intro - carrier screensCS vision Unique features BP solverSimulations

Distinctions from traditional CS ‘On a budget’ compressed sensing Not all pools were born equal Pooling imperfections Signal domain Intro - carrier screensCS vision Unique features BP solverSimulations

Distinctions from traditional CS ‘On a budget’ compressed sensing Not all pools were born equal Pooling imperfections Signal domain Intro - carrier screensCS vision Unique features BP solverSimulations

Distinctions from traditional CS ‘On a budget’ compressed sensing Not all pools were born equal Pooling imperfections Signal domain Intro - carrier screensCS vision Unique features BP solverSimulations

Distinctions from traditional CS ‘On a budget’ compressed sensing Not all pools were born equal Pooling imperfections Signal domain Intro - carrier screensCS vision Unique features BP solverSimulations