Derivation of a mathematical expression useful for the construction of complete genomic libraries

We present and derive a formula that is useful for the design and evaluation of gene cloning experiments in which a complete gene library of the entire genome of an organism is desired. The formula n = ln(1-phi f)/ln(1-f) (in which n is the number of recombinant clones required to ensure a probability, phi, of obtaining at least one of each of all possible gene sequences, and f is the fraction of the genome contained in an average-sized DNA fragment) applies to construction of libraries, in which at least one copy of all the genetic information of a genome is required. The use of this formula for quantitative evaluation of genomic libraries should give greater assurance that a given library would be complete.