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PoolingDesigns - Computational Molecular Biology Group...

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Computational Molecular Biology Group Testing – Pooling Designs
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My T. Thai [email protected] 2 Group Testing (GT) Definition : Given n items with at most d positive ones Identify all positive ones by the minimum number of tests Each test is on a subset of items Positive test outcome : there exists a positive item in the subset
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My T. Thai [email protected] 3 An Idea of GT _ _ _ _ _ _ _ + Positive Negative + _ _ _ _ _ _ _ _ _
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My T. Thai [email protected] 4 Example 1 Sequential Method  1  2  3  4   5   6  7  8  9 1  2  3   4   5     4      5
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My T. Thai [email protected] 5 Example 2 – Non-adaptive Method P 4 p p 6 p 1 1 2 3 p 2 4 5 6 p 3 7 8 9 Non-adaptive group testing is called pooling  design in biology
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My T. Thai [email protected] 6 Sequential and Non-adaptive Sequential GT needs less number of tests, but longer time. Non-adaptive GT needs more tests, but shorter time. In molecular biology, non-adaptive GT is usually taken. Why ?
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My T. Thai [email protected] 7 Because… The same library is screened with many different probes. It is expensive to prepare a pool for testing first time. Once a pool is prepared, it can be screened many times with different probes. Screening one pool at a time is expensive. Screening pools in parallel with same probe is cheaper. There are constrains on pool sizes. If a pool contains too many different clones, then positive pools can become too dilute and could be mislabeled as negative pools.
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My T. Thai [email protected] 8 Pooling Designs Problem Definition Given a set of n clones with at most d positive clones Identify all positive clones with the minimum number of tests Pool : a subset of clones Positive pool : a pool contains at least one positive clone Clones = Items
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My T. Thai [email protected] 9 Relation to Pooling Designs clones c 1 c 2 c c n p 1 0 0 … 0 … 0 … 0 … 0 0 p 2 0 1 … 0 … 0 … 0 … 0 1 pools . . . . p i 0 0 … 0 … 1 … 0 … 0 1 . . . . p t 0 0 … 0 … 0 … 0 … 0 0 t x n t x 1 M[ i, j ] = 1 iff the i th pool contains the j th clone Decoding Algorithm : Given M and V , identify all positive clones Testing V M t x n  =
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My T. Thai [email protected] 10 Observation clones c 1 c 2 c 3 c j p 1 1 1 1 0 0 0 0 0
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