Exploring the Free Energy Landscape of Nucleosomes
Bin Zhang,
†
Weihua Zheng,
†
Garegin A. Papoian,
‡
and Peter G. Wolynes*
,†,§
†
Department of Chemistry and Center for Theoretical Biological Physics and
§
Department of Physics and Astronomy, Rice
University, Houston, Texas 77005, United States
‡
Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College
Park, Maryland 20742, United States
*
S
Supporting Information
ABSTRACT: The nucleosome is the fundamental unit for
packaging the genome. A detailed molecular picture for its
conformational dynamics is crucial for understanding tran-
scription and gene regulation. We investigate the disassembly
of single nucleosomes using a predictive coarse-grained protein
DNA model with transferable force fields. This model
quantitatively describes the thermodynamic stability of both
the histone core complex and the nucleosome and predicts
rates of transient nucleosome opening that match experimental
measurements. Quantitative characterization of the free-energy
landscapes reveals the mechanism of nucleosome unfolding in
which DNA unwinding and histone protein disassembly are
coupled. The interfaces between H2A-H2B dimers and the
(H3-H4)
2
tetramer are first lost when the nucleosome opens releasing a large fraction but not all of its bound DNA. For the short
strands studied in single molecule experiments, the DNA unwinds asymmetrically from the histone proteins, with only one of its
two ends preferentially exposed. The detailed molecular mechanism revealed in this work provides a structural basis for
interpreting experimental studies of nucleosome unfolding.
■
INTRODUCTION
The genome, the blueprint of life, contains nearly all the
information needed to build and maintain an entire organism.
In higher organisms, at the chromosomal level, the three-
dimensional structural organization of the genome is crucial for
its function.
1−3
Large scale chromosome folding can bring into
proximity regulatory elements, i.e., enhancers and promoters,
that are separated far away in sequence in order to control gene
expression.
4,5
At a finer nanometer scale, the packaging of the
genome plays an important role in gene regulation as well.
6
For
eukaryotic cells, the fundamental unit of DNA organization is
the so-called nucleosome, in whose crystal structure the DNA
wraps approximately 1.7 times around a core made of histone
proteins.
7
We investigate the stability and conformational
dynamics of single nucleosomes by computing the free-energy
landscapes for nucleosome disassembly using a coarse-grained
model that includes a transferable protein force field suitable for
structure prediction
8,9
and a DNA force field that successfully
predicts its elastic properties.
10,11
The nucleosome structure itself presents a steric barrier for
gene transcription.
6
Approximately 147 base pairs of duplex
DNA wrap around each histone octamer, which is formed from
two copies of the histone heterodimers (H2A-H2B)
α,β
and
(H3-H4)
α,β
. The linker length between neighboring nucleo-
somes ranges from 20 to 90 base pairs long,
12
and
approximately 75% of the DNA is sterically occluded by
being bound in nucleosomes.
13,14
In order for other proteins,
including transcription factors and RNA polymerases, to access
their binding sites, the tightly bound DNA must at least
partially unwind from the histone core. Numerous mechanisms
inside the cell regulate the stability of the nucleosome and
thereby fine-tune the amount of accessible DNA. These
mechanisms range from passive histone modifications to active
remodeling that uses ATP.
15,16
A detailed characterization of
the molecular mechanism for nucleosome assembly will not
only improve our understanding of genome packaging but will
also shed light on the various pathways that regulate gene
expression kinetically.
Many experimental studies already have provided insight into
how the nucleosome assembles. Single molecule stretching
experiments using optical traps suggest that the DNA may
unwrap from the histone core following a three step process
that includes first (i) the release of the outer turn, next (ii) the
release of the inner turn, and finally (iii) irrev ersible
dissociation of the histone core.
17,18
When the three stage
picture was proposed, the histone core was assumed to be
rather rigid retaining a stable octamer conformation. Recently,
however single molecule Fo
rster resonance energy transfer
(FRET) experiments have revealed that the protein core is
rather flexible and disassembles with a loss of the (H3-H4)
2
tetramer/(H2A-H2B) dimer interface as the DNA unwraps.
7,19
Received: March 19, 2016
Article
pubs.acs.org/JACS
© XXXX American Chemical Society A DOI: 10.1021/jacs.6b02893
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX
Furthermore, in contrast to the symmetric unwinding of the
two DNA ends initially proposed, recent experiments on short
DNA suggest that the DNA unwraps asymmetrically with one
end being predominantly exposed. These experiments used an
assay that merges single molecule FRET together with optical
tweezers.
20
We show here that computational modeling of
nucleosome disassembly further elucidates the molecular
mechanism and provides a quantitative theoretical foundation
that is needed to unify these experiments.
Using computer simulations of a coarse-grained protein−
DNA model, we provide a comprehensive characterization of
free-energy landscapes for the histone complex and nucleosome
disassembly. We find that the histone core complex without the
DNA is unstable at physiologic al conditions. Instead an
intermediate stat e in which the (H3-H4)
2
tetramer is
sandwiched between the two H2A-H2B dimers with non-
specific interactions is favored thermodynamically. Though the
octamer structure is stable when the DNA is bound, a similar
intermediate state which has lost the (H3-H4)
2
tetramer/H2A-
H2B dimer interface is observed as the DNA unwinds,
supporting the idea that DNA unwrapping and histone core
complex unfolding are coupled processes. Finally, the free-
energy landscape of nucleosome disassembly supports asym-
metric conformations of DNA unwrapping that predominantly
expose only one of the two ends. Comparing the free-energy
landscapes of intact and tailless nucleosomes, we show that this
asymmetric unwrapping mainly arises from electrostatic
interactions between histone tails and the DNA, and we find
that the tails of histone H3 have the most profound effect. The
combined chemical accuracy and computational efficiency of
the coarse-grained model thus enables a rigorous energy
landscape analysis for a single nucleosome and paves the way
for further investigation of higher order structures formed by
oligonucleosomes.
■
METHODS
Coarse-Grained Protein−DNA Model. Computational modeling
promises to provide a detailed molecular characterization for the
assembly of a single nucleosome as well as the higher order structures
formed by oligonucleosomes. In fact, atomistic simulations have
already provided structural insight into the transient DNA unwrapping
near its entry/exit sites
21−23
and revealed the effect of post-
translational modific ations and di fferent histone variants on
nucleosomal dynamics.
22,24
The minimal systems are large in size
and involve a complex ensemble of molecular players having intricate
physicochemical interactions. These features make the modeling of
nucleosomes a challenge
25
and limit the time scale currently accessible
from fully atomistic simulations to microseconds.
22,23,26,27
This
limitation constrains the application of all atom models currently
providing a comprehensive landscape characterization. Instead, we
adopt a coarse-grained modeling approach, which has already proven
fruitful in investigating a wide range of biological systems.
28−30
To investigate protein−DNA interactions in the nucleosome, we
combine the associative memory, water-mediated, structure and energy
model (AWSEM) for protein
9
with an improved version of the three
site per nucleotide model (3SPN.2C) for DNA.
10,11
Each amino acid
in AWSEM is modeled with three atoms, C
α
,C
β
, and O, and the
transferable interactions among amino acids are parametrized
following the energy landscape theory prescription to maximize the
ratio of folding temperature over glass transition temperature for a set
of training proteins.
31−34
AWSEM has been shown to predict
monomer structures reasonably well from sequence alone and to
predict protein−protein interfaces in dimers with remarkable accuracy
when monomer structures are known.
8,35
The coarse-grained DNA
model developed by de Pablo and co-workers quantitatively
reproduces the persistence length of double-stranded DNA at varying
ionic concentrations and for different DNA sequences.
10,11
Thus, it
encodes DNA’s elastic properties in a predictive fashion. When we
combine the protein and DNA models, we preserve the original fine-
tuned force fields for protein−protein and DNA−DNA interactions by
themselves. In the present model, we introduce additional protein−
DNA interactions at a nonspecific level using a screened Debye−
Hu
ckel potential for the electrostatics along with a Lennard-Jones
potential for excluded volume (see Supporting Information (SI) for
details). A typical dielectric constant of 78.0 for water and an ionic
concentration of 100 mM at the physiological condition are used for
the electrostatic interactions in this study. Using this nonspecific
simplification of the protein−DNA interactions is not unreasonable for
the nucleosome assembly problem because the X-ray structure
indicates the lack of base-specific interactions between histone
proteins and the DNA as well as the predominance of water molecules
at the interface of the two.
7,36
We note this kind of simple treatment of
the direct protein−DNA interaction has already been applied
successfully to study protein−DNA interactions in a wide range of
biological systems,
37−39
including some studies of nucleosomes.
40,41
We introduce two modifications to the original AWSEM force field
presented in ref 8 in order to improve modeling the chemical
complexity of histone proteins. First, to better characterize long-range
electrostatic interaction among histone proteins, we explicitly include
Debye−Hu
kcel potential among charged amino acid residues
following ref 42 . Unfortunately, such a simple treatment of
electrostatics, though useful in capturing long-range interactions,
may give rise to some double counting at short-range. This double
counting arises since AWSEM, in its original form, already includes
short-range direct contact potentials between charged residues that
implicitly involve electrostatics. Another modification we employ
remedies to some extent the double counting issue. Additional weak
nonadditive Go
-potentials derived from the octamer conformation in
the nucleosome crystal structure were introduced for the histone
protein core. These partially counteract the repulsion among positively
charged residues in short range. Nonadditive Go
-potentials are further
helpful in quantitatively reproducing energetic barriers and sufficient
cooperativity while tuning an already funneled energy landscape more
completely toward native conformations.
43
It is important to note that
the strength of the nonadditive Go
-potential employed here is small
(<30% in the native state of the physically motivated AWSEM contact
potentials, i.e., λ
c
V
contact
in eq S1 of the SI), so the emergence of a basin
of attraction in calculated free-energy landscapes should be attributed
mostly to the original physical potentials. Most of the features seen in
the simulation also appear in simulations completely lacking the
nonadditive Go
term, albeit with somewhat less clarity (see Figure S1).
Details of the definition and the parametrization of the nonadditive
Go
-potential are provided in the SI.
Reaction Coordinates and Free-Energy Calculations. We
determine the free-energy profiles using reaction coordinates Q and
R
DNA
to monitor the disassembly of the histone core and the global
DNA portion of the nucleosome, respectively. The fraction of native
contacts Q is defined as
∑
σ
=
−−
−
−
<−
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
Q
NN
rr
2
(2)(3)
exp
()
2
ij
ij ij
N
2
2
2
(1)
with σ = 3 Å and N being the total number of nontail residues from all
eight histone proteins. The summation in eq 1 only includes C
α
atoms.
The native separation r
ij
N
is the distance between the two C
α
atoms
from amino acids i and j calculated using the coordinates from the
crystal structure.
36
Similar measures can be defined to study protein−
protein interfaces when only intermolecular contacts are included in
the summation. Q ranges from 0 to 1, with a higher value
corresponding to greater similarity to the native structure. For
funnele d surfaces, Q has bee n shown to provide an excellent
characterization of the progression of folding for single proteins
44,45
and binding for protein−protein complexes.
46
To study how the DNA
becomes unwrapped when the nucleosome unfolds, we use the radius
of gyration of the DNA R
DNA
defined as
Journal of the American Chemical Society Article
DOI: 10.1021/jacs.6b02893
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX
B
∑
=−
=
R
N
rr
1
()
i
N
iDNA
1
com
2
(2)
where r
com
is the center of mass, and the summation is conducted over
all the coarse-grained sugar beads of the DNA.
We used umbrella sampling together with replica exchange
techniques to enhance conformation sampling for free-energy
calculations.
47,48
Harmonic potentials 1/2K
q
(Q − Q
o
)
2
and 1/
2K
r
(R
DNA
− R
DNA
o
)
2
were introduced to restrain constant temperature
molecular dynamics simulations toward reference values, with K
q
=
1000 kcal/mol and K
r
= 0.8 kcal/mol/Å
2
. The reference values for Q
o
are equally spaced from 0.2 to 0.8 with a step size 0.1. For R
DNA
o
,12
references were chosen from 45 to 72.5 Å with an increment of 2.5 Å.
Twelve replicas were used for each umbrella window with temperature
ranging from 260 to 370 K with a step of 10 K. Data from different
windows were stitched together with the weighted histogram analysis
method (WHAM) to construct free-energy landscapes.
49
Simulation Details. All simulations were performed using the
software Large-Scale Atomic/Molecular Massively Parallel Simulator
(LAMMPS). Initial configurations of the simulation and the DNA
sequence are obtained from the crystal structure with PDB ID: 1KX5
(see Figure S2). Molecular dynamics trajectories were performed at
constant temperatur e and volume without p eriodic boundary
conditions for 5 million steps with a time step of 20 fs, and exchanges
among different replicas were attempted at every 100 steps. Due to the
coarse graining, we note the simulation time scale cannot be converted
precisely into real time units.
50
In any event, we checked the
convergence of the simulations by performing rigorous error analysis
of the calculated free-energy profiles (see SI Section: Convergence of
the Simulation for Details). Since the simulations were performed
without periodic boundary conditions, we introduced a constraint on
the radius of gyration of the histone core complex when the protein
assembly is studied without the presence of the DNA in order to
prevent molecules from diffusing too far away from each other
unproductively. De finition of this constraint and additional simulation
details are provided in the SI.
■
RESULTS AND DISCUSSION
Free-Energy Landscape of the Assembly of the
Histone Protein Core. Several coarse-grained models have
already been used for the investigation of nucleosome
dynamics.
40,41,51,52
In most of these studies, the histone core
complex was restrained to having the octamer conformation
found in the crystal structure because the models that were
employed lack a transferable force field for protein molecules.
These structural restraints prohibit large-scale conformational
changes away from the crystal structure, whether they are
artifactual and unphysical or physical and mechanistically
required. In our view, allowing protein flexibility is essential
because the histo ne octamer structure is unstable under
physiological conditions in the absence of the DNA.
53−55
Partial disassembly of the histone core complex as the
nucleosome unfolds has also been observed in single molecule
FRET experi ment s.
19,56
Conformational flexib ilit y of t he
histone core complex must therefore play a crucial role in
nucleosome dynamics. We first investigate whether the histone
core would assemble in the absence of the DNA using free-
energy landscape analysis.
Figure 1 presents the free-energy profile as a function of the
fraction of native contacts Q, with representative structures of
the protein complex at various Q values shown at the top.
Ther e are three free-energy basins i n this landscape at
approximately Q = 0.35, 0.45, and 0.75, respectively. At Q =
0.35, the system has disassembled into a tetramer (H3-H4)
2
and two H2A-H2B dimers, and no specific contacts between
H2A-H2B and the tetramer are present. Throughout our
simulation, we have not observed complete dissociation of any
of the four dimers into monomer structures. The stability of
this low Q basin is sensitive to protein concentrations due to
the entropic contributions from the free diffusion of proteins in
the solution.
54
At Q = 0.45, the two dimers H2A-H2B begin to
assemble around (H3-H4)
2
from two sides, and the tetramer is
seen to be sandwiched in between H2A-H2B dimers, as
illustrated in the top panel. Finally, specific contacts form
between the dimers and the tetramer at Q = 0.75, and the
histone core complex adopts the conformation captured in the
nucleosome crystal structure that contains DNA. Average
contact maps of protein structures at various Q values are
provided in Figure S3 .
Mechanistic insight about the assembly process can be
obtained by following the formation of interfacial contacts as a
function of Q . As shown in Figure 2A, the formation of contacts
between the two H3-H4 dimers (blue) precedes the formation
of contacts between H3-H4 and H2A-H2B (red and yellow).
The partially disassembled state at small Q values thus consists
of a (H3-H4)
2
tetramer and two H2A-H2B dimers. As the two
distinct interfaces between H3-H4 and H2A-H2B are chemi-
cally identical, it is reassuring that their average number of
contacts are found to be the same within numerical accuracy.
The attachment of the two H2A-H2B dimers to the (H3-
H4)
2
tetramer occurs largely sequentially, as shown in Figure
2B. The free-energy profile as a function of the two interfacial
contact numbers exhibits two parallel reaction channels from
the disassembled state to the octamer conformation, as
indicated by the arrows. Along either one of the reaction
pathways, the formation of each of the two interfaces is
decoupled from the formation of the other, suggesting two
parallel serial mechanisms.
The molecular picture for the assembly of histone proteins
revealed from our s imulation is consistent with prior
experimental observations. For example, in agreement with
Figure 2A, the histone proteins are known to stabilize into a
(H3-H4)
2
tetramer and two H2A-H2B dimers when
disassembled.
53−55,57
Furthermore, in support of the sequential
Figure 1. Free energy profile as a function of the fraction of native
contacts Q for the folding of the histone protein core. Error bars
shown in gray represent the standard deviation of the mean. Example
configurations of the histone complex at various values of Q are shown
in the top panel, with the two H3-H4 dimers drawn in blue and green
and the two H2A-H2B dimers in red and orange. Histone tails are not
displayed for clarity.
Journal of the American Chemical Society Article
DOI: 10.1021/jacs.6b02893
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX
C
pathway shown in Figure 2B, an intermediate hexameric
structure consisting of the H3-H4 tetramer and one copy of the
H2A-H2B dimer has been observed in ref 54.
Free-Energy Landscape of Full Nucleosome Disas-
sembly. The free-energy landscape for the histone core
complex quantifies the stability of the octamer state and
provides a detailed molecular pathway for the assembly process.
The remarkable agreement between the molecular mechanism
predicted from simulation and that proposed from experimental
observations on the histone complex by itself encourages the
application of AWSEM for studying full nucleosome
disassembly. We therefore now turn to investigate the coupling
between DNA unwrapping and the conformational changes of
the histone core complex as the nucleosome unfolds.
Figure 3 presents the free-energy profile (yellow) as a
function of the radius of gyration of the DNA (R
DNA
).
Unfolded nucleosome conformations with exposed DNA can
be seen from example snapshots shown in the top panel
together with Figures S5 and S6. The free-energy landscape
exhibits a single basin around the crystal structure at R
DNA
=45
Å, where the DNA is tightly bound to histone proteins. The
model thus reproduces the expected stability of the nucleosome
as a packaging unit for the genome. The free-energy cost of
unwrapping the outer layer of the DNA in intact nucleosomes
has been estimated to be around 7 to 10 kcal/mol.
17,18,58
As
detailed in the SI (Section: Thermodynamics and Kinetics of
DNA Unwrapping), by carefully defining the state in which the
outer layer DNA has been unwound, our simulation predicts
the free-energy cost for unwinding the DNA to be 8 kcal/mol.
Furthermore, using a diffusion constant of D = 5500 bp
2
/s
estimated experimentally,
59
we find the rate for unwrapping the
outer layer DNA for the intact nucleosome to be approximately
3.6 × 10
−4
s
−1
, which is in good agreement with reported rate
0.00038 s
−1
from single molecule pulling experiments.
18
The average number of DNA base pairs bound to histone
proteins (see the SI for a rigorous definition) as a function of
R
DNA
is also shown in Figure 3 as a blue curve. As R
DNA
increases, we find that the number of bound DNA base pairs
changes in a stepwise manner. For example, most of the DNA
base pairs remain bound over the range of extension 45 < R
DNA
< 47.5 Å, which is followed by a sudden drop of ∼10 bp,
followed again by another plateau region 48 < R
DNA
<52Å.
The stepwise unwinding is even clearer at lower temperature, as
shown in Figure S7. Step-wise DNA unwinding is expected
from the periodic contacts that form between histone proteins
and the DNA at a 10−11 bp frequency;
36,57,60,61
see SI Section:
Periodicity of Histone DNA Contacts for a detailed discussion.
Figure 4A presents a two-dimensional free-energy landscape
as a function of the DNA radius of gyration R
DNA
and the
fraction of native contacts Q. At small R
DNA
when the DNA is
fully bound, the histone core complex is highly stable around
the octamer conformation that is captured in the crystal
structure with Q ∼ 0.8. As the DNA unwraps at large R
DNA
, the
free-energy of the low and high Q conformations become
comparable, and the histone proteins begin to fall away from
the core and begin to deviate from the octamer X-ray structure.
Figure 4B further characterizes in detail the unfolding of various
protein−protein interfaces. The interface between the two
copies of H3-H4 f orming the tetramer remains stable
throughout the entire range of R
DNA
studied. On the other
hand, the two interfaces between H3-H4 and H2A-H2B
gradually disappear as the nucleosome unfolds. We note the
loss of the interface between H3-H4 and H2A-H2B is
consistent with the stability of different interfaces determined
from the free-energy landscape for histone core assembly
shown in Figure 2. The coupling between histone disassembly
Figure 2. Formation of different protein−protein interfaces as the
histone protein core assembles. (A) Average fraction of native contacts
for various protein−protein interfaces as a function of the global Q.
(B) Two-dimensional free-energy profile for the two chemically
identical interfaces formed between H3-H4 and H2A-H2B hetero-
dimers. The arrows indicate the two parallel reaction channels for
folding. Standard deviation is provided in Figure S4.
Figure 3. Free-energy profile as a function of the DNA radius of
gyration R
DNA
for the unfolding of the nucleosome (yellow). Error
bars shown in gray represent the standard deviation of the mean. The
blue line measures the average number of DNA base pairs bound to
histone proteins. Examples of nucleosome configurations at various
values of R
DNA
are shown in the top panel, with the DNA colored in
yellow and the same coloring scheme as in Figure 1 for proteins.
Journal of the American Chemical Society Article
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J. Am. Chem. Soc. XXXX, XXX, XXX−XXX
D
and DNA unwinding revealed in Figure 4 suggests that histone
proteins will remain bound to the DNA by disrupting protein−
protein interfaces at large R
DNA
, thus explaining the plateau of
average bound DNA base pairs shown in Figure 3.
As illustrated in the top panel of Figure 3B, the DNA
molecule unwraps asymmetrically, and only one of two ends is
preferentially exposed at large R
DNA
. Figure 5 further
consolidates this observation with a free-energy landscape as
a function of the R
DNA
for each of the two equally divided DNA
segments separated at the nucleosome dyad. This landscape
clearly illustrates that the energetic cost of opening the two
ends simultaneously, i.e., moving along the diagonal of the
landscape, is much higher than opening only one end following
the pathways highlighted with arrows. Two examples of
sampled half open nucleosome structures are shown in Figure
5A, with the two segments of the DNA colored in yellow and
purple, respectively. It is important to point out that the short
DNA sequence employed in our simulation is palindromic, and
thus the two segments of the DNA are identical chemically.
There is thus no preference for either one DNA end to unwrap
first or the other, as reflected in the symmetry of the two
reaction channels on the free-energy landscape.
The asymmetric DNA conformation having only one of its
two ends unwrapped allows the other end to interact more
favorably with histone proteins. This energetic preference can
be seen from Figure 5C, which plots the average protein−DNA
electrostatic interaction energy of various nucleosome con-
formations. The y-axis of this figure is a measure for DNA
asymmetry defined as ξ =(R
DNA
first
)/(R
DNA
first
+ R
DNA
second
). This
definition is motivated by the observation that the unwrapped
end has larger radius of gyration. From Figure 5C, we see that
as we pull the DNA apart, for R
DNA
between 58 and 62 Å, the
protein−DNA electrostatic interaction energy is indeed lower
either for ξ < 0.5 or for ξ > 0.5 compared with the symmetric
configuration with ξ ∼ 0.5.
Sampling becomes difficult at large distances, but we note
that at the R
DNA
= 62 Å, a new set of configurations, in which
the DNA folds back onto itself along with a completely
dissociated histone protein core occasionally appears in the
simulation (see Figure S8). These configurations also have a
low electrostatic energy. This multiplicity of observed structures
at large R
DNA
suggests that in vivo unwrapping is likely to be
mechanically coupled to large scale DNA motions that are
promoted by motor proteins.
62
The detailed molecular model for nucleosome disassembly
put forward by our simulation is well supported with
experimental single molecule studies. For example, the
predicted loss of the H3-H4 tetramer/H2A-H2B dimer
interface along with DNA unwinding was indeed observed in
single molecule FRET experiments.
19,56
Similarly, the sequen-
tial asymmetric unwrapping of the two DNA ends has been
detected in recent single molecule pulling experiments.
20
Figure 4. Coupling between DNA unwrapping and histone protein
core disassembling. (A) Two-dimensional free-energy profile as a
function of the DNA radius of gyration (R
DNA
) and the fraction of
native contacts for the histone protein core (Q). Energies in kcal/mol.
(B) Average fraction of native contacts for various protein−protein
interfaces as a function of R
DNA
.
Figure 5. Asymmetric unwrapping of the two DNA ends as the
nucleosome unfolds. (A) Example asymmetric nucleosome conforma-
tions with the first DNA segment colored in purple and the second in
yellow. The coloring scheme for proteins is identical to Figure 1. (B)
Two-dimensional free-energy profile for the radius of gyration of the
two chemically identical DNA segments separated at the nucleosome
dyad. (C) Average protein−DNA electrostatic interactions as a
function of the DNA radius of gyration R
DNA
and the asymmetry
measure ξ. Energy scales in both part (B) and (C) are kcal/mol.
Journal of the American Chemical Society Article
DOI: 10.1021/jacs.6b02893
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E