inhibitors_Hwang - JOURNAL OF COMPUTATIONAL BIOLOGY Volume...

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JOURNAL OF COMPUTATIONAL BIOLOGY Volume 10, Number 2, 2003 © Mary Ann Liebert, Inc. Pp. 231–236 Error-Tolerant Pooling Designs with Inhibitors F.K. HWANG and Y.C. LIU ABSTRACT Pooling designs are used in clone library screening to efŽ ciently distinguish positive clones from negative clones. Mathematically, a pooling design is just a nonadaptive group testing scheme which has been extensively studied in the literature. In some applications, there is a third category of clones called “inhibitors” whose effect is to neutralize positives. SpeciŽ cally, the presence of an inhibitor in a pool dictates a negative outcome even though positives are present. Sequential group testing schemes, which can be modiŽ ed to three-stage schemes, have been proposed for the inhibitor model, but it is unknown whether a pooling design (a one-stage scheme) exists. Another open question raised in the literature is whether the inhibitor model can treat unreliable pool outcomes. In this paper, we answer both open prob- lems by giving a pooling design, as well as a two-stage scheme, for the inhibitor model with unreliable outcomes. The number of pools required by our schemes are quite comparable to the three-stage scheme. Key words: nonadaptive group testing, inhibitors, error-tolerant. 1. INTRODUCTION S equencing a set of clones often relies on identifying the clones which contain a given probe. For examples, in physical mapping, the probe can be a sequence-tagged site which is a unique subsequence in the target sequence. The identiŽ cation of a clone containing this probe essentially locates the clone. In a DNA array, a probe is a given l -tuple and a positive identiŽ cation conŽ rms the existence of such an l -tuple in the target sequence. We will assume that the setting is in the Ž rst application, namely, to identify which clones in the given set contain the probe. A clone is called a positive if it contains the probe, and a negative if not. A pool is a subset of clones put together for a joint assay with two possible outcomes: a negative pool signiŽ es that there’s no positive in the pool, a positive pool signiŽ es otherwise, namely, that there is at least one positive in the pool. A pooling design is a 0-1 matrix where the columns are the set of clones, the rows are the set of pools, and a 1-entry in cell .i; j/ signiŽ es that clone j is in pool i . In some biological applications, there is a third category of clones called inhibitors whose presence in a pool dictates a negative outcome, regardless of the presence of a positive in the pool. While the pooling design corresponds to the classical nonadaptive group testing problem (Du and Hwang, 2000), the presence of inhibitors presents a new group testing model not considered in the group testing literature. Farach
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inhibitors_Hwang - JOURNAL OF COMPUTATIONAL BIOLOGY Volume...

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