Theoretical analysis of library screening using a N-dimensional pooling strategy

A solution to the problem of library screening is analysed. We examine how to retrieve those clones that are positive for a single copy landmark from a whole library while performing only a minimum number of laboratory tests: the clones are arranged on a matrix (i.e in 2 dimensions) and pooled according to the rows and columns. A fingerprint is determined for each pool and an analysis allows selection of a list containing all the positive clones, plus a few false positives. These false positives are eliminated by using another (or several other) matrix which has to be reconfigured in a way as different as possible from the previous one. We examine the use of cubes (3 dimensions) or hypercubes of any dimension instead of matrices and analyse how to reconfigure them in order to eliminate the false positives as efficiently as possible. The advantage of the method proposed is the low number of tests required and the low number of pools that require to be prepared [only 258 pools and 282 tests (258 + 24 verifications) are needed to screen the 72,000 clones of the CEPH YAC library (1) with a sequence-tagged site]. Furthermore, this method allows easy and systematic screenings and can be applied to a large physical mapping project, which will lead to an interesting map with a low, precisely known, rate of error: when fingerprinting a 150 Mb chromosome with the CEPH YAC library and 1750 sequence-tagged sites, 903,000 tests would be necessary to obtain about 20 contigs of an average length of 6.7 Mb, while only about one false positive would be expected in the resultant map. Finally, STSs can be ordered by dividing a clone library into sublibraries (corresponding to groups of microplates for example) and testing each STS on pooled clones from each sublibrary. This allows to dedicate to each STSs a fingerprint that consists in the list of the positive pools. In many cases these fingerprints will be enough to order the STSs. Indeed if large YACs (greater than 1 Mb) can be obtained, the combined screening of DNA families and YAC DNA pools would allow an integrated construction of both genetic and physical maps of the human genome, that will also reduce the optimal number of meioses needed for a 1 centimorgan linkage map.