Characterization of Nucleosome Unwrapping within …...tion requires insight into the folding properties of the chromatin ﬁber in molecular detail. Despite this, the structure and

Biophysical Journal Volume 107 July 2014 373–383 373

Article

Characterization of Nucleosome Unwrapping within Chromatin FibersUsing Magnetic Tweezers

Fan-Tso Chien1,* and Thijn van der Heijden21Institute of Physics, Academia Sinica, 128, Sec. 2, Academia Road, Nankang, Taipei, Taiwan, Republic of China; and 2Cambridge,Massachusetts

ABSTRACT Nucleosomal arrays fold into chromatin fibers and the higher-order folding of chromatin plays a strong regulatoryrole in all processes involving DNA access, such as transcription and replication. A fundamental understanding of such regula-tion requires insight into the folding properties of the chromatin fiber in molecular detail. Despite this, the structure and themechanics of chromatin fibers remain highly disputed. Single-molecule force spectroscopy experiments have the potential toprovide such insight, but interpretation of the data has been hampered by the large variations in experimental force-extensiontraces. Here we explore the possibility that chromatin fibers are composed of both single-turn and fully wrapped histoneoctamers. By characterizing the force-dependent behavior of in vitro reconstituted chromatin fibers and reanalyzing existingdata, we show the unwrapping of the outer turn of nucleosomal DNA at 3 pN.We present a model composed of two freely-jointedchains, which reveals that nucleosomes within the chromatin fiber show identical force-extension behavior to mononucleo-somes, indicating that nucleosome-nucleosome interactions are orders-of-magnitude smaller than previously reported andtherefore can be overcome by thermal fluctuations. We demonstrate that lowering the salt concentration externally increasesthe wrapping energy significantly, indicative of the electrostatic interaction between the wrapped DNA and the histone octamersurface. We propose that the weak interaction between nucleosomes could allow easy access to nucleosomal DNA, while DNAunwrapping from the histone core could provide a stable yet dynamic structure during DNA maintenance.

INTRODUCTION

Chromatin fibers are composed of strings of nucleosomecore particles that are connected by several 10s of basepairs(bp) of linker DNA (1). The nucleosome core particleconsists of an octamer of histone proteins and 147 bp ofDNA wrapped in 1.65 turns around the histone core (2).The tails of the histone proteins mediate the nucleosome-nucleosome interactions, which stabilize folding intohigher-order chromatin structures, such as the 30-nm fiber(3–5). Insight into the physical mechanisms that drive thehigher-order folding of chromatin is essential for under-standing the role of chromatin organization in all processesinvolved in the maintenance, transcription, and replicationof the eukaryotic genome.

In vivo, the chromatin structure can be regulated by DNA-sequence (6–8), ATP-dependent chromatin remodelers (9),posttranslational modifications (10), linker histones (11),and any other factors that bind to DNA or histones (12).The possible variations in size, composition, chemical,and mechanical properties of chromatin fibers render nativechromatin fibers challenging substrates for obtaining struc-tural information (13).

Submitted September 13, 2013, and accepted for publication May 16, 2014.

*Correspondence: [email protected]

Fan-Tso Chien and Thijn van der Heijden contributed equally to this work.

Editor: Jason Kahn.

� 2014 by the Biophysical Society

0006-3495/14/07/0373/11 $2.00

Reconstitution of chromatin fibers from purified histonesand arrays of nucleosome positioning elements results inhighly regular, stoichiometric fibers (10). This system pro-vides a controlled in vitro system for evaluating the contri-bution of individual components to folding independently ofone another. For example, by varying the linker lengthbetween positioning elements, a solenoidal folding wasobserved for linker lengths of 50 bp (14), whereas forshorter linker lengths of 20 bp a zig-zag structure hasbeen proposed (15). Furthermore, incorporating H5 linkerhistones not only stabilizes wrapped DNA in individualnucleosomes (16), but also contributes significantly to chro-matin compaction (14). Conversely, the higher-order foldingof chromatin fibers is inhibited by both ubiquitylated H2B(17) and acetylated H4 (3). Besides this variation in internalcomponents, chromatin compaction, at least in vitro, in-creases with ionic strength of the buffer conditions and/orincreasing amounts of divalent magnesium ions (4).

Single-molecule force spectroscopy has been used suc-cessfully to resolve force-induced transitions in chromatinfibers, in particular the transition from partially unwrappedto fully unwrapped nucleosomes, which occurs at forces>10 pN (18–21). The release of the inner wrap of DNA oc-curs in 25-nm steps corresponding to 74 bp. All these forcespectroscopy studies consistently demonstrate a plateau at 3pN for both native and reconstituted fibers. It has been sug-gested that the observed plateau is a characteristic of the

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374 Chien and van der Heijden

breaking of the bonds that hold neighboring nucleosomestogether, termed ‘‘unstacking’’ (21,22). However, forcespectroscopy studies on mononucleosome complexes alsoshow a transition at 3 pN, even though there are no nucleo-some-nucleosome bonds to break. In the case of mononu-cleosome complexes, the transition has instead beenattributed to unwrapping of the outer turn of DNA fromthe histone core (23,24).

To understand the force extension behavior of reconsti-tuted chromatin fibers in a magnetic tweezers setup, Krui-thof et al. (21) introduced an unstacking model to quantifythe force plateau based upon both a Hookean and a worm-like-chain description for the chromatin fiber and theunstacked configuration, respectively. This model assumedthat

1. all bound nucleosomes within the fiber are fully wrappedand stacked, and

2. all nucleosome positioning elements are occupied byhistone octamers.

Moreover, this model contains two interesting and testablephenomena:

1. the model assumes that the average distance between theextremities of the chromatin fiber is nonzero in theabsence of force; and

2. for forces >5 pN, the end-to-end distance of the tetherdecreases because the model predicts reentering of thehigher-folding domain by the chromatin fiber.

Finally, Kruithof et al. (21) concluded from their unstackingmodel that the higher-order folding in chromatin fibersfollows a solenoid structure for forces up to 3 pN. Basedon a reanalysis of the same experimental data using a two-angle model, Victor et al. (25) suggested that chromatinfibers follow a zig-zag instead of a solenoid configuration.Like Kruithof et al. (21), they assumed that all nucleosomepositioning elements were occupied by fully wrapped andstacked histone octamers. That these two studies reacheddifferent conclusions from the same data indicate that theinterpretation of the structure of higher-order nucleosomefolding varies greatly with the model and assumptionsapplied.

We now present an alternative model of chromatin exten-sion with the same number of fit parameters as used by Krui-thof et al. (21) that predicts the correct behavior even withoutdefining a priori the numbers of bound single-turn and fullywrapped histone octamers. This model (2FJC, for twofreely-jointed chains) contains two freely-jointed chainsdescribing the mechanical properties of fully wrapped nucle-osomes and nucleosomes with only one turn of wrappedDNA. We feel that the data analyzed with 2FJC resolvessome of the seemingly conflicting results in the field todate. We reanalyzed the data obtained by Kruithof et al.and collected single-molecule force spectroscopy data athigher forces for chromatin fibers reconstituted using the

Biophysical Journal 107(2) 373–383

same experimental conditions as in Kruithof et al. However,a key difference is that in our experiments we built-in longernaked DNA spacers to increase the distance between thechromatin fiber and the bead/glass. As the tether is alignedwith the force-axis in a magnetic tweezers setup, the positionof the magnetic bead has moved laterally due to an off-centerattachment to the tether through which the observed tetherlength decreases (26). Using longer naked DNA spacers,we are able to compensate for this decrease without affectingthe accuracy of the measured length of chromatin fibers.

Using the model of 2FJC generated from these analyses,we attribute the force-induced transition at 3 pN to a nonco-operative extension that results from 0.65 turns of DNAunwrapping from the fully wrapped nucleosomes. This re-sults in a fiber with octamers that contain only a singlewrap of DNA. At forces above 15 pN, this inner wrap ofDNA is also released. Furthermore, we show that minutesof exposure to forces as small as 4 pN leads to progressiveand irreversible unwrapping of the outer DNA turn likelycaused by dissociation of H2A/H2B dimers.

Finally, the previously reported interaction (21,22)between nucleosomes to induce higher folding within chro-matin fibers is not observed in our model, suggesting thatthermal fluctuations are sufficient to induce unstacking ofnucleosomes. Based on these findings, we therefore proposethat nucleosome-nucleosome interactions are weak inreconstituted chromatin fibers, at least in the buffer condi-tions utilized during in vitro chromatin pulling experiments.The weak interactions could allow regulatory elements suchas transcription factors easy access to nucleosomal DNA,while DNA unwrapping from the histone core could providea stable yet dynamic structure during DNA maintenance.

MATERIALS AND METHODS

DNA and chromatin fibers

The DNA construct for fibers with short 251-bp DNA spacers was prepared

as described in Kruithof et al. (21). The DNA spacers comprise the distance

between the chromatin fiber and the surface of either the magnetic bead

and/or bottom glass slide. For fibers with long DNA spacers, pUC18 con-

taining 25 copies of 197 bp of the 601-nucleosome positioning sequence

was applied (4). After digestion with BsaI and BseYI, the single-stranded

overhangs were filled with digoxigenin-labeled dUTP at the BsaI extremity

and biotin-labeled dUTP at the BseYI extremity. Chromatin fibers were re-

constituted through salt dialysis with competitor DNA (147 bp) and histone

octamers purified from chicken erythrocytes (4). Using an elution profile

and a protein-denaturing gel, only the fractions containing the well-formed

histone octamers were used, thus avoiding histone tetramers in subsequent

fractions (see Fig. S8 in the Supporting Material).

Magnetic tweezers

The details of the magnetic tweezers setup and the preparation of the flow

cell are as described in Kruithof et al. (21). The position of the bead was

measured by real-time image processing using the software LABVIEW

(National Instruments, Austin, TX) with an accuracy of 10 nm in three

dimensions. The force applied to the magnetic bead was calibrated by

Nucleosome Unwrapping within Chromatin 375

analyzing the power spectrum of measured lateral fluctuations (13). Based

on that analysis, we estimate the uncertainty in the measured force to

be 10%.

Data analysis

All data analysis was implemented in the software LABVIEW (National

Instruments). The uncertainty mentioned for each value is the standard de-

viation in the mean of the fitted parameter.

FIGURE 1 Force spectroscopy on chromatin fibers. (A) Schematic draw-

ing of outer- and inner-turn unwrapping from a nucleosome octamer

causing different end-to-end distances of the involved configurations.

(Red) Start and end of the nucleosome positioning element. (B and C)

Force-extension traces (black lines) with long and short DNA spacers,

respectively, are fit with the model of 2FJC (red line). The force-extension

of chromatin fibers with short or long DNA spacers behaves similarly. To

see this figure in color, go online.

Theory

Here, we first review the unstacking model from Kruithof et al. (21) and the

two-angle model from Victor et al. (25), which both describe the force-

extension of a chromatin fiber connected to bare double-stranded (ds)

DNA spacers.

In Kruithof et al. (21), the stacked chromatin fiber modeled as a Hookean

spring (HK) undergoes a force-dependent transition into a beads-on-a-

string (BoS) configuration consisting of only 1.65 turns wrapped, i.e., fully

wrapped, histone octamers connected to neighboring wrapped histone

octamers by linker DNA. The force-dependent extension z follows

z ¼ zDNAðWLCÞ þ nHKzHK þ ðM � nHKÞz1:65ðWLCÞ; (1)

with

nHK ¼ aM;

zHK ¼ lþ f

k;

a ¼ ½1þ expðbf ðz1:65 � zHKÞ � εÞ��1;

(2)

where both the DNA spacers and the BoS configuration are modeled using

the well-established wormlike-chain model described by their respective

contour, LDNA and LBoS, and persistence length, pDNA and pBoS (27).

Furthermore, the index 1.65 indicates the outer-turn wrapped configuration,

zDNA is the end-to-end distance of the DNA spacers, nHK is the number of

the stacked nucleosomes, zHK is the end-to-end distance of the stacked chro-

matin fiber, and z1.65 is the end-to-end distance of the outer-turn wrapped

configuration, f is the exerted force, l is the nucleosome line density, k is

the spring constant, M is the number of fully wrapped histone octamers,

ε is the free energy difference between both configurations, and b is the in-

verse thermal energy kBT.

In the two-angle model from Victor et al. (25), the chromatin fiber

undergoes a force-dependent transition from state v1 where the opening

angle between the entering and exiting DNA linkers of the nucleosome is

larger than 20� to state v2, where the opening angle is smaller than 20�.The force-dependent extension z follows

z ¼ zDNAðWLCÞþ nv1

�dv1 þ

f

kv1

�þ ðM � nv1Þ

�dv2 þ

f

kv2

�;

(3)

with

nv1 ¼ Mexpð�bDGÞ

expð�bDGÞ þ 1; (4)

and

DG ¼ 1

2f 2�

1

kv2� 1

kv1

�þ f ðdv2 � dv1Þ � ε; (5)

where dvi and kvi are the rest length and stiffness, respectively, of states vi in

the absence of force, with i denoting the two different states.

Both Kruithof’s model and Victor’s model are based on the assumption

that all nucleosomes in the chromatin fibers are fully wrapped. Here we

explore the possibility that chromatin fibers are composed of both fully

wrapped nucleosomes and histone octamers wrapped with only one turn

of DNA. In our description of the force-dependent extension of the chro-

matin fiber, we therefore consider three structures:

1. dsDNA spacers,

2. histone octamers with a single turn, or

3. 1.65 turns of dsDNA connected to neighboring wrapped histone

octamers by linker DNA in a BoS configuration (Fig. 1 A).

We consider the BoS configuration to be a flexible polymer with M ele-

ments in the fully wrapped configuration with length d0, able to release

independently the outer turn of wrapped DNA into a longer form d1, i.e.,

the inner or single-turn wrapped configuration under a free energy cost of

ε kBT (28). Furthermore, the BoS configuration contains N inner-turn



wrapped histone octamers, which are unable to transform into the outer-turn

wrapped configuration.

We model the BoS configuration as a freely-jointed chain where the

linker DNA acts as an inextensible rod and the bound histone octamers

as free swivel points. Because the linker DNA between nucleosomes is

much shorter than the persistence length of DNA, i.e., 50 and 150 bp,

respectively, we assume that thermal bending fluctuations of the linker

DNA are negligible compared to the breathing dynamics of a nucleosome

allowing different entry and exit angles of the wrapped DNA, especially

when the BoS configuration is aligned in the presence of an external force.

The force-dependent extension of such a BoS configuration was derived by

Cocco et al. (28), yielding

z ¼ zDNA þ z1:65 þ z1:0

¼ zDNAðWLCÞ þ v lnðZ1:65Z1:0Þvðbf Þ ;

(6)

with

z1:65 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pMd1bf0

s Z 1

�1

dt

2exp

�bMd1 f

2t2

2f0þ bMd0 ft

�

ð1þ exp½bftðd1 � d0Þ � ε�ÞM;(7)

ffiffiffiffiffiffiffiffiffiffiffiffiffis Z 1 �2 2

�
z1:0 ¼ 2pNd1
bf0 �1

dt

2exp

bNd1 f t

2f0; (8)

and t ¼ cosq, where q is the polar angle between the linker DNA and the

direction of the applied force. The index 1.0 corresponds to the inner-

turn wrapped configuration and f0 is an elastic constant that gives the

BoS configuration some elastic stretching due, for instance, to elastic

bending deformation of the linker DNA and peeling dsDNA of the histone

octamers.

RESULTS

In the force-spectroscopy experiments by Kruithof et al.(21), the length of the DNA spacer, and therefore the dis-tance between the nucleosomes and the surface of eitherthe magnetic bead and/or bottom glass slide, was 251 bp.The obtained end-to-end distance of the tethered chromatinfiber was used to extract changes in the higher-order struc-ture without taking into account the off-center binding posi-tion on superparamagnetic beads (26). This off-centerbinding always results in a shortening of the observedend-to-end distance of the tether up to the radius of theapplied bead size due to a (small) misalignment betweenthe tether and the center of the magnetic bead (26), andtherefore influences the reported end-to-end distance ofboth the DNA spacer and the chromatin fiber.

We hypothesized that longer DNA spacers would allow usto obtain the actual length of chromatin fibers despiteunderestimating the length of the DNA spacers themselves.Therefore, we used the same array containing 25 copies of601 positioning elements (29) but increased the length ofthe DNA spacers from the 251-bp spacer used by Kruithofet al. (21) to 2035 bp; this corresponds to a contour length


of 85 and 6.9 � 102 nm, respectively, by using a conversionof 0.34 nm/bp. These longer DNA spacers could providepotential binding sites for histone octamers and hence couldinfluence the reconstitution process of the chromatin fiberitself, therefore we carefully controlled for this as outlinedbelow. Although histone octamers do prefer a nucleosomepositioning element over a random DNA sequence (29), pre-vious force spectroscopy studies did not experimentallyconfirm the absence of histone octamers on the DNAspacers (18,24,30).

To confirm the absence of histone octamers on the longDNA spacers, we performed a parallel reconstitution on aconstruct with 25 copies of 197 bp of 601 positioningelements with long (2035-bp) DNA spacers. After reconsti-tution, the construct with the long spacers appeared as athick band in lane 1 followed by a gradual transition intoa slower migration species in lanes 2–8 in the native gel atincreasing histone octamer/DNA ratios (see Fig. S1 A),which is consistent with the fibers with short spacers (4).In addition, we also performed a postreconstitution diges-tion of the long DNA spacers. The subsequent native gelelectrophoresis showed that the EcoRI restriction siteswere well accessible and a band shift was absent, indicatingthat the spacers were nucleosome-free (see Fig. S1 B).These data demonstrate that during reconstitution, the his-tone octamers have a high preference for the 601 positioningsequences, leaving nucleosome-free DNA at the extremitiesof long (2035-bp) DNA spacers.

To determine any influence of the long DNA spacers onthe conformation of the chromatin fibers, we measured theforce-extension (FE) behavior of the construct in a magnetictweezers setup (21). We used samples with a histoneoctamers/DNA ratio of 0.6 (see lane 4, Fig. S1 A). Theconstruct was anchored between a glass surface and a super-paramagnetic bead. A pair of external magnets allowed us toexert a force on the tethered superparamagnetic bead. Theconstructs with short and long DNA spacers showed asimilar force extension behavior, albeit with a larger-lengthoffset for the long spacer construct. In both cases, weobserved a linear extension of the molecule at forces below3 pN followed by a force plateau between 3 and 4 pN, asobserved previously (18,21,22). Subsequently, the extensionbecomes linear again, until at high forces (F > 10 pN),where we observe distinct stepwise extensions. Becauseboth constructs show a similar behavior under these condi-tions, we summarize that the presence of longer spacers didnot influence the conformation of the chromatin fiber(Fig. 1, B and C).

Evaluation of the unstacking model

Wewill first show the shortcomings of the unstacking model(21) by highlighting a discrepancy in the fit results for thenumber of stacked nucleosomes, and the inability of the un-stacking model to correctly describe the force-extension


behavior above the force plateau. For this, we obtained theforce-extension behavior of individual fibers with shortand long spacers up to forces of 3 pN. All pulling curveswere repeated three times yielding overlapping FE tracesindicative of an equilibrated system. This indicates thatthe observed variations are intrinsic to the specific fiberand do not represent alternative conformations within eachfiber. Moreover, individual chromatin fibers have subtle var-iations in the position of the appearance of the plateau (seeFig. S6 and Fig. S7). The results after fitting the unstackingmodel to the short- and long-spacer constructs are summa-rized in Table S1 in the Supporting Material.

A typical fitting result is shown in Fig. S2, A and B, withthe experimental data in black and the obtained fit result inred. In the fitting process, we kept the persistence length ofDNA constant at 50 nm (31). Furthermore, data pointsbelow 0.2 pN were discarded in this analysis because inthe case of 2.8-mm-sized beads, at these small forces, theextension of the fiber in a dynamic force spectroscopyexperiment is dominated by the viscous drag on the super-paramagnetic bead (32). Although the chromatin fiber con-structs differ only by the length of their DNA spacers (seeabove), the unstacking model yields significantly differentvalues for the number of nucleosome positioning elementsand the persistence length of a beads-on-a-string array.Surprisingly, the change in DNA spacer length from 85 to6.9 � 102 nm is not observed in the fitted values.

Furthermore, the value we obtained for the nucleosomeline density is 8 5 4 nm per nucleosome, which is not inagreement with the values reported previously for chromatinfibers containing short DNA spacers (21) nor with valuesobtained from electron microscopy images (10) (see TableS1). Subsequently, the obtained contour length for the fullywrapped but unstacked state by fitting the model of 2FJC toour experimental data is 38 5 2 nm, which is much largerthan the expected value of 17 nm, i.e., the length of thelinker DNA (50 bp) between nucleosome positioning ele-ments. Finally, the unstacking model predicted a shorteningin the end-to-end distance at forces larger than 6 pN becausethe chromatin fiber reenters the higher-folding configurationdue to continuous stretching of the Hookean spring (see

stepwise rupture events in the high force regime between 12 and 18 pN. (Arro

with respect to the total number of bound histones as obtained from the mod

that the number of bound nucleosomes can be obtained accurately by fitting th

Fig. S5). This behavior is not observed in the experimentaldata; instead, it shows an increase in end-to-end distanceabove 6 pN (Fig. 2 A).

Absence of higher-order folding

As described above, we therefore concluded that the un-stacking model contains shortcomings and cannot describethe experimental data we generated. The unstacking modelassumed that all nucleosomes within the chromatin fiber areinitially fully wrapped but also stacked by nucleosome-nucleosome interactions creating a higher-order folding ofchromatin fibers (14). Applying an external force allowsthe nucleosome-nucleosome interactions to be overcome,eventually removing the higher-order folding and creatinga string of (fully) wrapped nucleosomes. We now addressthe possibility of absence of higher-order folding in a chro-matin fiber with a 50-bps linker length between adjacent nu-cleosomes for the force range probed here. Based on theirexperimental data and unstacking model, Kruithof et al.(21) suggested that such a chromatin fiber behaves as asolenoid.

Interestingly, Victor et al. (25) showed that using a two-angle model, the original data obtained by Kruithof et al.also allowed the existence of a zig-zag structure as ahigher-order folding. The results after fitting the two-anglemodel to our experimental data for the short- and long-spacerconstructs are summarized in Table S3. A typical fittingresult is shown in Fig. S3 with the experimental data in blackand the obtained fit result in red. Although the two-anglemodel yields similar values for the different constructs, theobtained spring constants are at least 10-fold larger thanexpected, i.e., 0.3 vs. 0.02, respectively. This significantincrease in the stiffness reflects a large change of the openingangle (>180�), indicating that nucleosome unwrappingoccurs in the linear extension regime (25). Such an outcomecannot explain the existence of a force plateau.

Furthermore, the obtained contour lengths for both thestacked and unstacked state are 32 5 2 nm and 15 53 nm, respectively, which are much larger than the expectedvalues of 17 and 1.8 nm. The latter is the nucleosome

FIGURE 2 FE traces obtained from stretching

individual chromatin fibers with 197-repeat 601

arrays. (A) The chromatin fibers were tethered to

2.8-mm superparamagnetic beads, allowing forces

up to 28 pN. The FE traces display five representa-

tive characteristics: an entropic extension below 1

pN followed by a linear extension until a force

plateau is reached at 3 pN. The plateau ends at 4

pN and a linear extension appears. Finally, above

8 pN, the FE trace shows stepwise rupture events

with an ~30-nm step size, revealing the number

of nucleosomes in the fiber. (B) Closeup of the

ws) Individual rupture events. (C) The number of counted rupture events

el of 2FJC. The high correlation of 0.95 between both methods indicates

e model of 2FJC to an FE trace below 6 pN.



density for a single nucleosome in a zig-zag structure (14).For our experimental data, Kruithof’s unstacking model andVictor’s two-angle model both yielded fitted structuralparameters significantly different from what is expectedfor a solenoidal or zig-zagged higher-order folding struc-ture, respectively. This indicates that such a higher foldingis also absent in the force regime below 3 pN. Thus weconclude that the force plateau in the experimental data isnot caused by a structural transition from a stacked to an un-stacked state, where the higher-order folding structure is dis-rupted by an external force.

Force plateau represents outer-turn unwrapping

Because both models fail to describe the force-extensionbehavior of reconstituted chromatin in our setup, we intro-duce here the model of 2FJC, which is based on theassumption that there is no higher-order folding caused bynucleosome-nucleosome interactions present (3). Moreover,the model includes the possibility that the chromatin fiberconsists initially of not only fully wrapped nucleosomes((ii) in Fig. 1 A), but also histone octamers wrapped withone turn of DNA ((iii) in Fig. 1 A). With the increase offorce, a nucleosome transits from a fully wrapped state toan inner-turn wrapped state while the initially bound one-turn wrapped histone octamers remain intact (18,24,33).The results of this model of 2FJC on the short- and long-spacer constructs are summarized in Table 1. Typical fittingresults are shown in Fig. 1, B and C.

We will first discuss the obtained parameters for the longDNA spacer constructs. The model of 2FJC discriminatesbetween two types of bound histone octamers, outer- andinner-turn wrapped, yielding 16 5 2 and 8 5 2, respec-tively. Their sum represents the total number of bound his-tone octamers, and is therefore 245 3, which is close to theexpected value of 25. Furthermore, the model of 2FJC fitsthe length of the DNA spacer yielding a value of (5.6 51.5) � 102 nm, which is shorter than the expected valueof 6.9 � 102 nm due to off-center attachment to the surfaceof the superparamagnetic bead (26). Subsequently, theelastic constant obtained is 8 5 3 pN.

TABLE 1 The mechanical properties of chromatin fibers with

a 197-bp repeat length of the nucleosome positioning element

601 connected to short or long DNA spacers

Properties 197 long spacers 197 short spacers

Number of FE traces 23 4

M þ N (nucleosomes) 24 5 3 23 5 6

d0 (nm) 18.2 5 1.7 20 5 7

d1 (nm) 38.2 5 0.9 36 5 2

ε (kBT) 15.2 5 1.4 11 5 4

f0 (pN) 8 5 3 11 5 7

LDNA (nm) (5.6 5 1.5) � 102 (7 5 4) � 101

Goodness of fit c2 1.1 1.6

The average and standard error of the mean of the fitted parameters of the

alternative model are shown.


Finally, the fit yielded values for the contour length of thefully wrapped and one turn wrapped state. The obtainedcontour length for the outer-turn wrapped configuration is18.2 5 1.7 nm. This is in good agreement with the 50-bplength of the linker DNA between the 601 repeats, whichis equivalent to 17 nm, being the contour length of a fullywrapped nucleosome (Fig. 1 A). Unwrapping of the outerturn results in the release of (0.65/1.65) � 147 ¼ 58 bp or20 nm (Fig. 1 A). Thus, the expected contour length ofsuch a configuration is 37 nm, in good agreement with theexperimentally obtained value of 38.2 5 0.9 nm. Further-more, the change in free energy between both states is15.2 5 1.4 kBT, close to the reported value of 12 kBT forthe change in free energy during first-turn unwrapping ofa mononucleosome (24). Taken together, the concordancebetween the model of 2FJC values and either our data ob-tained from chromatin fibers with long DNA spacers, orvalues reported in the literature, strongly indicates that theobserved force plateau in the force-extension behavior ofa chromatin fiber responds to outer-turn unwrapping of thebound histone octamers.

In the case of the short-spacer construct, we obtainedsimilar fitted values for the different parameters using themodel from 2FJC. The obtained contour length of theDNA spacer was (7 5 4) � 101 nm, in good agreementwith the expected value of 85 nm. Becaused only the fittedvalue for the DNA spacer differed between the short andlong spacer constructs, we can conclude that the length ofthe spacers does not influence the conformation of thechromatin fiber. More importantly, we are able to showthat the model of 2FJC is able to describe the obtainedforce-extension behavior as expressed in the goodness-of-fit value, i.e., 1.6 and 1.1 for the chromatin fiber with shortand long DNA spacers, respectively, where values are closeto 1.0 (Table 1).

Attachment position on the magnetic bead

In the force-extension data analysis presented by Kruithofet al. (21), the end-to-end distance of the chromatin fiberswas obtained directly from the length measurements byassuming that the attachment position of the chromatinfiber to the magnetic bead was at the closest position tothe glass surface. An extension in end-to-end distancewas interpreted as incomplete coverage of the nucleosomepositioning elements by histone octamers (see Fig. S4 A).However, a decrease in bound histone octamers shouldresult in a stiffening of the spring in the linear extensionregime (Eqs. 1 and 2). Instead, all our traces show an iden-tical behavior in this regime. Klaue and Seidel (26) showedthat the magnetic beads applied in a typical magnetictweezers setup are not superparamagnetic, but do containa small magnetic moment causing an off-centered attach-ment point to the magnetic bead. As a result, variationsup to the radius of the bead can be observed in the


end-to-end distance although a uniform DNA construct isapplied.

Kruithof et al. (21) did not measure experimentally theoffsets of the tethered chromatin fibers so their data couldcontain unknown offsets. To address the consequencecaused by the off-center attachment, we took Kruithof’sdata and speculated that the chromatin fiber has the largestoffset, which equals to 0.5 mm, the radius of the magneticbeads used. Fitting the model of 2FJC to Kruithof’s originaldata (see Fig. S4 A) resulted in a description of a chromatinfiber with only nine bound histone octamers and a negativevalue for the length of the DNA spacers (see Table S2),where a value of 25 bound histone octamers and at least apositive value for the contour length was expected. Addingan offset of 0.5 mm, the model of 2FJC fitting these cor-rected Kruithof’s data (see Fig. S4 B) yielded values in com-plete agreement with the values obtained for our chromatinfibers with short DNA spacers as summarized in Table S2.This clearly shows that the off-center binding to the mag-netic bead influences the outcome of the contour lengthmeasurement, and, therefore, any result directly obtainedfrom this, such as the number of bound nucleosomes (21).

FIGURE 3 The impact of ionic strength on the outer-turn unwrapping

from histone octamers within a chromatin fiber. In the presence of

10 mM Naþ, a single chromatin fiber was stretched in 10, 100, and

200 mM Kþ. The extension of the chromatin fiber is shown (black lines)

in the FE plots. (Solid red lines) Fits obtained from the model of 2FJC.

An increase in ionic strength not only reduces the height but also the size

of the force plateau. To see this figure in color, go online.

Inner-turn unwrapping

The model of 2FJC allows us to fit the number of bound his-tone octamers below 6 pN. In the force regime above 10 pNwe observe stepwise extension (see Fig. 2 B). Due to thehigh stiffness of DNA at these forces, the Brownian fluctu-ations of the tether are small compared to the observedstepwise extensions, allowing us to directly count the num-ber of nucleosomes in an individual chromatin, as shown inFig. 2 A (18). For this batch of reconstituted fibers with arepeat length of 197 bp, we have, on average, 25 5 2inner-turn unwrapping events and therefore 25 5 2 boundnucleosomes. This is in excellent agreement with the ex-pected number of 25 of 601 nucleosome positioning ele-ments in the DNA construct. Furthermore, the obtainedaverage step size for an unwrapping event above 10 pN is30.1 5 0.7 nm, obtained by dividing the increase in lengthby the number of counted steps. This is in excellent agree-ment with the release of the inner wrap of a nucleosomecontaining 147/1.65 ¼ 89 bp equivalent to 30 nm (2).

Although the force measurements above 10 pN resolvethe number of nucleosomes in a fiber, these forces alsoinduce histone dissociation (18). To resolve the fiber compo-sition in a potentially less-destructive manner, we used themodel of 2FJC to fit the FE curves between 0.5 and 7 pN.From the fits we obtained 25 5 2 bound nucleosomes inexcellent agreement with the numbers obtained abovefrom the inner-turn unwrapping events and the expectedvalue of 25 601-nucleosome positioning elements. Wealso observed a small fraction of fibers containing a signif-icantly different number of bound nucleosomes (Fig. 2 C). Apossible reason is that a small fraction of the DNA arrays

may contain a different number of nucleosome positioningelements, which could not be detected with partial digestionexperiments.

Furthermore, when seeking tethered fibers, we tend to usethose with the largest spatial fluctuations, which are inher-ently also the longest ones. We therefore skew the obtaineddistribution of nucleosome positioning elements presentwithin a fiber. For this fraction, the obtained numbers ofbound nucleosomes from the model of 2FJC and theinner-turn unwrapping events showed a high correlationcoefficient of 0.95, confirming the consistency betweenboth methods.

Outer-turn unwrapping is salt-dependent

Having established a model for describing the FE behaviorof single chromatin fibers, we were able to evaluate the saltdependence of outer-turn DNA unwrapping in detail. Bymeasuring the same chromatin fiber multiple times, weminimized heterogeneities in terms of fiber composition.Fig. 3 shows three FE traces at increasing salt concentration[Kþ]. These traces were obtained as follows: starting at aconcentration of 10 mM, three consecutive force cycleswere applied to test for hysteresis in the force-extensionbehavior. Absence of any hysteresis indicated that the chro-matin fiber was in equilibrium with its present bufferconditions.

Subsequently, a new buffer with an increased salt concen-tration was introduced into the flow cell and the measure-ments were repeated. Increasing the salt concentrationfrom 10 to 200 mM decreased the force plateau at which



unwrapping occurs from 3.5 to 2.3 pN. We also observed adecrease in the compaction of the folded fiber being propor-tional to the shortening of the plateau. Furthermore, thechange in free energy dropped from 19 5 3 kBT at10 mM to 11.1 5 1.7 kBT at 200 mM. All other mechanicalproperties remained constant and within the range that weobserved under standard conditions (Table 2). Althoughthe salt concentrations changed by an order of magnitude,we kept the persistence length of DNA fixed at 50 nm,because the persistence length of DNA does not changesignificantly over this concentration range (31).

Thus the 2FJC description of the nucleosome, beingwrapped by DNA by one or 1.65 turns, holds over a widerange of salt conditions. The free energy between both statesdecreases for an increase in ionic strength, possibly reflect-ing the enhanced screening of electrostatic interactions be-tween DNA and the histone octamer surface.

Irreversible outer-turn DNA unwrapping

To probe the stability of the inner-turn wrapped state, weapplied 15 successive stretching cycles up to 4 pN to a singlechromatin fiber containing long DNA spacers. The linearextension between 0.5 and 2.5 pN showed a gradual shifttoward a more extended structure unable to maintain itsoriginal conformation while the size of the plateau at 3pN decreased, but the end-to-end distance at 4 pN convergedfor all traces (Fig. 4 A).

The successive traces were fit with the model of 2FJCand the resulting outcome with respect to the number ofapplied stretching cycles is displayed in Fig. 4, B–F, for,respectively, the following:

Fig. 4 B, the number of bound histone octamers;Fig. 4 C, the contour length of one-turn and fully wrap-

ped histone octamers;Fig. 4 D, the elastic force;Fig. 4 E, the change in free energy; andFig. 4 F, the contour length of the DNA spacers.

All parameters shown in Fig. 4, B–F, remain constant, eventhe total number of bound histone octamers. Interestingly,the number of outer-turn wrapped histone octamers de-creases with respect to the number of applied force cycles,whereas the number of inner-turn wrapped histone octamersshows the reversed behavior (solid and open circles inFig. 4 B, respectively). This indicates that long-term expo-sure of the unwrapped state leads to irreversible outer-turn

TABLE 2 The mechanical properties of a chromatin fiber in

different monovalent salt conditions as obtained from the

model of 2FJC

[Kþ] (mM) M N d1 (nm) d0 (nm) f0 (pN) ε (kBT) LDNA (nm)

10 24 3 36.9 17.5 8.7 18.6 4.1 � 102

100 16 7 36.8 16.4 8.2 15.4 5.3 � 102

200 7 18 38.0 17.6 6.7 11.1 3.1 � 102


DNA unwrapping likely caused by H2A/H2B dimer dissoci-ation in agreement with other force spectroscopy experi-ments where only histone tetramers remain bound to theDNA molecule (34).

DISCUSSION AND CONCLUSIONS

We characterized the conformation of reconstituted chro-matin fibers by quantifying their FE traces in the forceregime below 4 pN and fitting the data to the model of2FJC. The fibers display a force plateau at 3 pN, indi-cating force-dependent outer-turn unwrapping events. Weconclude that chromatin fibers lack higher-order folding inthe experimental conditions utilized. Instead, the chromatinfibers are composed of histone octamers with either one or1.65 turns of wrapped DNA. As a result, both previouslypublished models—the unstacking model featuring a sole-noid (21) and the two-angle model using a zig-zag structure(25)—are not supported by the data obtained from stretch-ing chromatin fibers containing 50 bp of linker DNA, eitheras previously published (21) or from the study in hand (seeTable S1 and Table S3).

This is in contrast to the unstacking behavior proposed byKruithof et al. (21), as based on their data. Their unstackingmodel predicted a shortening in end-to-end distance forforces above 5 pN, which was not observed in our experi-mental data (Fig. 2 A). Furthermore, their model did nottake into account the degeneracy of states, where differentconfigurations of (un)stacked nucleosomes within a chro-matin fiber have identical free energy levels. Therefore,the observed extension of a chromatin fiber becomes amixture of configurations instead of a single defined config-uration. Subsequently, Kruithof et al. reported that the valuesof the nucleosome line density obtained from applying theunstacking model to their data are consistent with the valuesreported by Routh et al. (14), suggesting the existence of asolenoidal folding up to the force plateau of 3 pN. However,fitting the unstacking model to our data revealed a dramaticincrease in the nucleosome line density, being nonconsistentwith the reported values obtained from analyzing electronmicroscope images of chromatin fibers (14). Moreover, themechanical properties of the fiber obtained from the un-stacking model vary between the chromatin fibers with shortand long DNA spacers. Finally, applying a two-angle modeldid not reveal the existence of a zig-zag structure for a chro-matin fiber with a 197-bp repeat.

Kruithof et al. (21) argued that chromatin fibers with arepeat length of 167 bp have a zig-zag structure becausethey observed an increase in stiffness of 2.7 for the tetheredmolecule where a factor 4 was expected. Here, we note threediscrepancies in their arguments.

1. They assume that the stiffness of a single ribbon of thezig-zag folding is identical to that of the solenoidalfolding, which has a denser-packed configuration.

FIGURE 4 The change of the number of fully wrapped histone octamers in repeated force-cycle experiments. (A) A single chromatin fiber was stretched

for 15 times displaying a shift in the start of the force plateau at 3 pN of 0.4 mm between the first and last force cycles while the length converged at 4 pN. The

individual FE traces of the sequential pulling cycles are plotted in different colors. (Dashed arrow) Progression of the 15 pulling cycles. The quantification of

the subsequent FE traces by the model of 2FJC is shown in panels B–F. All parameters remained constant throughout the force cycles except for the number

of inner- and outer-turn wrapped histone octamers showing an opposite behavior. (B) Total bound nucleosomes (solid red circles) are the sum of fully wrap-

ped nucleosomes (solid black circles) and one-turn wrapped nucleosomes (open circles). (C) Contour length shown: (solid black circles) fully wrapped

nucleosomes; (open black circles) one-turn wrapped nucleosomes. (D–F) Elastic force, change in free energy, and contour length of the DNA spacers, respec-

tively. The error bars shown represent the uncertainties in the fit parameters. To see this figure in color, go online.


2. The obtained rest lengths for 167- and 197-bp repeatfibers are 79 5 21 nm and 50 5 6 nm, respectively,which do not differ significantly.

3. In both discrepancies 1 and 2, all nucleosome positioningelements are assumed to be occupied with fully wrappedand stacked histone octamers, but this is not experimen-tally supported; therefore, the changes in rest lengthand stiffness may be a product of chromatin fiber hetero-geneity.

In summary, the claim of a highly compliant helical foldingcannot be substantiated by the models and data presented byKruithof et al. (21).

Our analysis showed that nucleosomes in a chromatinfiber unwrap in two distinct steps in response to increasingstretching forces as observed for single nucleosomes(23,27), releasing first 0.65 turns followed by a full turn.This implies that the model presented here is independentof the linker length present between adjacent nucleosomes,because the amount of DNA released from the histone-octamer remains constant resulting in identical force-exten-sion curves. However, we would like to note that, to stretch a

beads-on-a-string array, the DNA length between nucleo-somes needs to be larger than the diameter of a nucleosome,i.e., 11 nm or 32 bp (2), to overcome any steric hindrance.Therefore, for chromatin fibers with a repeat length shorterthan 179 bp, this can result in a force-extension behaviordifferent than presented here.

The FE description for the chromatin fiber included afreely-jointed chain (FJC) contribution. Does an FJC mimicthe structure of chromatin fibers? Electron microscopystudies have shown that nucleosomes in the presence oflinker histone H5 are able to form a 30-nm chromatin fiberforming either a solenoid or zig-zag structure (14). How-ever, fibers in the absence of H5 resulted in a beads-on-a-string configuration lacking regular higher-order foldingand showing a lower compaction (14). This resembles ourassumption above for an FJC description for the BoS config-uration: the dsDNA linkers between histone octamers act asstiff rods due to their short length compared to the persis-tence length of dsDNA, whereas the bound histones act asa free swivel point at the DNA entry point.

What, then, happens to the nucleosome-nucleosome in-teractions to induce higher-order folding? In this study,



the observed force plateau at 3 pN resembles first-turn un-wrapping within the chromatin fiber in agreement with theforce spectroscopy behavior of mononucleosomes (24).Furthermore, the FE behavior is well described by twoFJCs in a force regime from 0.2 to 7 pN with a c2 valueat ~1.0. Any nucleosome-nucleosome interaction in thisforce regime should have resulted in a higher value for c2,indicating that not all force-dependent characteristics werecaptured by the model. This allows us to provide an upperlimit for the nucleosome-nucleosome interactions. Thetypical distance overcome between adjacent histone oc-tamers is the linker DNA: 50 bp for 197-repeat fibers.

Because the lowest force described with the model is 0.2pN, the free energy difference between stacked and un-stacked nucleosomes is at most 0.83 kBT, indicating thatthermal fluctuations are sufficient to overcome nucleo-some-nucleosome interactions. This estimation is smallerthan previously published values on nucleosome-nucleo-some interactions ranging between 3.8 and 14 kBT(21,22), where 14 kBT describes the free energy change ofouter-turn unwrapping as discussed here. The former value,3.8 kBT, is based upon estimation for the average distancebetween adjacent nucleosomes, which was not experimen-tally verified.

The model of 2FJC presented here can be expanded toinclude nucleosome-nucleosome interactions, to unravelthe higher-order folding of chromatin in the subpiconewtonforce regime. Differences in spring constant between a sole-noid and zig-zag superstructure should then be reflected inthe force-extension behavior or in the thermal fluctuationsat a given force due to constant stacking and unstackingbetween adjacent nucleosomes (14,35,36).

Posttranslational histone modifications have been sug-gested to play an important role in the regulation of DNA-based activities (37). We have shown that a combinationof low-force pulling experiments and quantitative analysiscan characterize the properties of outer-turn unwrappingevents within chromatin fibers. This method of analysiscan be used to unravel the effects of such histone modi-fications on chromatin folding, bringing us closer to a struc-tural understanding of the regulatory role of chromatinorganization.

SUPPORTING MATERIAL

Eight figures and three tables are available at http://www.biophysj.org/

biophysj/supplemental/S0006-3495(14)00600-6.

The experimental work described in this article was performed in the group

of Dr. Ir. S.J.T. van Noort at the Leiden institute of Physics, Leiden Univer-

sity, the Netherlands. We thank Daniela Rhodes for generous gifts of the

DNA constructs, Andrew Routh for help with chromatin reconstitutions

and the postreconstitution digestion, and Derek Stein, Paige Shaklee, and

Elizabeth Gaskell for valuable discussions.

This work was financially supported by the Netherlands Organization for

Scientific Research (NWO).


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Characterization of Nucleosome Unwrapping within Chromatin Fibers Using Magnetic Tweezers Fan-Tso Chien and Thijn van der Heijden

Figure S1:

Biochemical preparations examined with gel electrophoresis. (A) Chromatin

fibers with DNA spacers of 2035 bp were titrated in 8 steps with purified

histones and mixed with 147 bp competitor DNA. The histone octamers:DNA

ratio is 0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, and 1.4 from lane 1 to 8. (B) Chromatin fibers

of the 8 titrations shown in (A) were digested with EcoRV. The digested spacers

1 and 2 have a length of 673 and 1362 bp. Lane 4 displays the most condensed

band of chromatin without spacers.

Figure S2:

(A, B) Force-extension traces with respectively long (LS) and short (SS) DNA

spacers are fit with the unstacking model (red line).

Figure S3

(A, B) Force-extension traces with respectively long (LS) and short (SS) DNA

spacers are fit with the two-angle model (red line).

Figure S4:

Influence of the tether attachment point on the obtained mechanical properties

of the chromatin fiber. (A) The original data (black line) overlaid with the fit

result of the 2FJC model (red line). (B) The corrected original data containing an

offset of 0.5 μm (black line) with the overlaid fit (red line). The fit parameters are

summarized in Table S2.

Figure S5:

Simulated force-extension trace obtained from the unstacking model as

described by Equations 1 and 2. The following values were applied: the

persistence length of DNA and the BoS configuration are 50 and 18 nm

respectively. Furthermore, the number of fully wrapped histone octamers is 25, a

free energy difference of 12 kBT, a spring constant of 0.6 pN/nm, a nucleosome

line density of 2 nm-1, and a contour length of 17 and 80 nm for respectively the

BoS configuration and bare DNA.

Figure S6

Force-extension traces of chromatin fibers with a nucleosome repeat length of

197 bp containing short DNA spacers.

Figure S7

Force-extension traces of chromatin fibers with a nucleosome repeat length of

197 bp containing long DNA spacers.

Figure S8

Purification of intact histone octamers. (A) Elution profile of histone octamer

sample run on an S-200 gel filtration column pre-equilibrated in 2M NaCl, 10 mM

Cacodylate (pH 6.0). The two peaks correspond to the histone octamer and

H2B/H2A dimers that become dissociated during the purification protocol.

H3/H4 tetramers run in the ‘shoulder’ that can be seen in the first peak. (B) 4-

20% Tris-Glycine SDS polyacrylamide gel electrophoresis of each of the fractions

shown in (A).

Table S1:

Outcome of the mechanical properties of long (LS) and short (SS) spacer

chromatin fibers as obtained with the model of Kruithof et al.

197 LS

(Kruithof)

197 SS (Kruithof)

Expected

M (nucleosomes) 36 ± 7 24 ± 4 25

d1 (nm) 39 ± 3 38 ± 3 17

ε (kBT) 15 ± 5 12 ± 2 12

LDNA (nm) (6.6 ± 1.3)·102 (4.6 ± 1.0)·102 LS: 6.9·102

SS: 85

l (nm-1) 6 ± 3 9 ± 6 1.5-2.0

pBoS (nm) 29 ± 17 (6 ± 3)·101 18

kHK (pN/nm) 0.31 ± 0.08 0.4 ± 0.3 0.6

Goodness of fit χ2 2.0 0.72 1.0

Table S2:

Comparison between the outcomes of the fits results for the offset corrected data

and the values as summarized in Table 1.

No offset +0.5 μm 197 SS

M + N (nucleosomes) 9 24 23

d0 (nm) 11 18 20

d1 (nm) 41.7 37.4 36.1

ε (kBT) 22 15 11

f0 (pN) 6.1 26 11

LDNA (nm) -8·101 8·101 7·101


Table S3

Outcome of the mechanical properties of long (LS) and short (SS) spacer

chromatin fibers as obtained with the two-angle model.

197 LH (Victor)

197 SH (Victor)

Expected

M (nucleosomes) 28 ± 2 25 ± 2 25

(nm) 33 ± 2 31.5 ± 1.8 17

ε (kBT) 13.5 ± 1.4 10 ± 3 12

LDNA (nm) (4.5 ± 1.9)·102 (3.0 ± 1.8)·102 LS: 6.9·102

SS: 85

(nm) 15 ± 3 15.1 ± 1.8 1.8

(pN/nm) 0.23 ± 0.03 0.4 ± 0.2 0.02

(pN/nm) 0.29 ± 0.06 1.3 ± 1.2 0.02


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Characterization of Nucleosome Unwrapping within …...tion requires insight into the folding properties of the chromatin ﬁber in molecular detail. Despite this, the structure and