Computational Modeling Predicts the Structure and Dynamics of Chromatin Fiber  Daniel A. Beard, Tamar Schlick  Structure  Volume 9, Issue 2, Pages 105-114 (February 2001) DOI: 10.1016/S0969-2126(01)00572-X

Figure 1 Chromatin Model (a) Left: basic structure of chromatin consisting of core particles connected by linker DNA segments. Right: electrostatic parameterization of a dinucleosome model by Debye-Hückel charges placed on the core surface. The linker DNA (red beads) carries a uniform negative charge, and the core particle disks, along with the H3 tail (which extends between the gyres of the wrapped DNA [6]), are modeled by charges distributed over the surface: 253 for each nucleosome and 24 for the H3 tail. Parameterization of the charges is described in [8] . (b) A core disk is located at position ri, and linker DNA beads are located at ri−1, ri+1, and ri+2. Associated with each particle is a local coordinate system denoted by the orthogonal unit vectors {ai, bi, ci}. (c) The trajectory of the wrapped DNA exiting and entering the core disk is indicated by a+i and a−i Structure 2001 9, 105-114DOI: (10.1016/S0969-2126(01)00572-X)

Figure 2 Calculated versus Experimental Diffusion Coefficients, Dt, Plotted as a Function of Cs, the Monovalent Salt Concentration Computed values for dinucleosomes (open circles) and trinucleosomes (open triangles) are estimated based on 10 trajectories of length 100 ns. Error bars indicate standard error of the estimate. Also shown are data adapted from Yao et al. [20] for dinucleosomes (black diamonds) and from Bednar et al. [21] for dinucleosomes (black squares) and trinucleosomes (black circles) Structure 2001 9, 105-114DOI: (10.1016/S0969-2126(01)00572-X)

Figure 3 Dinucleosome Folding and Unfolding (a) Simulation snapshots (1 ns intervals over an 8 ns trajectory) of a dinucleosome at the higher salt concentration of Cs = 0.05 M. The core particles are depicted as idealized disks with effective charges distributed on the surface. In the final frame, the linker and core DNA is depicted as a continuous chain. (b) Snapshots of the dinucleosome at the lower salt concentration of Cs = 0.01 M. The initial structure is the compact for obtained at high salt Structure 2001 9, 105-114DOI: (10.1016/S0969-2126(01)00572-X)

Figure 4 Trinucleosome Folding and Unfolding (a) Simulation snapshots (1 ns intervals over an 8 ns trajectory) of a trinucleosome at the higher salt concentration of Cs = 0.05 M. (b) Simulation snapshots of the trinucleosome at the lower salt concentration of Cs = 0.01 M. The initial structure is the compact form of the trinucleosome obtained at Cs = 0.05 M. The final structure is rotated 90° relative to the other snapshots Structure 2001 9, 105-114DOI: (10.1016/S0969-2126(01)00572-X)

Figure 5 Model for the 30 nm Fiber Upper panel shows the nucleosome folding motif obtained for condensed dinucleosome at Cs = 0.05 M. The 48 nucleosome system in the middle panel is constructed from the repeating nucleosome motif above. A 50 ns Brownian dynamics trajectory at Cs = 0.05 M, applied to the initial structure, produces the refined structure illustrated in the lower panel. The images to the right are side views demonstrating the diameter of the fiber Structure 2001 9, 105-114DOI: (10.1016/S0969-2126(01)00572-X)

Figure 6 Instability of the 30 nm Fiber at Low Salt Demonstrated by BD Simulation (a) Using the refined condensed structure obtained at Cs = 0.05 M as the initial condition (Figure 5), the 48 nucleosome fiber unfolds at Cs = 0.01 M. (b) The low-salt equilibrium structure for the 48 nucleosome fiber obtained by Monte Carlo sampling. A comparison to the high salt condensed fiber (top) reveals a difference of several orders of magnitude. The scale bar is 100 nm Structure 2001 9, 105-114DOI: (10.1016/S0969-2126(01)00572-X)

Figure 7 Calculated Small-Angle X-Ray Scattering Profiles for 48 Nucleosome Systems at Salt Concentrations Ranging from 0.01 M to 0.05 M The scattered X-ray intensity was calculated as a function of s according to the Debye formula [50]: Is = ∑i,j fisfjs sin 2πsrij 2πsrij, where s = 2 sinθ λ, θ is the scattering angle, and λ is the X-ray wavelength. For our purpose, each particle in the system was treated as a symmetric Gaussian subunit, with structure factor fis = R3i exp−πsRi2. The effective radius Ri is set to Ri = 1.5 nm for linker beads and Ri = 4.5 nm for core particles. Scattering profiles were calculated as the mean intensity based on 100 independent equilibrium configurations for each salt concentration. Computed data plotted as log s(I(s)) versus s are shown as solid lines. The profiles obtained by Fujiwara [26] at 0.01 and 0.05 M salt concentration are shown as circles. The profiles are displaced vertically for clarity Structure 2001 9, 105-114DOI: (10.1016/S0969-2126(01)00572-X)