Intracellular nucleosomes constrain a DNA linking number difference of-1.26 that reconciles the Lk paradox

The interplay between chromatin structure and DNA topology is a fundamental, yet elusive, regulator of genome activities. A paradigmatic case is the linking number paradox of nucleosomal DNA, which refers to the incongruence between the near two left-handed superhelical turns of DNA around the histone octamer and the DNA linking number difference (Delta Lk) stabilized by individual nucleosomes, which has been experimentally estimated to be about -1.0. Here, we analyze the DNA topology of a library of mononucleosomes inserted into small circular minichromosomes to determine the average Delta Lk restrained by individual nucleosomes in vivo. Our results indicate that most nucleosomes stabilize about -1.26 units of Delta Lk. This value balances the twist (Delta Tw approximate to + 0.2) and writhe (Delta Wr approximate to -1.5) deformations of nucleosomal DNA in terms of the equation Delta Lk = Delta Tw + Delta Wr. Our finding reconciles the existing discrepancy between theoretical and observed measurement of the Delta Lk constrained by nucleosomes.