Elucidating Internucleosome Interactions and the Roles of Histone Tails
Steven C. Howell,†Kurt Andresen,‡Isabel Jimenez-Useche,§Chongli Yuan,§and Xiangyun Qiu†*
†Department of Physics, George Washington University, Washington, DC;‡Department of Physics, Gettysburg College, Gettysburg,
Pennsylvania; and§School of Chemical Engineering, Purdue University, West Lafayette, Indiana
DNA is wrapped around largely positively charged histone proteins. Interaction between nucleosomes is dominated by electro-
statics at long range and guided by specific contacts at short range, particularly involving their flexible histone tails. We have thus
quantified how internucleosome interactions are modulated by salts (KCl, MgCl2) and histone tail deletions (H3, H4 N-terminal),
using small-angle x-ray scattering and theoretical modeling. We found that measured effective charges at low salts are ~1/5th of
the theoretically predicted renormalized charges and that H4 tail deletion suppresses the attraction at high salts to a larger extent
than H3 tail deletion.
The nucleosome is the first level of genome organization and regulation in eukaryotes where negatively charged
Highly charged DNA is packaged into nucleosome core par-
ticles (NCP) in eukaryotic cells by wrapping every 147 per
~180 basepairs (bp) of DNA around a histone octamer. The
octamer is a protein complex comprising two copies of each
of the four histone proteins (named H2A, H2B, H3, and H4).
Each histone has one C-terminal and one N-terminal tail that
protrude out from the octameric core. Linked by ~20–60 bp
DNA like beads on a string, NCPs are further packaged into
chromatin whose conformation and dynamics underpins
gene maintenance and regulation. Thus, there has been
long-standing interest in physically understanding nucleo-
some structure and interaction fundamental to chromatin
Polyelectrolyte behavior and histone tail modulation are
among the key determinants of the multifactorial packaging
of nucleosomes (1). One NCP carries a net negative charge
of ~150 e with ?294 e from DNA and þ144 e from histone
proteins. Given its diameter of ~10 nm and height of ~6 nm,
this leads to an average charge density of ?0.43 e/nm2,
about half of the ?1 e/nm2of DNA. The expected polyelec-
trolyte behavior of NCP is demonstrated by cation-modu-
lated unfolding and compaction of NCP arrays (2,3).
Notably, divalent cations go beyond screening the electro-
static repulsion between NCPs and can mediate inter-NCP
attraction, e.g., Mg2þ- or Ca2þ-induced condensation of
mono- and polynucleosomes (4). In contrast, these divalent
cations are unable to condense DNA. This suggests signifi-
cant roles of the complex charge distribution of NCP
furnished by the histones (5). In particular, the tails of his-
tones (~30% of the histone mass), being highly positively
charged and flexible, are known to be crucial in modulating
nucleosome interaction and chromatin assembly (1).
There have been extensive experimental studies aiming to
elucidate the electrostatics of nucleosomes and the roles of
histone tails. The effects of cations of varied valences on the
nucleosome assembly have been well characterized (1–3,6),
e.g., by measuring the sedimentation coefficients of nucleo-
some arrays or the fraction of condensed nucleosomes (4,7).
Among the 16 histone tails, the eight N-terminal tails hold
the most positive charges and are considered more signifi-
cant, e.g., NCPs with all N-terminal tails deleted remain sol-
uble in high divalent salts (8). In an effort to dissect the
contribution from each N-terminal tail, all 16 possible tail-
deletion NCP mutants have been studied and it was found
that all N-terminal tails contribute to the condensation of
oligo-NCP arrays nonspecifically and additively (8). Still,
the histone tails vary in length and charge and thus differ
in strength in mediating nucleosome interactions, e.g., H3
and H4 tails, studied herein, were observed to be more
important than H2A and H2B tails (8,9).
Systematic measurements have promoted widespread
theoretical interests in mechanistically understanding the
structure and interaction of nucleosomes (10,11). At the
atomic level, enabled by the availability of high resolution
crystal structures (12), molecular dynamics simulations
have described the ion and solvent atmospheres of nucleo-
some and revealed rugged electrostatic surfaces (13,14).
The flexible histone tails have been analyzed in detail and
shown to display multistate conformational dynamics (15–
17). At the coarse-grain level, both nucleosome arrays and
chromatin have been modeled to recapture the conforma-
tional changes under varied conditions such as salt and me-
chanical stretching (18,19). However, to apply the detailed
NCP structures and energetics predicted by theoretical ap-
proaches, stringent experimental tests are required, but
largely lacking. For example, as the focus of this study,
one key factor to the assembly of NCPs is the effective in-
ter-NCP potential that is usually computed following the
Poisson-Boltzmann formulism for efficiency (11). However,
such theoretical treatment has not been validated experi-
mentally due to the lack of direct measurements of inter-
NCP potentials. Comparisons with previously measured
Submitted December 16, 2012, and accepted for publication May 6, 2013.
Editor: Gerhard Hummer.
? 2013 by the Biophysical Society
194 Biophysical JournalVolume 105July 2013194–199
quantities are often difficult, e.g., the interpretation of sedi-
mentation coefficient necessitates an ab initio hydrody-
Here, we report measurements of interactions between
monomeric nucleosomes using solution small-angle x-ray
scattering (SAXS) in conjunction with theories of polyelec-
trolytes. There are two outcomes we deem important: 1),
Quantification of inter-NCP pair potentials by modeling
full SAXS profiles; 2), Elucidation of the individual role of
H3 and H4 tails. Although SAXS (and small-angle neutron
scattering for neutron) has been used to study the structure
refinementoffullSAXSprofiles has been done to extract the
inter-NCP interactions, which we obtain here by refining
synchrotron SAXS data. One key advantage of full profile
modeling is quantification of the inter-NCP potential as a
function of inter-NCP distance (21), in contrast to single-
parameter measurements such as second virial coefficients
or osmotic pressures of NCP solutions. Bertin et al. (22)
have compared full SAXS profiles with theoretical calcula-
tions. However, refinements were not performed, possibly
due to the relatively dilute NCP concentrations (%
8 mg/ml, ~0.04 mM) and limited angular range of the in-
house SAXS data that lower SAXS sensitivity to inter-NCP
interactions. In addition, using recombinant NCP constructs
we report the first analysis of this kind on the respective role
of H3 and H4 tails in mediating inter-NCP interactions.
MATERIAL AND METHODS
Natural-source monomeric NCPs (NS-NCP) were prepared from adult
chicken erythrocytes as in (23). Gel electrophoresis was used to assess
the DNA length (147 5 5 bps) and the histone content (Fig. S1, a and b,
in the Supporting Material). Recombinant nucleosomes (RC-NCP) were re-
constituted by mixing 147-bp mouse mammary tumor virus DNA and his-
tone octamers with sequences from Xenopus laevis following standard
protocols (8) (Fig. S1, a and c). The globular H3 and H4 recombinant pro-
teins were truncated at their N-terminal ends (referred to as gH3 and gH4
RC-NCPs), by deleting the coding sequences of amino acids (1–27
with þ10 e of H3 and 1–10 with þ3 e of H4) via site-directed mutagenesis.
All NCP stockswere purified by size-exclusion chromatography (Sephacryl
S300-HR medium) and then dialyzed against 10 mM KCl 10 mM Tris
0.1 mM EDTA pH 7.5 buffer. Salts were adjusted to studied conditions
by adding concentrated salts. SAXS experiments were carried out at
20?C at the G1 station at the Cornell High Energy Synchrotron Source in
Ithaca, New York. The incident beam had an energy of 9.97 keV and size
of 250 ? 250 mm. Samples of ~30 ml were injected into an in-vacuum capil-
lary flow cell to enable windowless data collection for background reduc-
tion. Radiation damage was mitigated by optimizing x-ray exposure time
and oscillating the plug of sample solution. Six to eight two-second expo-
sures of the same sample were taken and verified to be reproducible, indic-
ative of the absence of radiation damage.
Measured SAXS profile I(Q) is a product of the form factor
P(Q) and the structure factor S(Q), i.e., I(Q) ¼ P(Q) ? S(Q),
with S(Q) becoming significant under conditions such as
high [NCP]s and strong inter-NCP interactions. I(Q) of a
dilute NCP solution (i.e., S(Q) ¼ 1) thus measures the struc-
ture of individual NCPs in terms of the form factor P(Q) ¼
I(Q). This can reveal differences between molecular struc-
tures in solution and in crystal. Fig. 1 shows excellent agree-
ment between the SAXS profile measured in solution and
the profile calculated from a crystal structure in Q range
of 0.01–0.28 A˚?1, indicative of high sample purify and
structural conformity. The same level of agreement was
observed for all NCP constructs (i.e., NS-NCP, wild-type,
gH3, and gH4 RC-NCPs). It is worth noting that the crystal
structure P(Q) shows an extra dip around Q of 0.14 A˚?1.
This discrepancy has been observed in previous reports
(22,24) and was attributed to the DNA unwrapping at the
ends by a few basepairs. Tail deletions lead to small changes
of the dip around Q ¼ 0.14 A˚?1that can be attributed to
increased DNA unwrapping (data not shown). Nonetheless,
these dips appear in relatively high Q and do not affect our
subsequent analysis. Guinier analysis of the low Q data
(Fig. 1, inset) gives the radius of gyration Rg¼ 44.4 (3)
A˚, which is nearly identical to previous SAXS measure-
ments of natural-source NCPs (25) and recombinant NCPs
with a-satellite DNA (24). Note that NCPs reconstituted
with the 601 sequence were reported to give slightly smaller
Rgby 2–3 A˚(22,24).
In addition to structure information, SAXS is capable of
quantifying intermolecular interactions, via the structure
factor S(Q) originating from spatial correlations between
molecules. Qualitatively, repulsive interaction leads to a
decrease of low Q intensities, i.e., a downturn, and attractive
interaction gives rise to an increase at low Q, i.e., an upturn.
Fig. 2 shows how SAXS profiles evolve with NCP and
salt concentrations. As expected from strong inter-NCP
and crystal structure (red, PDB ID: 1KX5). Q ¼ 4psin(q)/l is the scattering
vector, where 2q is the scattering angle and l is the x-ray wavelength. The
experiment form factor was measured at a dilute NCP concentration of
0.003 mM (~0.6 mg/ml) and an intermediate salt (40 mM KCl) to minimize
the influenceofinter-NCPinterferences. Errorbarsof I(Q)s, in thisand sub-
sequent plots, are smaller than symbol sizes except at high Qs. Inset shows
the Guinier fit (solid line) to obtain the radius of gyration (Rg). The linear
region extends well over the empirical Qmaxcutoff of 1.3/Rgfor globular
SAXS form factor P(Q) of NS-NCP from experiment (,)
Biophysical Journal 105(1) 194–199
Measuring Internucleosome Interactions195
repulsions at low salts (10 and 40 mM KCl, Fig. 2, a and b),
low Q downturns are observed and deepen upon increasing
[NCP]. In contrast, low Q upturns appear and heighten with
[NCP] at high salts (100 and 200 mM KCl, Fig. 2, c and d),
indicating inter-NCP attractions. These observations are
consistent with reports of negative virial coefficients at
>70 mM KCl (22). Divalent Mg2þ, known to condense
NCP at >2.5 mM [Mg2þ] (4), was also studied and the onset
of inter-NCP attraction was found to be between 1 and
2 mM [Mg2þ] (Fig. S3).
To gain quantitative insights into the underlying inter-
NCP interactions, we then applied the generalized one
component method (GOCM) with the mean spherical
approximation (21,26) to model the structure factors. As
both repulsion and attraction exist, the general form of
inter-NCP interaction potential as a function of inter-NCP
distance is given by
where s is the equivalent diameter of NCP, Zeffand Zattrare
the effective charges to be fitted, ε ¼ 80.4 is the dielectric
constant of water at 20?C, and k is the inverse Debye
screening length calculated from the salt condition. Namely,
the inter-NCP potential comprises a hard-sphere (HS) repul-
sive term, a Debye-Huckel (DH) electrostatic repulsive
term, and a DH-like attractive term. Although it is possible
to include both DH potentials in the fitting procedures, there
exist significant correlations between the fitted repulsiveand
attractive DH terms despite better fits (see the Supporting
Material for detailed results and discussions). Due to this
complication, the attractive DH potential is turned off
(i.e., Zattr¼ 0) under conditions where a net inter-NCP
repulsion is observed. Likewise, Zeffis set to 0 under condi-
tions where a net attraction is observed. As the physical
origin of the attraction is poorly understood, we chose a
short-range attraction of effective charge Zattrand 4.8 A˚
decay length for all data. The effect of NCP’s disk-like
shape (axis ratio ~2) on S(Q) only becomes significant at
Q > 0.036 A˚?1(22) where S(Q) ~1 as observed in the exper-
iments; it is thus not considered. Such GOCM fits are shown
in Fig. 2 as solid lines, noting that the form factor for each
NCP construct is calculated based on the crystal structure
(shown in Fig. S2). It is evident that the GOCM fits are in
good agreement with experimental data over the entire Q
range. Inter-NCP interactions are thus quantified in the
forms of HS and DH potentials.
Despite being quantitative, directly usable, and compara-
ble with theoretical studies, it should be noted that the sum
of HS and DH potentials describes an apparent inter-NCP
interaction that reproduces the measured structure factor.
In the case of inter-NCP repulsion, the effective charge
Zeff, as the only fitting parameter, differs from the bare
charge Zbaredue to the nonlinear nature of ion screening
and the validity of DH potentials in linear regime only.
For the same reason, the equivalent diameter s encloses
the vicinity with a large electrostatic field (e.g., >3.8
kBT/e was used for dsDNA by the authors (27)), which is
in the order of Debye length. Especially at low salt, s is
significantly larger than the 100 A˚ computed from the
NCP crystal structure (21). We determined the value of s
at different salts based on cell model numerical calculations
(27,28), and the same s value was then fixed for all data at
the same ionic condition for consistency. We show these
relevant interaction potential parameters in the figure cap-
tions and in Table S1.
Fig. 3 shows data from recombinant gH3 and gH4 RC-
NCPs at two salt conditions (10 and 100 mM KCl) together
with GOCM fits (data at 20 and 40 mM KCl are shown
in Fig. S4). We primarily focused on gH3 and gH4
concentrations. I(Q)s are normalized by NCP concentrations to assist com-
parison. Each panel shows experimental I(Q)s (symbols) at a series of
[NCP]s (0.1 mM gives ~20 mg/ml) as indicated in the legends, together
with their respective theoretical fits (lines). The residues are shown with
an offset at the same scale. The pertinent pair-potential parameters are (dis-
cussed in detail in the main text), (a) Zeff¼ 22 (1) e, s ¼ 140 A˚; (b) Zeff¼
23 (1) e, s ¼ 110 A˚; (c) Zattr¼150 (5) e, s ¼ 100 A˚; (d) Zattr¼ 200 (8) e,
s ¼ 100 A˚. Uncertainties of Z values originate from both curve fitting (via
variance-covariance matrix, ~1%) and small variations (~3%) between
values at different [NCP]s. The Zeffand Zattrvalues are poorly defined
when [NCP] is small (<0.03 mM, or 6 mg/ml) and their values given
here are from data at high [NCP]s.
SAXS profiles, I(Q) ¼ P(Q) ? S(Q), of NS-NCPs at four KCl
εð1 þ ks=2Þ2
εð1 þ kattrs=2Þ2
Biophysical Journal 105(1) 194–199
196Howell et al.
RC-NCPs because recombinant samples were relatively
limited in volume and previous studies have reported the
second virial coefficients (though no inter-NCP potentials)
of intact RC-NCPs and gH3gH4 RC-NCPs, i.e., with none
or both tails deleted (22). To enable cross-comparisons,
intact RC-NCPs were measured at a few selected conditions
(Fig. S5). At low salt of 10 mM KCl, essentially no differ-
ence in the effectivecharge Zeff(~22 e) was observed among
all NCP constructs (i.e., NS-NCP, gH3, gH4, and intact RC-
NCPs), noting that the negativity of Zeffis omitted for brev-
ity. We further calculated the second virial coefficient from
the inter-NCP potential using
?1 ? e?UðrÞ=kBT?4pr2dr;
and obtained avalue of 2.5(1) ? 10?4ml$mol/g2. This value
is in excellent agreement with the osmometry measurement
by Mangenot et al. (29). Bertin et al. (22) used theoretical
calculations of Zeffbetween 70 and 125 e and obtained
much larger A2values close to 5.0 ? 10?4ml$mol/g2. We
attribute the difference to the discrepancy between theoret-
ical and experimental Zeffvalues (discussed below) used by
Bertin et al. and us, respectively. At high salt of 100 mM
KCl, qualitative differences were observed: NS-NCP, gH3
and intact RC-NCPs show comparable levels of attraction;
whereas gH4 and gH3gH4 RC-NCPs show no attraction
(including observations in (22).). This suggests the major
role of H4 tail in mediating inter-NCP attractions.
We consider the quantification of inter-NCP pair potentials
from SAXS structure factors as the most interesting result of
our study. Compared with the traditional analysis of second
virial coefficients that relies on I(Q ¼ 0) only, the GOCM
(and methods alike) uses the full SAXS profiles and obtains
self-consistent pair potentials allowing quantitative compar-
isons with theoretical predictions. At low salts such as
10 mM KCl, NCP-NCP interactions are dominated by repul-
sion as expected. Essentially the same Zeffis obtained for all
four NCP constructs. The minimal effect of tail deletions on
inter-NCP repulsion is not surprising given that tail dele-
tions change NCP bare charges by <8% and that cations
can effectively fill in for the deleted monocharged amino
acids. Quantitatively, it is instructive to compare the
measured Zeff with the theoretical renormalized charge
Zrenthat can be calculated following the charge renormali-
zation theorem (28). For dsDNA with negatively charged
groups only, our previous work showed that the measured
Zeffis fairly consistent (within 10–25%) with its renormal-
ized charge Zrenin monovalent salts (27). However, for
the nucleosome, its Zeff(~22 e) is far smaller than theoret-
ical Zren(>100 e for all experimental conditions), noting
that Zbareis ~150 e and Zrenweakly depends on NCP and
salt concentrations (28). Given that the Zrenis calculated
by treating NCP as a uniformly charged sphere, such drastic
and physically significant discrepancy is likely due to the
charge nonuniformity of NCP in terms of spatial distribution
and sign, resulting in highly anisotropic behaviors where the
uniformly charged surface consideration breaks down.
Inter-NCP interactions at short range are further compli-
cated by the flexible histone tails (11,16). At elevated salts
where electrostatic repulsion is greatly weakened, histone
tail deletions can significantly affect NCP-NCP interactions.
At 100 mM KCl (Fig. 2 c, Fig. 3, b and d), NS-NCP shows
significant attraction (i.e., low Q upturn), gH3 RC-NCP
shows attraction of comparable magnitude, and gH4 RC-
NCP shows nearly no attraction. The difference between
gH3 and gH4 RC-NCPs, which have not been studied by
SAXS previously, suggests that H4 tail is more important
in mediating NCP-NCP attractions than H3 tail. This corre-
sponds well with the observedmost important role of H4 tail
in assembling the 30-nm chromatin fiber (7). Such trend is
also consistent with the repulsion between gH3gH4 RC-
NCPs up to 200 mM KCl (22). The more important role
of the H4 tail in mediating internucleosome interactions
has been suggested by Arya and Schlick (30) analyzing a
coarse-grained mesoscale structure model with a tailored
configurational-bias Monte Carlo method. As H4 tail dele-
tion removes fewer charges than H3 tail deletion (þ3
vs. þ10 e) but shows a larger effect, this alludes to specific
interactions of H4 tails with adjacent NCPs in close
approach. To probe the likely H4-tail-DNA interactions,
Korolev and Nordenskio ¨ld (31) performed all-atomic
NCPs at 10 and 100 mM KCl. Annotations follow that of Fig. 2. Inter-
NCP potential parameters are, (a) Zeff¼ 21 (1) e, s ¼ 140 A˚; (b) Zattr¼
123 (4) e, s ¼ 100 A˚; (c) Zeff¼ 20 (1) e, s ¼ 140 A˚; (d) Zattr¼ 100 (4)
e, s ¼ 100 A˚. It is worth noting that, although gH4 RC-NCP shows no inter-
action at 100 mM KCl, a significant Zattrexists so as to negate the hard
sphere repulsion with s ¼ 100 A˚, which makes Zattrvalues artificially large.
Zattrwould be zero if s is zero for gH4 RC-NCP in 100 mM KCl. It is thus
more appropriate to interpret Zattr-100 as contributed by the inter-NCP
SAXS profiles, I(Q) ¼ P(Q) ? S(Q), of gH3 and gH4 RC-
Biophysical Journal 105(1) 194–199
Measuring Internucleosome Interactions197
molecular dynamics simulations of DNA and H4 tails and
suggested possible lysine-mediated bridging and minor
groove dynamic binding. Another possible explanation is
H4-tail binding with the H2A/H2B anionic patch on neigh-
boring NCPs, as suggested by crystallography studies
(32,33). This is in agreement with recent experimental
studies of the effects of H4 tail lysine acetylation on nucle-
osome array folding that proposed site-specific lysine bind-
ing to the H2B histone (9). To fully establish the underlying
molecular mechanisms, experimental approaches probing
the local structure would be needed to resolve the physical
origins of inter-NCP short range attraction.
In conclusion, we have measured repulsive and attractive
NCP-NCP interactions under various salt conditions with
distinct NCP constructs. Quantitative knowledge of inter-
NCP pair potentials should aid theoretical studies of nucle-
osome and chromatin high-order structure and dynamics.
The physical understanding to be gained will shed light on
the broad class of multiphasic macromolecules with two
or more different interacting groups. Work is underway to
relate the inter-NCP interactions to the conformation and
energetics of nucleosome arrays through measurement and
Supporting data including nine figures and one table are available at http://
The authors thank Arthur Woll, Richard Gillian, Soren Nielsen, and Qi Xia
for assistance with experiment, and thank Yun Liu for discussions on data
modeling. C.Y. acknowledges Prof. Timothy Richmond (ETH, Zurich) for
generously providing us the plasmids of histone proteins and MMTV DNA.
This work was supported by George Washington University (to X.Q.),
Research Corporation for Science Advancement and Gettysburg College
(to K.A.), and the Purdue University (to C.Y.).
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