ON THE CONSISTENCY OF A PHYSICAL MAPPING METHOD TO RECONSTRUCT A CHROMOSOME IN-VITRO

During recent years considerable effort has been invested in creating physical maps for a variety of organisms as part of the Human Genome P roject and in creating various methods for physical mapping. The stati stical consistency of a physical mapping method to reconstruct a chrom osome, however, has not been investigated. In this paper, we first est ablish that a model of physical mapping by binary fingerprinting of DN A fragments is identifiable using the key assumption-for a large rando mly 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 optimizati on problem. By doing so, we prove epi-convergence of the physical mapp ing model and epi-convergence of the physical mapping method. Combinin g the identifiability of our physical mapping model and the epi-conver gence of a physical mapping method, finally we establish strong consis tency of a physical mapping method.