Nucleosome positioning by genomic
Pascale Milania,b,c, Guillaume Chevereaua,b,c, Cédric Vaillanta,b,c, Benjamin Audita,b,c, Zofia Haftek-Terreaua,b,
Monique Marilleya,b, Philippe Bouveta,b,d, Françoise Argoula,b,c, and Alain Arneodoa,b,c,1
aUniversitè Claude Bernard Lyon 1, Université de Lyon, F-69000 Lyon, France; andbLaboratoire Joliot-Curie,cLaboratoire de Physique, anddLaboratoire de
Biologie Moléculaire de la Cellule, Centre National de la Recherche Scientifique/Ecole Normale Supérieure de Lyon, F-69007 Lyon, France
Edited by Jonathan Widom, Northwestern University, Evanston, IL, and accepted by the Editorial Board October 28, 2009 (received for review August 21, 2009)
Recent genome-wide nucleosome mappings along with bioinfor-
matics studies have confirmed that the DNA sequence plays a more
important role in the collective organization of nucleosomes in
vivo than previously thought. Yet in living cells, this organization
also results from the action of various external factors like DNA-
binding proteins and chromatin remodelers. To decipher the code
for intrinsic chromatin organization, there is thus a need for in vitro
experiments to bridge the gap between computational models of
nucleosome sequence preferences and in vivo nucleosome occu-
pancy data. Here we combine atomic force microscopy in liquid and
theoretical modeling to demonstrate that a major sequence signal-
ing in vivo are high-energy barriers that locally inhibit nucleosome
formation rather than favorable positioning motifs. We show that
these genomic excluding-energy barriers condition the collective
assembly of neighboring nucleosomes consistently with equilib-
rium statistical ordering principles. The analysis of two gene pro-
moter regions in Saccharomyces cerevisiae and the human genome
indicates that these genomic barriers direct the intrinsic nucleo-
some occupancy of regulatory sites, thereby contributing to gene
nucleosome statistical ordering | chromatin-mediated gene regulation |
physical modeling | atomic force microscopy
opportunity to elucidate the extent to which the DNA sequence
participates in the positioning of nucleosomes observed in vivo
along eukaryotic chromosomes (4, 5). Among the results indicat-
odicity of some di- or trinucleotides (e.g., AA/TT) show higher
affinity for nucleosomes (6–9). The periodic positioning of these
motifs over a few helical pitches would contribute to a global
spontaneous curvature of DNA that would favor its wrapping
on the histone surface (10, 11). However, the statistical signif-
icance of this 10-bp periodicity nucleosomal positioning signal
remains a subject of great debate (4, 5, 12, 13). According to
previous reports (12, 13), in Saccharomyces cerevisiae (1, 2), no
more than 20% of the in vivo nucleosome positioning, above what
is expected by chance, is determined by intrinsic signals in the
genomic DNA. An alternative antipositioning signaling picture
has recently emerged from bioinformatic studies (13–16) that
bring to light the fact that the sequence is actually highly pre-
and nonlocally influence the overall nucleosomal chromatin orga-
nization according to equilibrium statistical ordering principles
(14, 17). Furthermore, by conditioning an activatory or inhibitory
nucleosomal chromatin environment, these genomic energy bar-
riers would contribute to gene regulation (18). In vivo genome-
wide nucleosome positioning data encompass the influence of
it is difficult to isolate the contribution of direct histone-DNA
he recent flowering of tiled micro-arrays (1, 2) and chip-
sequencing (3) approaches has provided an unprecedented
interaction in these data. To overcome this limitation, we per-
formed an experimental study based on atomic force microscopy
(AFM) imaging in liquid of nucleosome assembly on genomic
sequences, at different loading levels, that provides direct single-
molecule visualization and precise quantification of intrinsic
nucleosome positioning. To investigate the role of the DNA
sequence on nucleosome positioning and nucleosome organiza-
tion, we assisted our AFM experimentation by some physical
dependent DNA bending properties (14, 15) that remarkably
reproduces recent in vitro genome-wide nucleosome occupancy
Results and Discussion
Combining AFM Imaging and Physical Modeling. So far, except for a
few studies of telomeric (22) and centromeric (23) nucleosomes,
AFM was used to image, mainly in air, nucleosome assembly on
specific positioning sequences (e.g., Xenopus 5S rDNA and 601
DNA sequences) and arrays of concatenated repetitions of these
sequences (22–25). We carried out AFM experiments in aque-
ous solution (26) and imaged mononucleosomes reconstituted on
genomic yeast and human DNA templates by using standard salt
detailed in Data and Methods. As a theoretical guide, we devel-
oped a physical modeling of nucleosome assembly that relies on
the computation of the free-energy cost of bending a DNA frag-
ment of a given sequence from its natural curvature to the final
ods). Consistent with our previous works (14, 28, 29), we used the
“Pnuc” structural bending trinucleotide coding table, experimen-
tally established from nucleosome positioning data (30) to derive
the effective potential. Then we extended this theoretical mod-
eling to a grand canonical description of the equilibrium density
of nucleosomes in this effective potential (see Data and Meth-
ods). When imposing that ≈30% of the sequence was covered by
parable with the nucleosome occupancy profiles observed in vitro
(21): The mean Pearson correlation computed along the 12 mil-
lion bps of the yeast genome is r = 0.70; a comparable high value
r = 0.77 is obtained when using recent models based on statisti-
cal learning (16, 21) [actually, r = 0.81 between our model and
the Field et al. model (16)]. Note that when adjusting the chem-
ical potential to get 75% nucleosome coverage of the sequence,
we got significantly lower correlations with in vivo data, namely
Author contributions: P.B., F.A., and A.A. designed research; P.M., G.C., C.V., B.A., and
Z.H.–T. performed research; P.M. and C.V. contributed new reagents/analytic tools; P.M.,
G.C., C.V., B.A., Z.H.-T., M.M., P.B., F.A., and A.A. analyzed data; and A.A. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. J.W. is a guest editor invited by the Editorial Board.
1To whom correspondence should be addressed. E-mail: email@example.com.
This article contains supporting information online at www.pnas.org/cgi/content/full/
www.pnas.org/cgi/doi/10.1073/pnas.0909511106PNAS December 29, 2009vol. 106no. 52 22257–22262
nucleosome occupancy probability profiles (black) predicted by our physical
modeling, for the three small yeast DNA fragments (see Data and Methods).
(A) 394-bp fragment A. (B) 386-bp fragment B. (C) 387-bp fragment C. For
each fragment, the chemical potential μ was adjusted so that the average
number of nucleosomes is 1.
Theoretical nucleosome formation energy landscapes (blue) and
r = 0.50 with Kaplan et al. data (21) and r = 0.30 with Lee et al.
data (2). The weakest correlations observed for our model as for
theFieldetal.model(16)(r = 0.43withinvivoKaplanetal.data,
and r = 0.33 with Lee et al. data), likely result from NFRs that
are induced by external factors (transcription factors, remodelers,
etc.) and are not taken into account by models that are mainly
aimed to describe the effect of the DNA sequence on nucleosome
Thus the main advantage of the present study that combines
in vitro AFM imaging and physical modeling is that for a same-
DNA template, very instructive and complementary informations
are made available: (i) by comparing the statistical positioning
distribution of a single mononucleosome (which is not accessible
in vivo) with the theoretical nucleosome energy profile, we are
able to characterize the ability of the sequence to locally favor
nucleosome formation, and (ii) by comparing the experimental
loading with the theoretical grand canonical nucleosome equilib-
rium density, we are in position to understand and quantify the
extent to which the DNA sequence contributes to the collective
organization of nucleosomes observed in vivo.
Genomic Energy Barriers Locally Inhibit Nucleosome Formation. In a
first experiment, we reconstituted a single nucleosome on three
short (394, 386, and 387 bp) DNA templates (see Data and Meth-
ods). These three DNA fragments were selected in the yeast chro-
mosome 3 according to the nucleosome formation energy profiles
predicted by our physical modeling (Fig. 1). Two of these pro-
files display rather high-energy barriers corresponding to NFRs
observed in vivo (2); for the first fragment (A), there is a barrier
positioned at the center (Fig. 1A) whereas two energy barriers
are bordering the second fragment (B) (Fig. 1B). As a reference,
the third fragment (C) presents a flat energy profile without any
barrier susceptible to impair nucleosome formation (Fig. 1C). As
illustrated on a few characteristic single-molecule AFM images
(Fig. 2A), the nucleosome is mostly observed at the edges of
DNA fragment A. The statistical analysis of the (symmetrized)
dyad-positioning distribution obtained from N = 107 molecules
(Fig. 2D) confirms an enrichment at both extremities, whereas a
lack of positioning events is noticeable at the center where the
sequence- induced energy barrier is located (Fig. 1A). This exper-
imental distribution is in good agreement (up to free-end effects)
with the theoretical mononucleosome occupancy probability pro-
of the underlying control of the DNA sequence on nucleosome
formation. This observation is corroborated by the mononucleo-
some positioning observed (N = 102) on DNA fragment B (Fig.
the presence of inhibitory energy barriers (Fig. 1B). Indeed, the
agreement observed between the experimental and theoretical
Consistent with its featureless theoretical energy landscape (Fig.
1C), the experimental nucleosome occupancy profile (N = 105)
obtained for DNA fragment C (Fig. 2F) turns out to be rather flat
tribution (Fig. 2C). This result confirms that the observed nucle-
osome positioning at the edges of fragment A(Figs. 2 A and D) is
not due to some possible entropic advantage (31) but more likely
results from the exclusion from the energetically unfavorable cen-
tral region (13–16). Similarly, the remarkable positioning of the
the excluding role of the bordering energy barriers and not from
some positioning signal, as observed in a test AFM experiment
with a 255-bp DNA fragment containing the 601 DNA sequence
three small yeast (chr. 3) genomic DNA fragments. (A and D) Yeast DNA frag-
ment A with L = 394 bp, N = 107 molecules. (B and E) Yeast DNA fragment
B with L = 386 bp, N = 102. (C and F) Yeast DNA fragment C with L = 387
bp, N = 105. Frames A–C give examples of four single-molecule AFM images
for each of these DNA templates respectively. D–F show the corresponding
symmetrized dyad positioning distributions (see Data and Methods). A red
bar was positioned at each experimentally detected dyad location and at its
symmetrical position with respect to the center of the fragment; the cross-
hatching at the edges corresponds to unphysical dyad positioning. The exper-
imental nucleosome occupancy probability profile (red curve), obtained as a
moving average of the symmetrized dyad density over a window of length
43.2 nm, is compared with the theoretical nucleosome occupancy probability
profile (Fig. 1) after symmetrization (black curve). In the physical modeling,
the boundary conditions were such that no nucleosome could settle on the
sequence if not adsorbed on its total length (147 bp); the chemical potential
μ was adjusted so that the average number of nucleosomes is 1 (See Data
AFM imaging in liquid of mononucleosome positioning along the
22258www.pnas.org/cgi/doi/10.1073/pnas.0909511106Milani et al.
Mononucleosomes. (A and C) Dinucleosomes. (D) Statistical analysis of mononucleosome positioning (N = 113 molecules); red bars correspond to experimen-
tally detected dyad locations and to their symmetrical position with respect to the center of the fragment. The experimental nucleosome occupancy profile
(red curve) is compared to the theoretical predictions of our physical modeling after symmetrization (black curve). (E) Statistical analysis of dinucleosome
positioning (N = 62); for each image, green bars were drawn at both the two dyad positions and their symmetric locations with respect to the center of
the fragment. The experimental nucleosome occupancy probability profile (green curve) is compared with the symmetrized theoretical profile (black curve).
(F) Histogram of internucleosomal distances between dinucleosomes; the continous black line corresponds to the distribution predicted by the pair function
(Eq. 5). (G) Oriented nucleosome occupancy probability distribution observed in vivo (2) (black dots) and predicted by the physical modeling (black curve); in
red is shown the location of the YRG105W gene with the transcription start site (arrow) and the transcription termination site (cross). Theoretical nucleosome
formation energy landscape (blue curve) and oriented nucleosome occupancy probability profile observed in vitro (21) (circles). Theoretical mononucleosome
(D) and dinucleosome (E–G) nucleosome occupancy profiles were computed by adjusting the chemical potential μ in our physical modeling so that the average
number of loaded nucleosome is 1 and 2, respectively (see Data and Methods).
AFM imaging in liquid of mono- and dinucleosomes along the yeast (chr. 7) DNA fragment (L = 595 bp) containing the gene YRG105W. (A and B)
(Fig. S1 of the SI Appendix), which was recently shown to prevent
the nucleosome from sliding (32). This first series of experiments
demonstrates the excluding role of high-energy barriers that are
Genomic Excluding-Energy Barriers Condition the Collective Assembly
of Neighboring Nucleosomes Consistently with Equilibrium Statisti-
cal Ordering Principles. In a second series of experiments (Fig. 3),
we reconstituted nucleosomes on a slightly longer (L = 595 bp)
DNA fragment in yeast chromosome 7 that contains the gene
YRG105W coding for a vacuolar membrane protein (see Data
organized nucleosomal chromatin observed in a majority of yeast
genes that are constitutively expressed (2, 18, 33, 34). Two rather
one just upstream the transcription start site (TSS) facilitating
the permanent access of activator/repressor (1, 2, 18, 33, 34) and
another at the gene 3?end possibly involved in transcription ter-
mination, antisense initiation, and recycling of RNA polymerase
to the promoter by DNA looping (34). Our physical modeling
of the nucleosome formation energy profile along yeast chromo-
somes confirms that a large number of these in vivo NFRs are
actually coded in the DNA sequence via genomic energy barriers
that impair nucleosome formation (or at least favor nucleosome
eviction) (14, 15). Hence, these energy barriers participate in the
regulation of the accessibility of promoter to transcription factor
scription termination by promoting cleavage and polyadenylation
of the nascent mRNA transcript (34).
AFM imaging of mononucleosomes reconstituted on this 595-
bp DNA fragment (Figs. 3 A and B) shows a lack of position-
ing at the two extremities, consistent with the presence of two
inhibitory energy barriers. Indeed, the statistical (symmetrized)
dyad-positioning distribution obtained for N = 113 molecules
(Fig. 3D) is similar to the one previously observed for the short
yeast DNA fragment B (Figs. 2 B and E). The mononucleosome
the 5?promoter and 3?downstream regions appear to be signif-
icantly depleted in nucleosome. The experimental nucleosome
occupancy probability profile (Fig. 3D) is rather flat in the gene,
as predicted by our physical modeling. This profile attests to a
homogeneous statistical dyad positioning inside the gene without
any preferential location induced by the presence of an under-
lying sequence strongly favorable to nucleosome formation (Fig.
3G). This conclusion is corroborated by the nucleosome occu-
pancy distribution observed in vitro at low nucleosome density in
a genome-wide experiment (21) (Fig. 3G).
The statistical analysis of N = 62 dinucleosomes reconstituted
on the same L = 595-bp yeast DNA fragment (Figs. 3 A and C),
clearly reveals a bimodal (symmetrized) nucleosome occupancy
probability profile with two privileged intragenic dyad locations,
as expected from the physical modeling when fixing the chemical
(Fig. 3E). Because the physical modeling reproduces the oriented
of in vitro nucleosome positioning is remarkably consistent with
the one observed in vivo. Importantly, the two priviledged loca-
tions of maximal nucleosome occupancy observed in vivo (Fig.
3G) did not emerge in the in vitro AFM mononucleosome occu-
pancy distribution (Fig. 3D) as well as in the genome-wide in vitro
data (Fig. 3G). This observation strongly suggests that the in vivo
nucleosome positioning was not driven by the presence of some
a global equilibrium ordering of two nonoverlapping objects con-
ities (17). This nucleosome confinement scenario is confirmed by
the internucleosomal distance distribution obtained from AFM
oretical equilibrium distribution predicted by the grand canonical
small linker length (?10 nm), corresponding to one or two helical
pitches (extreme left and extreme right configurations in Fig. 3C),
and a lower secondary peak at larger linker length (≈25 nm)
Milani et al.PNASDecember 29, 2009vol. 106no. 52 22259
ing from our in vitro AFM imaging of nucleosome assembly on
ated from these stable “genomic boundaries”, likely imprinted in
the DNA sequence during evolution.
Genomic Energy Barriers Direct the Intrinsic Nucleosome Occupancy
of Regulatory Sites. Finally, we investigated nucleosome assem-
bly on a DNA fragment long enough to allow orientation by using
a DNA topography profile without the need for end labelling
susceptible to affect DNA structure and nucleosome position-
ing (see Data and Methods and Fig. S2 of the SI Appendix). We
selected a L = 898-bp DNA fragment in the human genome that
contains the promoter of the gene IL2RA, which plays a major
role in the control of the immune system response. This frag-
ment includes different functional elements: (i) the TSS, (ii) the
core promoter with the TATA box, (iii) two positive regulatory
regions (PRR), PRRI and PRRII lying at positions −289/–216
and –137/–64 upstream of the major TSS, respectively (Fig. 4B).
These regulatory elements are important for regulating inducible
transcription of the IL2RA gene (35). Previous in vivo study in
unstimulated T-cells (36) revealed that prior to transcription, an
inhibitory nucleosome was positioned on the TATA box and TSS
regions, therefore preventing both preinitiation complex (PIC)
formation on the TATA box. In addition, this critically posi-
tioned nucleosome may also take part in the prevention of uncon-
trolled DNA melting in the TSS region (37). These properties
make this promoter a suitable model to investigate the actual
role of the DNA sequence in this peculiar repressive chromatin
From the analysis of N = 100 oriented DNA molecules loaded
by a mononucleosome (Fig. 4A), we confirmed the repressive
nucleosome positioning on the TATA box and TSS as observed in
upstream of the TSS that covers the regulatory sequence PRRI
(Fig. 4B). More importantly, the observed in vitro nucleosome
theoretical profile obtained from our physical modeling. There
exists an energy barrier ≈150 bp upstream of the TSS that is
coded in the sequence and that extends over the PRRII regu-
latory region, thus explaining the lack of nucleosome positioning
recorded from −200 bp to −100 bp (Fig. 4B). This stable genomic
excluding-energy barrier further conditions, by classical parking
phenomenon close to a wall (17), the observed repressive nucleo-
(ii) at its left foot encompassing the PRRI region (Fig. 4B). These
results demonstrate the fundamental role of the DNA sequence
in conditioning a peculiar local nucleosome chromatin structure
that constitutively contributes to gene repression. Furthermore,
by inhibiting nucleosome formation in the PRRII region, the
sequence may favor DNA accessibility to HMGA proteins that
are known to induce a negative torsional stress and, by accumu-
lation, a negative supercoil that may help nucleosome remodel-
ing and/or eventually nucleosome ejection (37, 38). Altogether,
these experimental observations enlighten the importance of this
sequence-induced local nucleosomal organisation for regulating
inducible transcription of the IL2RA gene.
In conclusion, by combining physical modeling and AFM
imaging in liquid, we demonstrated that sequences coding for
high-energy barriers impair nucleosome formation and condi-
tion the collective assembly of neighboring nucleosomes consis-
tently with equilibrium statistical ordering principles. By direct-
ing the positioning of these energy barriers relative to the TSS,
the sequence contributes to the specification of the activatory or
inhibitory role of the local chromatin environment. These studies
are a step forward in imaging nucleosome assembly in various
functional regions (promoters, replication origins, etc.). In
particular, comparing in vivo nucleosome positioning data to
human ILR2A promoter DNA fragment (L = 898 bp). (A) Examples of mol-
ecules that were oriented using the DNA topography profile methodology
(see Data and Methods and Fig. S2 of the SI Appendix). (B) Statistical analysis
(N = 100 molecules) of dyad positioning (red bars) relative to the locations
of the two regulatory regions PRRI and PRRII, the TATA box, and the TSS.
The experimental nucleosome occupancy probability profile (red curve) is
compared with the theoretical prediction of our physical modeling (black
loaded nucleosomes is 1 (see Data and Methods). The blue curve corresponds
to the theoretical nucleosome formation energy landscape.
AFM imaging in liquid of mononucleosome positioning along the
intrinsic sequence-induced positioning will provide direct mea-
remodelers, etc.) on chromatin architecture. The strategy devel-
oped here can also be generalized to real-time dynamical studies
of nucleosome repositioning on genomic sequences.
Data and Methods
Preparation of DNA Fragments. The DNA fragments were selected
according to the energy landscape and nucleosome occupancy profile
obtained from the physical modeling of nucleosome positioning (see Phys-
ical Modeling). The short (A, 394 bp; B, 386 bp; C, 387 bp) DNA fragments
were obtained by PCR amplification with Taq polymerase (Promega) from
yeast S. cerevisiae genomic DNA. Templates were amplified from sequences
of yeast chromosome 3: A, 249050-249443; B, 61210-61595; C, 214107-
214493 (SGD assembly database). The 595-bp-long sequence containing the
gene YGR105W (698500-698950) located on yeast chromosome 7: 698436-
699030, was amplified by PCR from genomic DNA. The human IL2RA pro-
moter sequence (898 bp) on chromosome 10: 4433-5331 (NCBI, locus n◦
NG007403), was amplified by PCR with Taq polymerase (Sigma) from human
length histone proteins of Xenopus laevis were overexpressed in bacteria and
purified as previously described (39). Nucleosome reconstitution was per-
formed by the salt dialysis procedure (27). The reaction was stopped in TE
buffer (10 mM Tris-HCl, pH 7.4, 1 mM EDTA) and 10 mM NaCl. For all con-
sidered DNA templates, nucleosomes were reconstituted with histone/DNA
ratio 1/0.8. The saturating loading of yeast chromosome 7 DNA fragment was
obtained with a histone/DNA ratio of 1.1/0.8.
AFM. AFM was performed in solution by using a Nanoscope IIIa microscope
(Digital Instruments) equipped with a type-E scanner and in tapping mode,
essentially as described in previous work (26). Ten microliters of a 1-nM recon-
stitution solution in imaging buffer (10 mM Tris-HCl, 1mM NiCl2, pH 7.9) were
22260 www.pnas.org/cgi/doi/10.1073/pnas.0909511106Milani et al.
deposited onto freshly cleaved mica and incubated for two minutes. A 100-μl
drop of imaging buffer was added in the liquid cell prior to imaging. For scan-
ning directly in the adsorption buffer, commercial silicon nitride probes (type
NP-S, Veeco Instruments) were used at a drive frequency of 8–9.5 kHz and a
set point of 0.3–0.4 V at constant temperature. AFM images were recorded
from 1 × 1 μm or 2 × 2 μm frames, at a scan rate of 2.18 Hz and a resolution
of 512 × 512 pixels.
Image Analysis. AFM image treatment and analysis were done by using
the “Scanning Adventure” software (40). Briefly, line-by-line second-order
flattening was first applied, followed by thresholding and filtering. Zooms
on individual mono- or dinucleosomes were performed, and the molecule
path was skeletonized; then, topographical analysis and length measure-
ments were carried out (Figs. S2 A–C of the SI Appendix). The results enabled
a measurement of nucleosomal height and a mapping of the nucleosome
position along DNA fragments. The position x of each nucleosome was con-
sidered to be the length corresponding to the midpoint of the DNA wrapping
length named “dyad” (Fig. S2B of the SI Appendix).
The distributions of mononucleosome height obtained for the three short
yeast DNA templates A, B and C, all display two discrete peaks centered at
1 and 2.9 nm (Fig. S3A of the SI Appendix). The largest peak value is slightly
smaller than the expected height of 5.0 nm for the nucleosome core particle
(NCP), as previously estimated by AFM in liquid when using a (3-aminopropyl)
triethyoxysilane (APTES) surface treatment (23). The smallest peak value ≈1
nm corresponds to the height of subnucleosomal particles that do not con-
tain the full histone octamer but more likely the histone tetramer. In all our
AFM nucleosome positioning studies, nucleosomes were identified as peaks
in the topographical profiles of height h ≥ 2 nm. The nucleosome diam-
eter measured by AFM is usually larger than the real diameter because of
tip convolution, which means that the actual entry/exit sites of DNA in the
nucleosome cannot be unambiguously localized. For the sake of comparison
with previous AFM studies (22, 23), the entry/exit sites were empirically deter-
mined by positioning the NCP at the position M corresponding to the local
height maximum and fixing its diameter to the crystallographic value (41)
d = 11 nm (Fig. S2C of the SI Appendix). In this way, the length of free DNA
outside the nucleosome, namely L+ = LS− (?M+ d/2) for the longer arm
and L− = ?M− d/2 for the shortest one, could be measured as well as the
corresponding length Lcof DNA that was complexed into nucleosome
Lc= L − (L++ L−), 
where L is the total length of the considered DNA fragment. The distributions
of complexed DNA length obtained for the sets of nucleosomes reconsti-
tuted on the three small yeast DNA fragments looked quite similar (Fig.
S3B of the SI Appendix). The mean complexed length Lc was found ≈150
bp in agreement with the expected core particle length of 147 bp. Let us
point out that some peak at Lc = 135 bp was observed for DNA fragment
A where, as induced by the underlying sequence, a majority of nucleosomes
were found to be located at the edges of the fragment (see Figs. 2 A and D).
We checked that those nucleosomes were the ones that were effectively par-
tially wrapped by DNA. Note that, consistent with previous AFM studies in
liquid (40), the DNA length was converted in bp by considering 0.36 nm as
the average distance between the nearest neighbor bps in B-DNA (Fig. S3C
of the SI Appendix).
From the measurement of L+, L−, and Lc(Fig. S2C of the SI Appendix), we
positioned the dyad along the DNA fragment by adding Lc/2 to either L+or
L−. But to compare the so-obtained experimental dyad-positioning distribu-
tion to the nucleosome probability density predicted by our physical model-
ing, we needed to orient DNA. We succeeded doing it for the 898-bp-long
S2DandE oftheSI Appendix).ForalltheotherDNAfragments,foreachAFM
image, we counted twice the fragment by positioning the dyad according
to the two possible orientations, namely the 5?-end is on the longest arm side
or vice versa (Figs. 2 D–F, Figs. 3 D and E, and Fig. S1B of the SI Appendix).
PhysicalModeling.Nucleosome density profile. When focusing on the
dynamical assembly of histone octamers along the DNA chain, chromatin can
be reasonably modeled (14) by a fluid of 1D rods of finite extension l (the
DNA wrapping length around the octamer), binding and moving in an exter-
nal potential E(s,l) (the effective nucleosome formation potential at position
s), and interacting through a hard core potential of size l. Within the grand
canonical formalism, considering that the fluid is in contact with a thermal
bath (at reciprocal temperature β) and a histone octamer reservoir (at chem-
ical potential μ), the equilibrium density ρ(s) of hard rods in an external field
E(s,l) obeys the nonlinear integral equation (42):
βμ = βE(s,l) + lnρ(s) − ln
Nucleosome formation energy.
E(s,l), we assumed that (i) DNA is an unshearable elastic rod whose con-
formations are described by the set of three local angles Ω1(s) (tilt), Ω2(s)
(roll), Ω3(s) (twist), and (ii) the DNA chain along the nucleosome at posi-
tion s is constrained to form an ideal superhelix (41) of radius R = 4.19 nm
and pitch P = 2.59 nm over a total length l which fixed the distribution of
angular deformations (Ωnuc
(u))i=1,2,3,u = s,...,s + l. Within linear elasticity
approximation, the energy cost for nucleosome formation is given by
To compute the energy landscape
(u) − Ωo
where A1, A2and A3are the stiffnesses associated to the tilt, roll, and twist
deformations around their intrinsic values Ωo
sistent with our previous works (14, 28, 29), we used the “Pnuc” structural
bending table (30), which was experimentally derived from the propensity
of trinucleotides in nucleosomal sequences to be in phase with the helical
pitch. This table is mainly a trinucleotide roll coding table (Ωo
table were arbitrarily assigned between 0 and π/18 rad, we performed the
following affine rescaling Ωo∗
get a comparable range of energy landscape fluctuations as was obtained in
the experiments (14).
Nucleosome occupancy profile.
required numerical integration. We fixed the variance σ2(E) [σ(E) = 1.95 kT]
and l = 146 bp, to match in vivo nucleosome positioning data by Lee et al.
(2). The nucleosome occupancy probability profile P(s) was obtained by con-
volving the nucleosome density ρ(s) with the rectangular function Π of width
l = 146 bp:
P(s) = ρ ? Π146(s).
P(s) is the probability for a bp located at s to be occupied by a nucleosome
of length 146 bp.
The theoretical probability of linker size xlwas computed by using the pair
function associated with the underlying energy E(s,l):
where ? is a normalizing constant.
2, and Ωo
3, respectively. Con-
2), with zero tilt
1= 0) and constant twist (Ωo
3= 2π/10.5). As the values of this bending
2− η with γ = 0.4,η = 0.06, in order to
Eq. 2 has an explicit solution (43) that
P(x = l + xl) =1
eβ(μ−E(s,l))eβ(μ−E(s+x,l))ds , 
ACKNOWLEDGMENTS. This work was supported by the Conseil Régional
Rhône-Alpes (Emergence 2005) and the Agence Nationale de la Recherche
under project DNAnucl (ANR-06-PCVI-0026).
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