Most combinatorial libraries are 'sparse' in that only a tiny fraction
of the relevant class of compounds is represented. This sparseness ca
n be compensated in some measure by alternating rounds of selection wi
th rounds of mutagenesis. Thus, clones are selected from the initial l
ibrary by some criterion of 'fitness', such as affinity for a particul
ar receptor. The selected clones are then mutagenized to generate a mu
tant library, which serves as input to the next round of selection, an
d so on. If the first round of selection is too stringent, rejecting a
ll but the very fittest clone in the initial library (the 'initial cha
mpion'), we might miss 'dark horses': clones in the initial library th
at are inferior to the initial champion, yet can be mutated to even hi
gher fitness than can that champion. A more thoughtful strategy is to
alternate nonstringent selection with simultaneous mutagenesis of many
selected clones en masse.