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## Abstract

Linker histones are essential for DNA compaction in chromatin. They bind to nucleosomes in a 1:1 ratio forming chromatosomes. Alternative configurations have been proposed in which the globular domain of the linker histone H5 (gH5) is positioned either on- or off-dyad between the nucleosomal and linker DNAs. However, the dynamic pathways of chromatosome assembly remain elusive. Here, we studied the conformational plasticity of gH5 in unbound and off-dyad nucleosome-bound forms with classical and accelerated molecular dynamics simulations. We find that the unbound gH5 converts between open and closed conformations, preferring the closed form. However, the open gH5 contributes to a more rigid chromatosome and restricts the motion of the nearby linker DNA through hydrophobic interactions with thymidines. Moreover, the closed gH5 opens and reorients in accelerated simulations of the chromatosome. Brownian dynamics simulations of chromatosome assembly, accounting for a range of amplitudes of nucleosome opening and different nucleosome DNA sequences, support the existence of both on- and off-dyad binding modes of gH5 and reveal alternative, sequence and conformation-dependent chromatosome configurations. Taken together, these findings suggest that the conformational dynamics of linker histones and nucleosomes facilitate alternative chromatosome configurations through an interplay between induced fit and conformational selection.

## INTRODUCTION

In eukaryotic cells, DNA packs tightly into the nuclei by forming higher-order chromatin structures. In chromatin, DNA wraps around histone core proteins to form complexes called nucleosomes, which interact with each other and are connected by segments of linker DNA (L-DNA) (1–3). One of the proteins determining the conformation, compaction and dynamics of chromatin is the linker histone (LH). LH proteins bind to the nucleosome in a 1:1 ratio at a site located between the L-DNAs, forming a chromatosome (4,5).

The H1/H5 family of LH proteins contributes not only to the dynamic compaction of chromatin but also participates in the regulation of processes such as replication and transcription (6–8). The existence of two proposed structures of the 30 nm chromatin fiber, the interdigitated solenoid (9) and the two-start zig-zag helix (10), implies that the L-DNA connecting successive nucleosomes varies not only in length (11) but also in conformation. However, how LH proteins interact with the nucleosome and the L-DNA, and how they affect the conformation and dynamics of the L-DNA, is not yet sufficiently understood (12–16).

LH proteins are composed of a short flexible N-terminal tail (∼20 amino acid residues), a globular domain (∼80 amino acid residues) and a long disordered basic C-terminal tail (∼100 amino acid residues). Whereas the C-terminal tail appears to affect both the affinity and geometry of the LH-nucleosome interaction (17–20), and may undergo DNA-mediated folding (21), it appears that the N-terminal tail only affects the binding affinity and specificity (18,22). Interestingly, although the C-terminal tail determines the organization of higher-order chromatin structures (17,23) and the binding geometry of the linker DNA (17,18) it does not appear to affect the LH positioning around the dyad (17). Moreover, the full length LH and the isolated globular domain protect the same L-DNA from micrococcal nuclease digestion (24), indicating that the globular domain determines the binding geometry, whereas the C-terminal tail further refines the interaction with the linker DNA. H5 is an avian LH that differs in sequence from mammalian LH isoforms, but shares most similarity with human H1.0, which is mostly found in terminally differentiated cells (see sequence alignment in Supplementary Data). The unbound gH5 adopts a winged helix fold consisting of three α-helices in which the helix-turn-helix motif is followed by a β-hairpin (pdb ID: 1 hst, 2.5 Å resolution) (25). The closed (gH5B) and open (gH5A) conformations of gH5 revealed by the two subunits (B and A) in the asymmetric unit of this crystal structure differ in the structure of the β-hairpin and its orientation with respect to the third α-helix. In gH5B, the β-hairpin bends toward the third α-helix forming hydrophobic contacts with the helix (Figure 1A), whereas in gH5A, it is extended (Figure 1B). Interestingly, the β-hairpin sequence is highly conserved among human LH isoforms, suggesting that it may play an important functional role (Supplementary Data).

Figure 1.

Conformational flexibility of the free gH5. (A) Closed conformation gH5B. (B) Open conformation gH5A. On the left, the two conformations (chains B and A in pdb ID 1hst) are shown in A and B, respectively. Proteins are shown in cartoon representation and colored according to secondary structure: α helices in orange, β sheets in green and unstructured regions in gray. This coloring is used throughout the manuscript. The conformational space of gH5 is described by the angles ϕ1 and ϕ2 (see Materials and Methods). The following vectors are shown: vH along the axis of helix α3, vB threading through the β sheet; vBH connecting the centers of vH and vB; vBT connecting the center of vB with the β turn; vHT connecting the center of vH with the β turn. ϕ1 is the angle between vH and vHT; ϕ2 is the angle between vBH and vBT. For clarity, vH and vB are shown in red and longer than their actual definition marked with black thin lines. All other vectors are shown in blue and their endpoints as black spheres. On the right, two-dimensional histograms of the sampling of the ϕ12 conformational space for the corresponding gH5 conformation during CMD and AMD simulations (Table 1) are shown. The red and blue crosses mark the ϕ1 and ϕ2 values in the crystal structure for gH5B and gH5A, respectively. See also Supplementary Figures S1 and S2.

Figure 1.

Conformational flexibility of the free gH5. (A) Closed conformation gH5B. (B) Open conformation gH5A. On the left, the two conformations (chains B and A in pdb ID 1hst) are shown in A and B, respectively. Proteins are shown in cartoon representation and colored according to secondary structure: α helices in orange, β sheets in green and unstructured regions in gray. This coloring is used throughout the manuscript. The conformational space of gH5 is described by the angles ϕ1 and ϕ2 (see Materials and Methods). The following vectors are shown: vH along the axis of helix α3, vB threading through the β sheet; vBH connecting the centers of vH and vB; vBT connecting the center of vB with the β turn; vHT connecting the center of vH with the β turn. ϕ1 is the angle between vH and vHT; ϕ2 is the angle between vBH and vBT. For clarity, vH and vB are shown in red and longer than their actual definition marked with black thin lines. All other vectors are shown in blue and their endpoints as black spheres. On the right, two-dimensional histograms of the sampling of the ϕ12 conformational space for the corresponding gH5 conformation during CMD and AMD simulations (Table 1) are shown. The red and blue crosses mark the ϕ1 and ϕ2 values in the crystal structure for gH5B and gH5A, respectively. See also Supplementary Figures S1 and S2.

From experimental and computational studies, a range of different models for the chromatosome structure have been proposed (11,17,26–37,38). In most of these, the nucleosome was modeled either without any L-DNA, or with different lengths of static or coarse-grained L-DNAs. L-DNA fluctuations up to ±45° were measured in a recent 1 μs MD simulation of the nucleosome (39). Because of the highly dynamic nature of DNA in chromatin (40) it is likely that the binding of LH is influenced by the local chromatin conformation. To address the role of nucleosome dynamics and to obtain a unified model of LH-nucleosome interactions, we previously carried out computational docking of the globular domain of H5 in the closed conformation (gH5B) to the nucleosome (32). We accounted for the flexibility of two flanking 10 base pairs long L-DNAs by applying normal mode analysis (NMA) to generate a range of conformations. Then, with Brownian dynamics (BD) based docking, we generated structures of gH5B-nucleosome encounter complexes. For a wide range of nucleosomal conformations with the L-DNA ends less than 65 Å apart, we identified a single dominant binding mode, in which gH5B binds between the nucleosomal DNA (N-DNA) and one of the L-DNAs, asymmetrically with respect to the nucleosomal dyad axis in an off-dyad configuration (Figure 2A).

Figure 2.

Chromatosome configurations. (A) The off-dyad configuration proposed from BD docking by Pachov et al. (32). (B) The on-dyad configuration revealed in the crystal structure of Zhou et al. (36). The images on the right show the nucleosome aligned with the dyad axis pointing towards the viewer and were obtained by 2 rotations, first vertical and second horizontal, marked by the 2 curved arrows. The insets show schematic representations of the gH5-nucleosome binding configurations. The numbers represent the DNA grooves as follows: 0 = the minor groove at the dyad, −1,+1 = the neighboring major grooves of N-DNA toward L-DNA1 and L-DNA2, respectively, −2,+2 = the major grooves of L-DNA1 and L-DNA2, respectively, at the junction with N-DNA, −3,+3 = the following minor grooves of L-DNA1 and L-DNA2, respectively. Helix α3 is shown as an arrow oriented from the N- to the C-terminus, whereas the turn β1 is shown as a curved line representing the closed conformation.

Figure 2.

Chromatosome configurations. (A) The off-dyad configuration proposed from BD docking by Pachov et al. (32). (B) The on-dyad configuration revealed in the crystal structure of Zhou et al. (36). The images on the right show the nucleosome aligned with the dyad axis pointing towards the viewer and were obtained by 2 rotations, first vertical and second horizontal, marked by the 2 curved arrows. The insets show schematic representations of the gH5-nucleosome binding configurations. The numbers represent the DNA grooves as follows: 0 = the minor groove at the dyad, −1,+1 = the neighboring major grooves of N-DNA toward L-DNA1 and L-DNA2, respectively, −2,+2 = the major grooves of L-DNA1 and L-DNA2, respectively, at the junction with N-DNA, −3,+3 = the following minor grooves of L-DNA1 and L-DNA2, respectively. Helix α3 is shown as an arrow oriented from the N- to the C-terminus, whereas the turn β1 is shown as a curved line representing the closed conformation.

Asymmetric binding models of the LH have since been derived from NMR and site-directed mutagenesis studies of gH1 (35), and by cryo-electron microscopy of a 12 nucleosome-containing chromatin fiber with H1 bound (33). Although similar to the binding mode we proposed for gH5, these models differ in the details of the interaction, suggesting that the LH sequence may also contribute to the chromatosome configuration. Recently, Zhou et al. determined a crystal structure of the gH5 bound to the nucleosome (36). Interestingly, they showed that gH5 interacts with the nucleosome dyad and both L-DNAs in an on-dyad configuration (Figure 2B). In addition, based on their previous structural study on the gH1-nucleosome complex (35), they proposed that the binding mode of LH proteins depends on their sequence, with gH5 binding on-dyad and gH1 binding off-dyad. Further, they suggested that the two LH proteins contribute to different packing of chromatin fibers, with gH5 promoting tighter structures because of its on-dyad binding mode. Notably, the nucleosome sequence used in this study was different from that which we used in our original docking simulations. This raises the question whether the DNA sequence may play a role in establishing a specific chromatosome configuration. Earlier, Cui et al. revealed that binding of the LH to the nucleosome is stabilized by interactions with AT-rich DNA, and suggested the presence of sequence-specific hydrophobic interactions (28). However, these interactions could not be confirmed either by our first models for the gH5-nucleosome encounter complex or by the recent crystal structure (32,36). Therefore, a full understanding of how the sequences and the conformational dynamics of the LH and the nucleosome affect the chromatosome configuration, and ultimately, the chromatin structure, remains elusive.

Here, we employed classical molecular dynamics (CMD) and accelerated molecular dynamics (AMD) simulations to study the conformational plasticity of the nucleosome and of gH5 in free and off-dyad nucleosome-bound forms. In addition, we investigated the dynamic pathways of chromatosome assembly with BD simulations. We provide evidence that the chromatosome configuration and assembly pathways depend on conformational dynamics and are determined by an interplay between induced fit and conformational selection mechanisms. Importantly, in addition to the off-dyad configuration, by using BD simulations we were able to reconstitute the on-dyad configuration revealed in the latest crystal structure. Thus, we demonstrate that both the on- and off-dyad binding modes of gH5 are plausible. Our findings provide fundamental insights into chromatosome structure, dynamics and assembly pathways.

## METHODS

### Selection of starting structures

The structures of the closed and open conformations of gH5 were obtained from chains B (Figure 1A) and A (Figure 1B) of the crystal structure (pdb ID 1hst, 2.5 Å resolution) (25), respectively. The nucleosome core particle (NUC) was taken from the crystal structure (pdb ID 1kx5, 1.9 Å resolution) (41). The histone tails were removed and 10 base pairs of L-DNA were added to each end (see Pachov et al. (32) for details). Hydrogen atoms were added at pH 7 by using the tleap module of the AMBER software (42). The structure of the NUC-gH5B encounter complex with the dominant binding mode of gH5B as described by Pachov et al. (32) was taken as the starting configuration for the molecular dynamics simulations of the chromatosome. The initial superposition of the crystal structure of gH5A on the starting configuration of the NUC-gH5B chromatosome revealed significant steric clashes between gH5A and the L-DNA. To minimize the clashes, snapshots from an initial 20 ns of the CMD simulation of gH5A taken every 400 ps were superimposed by minimizing the root mean square deviation (RMSD) of the gH5 non-hydrogen atoms from the NUC-gH5B configuration. Next, two of the superimposed snapshots (corresponding to the structures at 2.4 and 11.2 ns of the gH5A simulation) were substituted instead of gH5B in the NUC-gH5B structure. We refer to the resulting two models as NUC-gH5A and NUC-gH5A*, respectively. We used both in the simulations to exclude potential bias due to the initial modeled configuration of the gH5A-nucleosome complex.

### Classical molecular dynamics simulations

The unbound structures of gH5B and gH5A, consisting of 74 residues, were neutralized with 11 Cl ions and solvated in a truncated octahedral box of explicit TIP3P (43) water molecules containing an additional ∼50 mM NaCl with a minimal distance between any solute and solvent atoms of 12 Å. The two systems had 24 345 and 22 134 atoms, respectively. The three models of the chromatosome (NUC-gH5B, NUC-gH5A and NUC-gH5A*) were neutralized with 226 Na+ ions and were solvated in a truncated octahedral box containing an additional ∼50 mM NaCl. For this, 50 Na+ and 50 Cl ions were first added, followed by the TIP3P water molecules. The total Na+ ion concentration was ∼200 mM. Only monovalent ions were added and the salt concentration was kept below physiological to avoid any potential artifacts due to inaccuracies in the force field parameters for ions (44,45). The minimal distance between the solute, including the neutralizing Na+ ions, and solvent atoms was 4 Å. Each chromatosome system had 198 303 atoms. In addition, a system with the free nucleosome having 197 127 atoms was setup by removing gH5B and 11 Cl ions from the solvated NUC-gH5B system.

We used the all-atom AMBER force field (46) modified for DNA (‘ff99’) (47) and proteins (‘ff99SB’) (48)) with further corrections for the DNA backbone (‘parmbsc0’) (49). Recent progress in force field development has corrected some of the limitations of these force fields (50–52). Based on previous evaluations (53,54), we estimate that the properties analyzed in this study are not affected by the known limitations of the force field versions we used. For ions, we used the Joung–Cheatham parameters optimized for TIP3P water (55). All systems were optimized by energy minimization with the AMBER software and equilibrated in NAMD (see Supplementary Methods) (56). Then, two independent CMD simulations were performed with a standard protocol (Table 1) (see Supplementary Methods).

#### Performed molecular dynamics simulations

Table 1.
Performed molecular dynamics simulations
Simulation Parameters gH5B gH5A NUC NUC-gH5B NUC-gH5A NUC-gH5A*
CMD-01 Time (ns) 600 600 100 324 324 324
VDIHED (kcal/mol) 749.1 ± 10.9 750.7 ± 10.9 16 095.7 ± 53.2 16 828.5 ± 52.7 16 844.2 ± 51.7 16 847.0 ± 53.2
CMD-02 Time (ns) 600 600 324 105 100 100
VDIHED (kcal/mol) 748.3 ± 11.2 749.9 ± 11.3 16 075.7 ± 50.5 16 844.6 ± 53.4 16 847.7 ± 55.4 16 853.7 ± 53.1
AMD-01 Time (ns) 200 208 108 100 100
α 44.4 44.4 850.5 850.5 850.5
EDIHED (kcal/mol) 976.8 976.8 21 097.0 21 101.2 21 101.2
ΔVDIHED (kcal/mol) 8.5 ± 3.8 8.6 ± 3.8 113.2 ± 7.4 114.0 ± 7.8 114.4 ± 7.8
AMD-02 Time (ns) 200 212 114 112 112
α 51.8 51.8 850.5 850.5 850.5
EDIHED (kcal/mol) 1005.7 1013.8 22 798.0 22 802.2 22 802.2
ΔVDIHED (kcal/mol) 11.5 ± 4.5 12.3 ± 4.7 193.6 ± 10.6 192.0 ± 10.9 192.4 ± 10.9
AMD-03 Time (ns) 200 208 108 112 112
α 59.2 59.2 850.5 850.5 850.5
EDIHED (kcal/mol) 1050.8 1050.8 24 499.0 24 503.2 24 503.2
ΔVDIHED (kcal/mol) 15.9 ± 5.4 16.2 ± 5.5 281.5 ± 14.4 281.8 ± 14.1 281.9 ± 14.3
AMD-04 Time (ns) 200 200
α 51.8 51.8
EDIHED (kcal/mol) 1109.3 1117.4
ΔVDIHED (kcal/mol) 18.4 ± 6.2 19.5 ± 6.4
AMD-05 Time (ns) 200 200
α 51.8 51.8
EDIHED (kcal/mol) 1212.9 1221.0
ΔVDIHED (kcal/mol) 26.9 ± 8.1 27.2 ± 8.1
Simulation Parameters gH5B gH5A NUC NUC-gH5B NUC-gH5A NUC-gH5A*
CMD-01 Time (ns) 600 600 100 324 324 324
VDIHED (kcal/mol) 749.1 ± 10.9 750.7 ± 10.9 16 095.7 ± 53.2 16 828.5 ± 52.7 16 844.2 ± 51.7 16 847.0 ± 53.2
CMD-02 Time (ns) 600 600 324 105 100 100
VDIHED (kcal/mol) 748.3 ± 11.2 749.9 ± 11.3 16 075.7 ± 50.5 16 844.6 ± 53.4 16 847.7 ± 55.4 16 853.7 ± 53.1
AMD-01 Time (ns) 200 208 108 100 100
α 44.4 44.4 850.5 850.5 850.5
EDIHED (kcal/mol) 976.8 976.8 21 097.0 21 101.2 21 101.2
ΔVDIHED (kcal/mol) 8.5 ± 3.8 8.6 ± 3.8 113.2 ± 7.4 114.0 ± 7.8 114.4 ± 7.8
AMD-02 Time (ns) 200 212 114 112 112
α 51.8 51.8 850.5 850.5 850.5
EDIHED (kcal/mol) 1005.7 1013.8 22 798.0 22 802.2 22 802.2
ΔVDIHED (kcal/mol) 11.5 ± 4.5 12.3 ± 4.7 193.6 ± 10.6 192.0 ± 10.9 192.4 ± 10.9
AMD-03 Time (ns) 200 208 108 112 112
α 59.2 59.2 850.5 850.5 850.5
EDIHED (kcal/mol) 1050.8 1050.8 24 499.0 24 503.2 24 503.2
ΔVDIHED (kcal/mol) 15.9 ± 5.4 16.2 ± 5.5 281.5 ± 14.4 281.8 ± 14.1 281.9 ± 14.3
AMD-04 Time (ns) 200 200
α 51.8 51.8
EDIHED (kcal/mol) 1109.3 1117.4
ΔVDIHED (kcal/mol) 18.4 ± 6.2 19.5 ± 6.4
AMD-05 Time (ns) 200 200
α 51.8 51.8
EDIHED (kcal/mol) 1212.9 1221.0
ΔVDIHED (kcal/mol) 26.9 ± 8.1 27.2 ± 8.1

### Accelerated molecular dynamics simulations

In AMD simulations (57), a positive boost potential is added to the system when the intrinsic potential energy is lower than a reference energy. In this way, the energy barriers for exploring different regions of the conformational space are lowered. The method has been shown to accurately describe biomolecular dynamics on time scales significantly shorter than those required by CMD (58). We applied a variant of the method in which only the dihedral potentials are boosted (57,59). The modified potential $${\rm{V}}_{{\rm{DIHED}}}^{\rm{M}}$$is:

\begin{equation*}{\rm{V}}_{{\rm{DIHED}}}^{\rm{M}} = \left\{ {\begin{array}{*{20}{c}} {{{\rm{V}}_{{\rm{DIHED}}}}{\rm{\ if\ }}{{\rm{V}}_{{\rm{DIHED}}}} \ge {{\rm{E}}_{{\rm{DIHED}}}}}\\ {{{\rm{V}}_{{\rm{DIHED}}}}{\rm{ + \Delta }}{{\rm{V}}_{{\rm{DIHED\ }}}}{\rm{if\ }}{{\rm{V}}_{{\rm{DIHED}}}} < {{\rm{E}}_{{\rm{DIHED}}}}} \end{array}} \right\}\end{equation*}
where $${{\rm{V}}_{{\rm{DIHED}}}}$$= the intrinsic dihedral potential, $${{\rm{E}}_{{\rm{DIHED}}}}$$= the reference potential, $${\rm{\Delta }}{{\rm{V}}_{{\rm{DIHED}}}}$$= the boost potential.
\begin{equation*}{\rm{\Delta }}{{\rm{V}}_{{\rm{DIHED}}}} = \frac{{{{\left( {{{\rm{E}}_{{\rm{DIHED}}}} - {{\rm{V}}_{{\rm{DIHED}}}}} \right)}^{\rm{2}}}}}{{{\rm{\alpha + }}\left( {{{\rm{E}}_{{\rm{DIHED}}}} - {{\rm{V}}_{{\rm{DIHED}}}}} \right)}},\end{equation*}
where α = the acceleration factor.

Accelerated simulations for the gH5B, gH5A, NUC-gH5B, NUC-gH5A and NUC-gH5A* were started after 100 ns of CMD simulation. The parameters used and the length of the simulations are shown in Table 1. Here, α = 1/5 · (3.5 · NR), where 3.5 is the recommended energy contribution per residue and NR is the number of residues. EDIHED = VDIHED + 3.5 · NR, where VDIHED is the average torsion potential after 100 ns CMD simulation. All parameters from the CMD simulations (Supplementary Methods) were kept.

### Analysis of structural dynamics

To describe the conformational plasticity of gH5, we first defined two vectors vH and vB that thread through the two structural elements involved, the helix α3 and the sheet β1, respectively (Figure 1): (i) vH connects the geometric centers of the second and third turns of the gH5 helix α3, defined by the backbone atoms (C, N, O, CA) of residues 67–71 and 71–75, respectively; (ii) vB connects the geometric center of the backbone atoms of residues 82 and 94 with the geometric center of the backbone atoms of residues 83 and 93. In addition, we defined the center of the turn between the two β strands as the geometric center of the backbone atoms of residues 87–91. The vectors vHT and vBT connect this point with the centers of vectors vH and vB, respectively. The latter two are connected by the vector vBH. Finally, we defined two angles ϕ1 and ϕ2 as follows (Figure 1): ϕ1 is the angle between vectors vH and vHT, ϕ2 is the angle between the vectors vBH and vBT.

To characterize the structural dynamics within the chromatosome (Figures 3–6), we setup a reference xyz coordinate system based on two vectors vN1 and vN2 (Figure 3A). vN1 connects the geometric centers of nucleotides 45–48, 287–290, 123–126, 209–212 and nucleotides 83–86, 249–252 whereas vN2 connects the geometric centers of nucleotides 100–103, 232–235, 24–27, 311–314 and nucleotides 144–147, 188–191, 66–69, 266–269. vN1 was defined along the dyad axis and crosses vN2, approximately in the center of the nucleosome. The origin of the xyz coordinate system was defined at the point where vN1 crosses the nucleosomal DNA at the geometric center of nucleotides 83–86, 249–252. Then, the x-axis was defined to extend along vN1, the y-axis was defined along the cross product of x and vN2, and the z-axis was defined along the cross product of x and y. The orientation of gH5 with respect to the N-DNA was described by the angles θ1 and θ2 (Figure 3B), where θ1 = the angle between the xy projection of vH and the x axis and θ2 = the angle between the yz projection of vH and the z-axis. The motions of the L-DNAs were described using the angles γ1 and γ2 (Figure 6A and B), where γ1 = the angle between the xz projection of the vector vL1 or vL2 and the z-axis, and γ2 = the angle between the xy projection of vL1 or vL2 and the y axis. vL1 and vL2 were defined based on selected DNA residues along the helical axis of the two L-DNAs. vL1 connects the geometric centers of nucleotides 12–15, 320–323 and 2–5, 330–333, whereas vL2 connects the geometric centers of nucleotides 153–156, 179–182 and 163–166, 169–172 (Figure 6A). The numbering of the DNA nucleotides starts from 1 and 168 at the 5′ ends of L-DNA1 and L-DNA2, respectively, and runs to 167 and 334 at the 3′ ends of L-DNA2 and L-DNA1, respectively. All non-hydrogen atoms were used to define the nucleotides. All vector-based angle calculations were performed in VMD (60).

Figure 3.

Orientation and dynamics of gH5 in the chromatosome. (A) Structure of the off-dyad chromatosome. A reference coordinate system, xyz, was constructed using the vectors vN1 and vN2. These were defined between selected DNA bases such as to cross as closely as possible to the center of the nucleosome (see Materials and Methods). vN1 points along the dyad axis. vN2 connects two points on opposite sides of the nucleosome DNA, above and below the dyad point, respectively. To construct the coordinate system, vN1 was translated on the x-axis, the y-axis was defined along the cross product of x and vN2, and the z-axis was defined along the cross product of x and y. The two linker DNAs (L-DNA1 and L-DNA2), nucleosomal DNA (N-DNA), gH5 and the vector vH (see Figure 1) are labeled. (B) Schematic representation of the definition of the two angles, θ1 and θ2, describing the orientation of helix α3 of gH5 with respect to N-DNA. θ1 is the angle between the xy projection of vH and the x axis. θ2 is the angle between the yz projection of vH and the z axis. (C and D) Orientation and dynamics of gH5B (C) and gH5A (D). The number of contacts of three structural regions of gH5 (turn β1, loop l1 and helix α3) with different DNA regions (N-DNA and L-DNA1) and the histograms of θ1 and θ2 distributions are plotted. See also Supplementary Figure S3.

Figure 3.

Orientation and dynamics of gH5 in the chromatosome. (A) Structure of the off-dyad chromatosome. A reference coordinate system, xyz, was constructed using the vectors vN1 and vN2. These were defined between selected DNA bases such as to cross as closely as possible to the center of the nucleosome (see Materials and Methods). vN1 points along the dyad axis. vN2 connects two points on opposite sides of the nucleosome DNA, above and below the dyad point, respectively. To construct the coordinate system, vN1 was translated on the x-axis, the y-axis was defined along the cross product of x and vN2, and the z-axis was defined along the cross product of x and y. The two linker DNAs (L-DNA1 and L-DNA2), nucleosomal DNA (N-DNA), gH5 and the vector vH (see Figure 1) are labeled. (B) Schematic representation of the definition of the two angles, θ1 and θ2, describing the orientation of helix α3 of gH5 with respect to N-DNA. θ1 is the angle between the xy projection of vH and the x axis. θ2 is the angle between the yz projection of vH and the z axis. (C and D) Orientation and dynamics of gH5B (C) and gH5A (D). The number of contacts of three structural regions of gH5 (turn β1, loop l1 and helix α3) with different DNA regions (N-DNA and L-DNA1) and the histograms of θ1 and θ2 distributions are plotted. See also Supplementary Figure S3.

To analyze the slow motions of the L-DNAs, we calculated the essential dynamics of the nucleosome core particle from principal component analysis (PCA) of the CMD simulations with the CPPTRAJ program (61). For this, we first removed gH5 and superimposed all non-hydrogen atoms of the nucleosome core particle. Secondly, we calculated the covariance matrix and diagonalized it to extract the first 25 eigenvectors and their eigenvalues. Then, we projected the trajectory onto the 25 calculated modes, and extracted the minimum and maximum projection values for each mode. Finally, we used these values to generate individual trajectories along each mode and analyze the motions of the L-DNAs in the trajectories of the first two modes that contributed most to the overall dynamics.

### Brownian dynamics simulations

Both gH5A and gH5B were docked using rigid body BD based docking simulations to eight nucleosome structures with different L-DNA1 conformations and L-DNA2 fixed in a specific, highly-populated conformation. These were selected from the CMD simulation without LH based on the γ1 and γ2 angles (Figure 7C and D). In addition, we docked gH5B in the nucleosome structure taken from the recent chromatosome structure by Zhou et al. (pdb ID 4qlc, 3.5 Å resolution) (36) using the protocol of Pachov et al. (32). In short, NMA was applied using the NOMAD-Ref web-server (62) to generate nucleosome conformations with different degrees of L-DNA opening. The original structure (conformation 0), as well as two conformations with RMSD of 1 and 2 Å, respectively (all non-hydrogen atoms superimposed) along the first mode (‘conformation 1’ and ‘conformation 2’), were selected. The RMSD of the L-DNAs in these two structures from the original structure was 4.7 and 9.2 Å (the non-hydrogen atoms of the core histones superimposed), respectively.

First, polar hydrogen atoms were added to the structures by using PDB2PQR 1.8 (63) and partial atomic charges and atomic radii were assigned from the AMBER99 force field. The electrostatic potential was calculated for all structures by solving the non-linear Poisson–Boltzmann equation on a grid with a 1 Å spacing and dimension of 1933 in APBS 1.4 (64) at temperature 298.15 K. The solvent and solute dielectric constants were 78.54 and 2, respectively and the ionic strength was 100 mM. Higher solute dielectric constants of 4, 6 and 8 were also tested for docking gH5 to the highly populated conformation of the nucleosome from snapshot 5 (Figure 7C and D). The results were insensitive to varying the solute dielectric constant in this range. To define dielectric boundary conditions, the van der Waals surface was used.

The BD simulations were performed with SDA7 (Simulation of Diffusional Association) (65) using electrostatic interaction forces. Short-range interactions were neglected, and a 0.5 Å excluded volume criterion to prevent overlap was applied. Effective charges were assigned to charged residues on the protein and to P atoms on the DNA using the ECM program (66). The trajectories were started randomly on a sphere at a center-to-center distance of b = 280 Å and stopped at a center-to-center distance of c = 500 Å. The time step was set to 1 ps for center-to-center distances up to 160 Å and increased linearly up to 100 ps at a distance of 260 Å. A total of 20 000 trajectories were generated for each pair of LH-nucleosome conformations simulated. The diffusional encounter complex was considered formed when the following two geometric conditions were satisfied: (i) the center-to-center distance of gH5 and the nucleosome <73 Å, and (ii) the nucleosome dyad point and gH5 separation <40 Å. The interaction energies and the coordinates of a complex were recorded if the RMSD to previously recorded complexes was >1 Å and the interaction energy was within the 5000 lowest (most favorable) energy complexes recorded. A complex with RMSD < 1 Å to a previously recorded complex but lower energy was recorded as a substitute of that complex. The 5000 recorded complexes were clustered into 10 groups according to the backbone RMSD values between them. Upon ranking the clusters by their population during the BD simulations, representative structures of the clusters were generated.

## RESULTS AND DISCUSSION

### The linker histone displays conformational plasticity

To describe the conformational plasticity of gH5 during the simulations (Table 1), we defined the Φ1 and Φ2 angles (Figure 1A and B, see Materials and Methods for details) using vectors with a small angular variance due to intrinsic internal motions (see Supplementary Methods and Figure S1A). In the crystal structure of gH5, the angles in the gH5B conformation are Φ1 = 103.62° and Φ2 = 53.06° whereas for the gH5A conformation, they are Φ1 = 95.00° and Φ2 = 91.73° (Figure 1).

In the CMD simulations, gH5B opened partially to a transient conformation characterized by an increase of Φ2 to about 70°–80° and a decrease of Φ1 (Figure 1A, Supplementary Figure S1B and C). In AMD simulations, gH5B opened to either partially or fully open conformations (Figure 1A, Supplementary Figure S1C). At the lowest boost (AMD-01), gH5B remained in the closed conformation for most of the time but opened irreversibly after ∼165 ns. Interestingly, at intermediate boosts (AMD-02, AMD-03), mainly reversible transitions between the closed and partially open conformations occurred, whereas at high boosts (AMD-04, AMD-05), we observed reversible (on the 200 ns timescale of the AMD simulations) transitions to fully open conformations. On the other hand, the open form, gH5A, adopted conformations characterized by Φ2 values greater than 120° in CMD simulations (Figure 1B, Supplementary Figure S1B and C). These differed from that observed in the crystal structure with turn β1 packing on the opposite side of the β sheet. Interestingly, in one CMD simulation gH5A closed irreversibly adopting a conformation similar to gH5B (Figure 1B). In AMD simulations, gH5A closed partially at the lowest boost (AMD-01) and adopted short lived fully closed conformations at intermediate to high boosts (AMD-02, AMD-03, AMD-04, AMD-05). In conclusion, on the timescale of the simulations, we observed both reversible and irreversible transitions between the different conformations of gH5 for both starting structures and we identified a partially closed conformation characterized by a defined range of Φ2 values (65°–80°). Furthermore, we found that the open conformation is an ensemble of conformations spanning a wide range of Φ2 values. Based on these findings, we propose that the unbound gH5 has a measurable preference for the closed conformation. The closed form is characterized by hydrophobic interactions between residues in turn β1 (V87, A89) and residues in the helix α3 as well as hydrogen bonds between polar sidechains (R47 in the helix α2, Q83 in the sheet β1) and the backbone of turn β1 (see Supplementary Methods and Figure S2). Of these residues, only A89 is conserved in H5 and human H1 LH proteins (Supplementary Data) suggesting that the LH sequence may influence the equilibrium between the two conformations. As residues in the turn β1 have been proposed to be important for nucleosome binding (26,35), it is possible that the changes in the equilibrium between the 2 conformations may result in different LH-nucleosome binding geometries.

### The open linker histone conformation forms a more rigid chromatosome structure

To characterize the binding mode of gH5 to the nucleosome, we adopted a schematic representation for which we aligned the nucleosome with the dyad axis perpendicular to the view plane and L-DNA1 and L-DNA2 on the left and right side, respectively (Figure 2). We then numbered the DNA grooves as follows: 0 = the minor groove at the dyad, −1,+1 = the neighboring major grooves of N-DNA toward L-DNA1 and L-DNA2, respectively, −2,+2 = the major grooves of L-DNA1 and L-DNA2 at the junction with N-DNA, −3,+3 = the following minor grooves of L-DNA1 and L-DNA2, respectively (Figure 2). In the off-dyad binding mode, the LH helix α3 binds in the major groove −1, the turn β1 interacts with groove −1 and −2, and the loop l1 interacts with groove −2 (Figure 2A). In the on-dyad binding mode, helix α3 binds in the minor groove −3, turn β1 in groove 0, and the loop l1 interacts with the groove 0 (Figure 2B).

To study the orientation and dynamics of the off-dyad bound gH5 in the simulations of the chromatosome, we monitored the number of contacts formed between different secondary structure elements of gH5 and the DNA. In addition, we defined the θ1 and θ2 angles (Figure 3A and B) to describe the rocking and tumbling motions, respectively, of helix α3 in the major groove of the N-DNA (see Materials and Methods). For this, a reference coordinate system was defined using the vectors vN1 and vN2. vN1 was defined along the dyad axis and vN2 in a direction approximately orthogonal to the dyad axis. Neither of these vectors was sensitive to the intrinsic internal fluctuations (Supplementary Figure S3A). From CMD simulations, we found that the pattern of contacts between gH5 and the nucleosome depends on the gH5 conformation. The closed gH5B formed more contacts between its loop l1 and L-DNA1 and fewer contacts between its turn β1 and L-DNA1 compared to the open gH5A (Figure 3C, D and Supplementary Figure S3B). Remarkably, the ranges of sampled θ1 and θ2 angles was greater in the CMD simulations of the NUC-gH5B chromatosome compared to the NUC-gH5A form (Figure 3C, D and Supplementary Figure S3B) indicating that the open form, gH5A, contributes to a more rigid chromatosome. This suggests that the open gH5A is the preferred conformation of gH5 in the off-dyad configuration of the chromatosome. The gH5A-nucleosome off-dyad binding geometry is in agreement with previous experiments that revealed residues involved in H1.0-nucleosome binding (26). H1.0 is the mammalian LH isoform most similar to H5 (Supplementary Data). Interestingly, an off-dyad configuration has also been obtained for the Drosophila H1 globular domain (35) but with a different orientation of the LH in which helix α3 does not dock in the major groove of N-DNA, suggesting that the detailed geometry of the off-dyad configuration may be LH-isoform dependent.

### The closed linker histone conformation opens in accelerated chromatosome simulations

To characterize the conformational dynamics of the LH while bound to the nucleosome, we monitored the Φ1 and Φ2 angles (Figure 1) during MD simulations of the chromatosome (Figure 4A, B and Supplementary Figure S4). In the CMD simulations of the NUC-gH5B, gH5B remained closed with a slight increase of both Φ1 and Φ2 (Figure 4A). In AMD simulations of NUC-gH5B, three open states were observed for gH5 in which both Φ1 and Φ2 angles increased by up to 40°. When the boost was low (AMD-01), we observed reversible transitions between closed and open conformations between 45 and 60 ns (Supplementary Figure S4). In the simulations with higher boosts (AMD-02, AMD-03), Φ2 increased irreversibly up to 120° (Figure 4A, Supplementary Figure S4). Interestingly, opening of gH5B was correlated with an increase in Φ1 (Figure 4A) in contrast to the simulations of the free gH5 (Figure 1). In the NUC-gH5A simulations, gH5A adopted a predominant open conformation with Φ2 larger than 105° and Φ1 smaller than 110° (Figure 4B, Supplementary Figure S4). The values of Φ2 were similar to those observed in CMD simulations of free gH5A (Figure 1) and reflect the packing of the turn β1 away from helix α3. Therefore, the extended structure of the β-turn observed in the crystal structure is not stable during the simulations. Importantly, gH5A did not close in any of the simulations of the chromatosome. These findings suggests that the closed conformation of gH5 is not stable in the fully bound complex with the nucleosome in the off-dyad configuration and provide further support for an induced fit mechanism, in which gH5B forms the encounter complex and opens in the fully bound complex.

Figure 4.

Conformational dynamics of gH5 in the chromatosome. (A) NUC-gH5B; (B) NUC-gH5A. The two-dimensional histograms for the sampling of the Φ12 conformational space during the four CMD and AMD simulations (Table 1) are shown. The graphs are colored as in Figure 1. See also Supplementary Figure S4.

Figure 4.

Conformational dynamics of gH5 in the chromatosome. (A) NUC-gH5B; (B) NUC-gH5A. The two-dimensional histograms for the sampling of the Φ12 conformational space during the four CMD and AMD simulations (Table 1) are shown. The graphs are colored as in Figure 1. See also Supplementary Figure S4.

### The open linker histone conformation interacts with thymidines in the linker DNA

To explore how the open gH5A conformation stabilizes the chromatosome, we analyzed the hydrophobic contacts between turn β1 of gH5 and thymidines in L-DNA1. We observed that residues V87 and A89 from gH5A form alternative networks of hydrophobic interactions with 1 to 3 thymidine bases in L-DNA1 (Figure 5A, Supplementary Figure S5). Although these interactions require a higher thymidine content in the L-DNA, the precise position of the bases may vary. Thus, the hydrophobic interactions are only partially DNA sequence specific. In CMD simulations of the NUC-gH5B complex, no hydrophobic contacts between gH5B and L-DNA1 were formed, whereas in the AMD simulations between 7 and 16% of the frames showed at least one such contact (Figure 5B, Supplementary Figure S5A). The formation of 1 or 2 hydrophobic contacts between 40 and 55 ns with low boost (AMD-01), and after ∼50 ns with higher boost (AMD-02, AMD-03) was correlated with the opening of the gH5B (Supplementary Figure S5B). In contrast, in over 60% of the trajectories of the NUC-gH5A complex (∼100% in the simulations with the highest boost), at least one such hydrophobic contact was formed (Figure 5B, Supplementary Figure S5C and D). Interestingly, the sampling efficiency of the hydrophobic contacts was greater in the AMD simulations in particular, for the NUC-gH5A* system (Supplementary Figure S5D). These findings indicate that the increased stability of the chromatosome with gH5 in the open conformation is due to additional hydrophobic contacts formed between gH5A (V87, A89) and thymidines in L-DNA1. These findings could explain the proposed higher preference of the LH for T-rich regions of DNA (28).

Figure 5.

Hydrophobic contacts between gH5 and L-DNA1 in the chromatosome. (A) Representative structures from the AMD-01 simulation of the NUC-gH5A chromatosome showing different hydrophobic contacts between V87 and A89 of gH5 and thymidine bases in L-DNA1. Protein residues are shown in cyan, whereas the thymidine bases are shown in yellow with the methyl group in red. (B) Percentages of MD trajectory frames in which at least one hydrophobic contact is established for NUC-gH5B (red) and NUC-gH5A (blue) chromatosomes. See also Supplementary Figure S5.

Figure 5.

Hydrophobic contacts between gH5 and L-DNA1 in the chromatosome. (A) Representative structures from the AMD-01 simulation of the NUC-gH5A chromatosome showing different hydrophobic contacts between V87 and A89 of gH5 and thymidine bases in L-DNA1. Protein residues are shown in cyan, whereas the thymidine bases are shown in yellow with the methyl group in red. (B) Percentages of MD trajectory frames in which at least one hydrophobic contact is established for NUC-gH5B (red) and NUC-gH5A (blue) chromatosomes. See also Supplementary Figure S5.

### Binding of the linker histone to the nucleosome remodels the linker DNA dynamics

To study how the binding of the LH influences the dynamics of the L-DNAs, we first defined the γ1 and γ2 angles which describe the motions of the L-DNAs in the xz and xy planes of the reference coordinate system respectively (Figure 6A, B and see Materials and Methods for details). Then, we calculated the essential dynamics from PCA of the CMD simulations and monitored the γ1 and γ2 angles in the trajectory projections along the first two modes.

Figure 6.

Effect of gH5 binding to the nucleosome on L-DNA motions. (A) Structure of the chromatosome showing vectors and angles defining the motions of the L-DNAs. The reference coordinate system xyz is shown in Figure 3. The vectors vL1 and vL2 were defined based on selected DNA bases to represent the helical axes of L-DNA1 and L-DNA2, respectively. The double headed arrows show the directionality of the L-DNA motions described by the two angles, γ1 and γ2 (see Materials and Methods for details). (B) Schematic representation of the definition of γ1 and γ2. γ1 is the angle between the xz projection of vL1 or vL2 and the z-axis, whereas γ2 is the angle between the xy projection of vL1 or vL2 and the y axis. (C) Motions of the L-DNAs (L-DNA1 in red and L-DNA2 in blue) along the first two essential dynamics modes of the CMD-trajectory. The data from the simulations of the nucleosome (NUC) and the chromatosome (NUC-gH5B and NUC-gH5A) are shown in the first, second and third columns, respectively. See also Supplementary Figure S6.

Figure 6.

Effect of gH5 binding to the nucleosome on L-DNA motions. (A) Structure of the chromatosome showing vectors and angles defining the motions of the L-DNAs. The reference coordinate system xyz is shown in Figure 3. The vectors vL1 and vL2 were defined based on selected DNA bases to represent the helical axes of L-DNA1 and L-DNA2, respectively. The double headed arrows show the directionality of the L-DNA motions described by the two angles, γ1 and γ2 (see Materials and Methods for details). (B) Schematic representation of the definition of γ1 and γ2. γ1 is the angle between the xz projection of vL1 or vL2 and the z-axis, whereas γ2 is the angle between the xy projection of vL1 or vL2 and the y axis. (C) Motions of the L-DNAs (L-DNA1 in red and L-DNA2 in blue) along the first two essential dynamics modes of the CMD-trajectory. The data from the simulations of the nucleosome (NUC) and the chromatosome (NUC-gH5B and NUC-gH5A) are shown in the first, second and third columns, respectively. See also Supplementary Figure S6.

In the CMD simulation of the free nucleosome, L-DNA1 moved predominantly along a path that is a combination of the two types of motions described by the two angles (Figure 6C, Supplementary Figure S6A). On the other hand, L-DNA2 moved predominantly in the xy plane along mode 1 showing little to no variation of γ1, whereas its motion along mode 2 differed in the 2 independent CMD simulations (Figure 6C, Supplementary Figure S6A).

In CMD simulations of the chromatosome, a clear separation between the xy and xz motions along different modes was not observed (Figure 6D, E and Supplementary Figure S6). Both L-DNAs sampled predominantly a combined path along all modes, suggesting that the presence of the LH alters the relative timescales of these motions. Interestingly, the closed gH5B conformation only marginally reduced the amplitude of the L-DNA motions (Figure 6D, Supplementary Figure S6B). In contrast, the open gH5A conformation suppressed greatly the L-DNA1 motion (Figure 6E, Supplementary Figure S6C, D and E). These findings are in agreement with the observation that gH5A showed less flexibility in its orientation when bound to the nucleosome compared to gH5B (Figure 3), providing further support for the induced fit mechanism described in previous paragraphs. The selective suppression of L-DNA1 in the fully bound gH5-nucleosome complex in the off-dyad configuration, has important implications for the assembly of higher-order chromatin structures (3) and it is analogous to the proposed change in DNA dynamics upon core histone protein binding in the nucleosome (67). Interestingly, our L-DNAs are asymmetric in sequence, L-DNA2 having a higher GC content, and we observed asymmetric dynamics of the L-DNAs (Figure 6A, Supplementary Figure S6A). These findings are in agreement with a recent study showing L-DNA sequence dependent, asymmetric flexibility and unwrapping of the nucleosome (68).

### Nucleosome dynamics determine the binding mode of the linker histone conformations

To explore the effect of the conformational dynamics on the chromatosome assembly, we performed BD simulations with different gH5 and nucleosome conformations. For this, we first calculated the electrostatic potential of gH5 and found that it differs between the two conformations. The large positive stripe on gH5A is perturbed on gH5B leading to a more evenly distributed potential (Figure 7A and B), suggesting that the gH5-nucleosome encounter complex may differ between gH5A and gH5B.

Figure 7.

Preparation of BD simulations. (A and B) Molecular electrostatic potentials of gH5B (A) and gH5A (B). (C and D) Snapshots from the CMD-01 simulation of the free nucleosome selected for BD simulations (labeled in red) on the γ12 histograms for L-DNA1 (C) and L-DNA2 (D). See also Supplementary Figure S7.

Figure 7.

Preparation of BD simulations. (A and B) Molecular electrostatic potentials of gH5B (A) and gH5A (B). (C and D) Snapshots from the CMD-01 simulation of the free nucleosome selected for BD simulations (labeled in red) on the γ12 histograms for L-DNA1 (C) and L-DNA2 (D). See also Supplementary Figure S7.

Then, we selected eight representative snapshots from the CMD simulation of the free nucleosome based on the distribution of the γ1 and γ2 angles. An increase of γ1 and a decrease of γ2 reflect the opening of L-DNA1 along the two types of motion described by the two angles (Figure 6A and B). Because in the off-dyad configuration, gH5 binds only to L-DNA1, we varied the conformation of L-DNA1 (Figure 7C), keeping the conformation of L-DNA2 fixed (Figure 7D). Our selection of snapshots was not affected by the limited sampling of the L-DNA dynamics in the 100 ns CMD simulation (Supplementary Figure S7A and B). With this selection, we cover the representative conformational space sampled by L-DNA1 in the absence of the LH. To evaluate the binding modes resulting from the BD simulations, we used the scheme described in Figure 2. In addition, we show the orientation of helix α3 with an arrow pointing from its N- to the C-terminus.

The closed gH5B conformation formed an off-dyad encounter complex with nucleosome conformations from snapshots 2, 3, 5 and 8 (Table 2). As snapshot 5 lies in the center of the γ12 histogram, this finding indicates that the off-dyad configuration is the predominant binding mode for gH5B. Moreover, it shows that closing of L-DNA1 along one direction (lower values of γ1) and the opening along the other (lower values of γ2) (snapshots 2 and 3), as well as opening of L-DNA1 along both directions simultaneously (snapshot 8), still permits binding of gH5B in this configuration. These findings confirm our previous observations based on NMA and BD simulations (32). The open gH5A conformation formed similar off-dyad encounter complexes in snapshots 3, 6 and 7 (Table 2). This indicates that opening of the L-DNA1 in either direction (higher γ1 or lower γ2), but not in both simultaneously, is required for the binding of gH5A in this configuration. The BD simulations also reveal other conformation-dependent configurations of the gH5-nucleosome encounter complex but not the on-dyad configuration (Table 2, Supplementary Figure S7C and D). Taken together, these findings indicate that besides the LH conformation, the nucleosome conformational dynamics determine the LH binding configuration. Therefore, we propose that the off-dyad encounter complex forms through a conformational selection mechanism in which different conformations of the LH bind to a subset of specific conformations of the nucleosome. Interestingly, the structure of a chromatin fiber (33) revealed different degrees of L-DNA opening in different regions with asymmetric binding of LH H1. This further suggests that the interplay between LH binding and L-DNA dynamics is important for the higher-order chromatin structures.

#### Binding configurations of gH5-nucleosome encounter complexes#

Table 2.
Binding configurations of gH5-nucleosome encounter complexes#

### Chromatosome assembly simulations reveal experimentally-determined configurations

Up to this point, we have focused on the off-dyad chromatosome configuration which we originally proposed based on BD simulations (32). Interestingly, the recent crystal structure of the chromatosome revealed the closed gH5B conformation bound in an on-dyad configuration contacting both L-DNA arms (Figure 2B) (36). Therefore, there is an apparent contradiction between the experimental and simulation-based configurations. However, it should be noted that the sequence of the nucleosome in the crystal structure differs from that used in our BD simulations (32). To test whether the DNA sequence may influence the chromatosome configuration, we applied our original protocol based on NMA and BD simulations to dock gH5B to the nucleosome taken from the new structure. With the very closed nucleosome conformation from the crystal structure, we could not reproduce the reference bound complex (Table 3). However, this is not surprising because it is unlikely that a diffusional encounter complex is formed with a tightly closed conformation of the nucleosome. Remarkably, when we docked gH5B to a nucleosome structure opened slightly along the lowest frequency mode obtained from NMA (see Methods), we obtained the on-dyad configuration in the two topmost ranking clusters (Table 3). Besides showing that BD simulations accurately describe chromatosome configurations, these findings suggest that the LH binding mode to the nucleosome may depend on DNA sequence as well as histone sequence. Therefore, we propose that both the off-dyad and on-dyad configurations are possible upon binding of gH5 to different nucleosomes with different nucleic acid sequences. A higher GC content around the dyad combined with a higher AT content in the L-DNA may favor the off-dyad configuration in which arginines from the third helix of gH5 form direct contacts with bases in the major groove of nucleosomal DNA (Supplementary Figure S8). Our proposal that a single LH isoform is able to bind to nucleosomes in different configurations depending on the sequence and conformation is supported by evidence for both on- and off-dyad binding modes for both gH1 (17,19,33,35) and gH5 (32,36).

#### Binding configurations of encounter complexes#

Table 3.
Binding configurations of encounter complexes#

### Concluding remarks

In this work, a series of classical and accelerated MD and BD simulations was performed to explore the dynamic nature of LH - nucleosome binding and chromatosome formation. In the MD simulations, we found that gH5 has the ability to switch from open to closed conformations and vice versa in solution. Interestingly, the free gH5 has a measurable preference for the closed form which is stabilized by a series of hydrophobic and hydrophilic interactions that involve residues from the turn β1. However, the open conformation stabilized the off-dyad encounter complex and significantly reduced the L-DNA motion through hydrophobic interactions with thymidines in the nearby L-DNA. This could explain the higher preference of the LH for T-rich regions (28), and provides further support for experimental observations (36). Moreover, the closed conformation opened in accelerated MD simulations of the chromatosome. Based on these findings, we propose an induced fit mechanism for the formation of the off-dyad chromatosome configuration. On the other hand, we show that the conformational plasticity of the nucleosome provides a framework for conformational selection during chromatosome assemby. Therefore, an interplay between induced fit and conformational selection mechanisms contribute to alternative chromatosome configurations which further affect the higher order chromatin structure. Finally, we show that when docking the closed gH5 conformation to the alternative DNA sequence used to solve the most recent crystal structure of the gH5-nucleosome complex, we observed the experimentally determined on-dyad binding mode of gH5. This opens up the possibility that, besides nucleosome and LH conformational plasticity, the DNA sequence may play a role in the chromatosome assembly without necessarily affecting the DNA binding affinity.

One potential limitation of our study may arise from not considering the highly flexible N- and C-terminal tails of the LH and the core histone proteins. It is notoriously challenging to sufficiently sample the conformational space of such highly flexible regions in molecular dynamics simulations. Especially the effect of the C-terminal tail of LH proteins may be of particular interest for future studies because, although it does not appear to affect the primary binding geometry around the dyad (17), it does affect the secondary positioning of LH proteins around the linker DNA (17–19) and the diversity of higher-order chromatin arrangements (17) through mechanisms that may involve DNA-mediated folding (20). The core histone H2A tails have been shown to affect the binding affinity of LH to the nucleosome (35). However, a recent long simulation of a free nucleosome (39) shows no significant overlap between the core histone H3 tails and the LH binding region, consistent with NMR data showing that the H3 tails are unaffected by binding of an H1 construct (35). This further suggests that the core histone tails may have little effect on the binding geometry of the LH whereas they may affect binding affinity through an induced fit mechanism in which the tails wrap around the LH after the initial binding. In conclusion, the chromatosome assembly pathways and final configurations may be significantly more complex than previously thought and further experimental and computational studies are necessary to elucidate them in the context of higher order chromatin structures.

## SUPPLEMENTARY DATA

Supplementary Data are available at NAR Online.

The authors thank Michael Martinez for helpful discussions and Alexey Shaytan and Anna Panchenko for providing their trajectory of the free nucleosome for analysis. V.C. is part of the Cells in Motion cluster of excellence of the University of Münster and thanks Hans Schöler for support.

## FUNDING

Klaus Tschira Foundation and the German Research Foundation [WA 1381/1-1 to R.C.W.]. Max Planck Society and the German Research Foundation [CO 975/1-1 to V.C.]. PRACE Research Infrastructure [computer resources for project LASIPROD to V.C.]. Funding for open access charge: HITS gGmBH.

Conflict of interest statement. None declared.

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# A number is chosen from 1 to 20. Find the probability that the number chosen is a prime number.

Last updated date: 19th Mar 2023
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Hint: First of all list down all the prime numbers from 1 to 20 that are 2, 3, 5, 7, 11, 13, 17, 19 and use probability of an event $=\dfrac{\text{Number of favourable cases}}{\text{Number of total cases}}$

Here favourable cases are total prime numbers from 1 to 20 and total cases are total numbers from 1 to 20.
Here we are given that a number is chosen from 1 to 20. We have to find the probability that the number chosen is the prime number.
Before proceeding with the question, we must know some basic terms like prime number, probability etc.
Prime numbers are the numbers that are divisible only by itself and 1. In other words we can say that prime numbers are numbers that have just two factors, 1 and itself.
Examples of prime numbers are 2, 3, 11, 5, 7, 17 etc. We must note that 2 is the only prime number as well even that is 2 is the only even prime number. All other prime numbers are odd.
Also the term ‘probability’ means the extent to which an event is likely to occur measured by ratio of favourable cases to the whole number of cases possible. In short we can say that ‘probability’ means possibility.
Probability of an event $=\dfrac{\text{Number of favourable outcomes/cases}}{\text{Number of total outcomes/cases}}$
Now, to select the prime number from 1 to 20. We must first note down all the prime numbers from 1 to 20.
The numbers that have 2 factors 1 and itself that is prime numbers from 1 to 20 are,
2, 3, 5, 7, 11, 13, 17, 19
Therefore, we have a total 8 prime numbers from 1 to 20.
Now the total numbers from 1 to 20 = 20
Here our favourable case is choosing the prime number from 1 to 20. Therefore, we get the number of favourable cases = 8.
Also here our total cases are all the numbers from 1 to 20. Therefore, the number of total cases = 20.
As we know that,
Probability of an event $=\dfrac{\text{Number of favourable cases}}{\text{Number of total cases}}$,
We get, probability of choosing a prime number from 1 to 20 $=\dfrac{8}{20}=\dfrac{2}{5}$.
Therefore, we get the probability of choosing a prime number from 1 to 20 as $\dfrac{2}{5}or\ 0.4$.

Note: Some students make this mistake of considering all the odd numbers as prime numbers but this is wrong. For example numbers like 9, 15, 21, 25 etc are odd but not prime. So this mistake must be avoided. Also apart from noting each prime number, students can remember that there are a total 25 prime numbers from 1 to 100 and 15 prime numbers from 1 to 50.

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