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We discuss recent observations of polymorphic chromatin packaging at the oligonucleosomal level and compare them with computer simulations. Our computations reveal two topologically different families of two-start 30-nm fiber conformations distinguished by the linker length L; fibers with L ≈ 10n and L ≈ 10n+5 basepairs have DNA linking numbers per nucleosome of ΔLk ≈ −1.5 and −1.0, respectively (where n is a natural number). Although fibers with ΔLk ≈ −1.5 were observed earlier, the topoisomer with ΔLk ≈ −1.0 is novel. These predictions were confirmed experimentally for circular nucleosome arrays with precisely positioned nucleosomes. We suggest that topological polymorphism of chromatin may play a role in transcription, with the {10n+5} fibers producing transcriptionally competent chromatin structures. This hypothesis is consistent with available data for yeast and, partially, for fly. We show that both fiber topoisomers (with ΔLk ≈ −1.5 and −1.0) have to be taken into account to interpret experimental data obtained using new techniques: genome-wide Micro-C, Hi-CO, and RICC-seq, as well as self-association of nucleosome arrays in vitro. The relative stability of these topoisomers is likely to depend on epigenetic histone modifications modulating the strength of internucleosome interactions. Potentially, our findings may reflect a general tendency of functionally distinct parts of the genome to retain topologically different higher-order structures.

Specific details concerning the spatial organization of nucleosomes in 30 nm fibers remain unknown. To investigate this, we analyzed all stereochemically possible configurations of two-start nucleosome fibers with short DNA linkers L = 13–37 bp (nucleosome repeat length (NRL) = 160–184 bp). Four superhelical parameters—inclination of nucleosomes, twist, rise, and diameter—uniquely describe a regular symmetric fiber. The energy of a fiber is defined as the sum of four terms: elastic energy of the linker DNA, steric repulsion, electrostatics, and a phenomenological (H4 tail–acidic patch) interaction between two stacked nucleosomes. By optimizing the fiber energy with respect to the superhelical parameters, we found two types of topological transition in fibers (associated with the change in inclination angle): one caused by an abrupt 360° change in the linker DNA twisting (change in the DNA linking number, ΔLk = 1), and another caused by overcrossing of the linkers ( ΔLk = 2). To the best of our knowledge, this topological polymorphism of the two-start fibers was not reported in the computations published earlier. Importantly, the optimal configurations of the fibers with linkers L = 10 n and 10 n + 5 bp are characterized by different values of the DNA linking number—that is, they are topologically different. Our results are consistent with experimental observations, such as the inclination 60° to 70° (the angle between the nucleosomal disks and the fiber axis), helical rise, diameter, and left-handedness of the fibers. In addition, we make several testable predictions, among them different degrees of DNA supercoiling in fibers with L = 10 n and 10 n + 5 bp, different flexibility of the two types of fibers, and a correlation between the local NRL and the level of transcription in different parts of the yeast genome.

To elucidate conformational dynamics of chromatin fibers, we compared available force-spectroscopy measurements with extensive Monte Carlo simulations of nucleosome arrays under external force. Our coarse-grained model of chromatin includes phenomenological energy terms for the DNA-histone adhesion and the internucleosome stacking interactions. We found that the Monte Carlo fiber ensembles simulated with increasing degrees of DNA unwrapping and the stacking energy 8 kT can account for the intricate force-extension response observed experimentally. Our analysis shows that at low external forces (F < 3.0 picoNewtons), the DNA ends in nucleosomes breathe by ∼10 bp. Importantly, under these conditions, the fiber is highly dynamic, exhibiting continuous unstacking-restacking transitions, allowing accessibility of transcription factors to DNA, while maintaining a relatively compact conformation. Of note, changing the stacking interaction by a few kT, an in silico way to mimic histone modifications, is sufficient to transform an open chromatin state into a compact fiber. The fibers are mostly two-start zigzag folds with rare occurrences of three- to five-start morphologies. The internucleosome stacking is lost during the linear response regime. At the higher forces exceeding 4 picoNewtons, the nucleosome unwrapping becomes stochastic and asymmetric, with one DNA arm opened by ∼55 bp and the other arm only by ∼10 bp. Importantly, this asymmetric unwrapping occurs for any kind of sequence, including the symmetric ones. Our analysis brings new, to our knowledge, insights in dynamics of chromatin modulated by histone epigenetic modifications and molecular motors such as RNA polymerase.

The spatial organization of nucleosomes in 30-nm fibers remains unknown in detail. To address this issue, we analyzed all stereochemically possible configurations of two-start nucleosome fibers with short DNA linkers L = 13 - 37 bp (nucleosome repeat length NRL = 160 - 184 bp). Four superhelical parameters – inclination of nucleosomes, twist, rise and diameter – uniquely describe a uniform symmetric fiber. The energy of a fiber is defined as the sum of four terms: elastic energy of the linker DNA, steric repulsion, electrostatics and a phenomenological (H4 tail - acidic patch) interaction between two stacked nucleosomes. By optimizing the fiber energy with respect to the superhelical parameters, we found two types of topological transition in fibers (associated with the change in inclination angle): one caused by an abrupt 360° change in the linker DNA twisting, and another caused by over-crossing of the linkers. (The first transition is characterized by change in the DNA linking number, ΔLk = 1, and the second one by ΔLk = 2.) To the best of our knowledge, this topological polymorphism of the two-start fibers was not reported in the computations published earlier. Importantly, the optimal configurations of the fibers with linkers L = 10n and 10n+5 bp are topologically different. Our results are consistent with experimental observations, such as the inclination 60-70° (the angle between the nucleosomal disks and the fiber axis), helical rise, diameter and left-handedness of the fibers. In addition, we make several testable predictions, among them existence of different degree of DNA supercoiling in the fibers with L = 10n and 10n+5 bp, different stiffness of the two types of fibers, and a correlation between the local NRL and the level of transcription in different parts of the yeast genome.

We are investigating correlation between the DNA folding in 30-nm chromatin fiber and the level of gene expression. The 30-nm fiber is generally characterized by the nucleosome repeat length (NRL) - that is, the length of the core DNA, 147 bp, plus the linker DNA length, L. We found previously that there are two families of the two-start chromatin fiber structures characterized by different DNA topology and flexibility. (Depending on the NRL value, the energetically optimal fiber structure belongs to one of the two families.) Here we analyze the high resolution nucleosome positioning data to find whether there is any correlation between the NRL and the gene expression level in yeast. We calculate the NRL values for the two groups of genes - 25% highly expressed and 25% lowly expressed genes (out of ∼3,500 yeast genes that are at least 1,000 bp long). Our results show that the average NRL=161-162 bp for the highly active genes (i.e., linker L=14-15 bp), whereas NRL=167-168 bp (i.e., linker L= 20-21 bp) for the lowly transcribed genes. Based on these findings, we conclude that the highly and lowly active gene sets have distinct nucleosome fiber organization with the linker L≈10n+5 and 10n, respectively. We hypothesize that organization of the most active genes in fibers with L≈10n+5 (which are more flexible than the fibers with L≈10n) facilitates formation of gene loops, thereby inducing transcription of these genes.