Quantitative analysis of single-molecule force spectroscopy on folded chromatin fibers

Abstract

Single-molecule techniques allow for picoNewton manipulation and nanometer accuracy measurements of single chromatin fibers. However, the complexity of the data, the heterogeneity of the composition of individual fibers and the relatively large fluctuations in extension of the fibers complicate a structural interpretation of such force-extension curves. Here we introduce a statistical mechanics model that quantitatively describes the extension of individual fibers in response to force on a per nucleosome basis. Four nucleosome conformations can be distinguished when pulling a chromatin fiber apart. A novel, transient conformation is introduced that coexists with single wrapped nucleosomes between 3 and 7 pN. Comparison of force-extension curves between single nucleosomes and chromatin fibers shows that embedding nucleosomes in a fiber stabilizes the nucleosome by 10 kBT. Chromatin fibers with 20- and 50-bp linker DNA follow a different unfolding pathway. These results have implications for accessibility of DNA in fully folded and partially unwrapped chromatin fibers and are vital for understanding force unfolding experiments on nucleosome arrays.

Figure 1.

Comparison between force-extension curves of (A) a chromatin fiber and (B) a mononucleosome. Dark circles represent the pulling trace, light gray circles represent the release trace. All force-extension measurements are reversible, but a significant hysteresis is observed when the the force exceeds 6 pN. The inset in (A) shows a force-extension experiment in which the force was limited to 6 pN; no hysteresis is observed. Light gray dashed lines represent WLC descriptions of the bare DNA and the state in which all nucleosomes are in the extended conformation (see Figure 2). A third dashed line in (B) represents a WLC with a contour length 147 bp shorter than the bare DNA. Black lines are fits to Equation (8) yielding for (A) n_fiber = 13, n_unfolded = 4, k = 0.28 pN/nm, _ext = 4.6 nm, ΔG₁ = 20.6 k_BT and ΔG₂ = 5.5 k_BT. For (B): _ext = 6.5 nm, ΔG₁ = 8.8 k_BT and ΔG₂ = 3.5 k_BT.

Figure 2.

Schematic representation of the transitions between all metastable conformations of the nucleosomes. The double-headed arrows depict the extension per nucleosome for each conformation. As force increases, a nucleosome unwraps part of its DNA until a single full turn of DNA remains wrapped around the histone core. The next conformation is slightly extended, which may be due to further unwrapping of the DNA, conformational changes within the nucleosome and/or deformation of the linker DNA. We propose the extended conformation may involve dissociation of H2A/H2B dimers from histone core (see the Discussion section). In the last conformation all histone proteins remain attached to the DNA, but the DNA can stretch fully. When a nucleosome is embedded in a chromatin fiber and interactions between nucleosomes fold the fiber into a dense structure, the extension per nucleosome is further reduced, tentatively depicted as a stack of nucleosomes in the bottom left. After the first transition, involving a change in free energy of ΔG₁, which may be different for a mono nucleosome and a nucleosome embedded in a fiber, all transitions will follow the same free energy landscape as schematically plotted in the inset.

Figure 3.

Detailed analysis of the unfolding of a single chromatin fiber. (A) A zoom in on the high-force region shows discrete steps in extension. Dashed gray lines represent the extensions of all states that are composed of extended and fully unwrapped nucleosomes. The fit match was obtained for _ext = 4.6 nm. The black line shows the best match between individual data points and the various states of unwrapping. (B) Step size distribution of the data shown in (A) obtained from a 10-point window t-test analysis. (C) Unfolding of a 15*197 NRL chromatin fiber at low force. Below 7 pN the extension starts to deviate from a string of extended nucleosomes (gray dashed lines). A single transition (black dashed line) does not capture the force-extension data. The black line shows a fit to Equation (8), while constraining L_wrap = 89 bp and _ext = 4.6 nm, yielding = 21.2±0.1 k_BT, ΔG₂= 4.3±0.1 k_BT. (D) The corresponding probability for a nucleosome to be in a fiber (low force), a single wrap (intermediate force) or in the extended conformation (high force).

Figure 4.

Different fibers show a large variation in condensation. (A) Ten chromatin fibers reconstituted on a 15*197 NRL DNA template. The high-force transitions align well with states that describe the last unfolding transition, plotted in gray dashed lines. All curves have a force plateau at 3 pN, but the size of the force plateau and the extension at lower forces varies significantly. Black lines represent fits to Equation (8). (B) Distribution of fit parameters obtained from (A). The stepsizes in the top histogram were determined independently using a t-test step finding algorithm. Except for the number of nucleosomes in the fiber, all parameters show a narrow distribution.

Figure 5.

Chromatin fibers with 167-bp NRL follow a qualitatively different unfolding mechanism than 197-bp NRL fibers. (A) A 15*197 NRL chromatin fiber fits well with Equation (8), black line. A model in which the degeneracy for the first transition is lifted, blue line, does not capture the unfolding transitions. (B) A 30*167 NRL chromatin fiber is better described by non-degenerate states for the first transition. This qualitative difference can be explained by a different structure of the fibers, as tentatively sketched in the insets, showing both the top and the side views of the maximally extended fibers. In particular, the nucleosomes that are embedded in the fiber, drawn in blue in the schematic drawing of a zig-zag folded fiber, are less susceptible for unfolding than the red nucleosomes at the ends of the fiber. In contrast, the nucleosomes arranged in a single stack are all equivalent, inset of (A), and rupturing of any of the nucleosomes will lead to the same amount of extension of the fiber. The top view in (A) depicts possible unwrapping of nucleosomal DNA in the folded 197-bp NRL fiber.