THE 30 NM CHROMATIN FIBER AS A FLEXIBLE POLYMER

Our analysis of the data of van den Engh, Sachs, and Trask (Science 25 7, 1410 (1992)), for the dependence of the mean square distance betwee n pairs of hybridization sites ( [L(n)(2)], mu m(2)) on the known geno mic 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 o f 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 c hromatin 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 (s imilar to 6 Mbp, 3 mu m diameter) loops of interphase chromatin attach ed to nuclear membrane sites. Using the constant (e.g., Widom, Ann. Re v. 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 (1 984); Biopolymers 27, 657 (1988)) for circular wormlike chains, we est imated the most favorable size of the small loops of the 30 nm fiber t o be 36-62 kbp with a diameter of 94-131 nm. Both the size and diamete r estimates are consistent with experimental measurements from the lit erature: 60 kbp for average loop size (van Holde, Chromatin, Ch. 7, Sp ringer-Verlag, New York 1989) and 125 nm for the diameter (Belmont et at, Chromosome 98, 129 (1989)).