Fig. 2: The stacking of nucleosomes is stabilized by the presence of rotational constraint.

a Force-extension (F–E) curves of 167-NRL chromatin fibers assembled on a rotationally constrained (red) or unconstrained (grey) 601-DNA template. Both curves were fit to the statistical mechanics model (black lines) derived in our earlier work⁴⁰. From these fits, the number of nucleosomes \({N}_{{\rm{nucleosomes}}}\) and the number of tetrasomes \({N}_{{\rm{tetrasomes}}}\) in the fibers were determined. These equaled 25 \(\pm 1\) and 1 \(\pm\) 1, respectively, in both tethers. The F–E response for 7.0 kb DNA according to the WLC model is co-plotted (dashed line). Below 1 pN, the response of the tethers to force reflects the entropic elasticity of the DNA handles that flank the folded chromatin fiber. Subsequently, in a linear regime between 1 and 4 pN, the stretching elasticity of the fiber dominates the F–E curve. Beyond 4 pN, in the rotationally unconstrained tether, the unstacking transition is observed, which results in a gain in the extension of nearly 0.5 \(\upmu\)m due to the release of linker DNA between nucleosomes and \(\sim\)56 bp of unwrapped DNA per nucleosome. In the rotationally constrained tether, the unstacking transition occurs at a higher force of 6.5 pN. Further increase of force results in a gradual increase in the extension (\(\sim\)10 bp per nucleosome)⁴⁰ and from \(\sim\)10 pN onwards, in a step-wise unwrapping of the remaining 80 bp of DNA from each octamer (or tetramer). Beyond 35 pN, the extension of the tether equals that of bare DNA, indicating complete unwrapping of DNA from the nucleosomes. The inset depicts the conformational changes of DNA and chromatin induced by the increasing force. b Distributions of parameters that result from quantitative analysis of rotationally constrained (n = 112, red) and unconstrained (n = 27, grey) 167-NRL fibers with the statistical mechanics model⁴⁰. The fibers contain on average 27 \(\pm\) 3 and 27 \(\pm\) 4 (mean \(\pm\) SD) assembled core particles (either nucleosomes or tetrasomes), respectively. The deduced stretching stiffnesses of 1.0 \(\pm\) 0.5 (for rotationally constrained fibers) and 0.9 \(\pm\) 0.4 pN\(\cdot {{\rm{nm}}}^{-1}\) (for rotationally unconstrained fibers) are similar to those obtained in our previous work^36,40. The mean unstacking energy of 27 \(\pm\) 4 \({k}_{{\rm{B}}}T\) in rotationally constrained fibers is significantly larger (Student t-test, p-value = 0.05) than in unconstrained fibers (21 \(\pm\) 2 \({k}_{{\rm{B}}}T\)). Source data are provided as a Source Data file.