SAMPLE-SIZE DETERMINATION IN COMBINATORIAL CHEMISTRY

Combinatorial chemistry is gaining wide appeal as a technique for gene rating molecular diversity, Among the many combinatorial protocols, th e split/recombine method is quite popular and particularly efficient a t generating large libraries of compounds. In this process, polymer be ads are equally divided into a series of pools and each pool is treate d with a unique fragment; then the beads are recombined, mixed to unif ormity, and redivided equally into a new series of pools for the subse quent couplings, The deviation from the ideal equimolar distribution o f the final products is assessed by a special overall relative error, which is shown to be related to the Pearson statistic, Although the sp lit/recombine sampling scheme is quite different from those used in an alysis of categorical data, the Pearson statistic is shown to still fo llow a chi(2) distribution, This result allows us to derive the requir ed number of beads such that, with 99% confidence, the overall relativ e error is controlled to be less than a pregiven tolerable limit L(1), In this paper, we also discuss another criterion, which determines th e required number of beads so that, with 99% confidence, all individua l relative errors are controlled to be less than a pregiven tolerable limit L(2) (0 < L(2) < 1.).