Theoretical study of the fraction of a long‐chain DNA that can be incorporated in a recombinant DNA partial‐digest library

Experimental evidence indicates that the cleavage sites for site‐specific DNA cleavage enzymes are randomly distributed throughout the DNA polymer [Botchan et al. (1973) Cold Spring Harbor Symp. Quantum Biol. 38 , 383–395; Hamer and Thomas (1973) Chromosoma 49 , 243–267]. Using this information we derive equations for the probability that a DNA base pair chosen at random can be found within the population of enzymatically generated partial cleavage products whose lengths fall between L + 1 and L + r base pairs. The results describe the fraction of a long‐chain DNA that can be incorporated in a recombinant DNA partial digest library. The weight‐fraction distribution of Kuhn (1930) is a special case of the distribution derived here.