On Cloning and Clone Libraries for Finite and Infinite Length Genomes

This paper develops mathematical theory to determine the representativeness of clone libraries for various models, defined below in the text. In particular, the means and variances of fragment lengths and the mean of the length of a randomly selected fragment are determined, as well as the probability of the event that a particular base pair of a given double-stranded DNA sequence is clonable. Further, some results are given for partial digestion where the digest is stopped before all cuts are made. A summary is given comparing the main biological conclusions from assuming that the length of the genome is (effectively) infinite with the corresponding conclusions from the more realistic assumption that the genome is of finite length.