Fingerprint Assembly

We now leave the world of estimates and enter that of exact results, but for model situations. The chain to be analyzed is imagined to be present as a set of cloned subchains with substantial but unknown overlap. In this section, we characterize a member of a clone by an ordered set of restriction fragments, or just a set of restriction-fragment lengths, or a set of lengths of special restriction fragments (e.g., those with certain characteristic repeats) called the fingerprint of the clone. We have, in many cases, a library of randomly chosen pieces of DNA or a section of DNA, each with a known fingerprint. Can we order these to produce a physical map of the full sequence? To examine the degree to which this is feasible (Lander and Waterman, 1988), let us first expand our notation. G will denote genome length (in base pairs, bp), L the clone length, N the number of distinct clones available, p = N/G the probability of a clone's starting at a given site, and c = LN/G = Lp the redundancy, the number of times the genome is covered by the aggregate length of all clones. In addition, and crucially, we let T be the number of base pairs two clones must have in common to declare reliably that they overlap, θ = T/L the overlap threshold ratio, and σ = 1 − θ = (L − T)/L; multiple overlap is fine.