Unveiling nucleosome dynamics: A comparative study using all-atom and coarse-grained simulations enhanced by principal component analysis

Abstract

The conformational dynamics of the DNA in the nucleosome may play a role in governing gene regulation and accessibility and impact higher-order chromatin structure. This study investigates nucleosome dynamics using both all-atom and coarse-grained (CG) molecular dynamics simulations, focusing on the SIRAH force field. Simulations are performed for two nucleosomal DNA sequences—alpha satellite palindromic and Widom-601—over 6 μs at physiological salt concentrations. A comparative analysis of structural parameters, such as groove widths and base pair geometries, reveals good agreement between atomistic and CG models, although CG simulations exhibit broader conformational sampling and greater breathing motion of DNA ends. Principal component analysis is applied to DNA structural parameters, revealing multiple free energy minima, especially in CG simulations. These findings highlight the potential of the SIRAH CG force field for studying large-scale nucleosome dynamics, offering insights into DNA repositioning and sequence-dependent behavior.

I. INTRODUCTION

Protein–DNA interactions are important for many essential processes inside the cell, such as organizing genetic information within the nucleus in eukaryotes, regulating gene expression, and DNA replication and transcription.^1–3 The nucleosome core particle (NCP), the elementary building block of chromatin, is a well-known protein–DNA complex that packages the genome inside eukaryotic cells.^4–6 The NCP comprises two copies of four histone subunits, i.e., H2A, H2B, H3, and H4. Each histone subunit consists of a highly ordered helical globular core region enclosed by flexible, disordered, positively charged tails known as the histone tails. The tails play an essential role in NCP–NCP interaction and the higher-level organization of chromatin. The NCP has a 147 base pair duplex DNA wrapped ∼1.7 times around a positively charged histone protein core in a left-handed helical fashion. It plays a pivotal role in several genomic processes, such as transcription, a process by which RNA polymerase copies DNA into RNA. During transcription, RNA polymerase must read the DNA sequence enclosed in the nucleosome. The timescale associated with transcription is from seconds to minutes. The positioning of nucleosomes along the DNA controls the accessibility to DNA binding factors, such as transcription factors and RNA polymerase.⁷ Hence, understanding the underlying sequence dependence that governs nucleosome positioning and dynamics, particularly the breathing motion, is crucial for gaining a broader mechanistic insight into genomic processes.

Nucleosome dynamics are associated with an extended range of timescales, such as unwrapping nucleosomes that range from milliseconds to seconds. Small-scale rearrangements, such as breathing or loop formation, happen at microsecond timescales.^8–12 The repositioning of the DNA on the nucleosome surface is associated with timescales of minutes to hours.^13–15 A single experimental technique cannot cover the extended ranges of timescales. Atomistic molecular dynamics (MD) simulation using state-of-the-art force fields can complement experimental findings, helping decipher molecular details underlying these events. Atomistic MD simulation has already been employed in several studies based on the nucleosome, such as the role played by hydration patterns and counterions around the nucleosome,¹⁶ the role of the histone tails,^8,17,18 and sequence-dependent nucleosome dynamics.^19–24 An increasing number of computational studies with atomistic details of nucleosomes are reported based on multiple microsecond timescales.^25–27 These studies have reported on the formation of twist defects,²⁶ loop formation,²⁵ etc. Characterizing higher-order nucleosome organization, such as the force between nucleosome dimers, the tetranucleosome free energy landscape (FEL), or simulations of chromatin fibers, requires implicit solvent approaches²¹ or coarse-grained (CG) models.²⁸ The plasticity of the nucleosome is also suggested to influence the phase behavior.²⁹ The underlying stability and structure of protein–DNA complexes largely depend on the accuracy of the force fields.³⁰ Atomistic MD simulations of nucleic acid (NA) complexes typically utilize either AMBER^31–33 or Chemistry at Harvard Molecular Mechanics (CHARMM)^34,35 force fields. Improvement of nucleic acid (NA) force fields mainly focuses on refining glycosidic torsion and backbone parameters^31,36,37 that may manifest deficiencies only over long simulation timescales. Both CHARMM and AMBER-based simulations of nucleic acids maintain the experimental double helical structure of DNA at tens of microseconds.^38,39 However, some artifacts have been reported for simulations of longer dsDNA fragments with the CHARMM36 force field in terms of structural stability.⁴⁰ Conversely, AMBER-based simulation force fields show good agreement with experiments with some minor and reversible distortions.⁴⁰ Tucker et al.⁴¹ developed a new DNA force field, DES-Amber, with refined non-bonded parameters. However, this force field cannot capture the BI/BII state correctly, whose population plays a key role in the flexibility of DNA and its ability to bind with proteins. Further advancements in force field development and the integration of multiscale modeling approaches will be essential to overcome these limitations and accurately capture the full spectrum of nucleosome dynamics.

Molecular dynamics studies of the NCP performed in our laboratory have observed correlated DNA motion of the DNA ends.²³ Indeed, at physiological salt concentrations, the timescales for nucleosome “breathing⁴²” are suggested to be in the range of 0.1–1 ms. To accelerate the dynamics of DNA motion, we simulated the NCP at salt concentrations ∼10 times the physiological ion concentrations with a 5 μs trajectory. We found DNA partial unwrapping starting with a spontaneous loop that forms in the SHL-5 region,²⁵ similar in location to that reported by Bilokapic et al.⁴³ We further report on large-scale DNA motion for two different nucleosomal DNA sequences— the “Widom-601” and alpha satellite palindromic “ASP” nucleosomal DNA sequences— based on 12 μs simulation trajectories performed on Anton 2 at a high salt concentration of 2.4M.²⁴ The two sequences exhibit different pathways, with the “ASP” sequence forming a loop, while the “Widom-601” shows large-scale breathing motion. We find that the motion of the H2A and H2B tails plays a key role in loop formation, while the H3 tail plays a critical role in breathing. Post translational modifications (PTMs) are also suggested to modify nucleosome breathing motion.⁴⁴ We further investigate the dynamics of the histone tails, considering the role of acetylation of the histone tails⁴⁵ and characterizing how salt modulates their conformational dynamics. Chemically accurate CG models are necessary to probe the role of the sequences in modulating nucleosome breathing at physiological salt concentrations.

It is well known that a simplified or “coarse-grained (CG)” representation of a complex system, such as a protein–DNA complex, is advantageous for characterizing the dynamics of these complexes and their phase behavior.^29,46 Insight into various biological problems can be obtained by choosing a resolution that fits the length and timescale of interest.⁴⁷ Force-induced unwrapping of the nucleosome has been characterized via polymer bead–spring models.⁴⁸ CG simulation was further explored to characterize the tension-dependent free energy profile of DNA as a function of extension.⁴⁹ Sun et al.⁵⁰ developed a CG model to characterize nucleosome phase separation with explicit divalent and polyvalent ions based on a “bottom-up” CG model. The nucleosomal DNA is modeled as five beads, representing every two base pairs; the histone protein is modeled as a single bead for each amino acid, and one bead represents one ion for all ion species. Chakraborty et al.⁵¹ developed a CG model known as COFFEE (CG force field for energy estimation) based on a self-organized polymer model. This model was used to study the salt-induced unwrapping of the nucleosome. Apart from polymer-based models of the nucleosome, higher-resolution CG models have been introduced to study nucleosome dynamics. For example, the Schlick group^52,53 used Brownian dynamics (BD) simulation to simulate fibers with a mesoscale model of chromatin. In this model, the histone core is treated as a cylinder with 300-point charges distributed on its irregular surface,⁵⁴ linker DNAs are represented by 1 bead per 3 nm,⁵⁵ and flexible histone tails⁵⁶ are explicitly incorporated along with the flexible linker histone.⁵⁷ Zhang et al.²² investigated nucleosome unwrapping by combining the associative memory, water-mediated, structure, and energy model (AWSEM) force field⁵⁸ for protein and the 3SPN model⁵⁹ for DNA. The sequence-dependent dynamics of the nucleosome were probed using CG modeling by de Pablo’s group.⁶⁰ They captured sequence-dependent dynamics of the nucleosome and showed that nucleosome repositioning occurs either by loop propagation or twist diffusion. Based on de Pablo's CG model, Takada’s group shows further aspects of sequence-dependent repositioning dynamics,^61–63 demonstrating two sliding modes based on the nucleosomal DNA sequence.⁶¹ Collepardo et al. have shown that DNA breathing can modify the nucleosome–nucleosome interaction and promote liquid–liquid phase separation (LLPS).²⁹

Higher-resolution chemistry-based CG force fields, such as SIRAH and MARTINI, have successfully described DNA–protein interactions.^64,65 Parameterization follows one of the two main strategies: a bottom-up approach, where the model focuses on reproducing microscopic features based on a more theoretical model such as an atomistic or quantum mechanical model, or a top-down approach, where the model is built in such a way that it can reproduce a set of experimental macroscopic properties such as surface tension and density.⁶⁶ MARTINI uses a bottom-up strategy for bonded interactions and a top-down strategy for non-bonded interactions as a parameterization strategy, while SIRAH uses a bottom-up structure-based approach. The limitation of the MARTINI model lies in base-pairing, which is not specific and requires an elastic network to keep dsDNA in its canonical representation.⁶⁷ However, the SIRAH CG DNA model does not require an elastic network. Furthermore, the model shows good agreement with the structural properties of DNA.⁶⁸ The SIRAH CG^68–70 force field has also been applied to numerous biomolecular systems, including protein–nucleic acid complexes.^71–75 For example, Machado and Pantano⁷⁶ used a hybrid CG atomistic approach to probe the conformational dynamics of the lac repressor–DNA complex. Due to the versatility of the force field, modified parameters to include salt bridges, and previous success in characterizing protein–nucleic acid complexes, we choose the SIRAH force field to characterize the dynamics of nucleosomal DNA in the nucleosome core particle.

Understanding DNA dynamics at the base pair level gives crucial insights into the repositioning of DNA along the histone core. Here, we probe whether nucleosome dynamics is sequence-dependent by comparing six-microsecond atomistic simulations with multiple replicas of the same systems using the SIRAH force field. We consider two different NCP nucleic acid sequences: (i) the human α-satellite palindromic (ASP) sequence and (ii) the strong positioning “Widom-601” DNA sequence. An earlier study using the SIRAH CG force field shows good agreement with atomistic simulation for the Drew–Dickerson dodecamer (DD) at the base pair level.⁷⁷ Motivated by this, we address base pairs and local geometry, such as intra- and inter-base pair parameters, for these two nucleosomal DNA sequences. First, we compare various structural parameters of the nucleosomal DNA based on the radius of gyration, groove width, and intra- and inter-base pair parameters. We find good structural similarity in atomistic and CG simulation base-pair parameters. Next, we quantify the breathing motion of DNA End1 and End2 for both atomistic and CG simulations. We find significant breathing motion at physiological salt concentration for CG simulations compared to AA simulations. We also characterize DNA repositioning around the histone protein in terms of translational and rotational order parameters, as first described by Lequieu et al.⁶⁰ Overall, our study on the nucleosome core particle establishes the accuracy of the SIRAH CG force field in characterizing large-scale motion, including breathing of the DNA. We also demonstrate that this model can probe the translocation and rotation of the DNA in the nucleosome core particle. We demonstrate that methods in dimensionality reduction, such as principal component analysis (PCA), can be applied to DNA order parameters to extract conformations of the DNA where the breathing motion occurs, finding that these conformations correspond to key states in the translocation and rotational space of the free energy landscape.

II. METHODS

A. System preparation

Here, we consider two different sequences of nucleosome DNA in complex with the histone in the nucleosome core particle (NCP): (i) the human α-satellite palindromic (ASP) sequence and (ii) the strong positioning “Widom-601” DNA sequence. The initial coordinates for the ASP NCP are taken from the protein data bank (PDB) ID 1KX5.⁷⁸ The crystal structure of 1KX5 contains 14 Mn²⁺ ions. Because of the absence of force fields for Mn²⁺, we replace these ions with Mg²⁺. For the “Widom-601” sequence, we consider the initial coordinates obtained from the protein data bank having a PDB ID of 3LZ0.⁷⁹ This crystal structure has missing histone N-terminal tails. So, we model these missing tails and other missing residues using the Prime module of the Schrödinger software suite, as previously reported.^80,81 The ASP structure is used as the template for homology modeling. We replace the 8 Mn²⁺ ions in the crystal structure of the homology-modeled 3LZ0 system with Mg²⁺ ions to use the available force fields for Mg²⁺ ions.

B. All-atom simulation of the NCP

Next, we simulate both NCP sequences using an all-atom molecular dynamics simulation using 0.15M NaCl salt. The histone proteins are parameterized using the AMBER19SB force field,⁸² whereas DNA is parameterized using OL15.³³ The Optimal Point Charge (OPC) water model⁸³ is used as solvent around the NCP in an orthorhombic box. Na⁺ and Cl⁻ ions are parameterized using Joung and Cheetham parameters (2008),⁸⁴ while the Li/Merz compromised parameter set⁸⁵ was used for Mg²⁺ ions. According to Kulkarni et al., the Lennard-Jones interaction of Na+/OPC (OW) was improved to better estimate osmotic pressure.⁸⁶ After parameterization, both systems are minimized for 15 000 steps, following the steepest descent and conjugate gradients in the AMBER18 package.⁸⁷ Then, both systems are heated at a constant volume, slowly varying the temperature to 310 K. All bonds involving hydrogen atoms are constrained using the SHAKE algorithm.⁸⁸ The heated structures are further equilibrated for 100 nanoseconds (ns), maintaining a constant pressure of 1 bar using a Berendsen barostat and a constant temperature around 310 K using a Langevin thermostat with a collision frequency of 1.0 ps. The total electrostatic interaction is calculated using a Particle Mesh Ewald (PME) algorithm under full periodic boundary conditions. A cutoff value of 12 Å was considered for the van der Waals interaction, while bonded atoms were excluded from non-bonded atom interactions using a scaled 1–4 value. The Gaussian split Ewald method was used to accelerate the electrostatic calculations. The final production runs are carried out for 6 μs on Anton 2.⁸⁹ The system-specific description is given in Table I.

TABLE I.

Summary of the initial setup of both all-atom (AA) and coarse-grained (CG) simulations.

NCP systems	1KX5-AA	3lZ0-AA	1KX5-CG	3LZ0-CG
Box dimensions (Å)	159 × 191 × 112	171 × 185 × 124	210 × 210 × 210	213 × 213 × 213
No. of atoms	444 888	448 776	114 459	117 837
No. of solvent molecules	104 740	105 816	26 587	27 448
No. of Na+ ions	472	486	896	930
No. of Cl− ions	356	358	783	805
No. of Mg2+ ions	14	8	14	8
Salt concentration (M)	0.15	0.15	0.15	0.15

C. Coarse-grained simulation of the NCP

Next, both NCP systems are simulated using the SIRAH CG force field in the GROMACS package.⁹⁰ Instead of the “four heavy atoms to one CG bead” rule according to the well-known CG MARTINI force field, the SIRAH CG force field handles the peptide bonds in the protein with a high level of detail by maintaining the coordinates of nitrogen (N), α-carbon (Cα), and oxygen (O). SIRAH models the side chain of the protein more coarsely. In the case of DNA, SIRAH reduces the complexity of nucleotides by considering six effective beads for each canonical nucleotide in DNA (A, T, C, and G). Each of the six nucleotide beads are placed in the exact Cartesian coordinates of the corresponding atoms from the atomic representations. Two beads at the phosphate and C5’ carbon position represent the DNA backbone. The phosphate bead carries a −1 charge. Three beads represent the Watson–Crick edge. A–T and G–C base pairs identify each other through electrostatic complementarity. The partial charges add to zero on these CG beads at Watson–Crick edges. In the SIRAH CG representation, the details of sugar moiety are completely ignored, with the five-member ring replaced with one bead at the C1 position, which connects the backbone to the Watson–Crick edge. SIRAH uses a WT4 water model formed by four linked beads, each having a partial charge. This charge pattern is allowed to generate its dielectric permittivity. This CG water model can include ionic strength effects by including explicit salt and reproduces the osmotic pressure of water. To maintain the transferability between different MD packages, SIRAH uses the commonly found classical Hamiltonian function, which typically includes bonded (bond stretching, bending, torsion angle, etc.) and non-bonded (Lennard-Jones and Coulombic potentials) interactions.

Here, we simulate both NCPs following the protocol mentioned by Machado et al.⁷⁰ for three sets of six-microsecond simulations for both nucleic acid sequences—the ASP and Widom-601 sequences. SIRAH tools were extensively used for mapping and analysis purposes. Before mapping to the CG model, the PDB2PQR server⁹¹ sets the protonation state based on the assumption of neutral pH by the AMBER naming scheme. After mapping into the CG model, the protein–DNA complex is solvated in a cubic box of SIRAH WT4 water.⁹² The system is neutralized by adding Na⁺ and Cl⁻ ion at a 0.15M salt concentration. The required number of ions, box dimensions, and total number of atoms and solvent molecules are tabulated in Table I for the 1KX5 and 3LZ0 structures. The box size is chosen to be sufficiently large so that the complex does not interact with its periodic image. Two steps of minimization are performed during system preparation. At first, the protein side chains are energy minimized by restraining the backbone for 50 000 steps using the steepest decent algorithm. This step improves the structural stability of the protein by avoiding significant distortions to the secondary structure of the protein. Then, the whole system was energy minimized for 5000 steps following the steepest descent. Next, solvent molecules are equilibrated around the complex by simulating each complex for 5 ns while placing a harmonic restraint on the position of all CG beads. The temperature of the system is set at 310 K using a V-rescale thermostat.⁹³

To improve the solvation of protein side chains, a further 25 ns equilibration is performed, maintaining the temperature at 310 K. Finally, an unrestrained simulation is carried out for 6 μs, maintaining the pressure at 1 atm using Parrinello–Rahman barostat with isotropic pressure coupling. The time step for all the simulations is fixed at 20 fs. The particle mesh Ewald algorithm with a cutoff of 12 Å and a grid spacing of 2 Å is used for electrostatic interactions. For van der Waals interaction, the cutoff is set at 12 Å. All the parameters during the simulations are kept the same for the 1KX5 and 3LZ0 systems. Each system is simulated for three different replicas. All analyses are done by averaging all available replicas for each NCP system.

The back-mapping from CG to all-atom is performed using the SIRAH back-mapping⁹⁴ tools. All the analyses are done on the obtained back-mapped trajectories to compare with all-atom trajectories. The atomistic positions in the back-mapped trajectories are built on a by-residue basis, maintaining the geometrical reconstruction (internal coordinates) following Parsons et al.⁹⁵ The structures from the initial stage are protonated and minimized using the ff14SB⁹⁶ atomistic force field within the tleap module of AmberTools.⁹⁷

III. ANALYSIS

Each analysis is performed for both NCP systems, comparing the all-atom and back-mapped trajectories obtained from CG simulations. In the rest of the paper, “AA” denotes the all-atom trajectory, while “CG” is used for the back-mapped CG trajectory.

A. Radius of gyration (R_g)

We calculate the radius of gyration (R_g) to compare the structures in the NCP in both AA and CG trajectories for both the protein and the DNA. We consider the backbone phosphate (P) atom for DNA and the α-carbon (C_α) atom for the protein. R_g is defined as the average distance of P/C_α atoms from their centers of mass (R_CM). The square of R_g is defined as

$$R_g^2=\frac{\sum _i{m}_i{\left(r_i-R_{CM}\right)}^2}{\sum _i{m}_i\cdot },$$

where m_i and r_i are the mass and position of the i-th P/C_α atom, respectively.

B. Secondary structure analysis

The secondary structure of the histone protein is analyzed for both CG and atomistic trajectories. For the atomistic trajectory, we used the AmberTools21⁹⁷ secstruct tool, which employs the DSSP algorithm.⁹⁸ In Dictionary of Secondary Structure in Proteins (DSSP), the hydrogen bonding pattern in the backbone amide (N–H) and carbonyl (C=O) positions determines the secondary structure of the protein. We use the sirah_ss tool of SIRAH tools to calculate the secondary structure for the CG trajectory. The secondary structure includes helix, extended-β sheet, and coil conformations. It calculates secondary structure based on hydrogen bond-like (HB) interactions and instantaneous values of the backbone’s torsional angles.^69,94 The secondary structure propensity is calculated based on averaging over all trajectories for both CG and atomistic trajectories.

C. Structural properties for nucleosomal DNA

We evaluate well-known structural parameters applicable to DNA to compare AA and CG trajectories. These are (i) the major and minor groove widths, (ii) the helical base pair step (inter-base pair) parameters, and (iii) the helical base pair (intra-base pair) parameters. All analyses were performed using the Curves+ software.⁹⁹ The inter-base pair parameters consist of three translations, i.e., shift (D_x), slide (D_y), and rise (D_z), and three rotations, i.e., tilt (ϕ_X), roll (ϕ_Y), and twist (ϕ_Z). Schematics are shown in Fig. S1(a). These parameters explain the relative position of two successive base pairs with respect to their short axis, long axis, and their normal.

We also calculate intra-base pair parameters, which comprise three translations, i.e., shear (S_X), stretch (S_Y), and stagger (S_Z), and three rotations, i.e., buckle (θ_X), propeller (θ_Y), and opening (θ_Z). Schematics are shown in Fig. S1(b). These parameters are calculated by determining the rigid-body transformations that map one base reference system to the others.

D. Principal component analysis

Principal Component Analysis (PCA) is a technique to characterize the collective motions of a molecule. It is a technique in dimensionality reduction by which one can identify configurational space having few degrees of freedom. This configurational space can be built by generating a 3N × 3N covariance matrix (C). Therefore, the C matrix is diagonalized, where the elements of the matrix are represented as $\text{C}=⟨{\left(\text{q}-⟨\text{q}⟩\right)}^{\text{T}}\left(\text{q}-⟨\text{q}⟩\right)⟩$, in which q corresponds to the coordinates and $⟨\cdots ⟩$ indicates the average over time. The diagonalization of this matrix gives the i-th eigenvector and i-th eigenvalues. The projection of the trajectory on the eigenvector provides the principal components (PCs). We also calculate the explained variance ratio, which quantifies the proportion of the total variance in the input data captured by each PC. It is calculated based on the ratio of each PC’s eigenvalue to the total sum of eigenvalues. This parameter indicates the importance of each PC. Here, we use dinucleotide base pair parameters as input coordinates for the PCA. The first two PCs were used to plot a two-dimensional free energy landscape. The free energy landscape can be obtained using the following equation:$\mathrm{\Delta }G\left(\text{PC}1,\text{PC}2\right)=-{\text{k}}_{\text{B}}\text{Tln}\left[\text{P}\left(\text{PC}1,\text{PC}2\right)/{\text{P}}_{\max }\right]$. Here, ΔG represents the free energy of the state, $\text{P}\left(\text{PC}1,\text{PC}2\right)$ is the joint probability distribution for PC1 and PC2, k_B is Boltzmann’s constant, T is the temperature, and P_max represents the maximum probability density.

E. Nucleosome dynamics

1. Breathing motion of nucleosomal DNA

We characterize the breathing motion of the nucleosomal DNA occurring in the DNA end regions due to the transient opening/closing of DNA entry/exit regions or in between the inner gyres, where two gyres come closer or move away from each other due to the modulation of histone–DNA contacts. We quantify the scope of DNA end breathing by calculating the breathing distance in the simulated structure, defined as the distance between the center of mass of the SHL0 bp and the terminal bp present in the entry/exit region. Here, we represent the change in end breathing with respect to the crystal structure. Positive values of end breathing distance indicate outward breathing with respect to the crystal structure, while negative values indicate inward breathing. We further quantify the breathing motion^24,25 by calculating the displacement of each bp’s average distance (ΔR) over the last 3 μs of the simulated trajectories relative to the center of mass of nucleosomal DNA non-hydrogen atoms in the crystal structure.

2. Translocation and rotational order parameters

To quantify the movement of nucleosomal DNA around the histone protein, we observe the translocation and rotation of DNA position relative to the protein dyad through the translocation order parameter (S_T) and the rotational order parameter (S_R).⁶⁰ Here, S_T is defined as

$$S_T=\frac{1}{\lambda }⟨\pm \arccos \left(\frac{\mathit{P}\cdot {\mathit{P}}_0}{|\mathit{P}\Vert {\mathit{P}}_0|}\right)⟩,$$

where P is a vector for a specific base pair that connects the histone center of mass to the center of mass of the respective base pair, P₀ is the value of the respective P in the crystal structure, and λ is a conversion factor that converts radians into the base pairs of DNA translocation. The value of λ is 0.08 rad/bp, as mentioned in Ref. 60. The sign of S_T is positive if (P × P₀).f ≤ 0 (negative if > 0), where f is a vector whose direction is along the center of the nucleosomal DNA superhelix. The positive value of S_T signifies forward translocation of nucleosomal DNA toward the 5′ end, whereas the negative value describes backward translocation toward the 3′ end. The schematic is shown in Fig. S1(c).

The S_R order parameter due to the rotational position of DNA is defined as

$$S_R=⟨\pm \arccos \left(\frac{\mathit{P}\cdot \mathit{B}}{|\mathit{P}\Vert \mathit{B}|}\right)⟩,$$

where B is a vector connecting the center of the given base step on the sense strand to its complementary base step on the antisense strand. All other terms are defined the same way S_T. The value of S_R is positive if (P × B).D ≤ 0 (negative if > 0), where D is a vector from the 5′ to 3′ direction along the sense strand. If S_R = 1/2, then the minor groove is oriented away from the histone core, whereas S_R = −1/2 signifies the orientation of the minor groove toward the histone core. The schematic is shown in Fig. S1(d). S_T and S_R order parameters have been used earlier to quantify the spatial positioning of DNA around histone proteins.⁶⁰

3. Minimum free energy path calculation

To identify the minimum free energy path between two conformations over a 2D free energy surface, we use the string method,¹⁰⁰ as implemented in MEPplot.¹⁰¹ This method describes the pathway between two conformational states as a discrete set of points (known as beads) that evolve iteratively until they converge to a minimum free energy path. First, we identify two initial conformations from two different energy minima of a 2D free energy surface. Finally, we obtain a path between two conformations using a gradient descent method, where each point moves in the direction of the local gradient of the free energy surface in an iterative way.

IV. RESULTS

We perform comparative simulations of two well-known sequences of the NCP with the SIRAH force field and compare them against fully atomistic simulations. We use the ASP and the Widom-601 NCP sequences. Figure 1(a) shows the ASP sequence's crystal structure and its CG representation. The orientation of the nucleosomal DNA base pairs is represented with respect to the central base pair, commonly known as superhelical location (SHL) zero. In general, each SHL contains ∼10 base pairs. It starts with SHL0 and ends at SHL ±7. Figure 1(b) shows a comparison of the sequence of the nucleosomal DNA for both the ASP and the Widom-601 sequences. Several flexible dinucleotide steps, such as TA in the minor groove block, exist for the Widom-601 sequence, forming narrow conformations of the DNA. Both the minor grooves at SHL ±1.5 for the Widom-601 sequence contain the strong positioning motif TTTAA, which enhances its positioning affinity. Overall, there is a 15% greater G|C content in the Widom-601 sequence than in the ASP sequence. However, both sequences have similar G|C content in the minor grooves. Notably, the G|C content in the 601-R and 601-L halves of the DNA are different, with the right half containing a higher G|C content, which is thought to make it more rigid with fewer contacts with the DNA and easier to open up under force, as shown by Ngo et al.¹² Overall, both the presence of the G|C content and the strong positioning motif TTTAA at SHL ±1.5 makes the Widom-601 one of the strongest positioning nucleosome sequences.

FIG. 1.

(a) Crystal structure of the human α-satellite palindromic (ASP) sequence (PDB ID:1KX5) and its CG representation. The DNA is shown in blue, while the histone is shown in red. (b) Comparison of the Widom-601 and the human α-satellite (ASP) DNA sequences. The blue color indicates a minor groove in the DNA sequence, while the black color represents a major groove. Both halves of the Widom-601 (601-R and 601-L) sequence are shown, while for the ASP sequence, only one half is present as it is a palindromic sequence.

A. Structural comparison

A comparison of the radii of gyration (R_g) of both fully atomistic and CG trajectories shows a direct comparison of the DNA at CG and all-atom levels. Figure 2(a) shows the change in R_g over time for the ASP DNA sequence. Here, we characterize three independent replicas of CG trajectories (Rep1, Rep2, and Rep3) with a single trajectory using all-atom (AA) force fields. In Fig. 2(b), we present the R_g histogram for all-atom and CG trajectories. The blue line indicates the average histogram over three independent CG trajectories. We perform block averaging to calculate the average value and error value for each quantity. The average values of the R_g for the DNA over AA and CG trajectories are 45.69 ± 0.06 and 47.37 ± 0.05 Å, respectively. The small value of the error suggests that each simulation is statistically converged. Figure 2(c) depicts the overlapped equilibrium conformation of DNA for both the AA (green) and the CG (blue) trajectories. The values of R_g for the equilibrium AA and CG structures are 45.77 and 46.13 Å, respectively. We further compare the R_g of the DNA over time for the Widom-601 sequence [Fig. 2(d)]. Figure 2(e) illustrates the distribution of R_g for that sequence. The average R_g values are 45.52 ± 0.03 Å for CG and 47.39 ± 0.05 Å for AA. A representative equilibrium conformation for the Widom-601 DNA sequence is shown in Fig. 2(f). Here, the values of R_g for AA and CG structures are 45.64 and 46.08 Å, respectively. The average R_g value of DNA obtained using the CG SIRAH force field for both sequences increases compared to the AA force field, indicating that the DNA samples have more conformational states in the CG trajectories.

FIG. 2.

(a) Time evolution of the radius of gyration (R_g) of the DNA considering phosphate atoms for the ASP sequence. The results for three different replicas for the CG and all atom trajectories are shown. (b) Histogram of R_g for the three different CG replicas, including atomistic data. (c) Representative equilibrium structures for the ASP DNA obtained from the CG and AA trajectories. Here, the green color represents the structure obtained from atomistic simulations, while the blue color represents the back-mapped structure from the CG trajectory. (d) Time evolution of the R_g of DNA for the Widom-601 sequence, including three different CG replicas and atomistic simulation. (e) Histogram of the R_g for the Widom-601 sequence. (f) Representative overlapped structure for the Widom-601 DNA. The blue color represents the back-mapped atomic structure of the CG trajectory, while the green color represents the structure obtained using atomistic simulations.

Next, we compare the R_g of the histone protein, considering the C_α atom at different levels of detail. Figure S2(a) illustrates the change in the R_g over time for the ASP histone protein, displaying three independent replicas of CG trajectories alongside trajectories using the all-atom force fields. In Fig. S2(b), we present the histograms of R_g for both trajectory types. The average R_g values for the histone over the AA and CG trajectories are 34.26 ± 0.03 and 37.09 ± 0.14 Å, respectively. Figure S2(c) depicts the overlapped equilibrium conformation of the histone for both AA (green) and CG (blue) trajectories. We compare the R_g of the histone over time for another NCP sequence, the Widom-601, in Fig. S2(d). Figure S2(e) further details the distribution of R_g for that sequence, with average R_g values of 34.04 ± 0.1 for AA and 36.54 ± 0.09 Å for CG. Figure S2(f) shows an overlapped equilibrium conformation of the histone proteins. For the histone, the average R_g value based on the CG force field shows good agreement with the atomistic force field results. Although similar to the DNA, the distribution of R_g states sampled for the protein CG trajectories is broader than that of the AA counterparts. Next, we compare the secondary structure percentage over the CG and AA trajectories. Figure S2(g) shows the average percentage of the helix, extended, and coil conformations for the ASP sequence. The percentage of helix conformation is lower for the CG compared to the AA simulation. The extended and coil conformation percentage is higher for the CG simulation than for the atomistic counterpart. A similar scenario also holds for the Widom-601 [Fig. S2(h)], i.e., a lower helical percentage in CG and a higher percentage of extended and coil conformations compared to the atomistic simulation.

Next, we characterize the DNA structure regarding groove width and dinucleotide base-pair step parameters. Figure S3(a) shows the schematic of DNA major and minor groove widths over the overlapped equilibrated DNA conformation for both AA (green) and CG (blue) trajectories. The distribution of the major groove width (d_Majw) for the ASP DNA [Fig. S3(b)] suggests larger widths for the CG trajectories (blue) with an average value of 11.88 ± 0.07 Å as compared to the AA trajectory (green). The average d_Majw over the AA trajectory is 11.44 ± 0.04 Å. The average minor groove width (d_Minw) for the ASP DNA over the CG trajectory and the AA trajectory is 5.44 ± 0.02 and 5.8 ± 0.01 Å, respectively. Figure S3(c) depicts that the distribution peak of the minor groove width distribution is lower for the CG (blue) trajectory than for the AA (green) trajectory. The distribution of groove widths for the Widom-601 shows a similar behavior to that of the ASP sequence for d_Majw [Fig. S3(d)] and d_Minw [Fig. S3(e)]. The average d_Minw is 5.63 ± 0.01 Å over the CG trajectory, while for the all-atom trajectory, the average d_Minw is 5.68 ± 0.02 Å. Along the CG trajectory, the d_Majw average is 11.67 ± 0.01 Å, slightly higher than the average of 11.43 ± 0.01 Å observed over the all-atom trajectory. The similarity in major and minor groove widths suggests that the SIRAH CG force field can reliably approximate the groove widths of the DNA in both systems.

Next, to better understand the orientation of the DNA at the base pair level, we focus on the DNA inter-base pair parameters, which provide valuable insights into the structure and function of DNA molecules. Figure 3 shows a histogram of different inter-base pair parameters obtained from CG and AA trajectories for the ASP DNA sequence. The experimental value measured from the x-ray structure of the corresponding quantity is shown as a vertical dashed line. Table II tabulates the average inter-base pair parameter values obtained from CG and AA trajectories. The distributions of shift (D_X) [Fig. 3(a)] parameters obtained from CG (blue) and AA (green) trajectories show close overlap. The average D_X value obtained from CG trajectories is 0.02 Å, whereas for AA trajectories, it is 0.0006 Å (see Table II). Conversely, while the distributions of slide (D_Y) [Fig. 3(b)] parameters and rise (D_Z) parameters [Fig. 3(c)] from CG and AA trajectories did not overlap, the average value of these parameters across CG and AA trajectories shows minimal disparity (see Table II). Figures 3(d)–3(f) show a histogram of rotational inter-base pair parameters, i.e., tilt (ϕ_X) [Fig. 3(d)], roll (ϕ_Y) [Fig. 3(e)], and twist (ϕ_Z) [Fig. 3(f)]. The histogram of tilt for CG (blue) and AA (green) trajectories exhibits complete overlap. CG trajectories yield an average tilt value of −0.28°, whereas the average tilt value of the AA trajectory stood at −0.14° (see Table II). The average twist value over the CG and AA trajectories is 32.00° and 34.02°, respectively. The roll order parameter shows a distinct behavior compared to the other parameters. The average value of roll over the CG trajectory is −8.42°, while for the AA trajectory, the average value of roll is 2.19°. Figure 4 shows similar distributions of inter-base pair parameters for the Widom-601 sequence. The distribution of the shift (D_X) parameter [Fig. 4(a)] for CG overlaps with that of the AA trajectory. The average shift value obtained from CG is nearly equal to the AA average (Table II). While the distributions of the slide [Fig. 4(b)] and rise [Fig. 4(c)] parameters from CG and AA trajectories do not overlap, the average values of these parameters along CG and AA trajectories show minor deviations. The rotational inter-base pair parameter tilt exhibits a perfect overlap in distributions between the CG and AA trajectories [Fig. 4(d)]. In addition, the average value of the twist parameter [Fig. 4(f)] over CG and AA trajectories is 31.62° and 34.33°, respectively. The roll parameter shows a similar behavior to that of the ASP sequence. The distributions of roll over the CG and the AA simulations are shown in Fig. 4(e). The average roll over the CG trajectories is −7.64°, while for the AA trajectory, it is 1.57°. Generally, the agreement of inter-base pair parameters between the CG and AA force fields is good. The deviation is mainly observed for the roll order parameter for both sequences. The vertical dashed line in each figure represents the value of the corresponding quantity obtained from the experimental x-Ray structure.

FIG. 3.

Histogram of DNA inter-base pair parameters for the ASP sequence: (a) shift, (b) slide, (c) rise, (d) tilt, (e) roll, and (f) twist. The results for both the atomistic and three different CG replicas are shown. The mean and standard error of the mean are tabulated in Table II. The dashed line shows the value of the corresponding quantity obtained based on the 1KX5 crystal structure.

TABLE II.

Average values of inter-base pair parameters obtained from AA and CG trajectories using Curves+.⁹⁹ The standard error of the mean is shown in parentheses.

NCP systems	1KX5-CG	1KX5-AA	3LZ0-CG	3LZ0-AA
Shift (DX) (Å)	0.02 (0.01)	0.0006 (0.001)	−0.02 (0.01)	0.03 (0.003)
Slide (DY) (Å)	−0.58 (0.01)	−0.01 (0.008)	−0.59 (0.02)	−0.03 (0.02)
Rise (DZ) (Å)	3.54 (0.01)	3.36 (0.02)	3.6 (0.02)	3.34 (0.004)
Tilt (ϕX°)	−0.28 (0.14)	−0.14 (0.05)	0.55 (0.14)	0.19 (0.02)
Roll (ϕY°)	−8.42 (0.3)	2.19 (0.11)	−7.64 (0.37)	1.57 (0.08)
Twist (ϕZ°)	32.00 (0.36)	34.02 (0.11)	31.62 (0.19)	34.33 (0.03)

FIG. 4.

Histogram of DNA inter-base pair parameters for the Widom-601 sequence: (a) shift, (b) slide, (c) rise, (d) tilt, (e) roll, and (f) twist. The results for both the atomistic and three different CG replicas are shown. The mean and standard error of the mean are tabulated in Table II. The dashed line shows the value of the corresponding quantity obtained based on the 3LZO crystal structure.

Next, the structural comparison between CG and AA is examined based on intra-base pair step parameters. Table III tabulates the average values of the intra-base pair parameters for the CG and AA trajectories. Figure S4(a) shows distributions of the shear parameters for CG (blue) and AA (green) trajectories for the ASP sequence. The average value of the parameter over the CG trajectory is 0.13 Å, while for AA, the value is 0.03 Å (Table III). The conformations sampled for the CG trajectory are much broader than those for the AA trajectory. The distribution overlaps for the stretch parameter [Fig. S4(b)], although the CG trajectory exhibits a significantly broader range of conformations than AA. In the CG trajectory, the parameter averages −0.02 Å, while for the AA trajectory, the average value is 0.03 Å. The distribution of the stagger parameter [Fig. S4(c)] for CG and AA does not overlap, although the average value of the stagger over CG and AA trajectories is 1.50° and 0.02°, respectively. The rotational intra-base pair parameter buckle exhibits overlaps between the AA (green) and CG (blue) trajectories [Fig. S4(d)]. The propel parameter shows distinct behaviors for the AA and CG simulations [Fig. S4(e)]. The average value of the propel parameter for CG is −2.57°, while for AA, the value is −13.05°. For the opening parameter [Fig. S4(f)], the average value for CG is 8.00°, and for AA, it is 2.85°. Most rotational inter-base pair parameters show good agreement in the average values along CG and AA trajectories, except for propel and opening. We further investigate the inter-base pair step parameter for the Widom-601 sequence. Figure S5 shows the distribution of the parameters for both CG and AA trajectories. The distributions of the CG and AA trajectories partially overlap for the shear [Fig. S5(a)] and stretch parameters [Fig. S5(b)]. The average value of both quantities along the CG and AA trajectories is nearly equal (Table III). The distribution [Fig. S5(c)] does not overlap for the stagger parameter, although the average value for CG is 0.98 Å, and for AA, it is 0.07 Å. The distribution for the buckle parameter [Fig. S5(d)] overlaps for CG and AA. The average propel parameter [Fig. S5(e)] value for CG is −0.56°, contrasting with AA's value of −11.68°. As for the opening parameter [as depicted in Fig. S5(f)], CG averages 5.59°, whereas AA averages 2.32°. Most intra-base pair parameters exhibit consistent average values along the CG and AA trajectories, except for propel and opening, where notable differences are observed, similar to the ASP sequence.

TABLE III.

Average values of intra-base pair parameters obtained from AA and CG trajectories. The standard error of the mean value is shown in parentheses.

NCP systems	1KX5-CG	1KX5-AA	3LZ0-CG	3LZ0-AA
Shear (SX) (Å)	0.13 (0.01)	0.03 (0.01)	−0.12 (0.01)	−0.02 (0.01)
Stretch (SY) (Å)	−0.02 (0.05)	0.03 (0.006)	0.01 (0.02)	0.07 (0.03)
Stagger (SZ) (Å)	1.50 (0.008)	0.02 (0.02)	0.98 (0.02)	0.07 (0.009)
Buckle (θX°)	0.95 (0.44)	−0.49 (0.08)	0.63 (0.26)	0.77 (0.06)
Propel (θY°)	−2.57 (0.16)	−13.05 (0.16)	−0.56 (0.6)	−11.68 (0.17)
Opening (θZ°)	8.00 (0.88)	2.85 (0.07)	5.59 (0.54)	2.32 (0.07)

B. Breathing motion of nucleosomal DNA

Here, we quantify the extent of end-breathing by computing the breathing distance in the simulated structure, defined as the distance between the center of mass of the SHL0 bp and the terminal bp present at the entry/exit region. We compare the breathing motion of the nucleosomal DNA ends for both sequences. Figure 5 shows a histogram of the breathing distance for both End1 and End2, depicted as the difference with respect to the crystal structure. For the atomistic trajectory, the breathing distance for both the DNA ends [Figs. 5(a) and 5(b), marked in green] fluctuates near zero for the ASP sequences. The average value of the breathing distance for End1 is 1.22 Å, and for End2, it is 0.46 Å. For the CG trajectory, the breathing distance increases for both ends [Figs. 5(a) and 5(b), marked in blue]. The average breathing distance for End1 is 17.69 Å, and for End2, it is 6.31 Å. The extent of breathing for both ends is different, with End1 displaying more extensive breathing since breathing motion is asymmetric, as suggested by earlier theoretical and experimental studies.^11,22,23 Figure 6 further displays the time evolution of the breathing distance for both End1 and End2, represented as the difference with respect to the crystal structure. Figures 6(a)–6(c) show snapshots of the nucleosomal DNA at different times from the atomistic simulation, indicating negligible breathing motion.

FIG. 5.

Normalized probability distribution of the breathing distance for the nucleosomal DNA for (a) End1 (ASP-L) and (b) End2 (ASP-R) for the ASP sequence and (c) End1 (601-L) and (d) End2 (601-R) for the Widom-601 sequence. The results for both the atomistic and three different CG replicas are shown.

FIG. 6.

Snapshots illustrating the motion of the nucleosomal DNA along the trajectory at 0, 3, and 6 μs. ASP DNA sequence obtained from (a)–(c) atomistic simulations and (d)–(f) CG simulations. Widom-601 sequence obtained from (g)–(i) atomistic and (j)–(l) CG simulations.

On the contrary, for the CG simulation [Figs. 6(d)–6(f)], the nucleosomal DNA shows substantial breathing motion at both t = 3 μs [Fig. 6(e)] and t = 6 μs [Fig. 6(f)]. We further check the breathing distance for both ends of the Widom-601 sequence. The histogram of the breathing distance for End1 (601-L) [Fig. 5(c)] suggests a greater extent of breathing for the CG than for the all-atom trajectories. The average value of the breathing distance for CG is 14.84 Å, while for AA, the average breathing distance is 3.24 Å. End2 (601-R) of the Widom-601 sequence shows a similar behavior, i.e., a higher range of breathing distance for CG than for AA [Fig. 5(d)]. The average breathing distance for End2 is 6.84 Å. In contrast, for AA, the average value of breathing distance is 1.75 Å. Here, different ends also show differential breathing, similar to the ASP sequences. End1 (601-L) shows a higher distribution of breathing distances than End2, indicating asymmetric breathing. Figures 6(g)–6(i) show the motion of DNA at different times for the Widom-601 sequence. The breathing motion is insignificant for the structures obtained from the atomistic trajectory over the entire simulation of 6 μs. Meanwhile, structures obtained from CG simulations show substantial breathing motion [Figs. 6(k) and 6(l)]. The SIRAH CG force field exhibits higher breathing than the AA simulations, with differential breathing motion at both ends of the DNA for both ASP and Widom-601 sequences.

We further quantify the breathing by calculating ΔR, which is the displacement in the average distance of each DNA base pair center represented in SHL notation over the simulated trajectory compared to the crystal structure in Fig. S6. We find a higher value of ΔR (nearly 10 Å) at SHL -7 for the ASP CG trajectories in one end, while the other has a lower value of ΔR [Fig. S6(a)]. We did not find large values of ΔR in the atomistic simulation of ASP as in the CG trajectories, suggesting negligible breathing motion for both ends. The significant breathing motion is also visible for the Widom-601 sequence at both ends of DNA [Fig. S6(b)]. However, the SHL +7 region (601-L) shows a much higher breathing for the Widom-601 sequence than for the ASP sequence (ASP-L).

C. Principal component analysis (PCA) based on base-pair parameters

We further perform a conformational analysis of DNA based on the free energy landscape (FEL) obtained by projecting MD trajectories onto the principal components for the DNA inter-base pair parameters (detailed in Sec. II). At first, we compare the CG and AA trajectories in principal component space by quantifying the overlap of the covariance matrices.¹⁰² We use the correlation matrix distance (CMD) method to characterize the equivalence of both CG and AA trajectories. The method of calculating the CMD is given in the supplementary material. The CMD has a value of 0 when covariance matrices are identical, while the value of 1 indicates a higher extent of difference between the two matrices. The value of the CMD between covariance matrices is 0.87 for the ASP sequence, while for Widom-601, the value is 0.89, suggesting dissimilarity in PC space between CG and AA simulations for both sequences. We further tried to understand the dissimilarity in PC space by quantifying the breathing motion in the system, as breathing motion is more prominent in the CG simulations than in the AA simulations. Using an explained variance ratio plot, we plot the contribution of the first 10 PCs, as shown in Fig. S7(a) (sequence ASP, AA simulation) and Fig. S7(b) (sequence ASP, CG simulation). This suggests that the contribution of the first two PCs captures ∼34% of the conformational dynamics of the ASP DNA, as characterized by the dinucleotide inter base-pair parameters. Figure 7(a) shows the FEL for the CG trajectory of the ASP sequence, suggesting three different energy minima. We extract conformations from each minimum to better understand the conformation of the nucleosomal DNA. The end breathing distance for three different conformations from different clusters is substantially different. The extent of the distance for End1 is the maximum for the conformation from region ii (conformation $i{i}_{\mathit{ASP}}^{CG}$), i.e., 22.79 Å. In contrast, from region iii (conformation $ii{i}_{\mathit{ASP}}^{CG}$), the value is lower, i.e., 1.04 Å [Fig. 7(a)]. The DNA conformation from region i (conformation $i_{\mathit{ASP}}^{CG}$) also shows a more significant breathing, i.e., 16.7 Å. The extent of breathing for End2 is lower than for End1 for conformation from regions i and ii, but for region iii, the extent of breathing is higher. The conformation in region ii indicates inward movement as compared to the crystal structure. The change in the breathing distance for End2 is higher for conformations from region ii, i.e., 11.93 Å, and from region i, it is 5.31 Å. Overall, the FEL suggests that conformations from different free energy minima show different levels of extent in breathing motion for both ends of the nucleosomal DNA. We find two different energy minima for the atomistic simulation for the ASP sequence [Fig. 7(b)]. The conformation obtained from region i (conformation $i_{\mathit{ASP}}^{AA}$) shows inward movement with respect to the crystal structure for both ends. End2 is showing a much larger extent than End1. The structure from region ii (conformation $i{i}_{\mathit{ASP}}^{AA}$) shows the opposite behavior, i.e., End1 shows a more significant extent of breathing motion than End2. For the atomistic simulations, the extent of breathing on both ends is lower than in the CG simulation, but the asymmetry in the breathing distance between the two ends is maintained.

FIG. 7.

Principal component analysis (PCA) based on DNA inter base pair parameters. Free energy landscape (FEL) based on PC1 and PC2 for (a) the CG trajectory and (b) atomistic simulation for the ASP sequence. FEL for (c) the CG trajectory and (d) the atomistic simulation for the Widom-601 sequence. The energy minima are marked, and structures with the minimum energy are shown.

Next, we extract conformations from the FEL for the Widom-601 sequence. The contribution of the PCs is shown in Fig. S7(c) (sequence Widom-601, AA simulation) and Fig. S7(d) (sequence Widom-601, CG simulation). This suggests that the contribution of the first two PCs captures ∼42% of the conformational dynamics of the Widom-601 DNA, as characterized by the dinucleotide inter base-pair parameters. Figure 7(c) shows the FEL for the CG trajectories based on the first two PCs. We find two different minima (marked as i and ii) in the PCA space. The DNA conformation from region i (conformation $i_{\mathit{Widom601}}^{CG}$) shows a breathing distance of 11.88 Å at End1 (601-L), while End2 (601-R) shows a breathing distance of 1.72 Å in the reverse direction. The conformation from region ii (conformation $i{i}_{\mathit{Widom601}}^{CG}$) possesses a nearly equal breathing distance at End1 (601-L). It shows a distance of 11.49 Å, although End2 (601-R) shows a breathing distance of 2.51 Å. The atomistic simulation of Widom-601 indicates a single minimum [Fig. 7(d), conformation $i_{\mathit{Widom601}}^{AA}$]. The breathing distance at both ends shows an inward breathing with respect to the crystal structure. End1 (601-L) and End2 (601-R) show breathing distances of 3.87 and 0.81 Å, respectively. The atomistic simulation for Widom-601 shows a lower amount of breathing than the CG simulation within the simulated timescale. Still, the higher breathing distance of End1 (601-L) is maintained in both AA and CG simulations.

D. DNA repositioning around the histone core

To further understand nucleosomal dynamics, we probe nucleosomal DNA repositioning around the histone core using translocation (S_T) and rotational (S_R) order parameters (see Sec. III). Figure 8(a) shows a two-dimensional free energy plot for the ASP sequence as a function of S_T and S_R, considering back-mapped CG trajectories using the SIRAH force field. The free energy surface suggests a strong tendency for rotational repositioning. However, translational repositioning is limited mostly within −0.4 to 0.4. The free energy minimum corresponds to S_T ≈ 0 with the minor groove toward the histone core. For the atomistic simulation [Fig. 8(b)], the free energy landscape indicates two distinct free energy minima around S_T ≈ 0, with minor grooves toward the histone core. The free energy landscape for both S_T and S_R for the Widom-601 sequence shows multiple minima [Fig. 8(c)] for this sequence around positive values of S_T. These free energy minima correspond to both S_R > 0 and S_R < 0. This suggests that the minor groove is aligned toward and away from the histone core in the free energy minima, respectively. The FEL for the atomistic force field for the Widom-601 sequence [Fig. 8(d)] suggests two distinct minima in the free energy landscape. The difference with the CG counterpart is for AA, the energy minima correspond to S_T < 0, suggesting backward translocation of the nucleosomal DNA. Two distinct minima are observed at S_R > 0 and S_R < 0, suggesting a tendency to align minor grooves toward and away from the histone core, respectively. This behavior is similar to that of the ASP sequence [Fig. 8(b)]. Overall, the result suggests that the CG force field can sample an extended range of possible states in the free energy landscape for both sequences, indicating multiple minima. In contrast, the AA force field restricts the system from exploring the available free energy landscape.

FIG. 8.

Free energy surface for DNA repositioning around histone based on (a) the CG trajectory, (b) the atomistic trajectory for the ASP sequence, (c) the CG trajectory, and (d) the atomistic trajectory for the Widom-601 sequence.

V. DISCUSSION

Overall, in this study, we focus on how the CG SIRAH force field can reproduce the conformations of nucleosomal DNA obtained using long-time molecular dynamics simulations using a state-of-the-art atomistic force field. Figure 2(b) indicates a minimal difference in R_g for the ASP nucleosomal DNA between the CG and AA models. The behavior of R_g is still preserved for the Widom-601 nucleosomal DNA [Fig. 2(e)]. For the histone, we obtain a similar behavior, i.e., the difference in the average R_g value between CG and AA trajectories is minimal. This indicates little deviation in R_g for both the nucleosomal DNA and the histone protein using the SIRAH ff compared to the AA force field. The CG indicates a slight expansion tendency, while the AA indicates compaction for both the DNA and the histone. This discrepancy is likely due to the solute–solvent interaction in the SIRAH CG force field, which is not finely parameterized as in AA, and the higher flexibility of CG force fields. Next, we focus on various structural parameters, which mainly focus on the local geometry of the DNA. We characterize the groove width for the nucleosomal DNA. Figure S3 indicates that average major and average minor width values do not deviate much between CG and AA trajectories. We compare inter-base pair parameters obtained from CG and AA trajectories for the ASP and the Widom-601 DNA sequences. We show the experimental value of each parameter obtained based on the x-ray crystal structure. The atomistic simulation results are more aligned with the experimental value as compared to the CG simulations. Most inter-base pair parameters show good agreement between CG and AA trajectories except for the roll inter-base pair parameter for both sequences, which tends to sample more negative value. This study is consistent with earlier studies of DNA based on the SIRAH force field.^74,77 Sometimes, the calculation of these numerical order parameters is biased toward the used mathematical formalism as well as the reference coordinate system, such as the roll parameter that is mathematically dependent on helix inclination¹⁰³ and the coordinate system used.¹⁰⁴ To address this issue, we perform both AA and CG simulations of B-DNA dodecamer (details are provided in the supplementary material) using the OL15 force field and the SIRAH CG force field. We use both Curves+ and the NUPARM software¹⁰⁵ to calculate the inter-base pair parameters for the B-DNA dodecamer. The analysis indicates that the average value of the roll parameter remains negative for the SIRAH CG force field, independent of the Curves+ and NUPARM software. Hence, the deviation for roll mainly occurs since the SIRAH CG force field tends to sample more negative values. For both NCP sequences, the twist value for the SIRAH CG force field samples lower values as compared to the crystal structure [Figs. 3(f) and 4(f)]. The B-DNA analysis also indicates similar trends independent of the software used for the calculation (Figs. S8 and S9, Table S1). Hence, the SIRAH CG force field indicates an under twisted behavior as compared to the experimental structure. We further compare various intra-base pair parameters of the nucleosomal DNA to understand better the structural similarity between AA and CG force fields. All intra-base pair parameters mainly show good similarity between AA and CG trajectories; nevertheless, the AA results agree quite well with the experimental values as compared to the CG results. However, propel and opening show a more significant deviation between the CG and AA trajectories for both sequences. Despite some disparity in roll, propel, and opening order parameters between CG and AA trajectories, the SIRAH force field effectively captures most structural parameters. This motivates us to observe the extent of breathing motion for both End1 and End2 of the nucleosomal DNA. Neither sequence shows significant breathing motion within the simulated timescales using the atomistic force field at physiological salt concentrations. However, the CG trajectory based on the SIRAH force field shows a reasonable breathing motion for both End1 and End2 within the simulated timescale. This extent of breathing motion is observed for both sequences. For the ASP sequence, End1 (ASP-L) shows a more significant breathing motion than End2 (ASP-R). This result is consistent with earlier simulation results.^23,24 Chakraborty and Loverde²³ showed that for the ASP sequence, a loop was formed at this same end [End1 (ASP-L)] as compared to End2 (ASP-R). This asymmetric breathing motion in our CG simulation also aligns with earlier experimental studies by Ngo et al.¹² Using a single molecule optical trapping technique, they showed that one end interacts with the histone more strongly than the other, as it is more flexible (601-L). Hence, a higher force is required to unwrap that end. Such an asymmetrical nature of DNA breathing is essential to understand, as it might be a gene expression control factor affecting DNA exposure. In the work of Khatua et al.,²⁴ we find a similar result for the ASP sequence based on our 12 μs simulation under high salt conditions. However, we find a much larger breathing in the case of the Widom-601 sequence. End2 (601-R) shows more extensive breathing than End1 (601-L); furthermore, the overall breathing motion is higher in the Widom-601 sequence than in the ASP sequence. Conversely, in our CG study for both sequences, we found no sequence-specific bias regarding the breathing distance; indeed, End1(601-L) shows a more significant breathing motion than End2 (601-R).

We next conduct further analysis of the breathing distance in DNA conformations obtained after performing PCA on the DNA base pair parameters. We identify both outward and inward breathing motions with respect to the crystal structure for both sequences at both Ends. Multiple minima with higher breathing distances have been observed for CG trajectories compared to atomistic simulation. Hence, the SIRAH CG force field can efficiently sample multiple minima relative to the atomistic force field. Next, we investigate the repositioning of the nucleosomal DNA around histone. To understand the DNA repositioning around a histone, we calculate two additional order parameters, i.e., S_T and S_R. We show the free energy surface based on both S_T and S_R. The SIRAH CG force field can sample multiple minima of the free energy landscape, while the AA force field shows restricted dynamics within specific regions of the free energy landscape. This result is consistent with earlier results of the FEL based on PCA of inter-base pair parameters.

We further elucidate the DNA repositioning mechanism from these free energy surfaces. In the free energy surface based on the base pair parameter, we find different free energy minima at different positions of the free energy surface [Figs. 7(a) and 7(c)]. We next identify the conformations at different minima and identified these conformations on the free energy surface obtained using translation (S_T) and rotation (S_R) order parameters (Fig. 8). Different conformations are marked on the free energy surface in Fig. 8. For the ASP sequence, one conformation belongs to energy minima for the CG trajectory (conformation $i_{\mathit{ASP}}^{CG}$) [Fig. 8(a)]. For the ASP atomistic simulation, we find two conformations at two different energy minima [Fig. 8(b)] at two different regions, suggesting restricted sampling in those energy minima. For the Widom-601 atomistic simulation, we find a similar behavior, i.e., two distinct conformations at two different energy minima [Fig. 8(d)]. For the case of the Widom-601 sequence, we find two distinct conformations at two different energy minima [Fig. 8(c)] along with possible multiple paths between these two conformations. Conformation $i{i}_{\mathit{Widom601}}^{CG}$ belongs to a region where S_R<0, while the other conformation $i_{\mathit{Widom601}}^{CG}$ belongs to the S_R > 0 region. We identify a minimum free energy path between those two conformations (Fig. 9) using the “string method.” We plot the minimum free energy path between the two conformations in Fig. 9. Figure 9 also shows the structures over the free energy path, suggesting that the breathing motion of DNA is accompanied by DNA rotation around the histone core. In contrast, Lequieu et al.⁶⁰ reported that the DNA repositioning mechanism for Widom-601 is almost independent of rotational position. This difference in mechanism suggests a more careful analysis of the local twisting of DNA; in particular, SHL regions may be necessary to elucidate the mechanism further. For example, Armeev et al.²⁶ have observed twist defects, etc. We have also observed twisting in particular regions²⁴ of the DNA at high salt concentrations. Notably, we have not observed loop propagation for this set of simulations as we have observed at high salt concentrations. Both loop propagation^106–109 and twist diffusion^110–112 have been reported. Some experimental evidence supports both mechanisms.^110–114

FIG. 9.

Minimum free energy path corresponding to DNA rotation for the Widom-601 sequence. The stars correspond to different conformational states of the DNA obtained from energy minima of the free energy landscape based on PCA of the inter-base pair parameters.

VI. CONCLUSIONS

Herein, we have shown that the SIRAH force field can capture small-scale rearrangements of nucleosomal DNA, such as breathing,^8–12 at microsecond timescales at physiological salt concentrations. Our study indicates substantial computational efficiency gained using the SIRAH CG force field in simulating the nucleosome core particle. The speed-up obtained using the SIRAH force field is reported in the supplementary material, Table S2. The SIRAH CG force field significantly reduces the computational time compared to the atomistic simulation while exploring the conformational dynamics of the DNA. Simulations of the two nucleosome systems containing different DNA sequences, the ASP and Widom-601 sequences, using the SIRAH CG force field, capture major conformations of nucleosomal DNA. We obtain a greater extent of breathing motion at both ends of the DNA in CG simulations relative to atomistic simulations. Principal component analysis based on DNA dinucleotide base pair parameters aids in identifying multiple minima in the free energy landscape for both the CG and atomistic force fields. The SIRAH CG force field explores multiple minima relative to atomistic trajectories. CG simulations preserve the asymmetric motion observed for the DNA ends. Next, we construct a minimum energy path based on the free energy landscape for nucleosome repositioning. For this set of simulations, we find that the Widom-601 sequence involves rotational repositioning. We hypothesize that the transition between different states can be probed using Markov State Models (MSMs).^115,116 This approach can provide information based on kinetic exchange between different conformational states of nucleosomal DNA. The SIRAH CG force field has a significant potential to address the dynamics of larger protein–DNA complexes, such as tetranucleosomes,²⁸ or address the shift in DNA repositioning with the binding of transcription factors¹¹⁷ and chromatin remodelers.¹¹⁸

SUPPLEMENTARY MATERIAL

See the supplementary material for schematics of inter-base pair parameters, intra-base pair parameters, translocation, and rotational movement of nucleosomal DNA around histone (Fig. S1); the time evolution and histogram of R_g of the histone and secondary structure percentage over CG and AA trajectories (Fig. S2); distributions of the DNA’s major and minor groove widths over both AA and CG trajectories (Fig. S3); the histogram of intra-base pair parameters for both sequences (Figs. S4 and S5) for both atomistic and CG trajectories; the change in the average distance of each DNA base pair center represented in SHL notation over the simulated trajectory compared to the crystal structure for both sequences (Figure S6); the explained covariance ratio for each PC (Fig. S7); B-DNA dodecamer inter- and intra-base pair parameters (Figs. S8 and S9); a comparison of B-DNA inter-base pair parameters as calculated using Curves+ and NUPARM (Table S1); the relative speed-up using CG simulations (Table S2); and the SIRAH CG trajectories for both sequences (Movies 1 and 2).

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Abhik Ghosh Moulick: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Rutika Patel: Data curation (equal); Formal analysis (equal). Augustine Onyema: Data curation (equal); Formal analysis (equal). Sharon M. Loverde: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

DATA AVAILABILITY

Analysis codes are available on https://github.com/CUNY-CSI-Loverde-Laboratory/GhoshMoulick_2024-. Trajectories are available on https://zenodo.org/records/14033991.