The Impact of Charge Regulation and Ionic Intranuclear Environment on the Nucleosome Core Particle

Abstract

We theoretically investigate how the intranuclear environment influences the charge of a nucleosome core particle (NCP) - the fundamental unit of chromatin consisting of DNA wrapped around a core of histone proteins. The molecular-based theory explicitly considers the size, shape, conformations, charges, and chemical states of all molecular species - thereby linking the structural state with the chemical/charged state of the system. We investigate how variations in monovalent and divalent salt concentrations, as well as pH, affect the charge distribution across different regions of an NCP and quantify the impact of charge regulation. The effective charge of an NCP emerges from a delicate and complex balance involving the chemical dissociation equilibrium of the amino acids and the DNA-phosphates, the electrostatic interaction between them, and the translational entropy of the mobile solution ions, i.e., counter ion release and ion condensation. From our results, we note the significant effect of divalent magnesium ions on the charge and electrostatic energy as well as the counterion cloud that surrounds an NCP, as a function of magnesium concentration, charge neutralization, and even charge inversion is predicted - in line with experimental observation of NCPs. The strong Mg-dependence of the nucleosome charge state arises from ion bridges between two DNA-phosphates and one Mg₂ ⁺ ion. We demonstrate that to describe and predict the charged state of an NCP properly, it is essential to consider molecular details, such as DNA-phosphate ion condensation and the acid-base equilibrium of the amino acids that comprise the core histone proteins.

FIG. 1.

Molecular representation of a single nucleosome without (top) and with disordered histone tails (bottom). Observe that our system explicitly contains the most prevalent intranuclear ions, including Na⁺, ${\mathrm{K}}^{+}$, ${\mathrm{M}\mathrm{g}}^{2+}$, and Cl⁻ as well as water, OH⁻ and H⁺, to account for charge regulation and acid-base equilibrium as well as ion-condensation effects.

FIG. 2.

Total charge of a nucleosome with (WT) and without (NT) tails as a function of monovalent ${\mathrm{K}}^{+}$ concentration, in physiological conditions without divalent cations (pH = 7.4, [NaCl] = 10 mM). The vertical dotted line at 140 mM marks the physiological concentration of ${\mathrm{K}}^{+}$.

FIG. 3.

The total nucleosome charge with (WT) and without tails (NT) as a function of divalent ${\mathrm{M}\mathrm{g}}^{2+}$ concentration for physiological conditions: pH=7.4, [KCl]=140 mM, and [NaCl]=10 mM. The vertical dotted lines at 0.5 mM and 50 mM mark the physiological range for magnesium, while the horizontal dotted line at 0 marks the charge inversion point.

FIG. 4.

The net positive charge of the phosphates, the charge of the histone octamer, and the total effective charges of the nucleosome presented as a function of Mg-concentration for a nucleosome without disordered tails. As ${\mathrm{M}\mathrm{g}}^{2+}$ concentration increases, the total nucleosome charge becomes less negative, reflecting increased charge screening and partial neutralization of the phosphate backbone. The vertical dotted lines at 0.5 mM and 50 mM mark the physiological range for magnesium. The conditions are pH=7.4, [KCl]=140 mM, and [NaCl]=10 mM.

FIG. 5.

The average fraction of chemical states of the phosphates as a function of ${\mathrm{M}\mathrm{g}}^{2+}$ concentration. The deprotonated (charged) state is labeled $P^{-}$, the magnesium bridge ($P_2\mathrm{M}\mathrm{g}$), the phosphates bound with ${\mathrm{K}}^{+},{\mathrm{N}\mathrm{a}}^{+}$, or ${\mathrm{M}\mathrm{g}}^{2+}$ are denoted as $PK,P\mathrm{N}\mathrm{a}$, and $P{\mathrm{M}\mathrm{g}}^{+}$, and the protonated state is labeled $PH$. As ${\mathrm{M}\mathrm{g}}^{2+}$ concentration increases, magnesium dominates the binding and significantly influences the chemical states of the phosphates, particularly in the physiological range $(0.5\mathrm{m}\mathrm{M}$ to 50 mM), as seen by the increased fraction of $P_2\mathrm{M}\mathrm{g}$ and ${\mathit{P}\mathrm{M}\mathrm{g}}^{+}$. The conditions are $\mathrm{p}\mathrm{H}=7.4,\left[\mathrm{K}\mathrm{C}\mathrm{l}\right]=140\mathrm{m}\mathrm{M}$, and $\left[\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{l}\right]=10\mathrm{m}\mathrm{M}$.

FIG. 6.

The ion excess of free ${\mathrm{K}}^{+},{\mathrm{N}\mathrm{a}}^{+},{\mathrm{M}\mathrm{g}}^{2+}$ and ${\mathrm{C}\mathrm{l}}^{-}$ions as function of ${\mathrm{M}\mathrm{g}}^{2+}$ concentration for $\mathrm{p}\mathrm{H}=7.4,\left[\mathrm{K}\mathrm{C}\mathrm{l}\right]=140\mathrm{m}\mathrm{M}$, and $\left[\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{l}\right]=10\mathrm{m}\mathrm{M}$. As the nuclesome's charge flips from positive to negative chloride ions replace potassium ions as counterions. The vertical dotted lines at 0.5 mM and 50 mM mark the physiological range for magnesium.

FIG. 7.

Distribution of (a) electrostatic potential, (b) local position-dependent proton concentration (c) local concentration of KCl, (d) local total volume fraction of the nucleosome at physiological conditions. Namely pH=7.4, [KCl]=140 mM, [NaCl]=10 mM, and [MgCl₂]= 1 mM. Each plot compares nucleosomes without tails (left) and with tails (right), highlighting the increased heterogeneity within the structure. The graphs, generated using the Plotly-Python package, are semi-transparent to improve visualization and contrast the distribution against the reservoir values. (Opacity = 0.1). The height, width, and depth are respectively 19.5 nm, 22.75 nm, and 26 nm for all graphs.

FIG. 8.

The total nucleosome charge of a nucleosome without tails as a function of divalent ${\mathrm{M}\mathrm{g}}^{2+}$ concentration at different pH values. The vertical dotted lines at 0.5 mM and 50 mM mark the physiological range for magnesium. Remaining conditions: [KCl]=140 mM, and [NaCl]=10 mM.