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 (∆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 ∆Lk restrained by individual nucleosomes in vivo. Our results indicate that most nucleosomes stabilize about −1.26 units of ∆Lk. This value balances the twist (∆Tw ≈ + 0.2) and writhe (∆Wr ≈ −1.5) deformations of nucleosomal DNA in terms of the equation ∆Lk = ∆Tw + ∆Wr. Our finding reconciles the existing discrepancy between theoretical and observed measurement of the ΔLk constrained by nucleosomes.