THE 30 NM CHROMATIN FIBER AS A FLEXIBLE POLYMER

Our analysis of the data of van den Engh, Sachs, and Trask (Science 257, 1410 (1992)), for the dependence of the mean square distance between pairs of hybridization sites ( [L(n)(2)], mu m(2)) on the known genomic distance (n, bp) separating these sites on chromosome number 4 in G1 human fibroblast nuclei, shows that [L(n)(2)] is proportional to n(2y) with v = 3/5 for n < 1 Mbp. The v-value of 3/5 is characteristic of flexible polymer chains with excluded volume effects in dilute good solutions. Since the DNA concentration in nuclei is very high(ca. 1-10 mg/ml), and theory (Flory, J. Chem. Phys. 17, 303, 1949) predicts v = 1/2 for overlapping polymers, the finding of v = 3/5 means that the chromatin fibers do not overlap in interphase nuclei. The dependence of [L(n)(2)] On n for n < 4 Mbp is consistent with the model of large (similar to 6 Mbp, 3 mu m diameter) loops of interphase chromatin attached to nuclear membrane sites. Using the constant (e.g., Widom, Ann. Rev. Biophys. Biophys. Chem. 18, 365 (1989)) and variable (Williams and Langmore, Biophys. J. 59, 606 (1991)) diameter fiber models, the Kuhn statistical segment of the 30 nm chromatin fiber was estimated to have a length of 196-272 nm with a corresponding DNA content of 21-37 kbp. Based on the model of Shimada and Yamakawa (Macromolecules 17, 689 (1984); Biopolymers 27, 657 (1988)) for circular wormlike chains, we estimated the most favorable size of the small loops of the 30 nm fiber to be 36-62 kbp with a diameter of 94-131 nm. Both the size and diameter estimates are consistent with experimental measurements from the literature: 60 kbp for average loop size (van Holde, Chromatin, Ch. 7, Springer-Verlag, New York 1989) and 125 nm for the diameter (Belmont et at, Chromosome 98, 129 (1989)).