Recent observations suggest that the basic supranucleosomal structure of chromatin is a zigzag helical ribbon with a repeat unit made of two nucleosomes connected by a relaxed spacer DNA. A remarkable feature of one particular ribbon is that it solves the apparent paradox between the number of DNA turns per nucleosome and the total linking number of a nucleosome-containing closed circular DNA molecule. We show here that the repeat unit of the proposed structure, which contains two nucleosomes with -13/4 DNA turns per nucleosome and one spacer crossover per repeat, contributes -2 to the linking number of closed circular DNA. Space-filling models show that the cylindrical 250-A chromatin fiber can be generated by twisting the ribbon.It is now well-established that the unit structure of chromatin, the nucleosome (1-3), is a flat cylindrical particle (110 X 110 x 57 A) with DNA wrapped around a histone octamer in a lefthanded toroidal supercoil of approximately 80 base pairs (bp) per turn (4). There are 146 bp of DNA in the nucleosome core describing -13/4 superhelical turns (5) and 20-95 bp of spacer DNA between neighboring nucleosome cores (6).The nature of the supranucleosomal structure of chromatin is less clear. Electron microscopic studies of eukaryotic nuclei have revealed a "thin" 100-A chromatin fiber and a "thick" 250-A fiber (7-9). Many past models have assumed that neighboring nucleosomes are stacked side by side to generate a 100-A nucleofilament, which is further coiled into a 250-A "solenoid" (10, 11). The unstacked 100-A fiber ("beads on a string") can be readily observed in nuclei and chromatin preparations spread under isotonic conditions (1, 2, 12). A stacked 100-A nucleofilament also has been detected, but only at high salt concentrations (11). Although the 100-A fiber is present in histone Hi-depleted chromatin, the 250-A fiber is never observed under these conditions (11, 12). Thus, histone HI must play a role in the further compaction of the linear chain of beads (12, 13). Reconstitution studies with the four intranucleosomal histones and small circular DNAs in the presence of nicking-closing enzyme have revealed that the DNA coiling around a nucleosome changes the DNA linking number by -1 (14). The histone Hl-induced compaction of the "beads on a string" into a 250-A-diameter supranucleosomal structure (15) does not cause further changes in the linking number (16). Because the nicking-closing enzyme relaxes the spacer DNA (16), the observed change in the linking number must be due to the particular DNA structure in the nucleosome.The linking number L of a closed circular DNA (ccDNA) molecule is the number of topological revolutions made by one strand about the other [counted after the molecule is constrained to lie in a plane (17)]. L is a topological invariant (i.e., an integer which is unchanged by all deformations that leave the strands intact). Moreover, it is related to the writhing number W and the twist number T by the equation (18-21)W is a real number that measures the shape...