In their efforts to define the rules for nucleosome positioning on DNA, Lowary and Widom obtained a library of 5 × 10¹² DNA molecules, each with a different randomized sequence. All of the molecules were assembled from three synthesized segments of 72, 76, and 72 bp each, with two different 6 bp linkers that contained restriction sites. Each molecule was flanked by short segments of DNA that served as targets for PCR amplification. The total length of all the random DNA segments was 220 bp. The entire library was PCR-amplified to increase the total amount of DNA. Then, histone octamers were mixed with the DNA, in a ratio of 10 DNA molecules per histone octamer. The nucleosome-DNA complexes were isolated after dialysis into a relatively high concentration of salt, the bound DNA was amplified by PCR, and the procedure was repeated. The same cycle was repeated 12 to 15 times, and eventually the bound DNAs that came through the selection were cloned and sequenced to determine which DNA sequences bound most tightly to nucleosomes. This led to a series of nucleosome positioning rules. For example, the dinucleotide TA tended to appear at 10- or 20-nucleotide intervals in sequences that were strongly bound by nucleosomes.