model of nucleosome arrays

In our CG model, each nucleosome, inclusive of the histone core and the ∼1.65-turn wrapped DNA, is constructed from nc = 26 charged beads, each of size σc = 2.0 nm (Fig. S1a). The beads are arranged in three stacks, where the top and bottom stacks each contain 9 beads evenly placed along a circumference of radius ro = 4.30 nm and the middle stack contains 8 beads evenly placed along a circumference of radius ri = 2.64 nm. The relative positions of these beads are held fixed to treat the entire nucleosome as one rigid body. Each linker DNA is modeled as a discretized wormlike chain composed of six charged beads to mimic the 62-bp linkers of chicken erythrocyte chromatin, where each bead represents a l0 = 3 nm-long strand of relaxed B-DNA. Each nucleosome is attached to two linker DNAs, termed “entry” and “exit” linkers, at sites consistent with the 1KX5 crystal structure of the nucleosome [1] subtending an entry/exit angle of θ0 = 120◦ and separated by a distance of 2w0 = 3.6 nm along the nucleosome axis (Fig. S1a and b). We do not explicitly model histone tails, as we examine the arrays under low salt conditions, similar to twisting experiments [2, 3]. Under these conditions, the arrays exhibit unfolded conformations and histone tail interactions become relatively unimportant [4]. The model geometry is shown in Fig. S1b. The positions of linker DNA beads and nucleosome centers are represented by vectors ri (i = 1, ..., N), where N is the total number of linker DNA beads and nucleosomes in the array. The positions of linker DNA entry and exit sites at nucleosomes i are described by vectors ri and r+i , respectively. The orientation of the nucleosomes and the linker DNA beads are described by the orthonormal unit vectors frame {ai,bi, ci}, where ai is the tangent vector, and bi and ci are the binormal and normal vectors, respectively [5]. When index i represents a nucleosome, the vectors ai and bi lie in the plane of the nucleosome, where ai points along the tangential direction of the wrapped DNA at the nucleosomal exit site, bi points towards the nucleosome center from the exit site, and ci = ai × bi. The entry/exit site positions ri and r + i can be obtained in terms of ri, ai, bi, ci, w0, and θ0 from geometry. The orientation of linker DNA exiting nucleosome i is described by the vector frame {a i ,b i , c i }, where a i points along the vector connecting the nucleosomal exit site to the first bead of the exiting linker DNA, b i is the binormal vector, and c i = a i × b i . We define two additional vector frames {ai ,b − i , c − i } and {a + i ,b + i , c + i } to describe the orientation of the wrapped DNA at the entry and exit sites of nucleosome i, respectively. The vector ai points along the tangential direction of the wrapped DNA at the nucleosomal entry site and is a geometrical function of ai, bi, and θ0, while bi points towards the nucleosome center from the entry site, and ci = ci. Since {ai,bi, ci} are defined according to the nucleosome exit site, the frame {a+i ,b + i , c + i } = {ai,bi, ci}. When i represents a linker DNA bead, ai defines the unit vector connecting linker bead i to either the next linker DNA bead i+ 1 or the entry site on nucleosome i+ 1, bi represents the binormal vector, and ci = ai × bi. The bending and twisting of the linker DNAs is determined in terms of Euler angles {αi, βi, γi} describing the relative orientations of adjacent coordinate frames. Specifically, when both i and i + 1 represent