Planning the purification process of active cDNA in expression cloning strategies

In principle, it is possible to clone the gene for any receptor that can be expressed in the Xenopus laevis frog oocyte and assayed electrophysiologically (E. S. Levitan, 1988, TINS 11, 41-43). Repeated fractionation of a lambda vector cDNA library made from mRNA which encodes the receptor protein will eventually lead to a single cDNA clone. This strategy poses the question as to how large should a lambda vector cDNA aliquot be at any fractionation stage in order that one may be relatively certain that the aliquot contains the clone of interest, and how many times should the fractionation be repeated in order that one isolate the single clone of interest? The purification of active cDNA is an iterative process. At each fractionation stage we specify the probability of at least one active cDNA in the total aliquot to be high. The required size of the aliquot taken depends upon this specified probability and the additional probability of selecting at random an individual cDNA which is active. We require an estimate of the latter probability for the initial stage. For subsequent stages Baye's estimators of these probabilities are used in the formula for calculating the aliquot size at each stage. We show how to perform this calculation when there is equal amplification of the active and remaining sequences and when the active sequence has a non-representative (unequal) amplification. When equal amplification holds a relatively simple formula is provided for calculating the expected number of stages needed in the process. When unequal amplification holds there is no simple calculation for this quantity and the entire sequence of calculations leading to termination of the process must be performed. In either case the minimum lambda vector amplification (growth) factor required at each stage to yield an adequate amount of cDNA for analysis is calculable.