title: On the consistency of a physical mapping method to reconstruct a chromosome in vitro.
abstract: During recent years considerable effort has been invested in creating physical maps for a variety of organisms as part of the Human Genome Project and in creating various methods for physical mapping. The statistical consistency of a physical mapping method to reconstruct a chromosome, however, has not been investigated. In this paper, we first establish that a model of physical mapping by binary fingerprinting of DNA fragments is identifiable using the key assumption-for a large randomly generated recombinant DNA library, there exists a staircase of DNA fragments across the chromosomal region of interest. Then we briefly introduce epi-convergence theory of variational analysis and transform the physical mapping problem into a constrained stochastic optimization problem. By doing so, we prove epi-convergence of the physical mapping model and epi-convergence of the physical mapping method. Combining the identifiability of our physical mapping model and the epi-convergence of a physical mapping method, finally we establish strong consistency of a physical mapping method.
authors.affiliation: Department of Mathematics and Molecular Biology, University of Southern California, Los Angeles 90089, USA.
authors.forename: M
authors.initials: M
authors.lastname: Xiong
authors.forename: H J
authors.initials: HJ
authors.lastname: Chen
authors.forename: R A
authors.initials: RA
authors.lastname: Prade
authors.forename: Y
authors.initials: Y
authors.lastname: Wang
authors.forename: J
authors.initials: J
authors.lastname: Griffith
authors.forename: W E
authors.initials: WE
authors.lastname: Timberlake
authors.forename: J
authors.initials: J
authors.lastname: Arnold
mesh_terms: D001233:Aspergillus nidulans / Q000235:genetics; D002874:Chromosome Mapping / Q000379:methods* / Q000706:statistics & numerical data; D015825:Chromosomes, Fungal / Q000235:genetics; D003001:Cloning, Molecular; D016172:DNA Fingerprinting / Q000379:methods; D015723:Gene Library; D016045:Human Genome Project; D006801:Humans; D008433:Mathematics; D008957:Models, Genetic; D015335:Molecular Probes; D013269:Stochastic Processes
chemical_list: D015335:Molecular Probes