Sample size determination in combinatorial chemistry.

Combinatorial chemistry is gaining wide appeal as a technique for generating molecular diversity. Among the many combinatorial protocols, the split/recombine method is quite popular and particularly efficient at generating large libraries of compounds. In this process, polymer beads are equally divided into a series of pools and each pool is treated with a unique fragment; then the beads are recombined, mixed to uniformity, and redivided equally into a new series of pools for the subsequent couplings. The deviation from the ideal equimolar distribution of the final products is assessed by a special overall relative error, which is shown to be related to the Pearson statistic. Although the split/recombine sampling scheme is quite different from those used in analysis of categorical data, the Pearson statistic is shown to still follow a chi2 distribution. This result allows us to derive the required number of beads such that, with 99% confidence, the overall relative error is controlled to be less than a pregiven tolerable limit L1. In this paper, we also discuss another criterion, which determines the required number of beads so that, with 99% confidence, all individual relative errors are controlled to be less than a pregiven tolerable limit L2 (0 < L2 < 1).

Compositional differences within and between eukaryotic genomes

Eukaryotic genome similarity relationships are inferred using sequence information derived from large aggregates of genomic sequences. Comparisons within and between species sample sequences are based on the profile of dinucleotide relative abundance values (The profile is ρ*XY = f*XY/f*Xf*Y for all XY, where f*X denotes the frequency of the nucleotide X and f*XY denotes the frequency of the dinucleotide XY, both computed from the sequence concatenated with its inverted complement). Previous studies with respect to prokaryotes and this study document that profiles of different DNA sequence samples (sample size ≥50 kb) from the same organism are generally much more similar to each other than they are to profiles from other organisms, and that closely related organisms generally have more similar profiles than do distantly related organisms. On this basis we refer to the collection {ρ*XY} as the genome signature. This paper identifies ρ*XY extremes and compares genome signature differences for a diverse range of eukaryotic species. Interpretations on the mechanisms maintaining these profile differences center on genome-wide replication, repair, DNA structures, and context-dependent mutational biases. It is also observed that mitochondrial genome signature differences between species parallel the corresponding nuclear genome signature differences despite large differences between corresponding mitochondrial and nuclear signatures. The genome signature differences also have implications for contrasts between rodents and other mammals, and between monocot and dicot plants, as well as providing evidence for similarities among fungi and the diversity of protists.