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, conformation, charge, and chemical state 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.

1.
D. A.
Walker
,
B.
Kowalczyk
,
M. O.
de la Cruz
, and
B. A.
Grzybowski
,
Nanoscale
3
,
1316
(
2011
).
2.
R. H.
French
,
V. A.
Parsegian
,
R.
Podgornik
,
R. F.
Rajter
,
A.
Jagota
,
J.
Luo
,
D.
Asthagiri
,
M. K.
Chaudhury
,
Y.-m.
Chiang
,
S.
Granick
,
S.
Kalinin
,
M.
Kardar
,
R.
Kjellander
,
D. C.
Langreth
,
J.
Lewis
,
S.
Lustig
,
D.
Wesolowski
,
J. S.
Wettlaufer
,
W.-Y.
Ching
,
M.
Finnis
,
F.
Houlihan
,
O. A.
von Lilienfeld
,
C. J.
van Oss
, and
T.
Zemb
,
Rev. Mod. Phys.
82
,
1887
(
2010
).
3.
K.
Maeshima
,
S.
Iida
, and
S.
Tamura
,
Cold Spring Harbor Perspect. Biol.
13
,
a040675
(
2021
).
4.
D. M.
Hinckley
and
J. J.
de Pablo
,
J. Chem. Theory Comput.
11
,
5436
(
2015
).
5.
G. M.
Giambaşu
,
M. K.
Gebala
,
M. T.
Panteva
,
T.
Luchko
,
D. A.
Case
, and
D. M.
York
,
Nucleic Acids Res.
43
,
8405
(
2015
).
6.
M.
Gebala
,
S. L.
Johnson
,
G. J.
Narlikar
, and
D.
Herschlag
,
eLife
8
,
e44993
(
2019
).
7.
A.
Zinchenko
,
N. V.
Berezhnoy
,
S.
Wang
,
W. M.
Rosencrans
,
N.
Korolev
,
J. R.
van der Maarel
, and
L.
Nordenskiöld
,
Nucleic Acids Res.
46
,
635
(
2017
).
8.
K.
Maeshima
,
T.
Matsuda
,
Y.
Shindo
,
H.
Imamura
,
S.
Tamura
,
R.
Imai
,
S.
Kawakami
,
R.
Nagashima
,
T.
Soga
,
H.
Noji
,
K.
Oka
, and
T.
Nagai
,
Curr. Biol.
28
,
444
(
2018
).
9.
10.
J.
Tanase
,
T.
Yokoo
,
Y.
Matsumura
,
M.
Kinoshita
,
Y.
Kikuchi
,
H.
Suemori
, and
T.
Ohyama
,
Biochem. Biophys. Res. Commun.
482
,
764
(
2017
).
11.
J. C.
Hansen
,
K.
Maeshima
, and
M. J.
Hendzel
,
Epigenet. Chromatin
14
,
50
(
2021
).
12.
X. W.
Guo
and
R. D.
Cole
,
J. Biol. Chem.
264
,
11653
(
1989
).
13.
M.
de Frutos
,
E.
Raspaud
,
A.
Leforestier
, and
F.
Livolant
,
Biophys. J.
81
,
1127
(
2001
).
14.
E.
Raspaud
,
I.
Chaperon
,
A.
Leforestier
, and
F.
Livolant
,
Biophys. J.
77
,
1547
(
1999
).
15.
A.
Bertin
,
S.
Mangenot
,
M.
Renouard
,
D.
Durand
, and
F.
Livolant
,
Biophys. J.
93
,
3652
(
2007
).
16.
A.
Zinchenko
,
N. V.
Berezhnoy
,
Q.
Chen
, and
L.
Nordenskiöld
,
Biophys. J.
114
,
2326
(
2018
).
17.
C. G.
Triandafillou
,
C. D.
Katanski
,
A. R.
Dinner
, and
D. A.
Drummond
,
eLife
9
,
e54880
(
2020
).
18.
L. M.
Almassalha
,
G. M.
Bauer
,
W.
Wu
,
L.
Cherkezyan
,
D.
Zhang
,
A.
Kendra
,
S.
Gladstein
,
J. E.
Chandler
,
D.
VanDerway
,
B.-L. L.
Seagle
,
A.
Ugolkov
,
D. D.
Billadeau
,
T. V.
O’Halloran
,
A. P.
Mazar
,
H. K.
Roy
,
I.
Szleifer
,
S.
Shahabi
, and
V.
Backman
,
Nat. Biomed. Eng.
1
,
902
(
2017
).
19.
N.
Korolev
,
Y.
Fan
,
A. P.
Lyubartsev
, and
L.
Nordenskiöld
,
Curr. Opin. Struct. Biol.
22
,
151
(
2012
).
20.
N.
Korolev
,
L.
Nordenskiöld
, and
A. P.
Lyubartsev
,
Adv. Colloid Interface Sci.
232
,
36
(
2016
), part of the Special Issue: Proceedings from the International Workshop on Polyelectrolytes in Chemistry, Biology and Technology.
21.
H.
Schiessel
,
J. Phys.: Condens. Matter
15
,
R699
(
2003
).
23.
Z.
Li
,
S.
Portillo-Ledesma
, and
T.
Schlick
,
Biophys. J.
122
,
2884
(
2023
).
24.
H. H.
Gan
and
T.
Schlick
,
Biophys. J.
99
,
2587
(
2010
).
25.
J.
Moller
,
J.
Lequieu
, and
J. J.
de Pablo
,
ACS Cent. Sci.
5
,
341
(
2019
).
26.
J.
Lequieu
,
A.
Córdoba
,
J.
Moller
, and
J. J.
de Pablo
,
J. Chem. Phys.
150
,
215102
(
2019
).
27.
G. S.
Freeman
,
J. P.
Lequieu
,
D. M.
Hinckley
,
J. K.
Whitmer
, and
J. J.
de Pablo
,
Phys. Rev. Lett.
113
,
168101
(
2014
).
28.
T.
Sun
,
V.
Minhas
,
A.
Mirzoev
,
N.
Korolev
,
A. P.
Lyubartsev
, and
L.
Nordenskiöld
,
J. Chem. Theory Comput.
18
,
3948
(
2022
).
30.
J.
Sun
,
Q.
Zhang
, and
T.
Schlick
,
Proc. Natl. Acad. Sci. U. S. A.
102
,
8180
(
2005
).
31.
G.
Arya
and
T.
Schlick
,
J. Phys. Chem. A
113
,
4045
(
2009
).
32.
R.
Collepardo-Guevara
,
G.
Portella
,
M.
Vendruscolo
,
D.
Frenkel
,
T.
Schlick
, and
M.
Orozco
,
J. Am. Chem. Soc.
137
,
10205
(
2015
).
33.
O.
Perišić
and
T.
Schlick
,
Phys. Biol.
13
,
035006
(
2016
).
34.
G.
Wedemann
and
J.
Langowski
,
Biophys. J.
82
,
2847
(
2002
).
35.
R.
Stehr
,
N.
Kepper
,
K.
Rippe
, and
G.
Wedemann
,
Biophys. J.
95
,
3677
(
2008
).
36.
T.
Zülske
,
A.
Attou
,
L.
Groß
,
D.
Hörl
,
H.
Harz
, and
G.
Wedemann
,
Biophys. J.
123
,
847
(
2024
).
37.
S.
Donnini
,
F.
Tegeler
,
G.
Groenhof
, and
H.
Grubmüller
,
J. Chem. Theory Comput.
7
,
1962
(
2011
).
38.
J.
Landsgesell
,
L.
Nová
,
O.
Rud
,
F.
Uhlík
,
D.
Sean
,
P.
Hebbeker
,
C.
Holm
, and
P.
Košovan
,
Soft Matter
15
,
1155
(
2019
).
39.
Y.
Cote
,
I. W.
Fu
,
E. T.
Dobson
,
J. E.
Goldberger
,
H. D.
Nguyen
, and
J. K.
Shen
,
J. Phys. Chem. C
118
,
16272
(
2014
).
40.
N. E.
Jackson
,
B. K.
Brettmann
,
V.
Vishwanath
,
M.
Tirrell
, and
J. J.
de Pablo
,
ACS Macro Lett.
6
,
155
(
2017
).
41.
42.
T.
Sun
,
N.
Korolev
,
V.
Minhas
,
A.
Mirzoev
,
A. P.
Lyubartsev
, and
L.
Nordenskiöld
,
Biophys. J.
123
,
1414
(
2024
).
43.
E.
Gonzalez Solveyra
,
R. J.
Nap
,
K.
Huang
, and
I.
Szleifer
,
Polymers
12
,
2282
(
2020
).
44.
P.
Gong
,
T.
Wu
,
J.
Genzer
, and
I.
Szleifer
,
Macromolecules
40
,
8765
(
2007
).
45.
M.
Tagliazucchi
,
O.
Peleg
,
M.
Kröger
,
Y.
Rabin
, and
I.
Szleifer
,
Proc. Natl. Acad. Sci. U. S. A.
110
,
3363
(
2013
).
46.
R. J.
Nap
and
I.
Szleifer
,
Biophys. J.
95
,
4570
(
2008
).
47.
R. J.
Nap
,
A.
Božič
,
I.
Szleifer
, and
R.
Podgornik
,
Biophys. J.
107
,
1970
(
2014
).
48.
D.
Wang
,
R. J.
Nap
,
I.
Lagzi
,
B.
Kowalczyk
,
S.
Han
,
B. A.
Grzybowski
, and
I.
Szleifer
,
J. Am. Chem. Soc.
133
,
2192
(
2011
).
49.
T. V.
Andreeva
,
N. V.
Maluchenko
,
A. L.
Sivkina
,
O. V.
Chertkov
,
M. E.
Valieva
,
E. Y.
Kotova
,
M. P.
Kirpichnikov
,
V. M.
Studitsky
, and
A. V.
Feofanov
,
Microsc. Microanal.
28
,
243
(
2021
).
50.
D. M.
Hinckley
,
G. S.
Freeman
,
J. K.
Whitmer
, and
J. J.
de Pablo
,
J. Chem. Phys.
139
,
144903
(
2013
).
51.
K.
Luger
,
A. W.
Mäder
,
R. K.
Richmond
,
D. F.
Sargent
, and
T. J.
Richmond
,
Nature
389
,
251
(
1997
).
52.
R. J.
Nap
,
S. H.
Park
, and
I.
Szleifer
,
Soft Matter
14
,
2365
(
2018
).
53.
R.
Nap
,
P.
Gong
, and
I.
Szleifer
,
J. Polym. Sci., Part B: Polym. Phys.
44
,
2638
(
2006
).
54.
R. J.
Nap
,
B.
Qiao
,
L. C.
Palmer
,
S. I.
Stupp
,
M.
Olvera de la Cruz
, and
I.
Szleifer
,
Front. Chem.
10
,
852164
(
2022
).
55.
A. C.
Hindmarsh
,
P. N.
Brown
,
K. E.
Grant
,
S. L.
Lee
,
R.
Serban
,
D. E.
Shumaker
, and
C. S.
Woodward
,
ACM Trans. Math. Software
31
,
363
(
2005
).
56.
K. M.
Dean
,
Y.
Qin
, and
A. E.
Palmer
,
Biochim. Biophys. Acta, Mol. Cell Res.
1823
,
1406
(
2012
).
57.
K. P.
Carter
,
A. M.
Young
, and
A. E.
Palmer
,
Chem. Rev.
114
,
4564
(
2014
).
58.
A. M. P.
Romani
,
Arch. Biochem. Biophys.
512
,
1
(
2011
).
59.
A.
Romani
and
A.
Scarpa
,
Arch. Biochem. Biophys.
298
,
1
(
1992
).
60.
Plotly Technologies Inc.
, Collaborative data science,
2015
.
61.
CRC Handbook of Chemistry and Physics
, 94th ed., edited by
W.
Haynes
(
CRC Press
,
Boston
,
2013
).
62.
A.
Allahverdi
,
Q.
Chen
,
N.
Korolev
, and
L.
Nordenskiöld
,
Sci. Rep.
5
,
8512
(
2015
).
63.
L. M.
Neri
,
S.
Capitani
,
A.
Valmori
,
B. M.
Riederer
, and
A. M.
Martelli
,
J. Histochem. Cytochem.
45
,
1317
(
1997
).
64.
H.
Matsuda
,
G.
Putzel
,
V.
Backman
, and
I.
Szleifer
,
Biophys. J.
106
,
1801
(
2014
).
65.
R. K. A.
Virk
,
W.
Wu
,
L. M.
Almassalha
,
G. M.
Bauer
,
Y.
Li
,
D.
VanDerway
,
J.
Frederick
,
D.
Zhang
,
A.
Eshein
,
H. K.
Roy
,
I.
Szleifer
, and
V.
Backman
,
Sci. Adv.
6
,
eaax6232
(
2020
).
66.
R. J.
Nap
,
M.
Tagliazucchi
, and
I.
Szleifer
,
J. Chem. Phys.
140
,
024910
(
2014
).
You do not currently have access to this content.