Histone Depletion Facilitates Chromatin Loops on the Kilobasepair Scale

Histone Depletion Facilitates Chromatin Loops on the Kilobasepair Scale Philipp M.Diesinger,??*Susanne Kunkel,§Jo¨rg Langowski,?§and Dieter W.Heermann??

?Institut fu¨r Theoretische Physik and?Interdisziplina¨res Zentrum fu¨r Wissenschaftliches Rechnen,Universita¨t Heidelberg,Heidelberg, Germany;and§Division of Biophysics of Macromolecules,German Cancer Research Center,Heidelberg,Germany

ABSTRACT The packing of eukaryotic DNA in the nucleus is decisive for its function;for instance,contact between remote genome sites constitutes a basic feature of gene regulation.Interactions among regulatory proteins,DNA binding,and transcrip-tion activation are facilitated by looping of the intervening chromatin.Such long-range interactions depend on the bending?ex-ibility of chromatin,i.e.,the ring-closure probability is a directly measurable indicator of polymer?exibility.The applicability of a wormlike chain model to naked DNA has been widely accepted.However,whether this model also suf?ces to describe the ?exibility of eukaryotic interphase chromatin is still a matter of discussion.Here we compare both5C data from a gene desert and data from?uorescence in situ hybridization with the results of a Monte Carlo simulation of chromatin?bers with and without histone depletion.We then estimate the ring-closure probabilities of simulated?bers with estimates from analytical calculations and show that the wormlike chain model grossly underestimates chromatin?exibility for sharp bends.Most importantly,we?nd that only?bers with random depletion of linker histones or nucleosomes can explain the probability of random chromatin contacts on small length scales that play an important role in gene regulation.It is possible that missing linker histones and nucleosomes are not just simple,unavoidable,randomly occurring defects,but instead play a regulatory role in gene expression. INTRODUCTION

The eukaryotic genome is compacted into chromatin.In this structure,the DNA is wrapped at~200basepair intervals around histone octamers,forming a string of beads that can be further compacted into a linear structure known as the chromatin?ber.How the nucleosomes are arranged to form this higher-order structure is still a matter of discussion (3–6).Different models have been proposed,including zigzag ribbon(or crossed-linker)models(7–11),helical solenoid models(12–14),and irregular structures(5).The solenoid models and the crossed-linker structures are the main competing classes of chromatin models for the nonde-pleted state.In the solenoid model,two consecutive nucleo-somes linked by a stretch of DNA are located at the same side of the?ber,requiring the linker DNA to bend,whereas in the crossed-linker case they sit on opposite sides of the ?ber and the DNA linker that connects them is straight.In the solenoid model,the nucleosome chain forms a helical structure with the axis of the core particles being perpendic-ular to the solenoidal axis.The crossed-linker pattern of the model with the straight linkers,peripherally arranged nucle-osomes,and internal linker DNA allows dramatic changes in the compaction level to occur without major changes in the topology.The crystal structure of a tetranucleosome (without linker histones)was solved in2005(7)and supports the helical ribbon structure.A more recent approach(15)starts with the nucleosome arrangement and seeks to determine which kinds of chromatin structures are possible.(For a profound discussion of different chro-matin models,see Schiessel(16).)

Nucleosomes are in a dynamic equilibrium with the chro-matin?ber.They can dissolve entirely by unwrapping the DNA,leaving naked DNA stretches behind,and later they can form again.This leads to an average nucleosome occu-pation(i.e.,the probability that a basepair will be covered by a nucleosome)of<75%(which corresponds to a entirely saturated chromatin?ber),an effect that has to be taken into account in structural models.

In addition to its structural role,this compaction is cen-trally important in the regulation of transcription.Access to DNA wrapped in a nucleosome is obstructed(17)for poly-merase,regulatory,repair,and recombination complexes, yet nucleosomes also bind other proteins through interactions with their histone tail domains(18).The detailed locations of nucleosomes along the DNA may have important inhibitory or facilitatory roles in regulating gene expression(19,20). Several enzymes can reposition nucleosomes along the DNA(21)and thus in?uence chromatin structure.

The salt concentration(12)and the presence of linker histones(8,22)can change the degree of chromatin compac-tion.The linker histones H1and H5compact the chromatin chain from the beads-on-a-string structure into the30nm ?ber.It binds to the in-and outgoing DNA strands and thus stabilizes the nucleosome.H1depletion changes the chromatin structure profoundly(23).

Linker histones are not necessary for the formation of the 30nm?ber(24),although they increase its compaction. Chromatin compaction also depends on the so-called nucle-osome repeat length(NRL)(25).The NRL is de?ned as the length of the DNA stretch that is wrapped around

Submitted February1,2010,and accepted for publication August5,2010.

*Correspondence:p.m.diesinger@gmx.de

Philipp Diesinger’s present address is Laboratory for Computational Cell

Biology&Biophysics,Department of Biological Engineering,Massachu-

setts Institute of Technology,77Massachusetts Avenue,Cambridge,MA

02139.

Editor:Laura Finzi.

ó2010by the Biophysical Society

0006-3495/10/11/2995/7$2.00doi:10.1016/j.bpj.2010.08.039 Biophysical Journal Volume99November20102995–30012995

a nucleosome plus the length of the linker DNA the nucle-osome with its neighbor.Widom(25)performed many measurements on NRLs and discovered that the NRL distri-butions show a preferential quantization to a set of values related by integral multiples of the helical twist of DNA. Model calculations of possible chromatin structures as a function of NRL by a combination of static model building on the atomic scale and Monte Carlo simulations(26)were in agreement with those earlier studies.

In a comparison between two DNAs with168and197bp NRL,it was found that only the197bp NRL could form a30nm higher-order chromatin structure(24).This structure also showed a cooperative linker histone-dependent compac-tion.Chromatin strands with a repeat length of167bp displayed a limited linker histone-dependent compaction, which led to a topologically different thinner?ber.

The?exibility of the chromatin?ber has a profound in?u-ence on its biological function.To start transcription,the RNA polymerase II complex associated with general transcription factors has to assemble at the promoter.In particular,in eukaryotic cells the basal transcription rate is low unless regulatory proteins bind to distant sequences (enhancers),hundreds to thousands of basepairs away from the transcription start,and then contact the transcrip-tion complex.These long-range interactions between regu-latory proteins and the transcription complex are mediated by bending of the intervening chromatin,which forms a loop.

Beyond simple looping,the overall folding topology of the genome is thought to play an important part in the coor-dination of transcription and other processes that act on DNA.Chromosome conformation capture(3C)technology allows one to analyze chromatin folding in the native cellular state by cross-linking parts of the genome that are close in space(27).The technique allows the identi?cation of physical interactions between distant DNA segments and of chromatin loops that are formed as a consequence of these interactions—for example,between transcriptional regulatory elements and distant target genes(28–32). Cross-linking techniques have become a standard research tool for studying the relationship between nuclear organization and transcription in the native cellular state. For instance,3C has been used to show that regulatory DNA elements communicate with distant target genes through direct physical interactions that loop out the inter-vening chromatin?ber.Other technologies(33,34)based on the3C principle have been designed to increase the throughput:4C technology allows for an unbiased genome-wide screen for interactions with a locus of choice, and5C technology permits parallel analysis of interactions between many selected DNA fragments.

Whereas3C technology measures cross-linking probabil-ities,?uorescence in situ hybridization(FISH)provides direct information about the spatial distribution of chromo-somes.Speci?c parts of the genome,ranging in size from a few kilobasepairs to100kbp,are?uorescently labeled. These labels can then be localized with a light microscope. Thus,a relationship between the mean-square distance and genomic separation of two or more markers can be estab-lished(2,35,36).

In general,the interaction probability of two loop-form-ing sites is a function of their distance and the?exibility of the chromatin?ber,expressed as the persistence length (37).For equal genomic distance,chromatin?bers with shorter persistence length will exhibit higher interaction probabilities.For a wormlike polymer chain with isotropic bending elasticity,the interaction probability is directly related to the persistence length and the genomic distance (38).However,for a complex structure such as the chro-matin?ber,this simple description may not be suf?cient. Therefore,in this work we used numerical simulations to calculate the looping probabilities for various chromatin chain models.

Even for simple DNA,it was recently suggested that tight bends are more probable than predicted from the wormlike chain(WLC)model(39).In that case,the interaction probability for DNA fragments shorter than the persistence length can be signi?cantly elevated.Our calculations show that both for chromatin chains randomly depleted of histone H1and for homogeneous chains at high bending angles,the looping probability may be substantially higher than for a presumed homogeneously elastic chain.In fact,it turns out that the30nm chromatin?ber can form sharp bends very easily.This means that the persistence length measured for small bending?uctuations close to thermodynamic equi-librium will give too low an estimate for the looping proba-bility,and vice versa.Measurements of the interaction probability will lead to estimates of the persistence length that are signi?cantly too low.

Here,we simulate conformations of chromatin?bers with the two-angle model originally proposed by Woodcock et al.

(9)and later used in several chromatin models(40–43).

In a previous publication(44)we discussed how different depletion effects change the properties of chromatin?bers. We simulated chromatin?bers across a large range of H1 and nucleosome depletion probabilities,and found that ?bers that match the experimental probabilities are very close to optimization in compaction.We also found that the concept of a regular30nm structure is not valid any more if one includes reasonable depletion rates.In this work,we use?xed depletion rates that equal average values estimated from experimental distributions(25,44)and focus entirely on chromatin looping probabilities.We compare the simulation results of chromatin?bers with and without histone depletion with5C data(1)from a gene desert as well as data obtained by FISH(2).We compare experi-mental with theoretical loop formation probabilities and ?nd that only?bers that are partially depleted of linker histones or entire nucleosomes can explain random chro-matin contacts on the small length scales that play an

Biophysical Journal99(9)2995–3001

2996Diesinger et al.

important role in gene regulation.It is possible that missing linker histones and nucleosomes are not just simple,unavoidable,randomly occurring defects,but instead play an important regulatory role in gene expression.MATERIALS AND METHODS

The model of the chromatin chain is based on the two-angle model origi-nally proposed by Woodcock et al.(9).In their model,the conformation of the chain is determined by two parameters:1),the opening angle between the linker DNA arms;and 2),the twisting angle between adjacent nucleo-somes (which is directly related to the linker DNA length through the DNA helical pitch).This model is extended by a more precise description of the local nucleosome geometry in the linker DNA region and by the presence or absence of histone H1,as described in previous publications (43–45).This extended model,termed the E2A model,can take two different depletion effects into account (Fig.1):1),linker histone depletion (i.e.,missing linker histones that normally would ?x the in-and outgoing DNA strand in front of the nucleosome);and 2),nucleosome depletion.In the latter case,not only the linker histone but also the whole nucleosome core particle (i.e.,the histone octamer)is missing,leaving a stretch of naked DNA behind.This stretch of DNA can then be covered with proteins again.One mechanism that might lead to nucleosome depletion is nucleosome replacement by other DNA-binding proteins,such as transcription factors.

The linker histone H1is positioned at the nucleosome dyad.Cryoelectron microscopy shows that the two linkers cross symmetrically in front of the linker histone (46).Thus,our model assumes a ?xed length of each linker clamped by the presence of H1.All chromatin ?ber components are modeled as segments interacting through bending and torsion potentials,as described previously (41).In simulations of tight chromatin bends,the model contained a slightly attractive potential between nucleosomes (41),whereas a cylindrical hard-core potential was used for the larger chains in the depletion studies (43).Chain conformations are generated by means of a Metropolis Monte Carlo procedure (47,48),and the averages presented here are based on at least 3?106chromatin conformations after a prerelax-ation period.

In the following text,chromatin ?bers without any depletion effects will be called regular ?bers,and ?bers with depletion effects will be called disturbed or irregular (Fig.2).In the case of the E2A model,the linker

histone skip rate was ?xed to 6%(45)and the nucleosome skip rate was ?xed to 8%(44)in accordance with experimental results (49).

The ?bers without depletion effects have lengths of 1.6Mbp,800kbp,and 160kbp (i.e.,8000NRLs,4000NRLs,and 800NRLs,respectively),and the ?bers with depletion effects have contour lengths of 160kbp and 80kbp.In the case of ?bers with depletion effects,smaller ?ber

lengths

FIGURE 1The two different types of histone depletion.(a )Linker histone depletion gives the ?ber more ?exibility locally.Normally the linker histone ?xes the in-and outgoing DNA strand.If the histone is gone,the DNA arms can move freely with respect to excluded volume potentials.(b )In this case,not only the linker histone but also the whole nucleosome core particle is missing,and hence a long,blank stretch of naked DNA

remains.

FIGURE 2(a )A regular chromatin ?ber without any depletion effects.(b )Disturbed chromatin ?bers with linker histone depletion (orange nucle-osomes)and nucleosome depletion.One can see that the disturbed chro-matin ?ber is much more irregular.The regular ?ber has a persistence length of ~280nm,whereas the disturbed ?ber is much more ?exible,with a persistence length of only ~140nm.If reasonable histone skip rates are taken into account,the regular 30nm chromatin ?ber is replaced by a very irregular structure with a much higher loop frequency.

Biophysical Journal 99(9)2995–3001

Chromatin Looping by Depletion Effects 2997

are suf?cient to resolve the loop distributions,as demonstrated further below.Furthermore,they are harder to sample,and sometimes conditional probabilities are needed for the analyses presented here.Unfortunately,these analyses require huge sample sizes (e.g.,to evaluate the conditional probability distribution of the loop end position over the set of all ?bers with a loop that starts a given position along the ?ber).It will be shown that the total length of a ?ber does not change the loop statistics very much as long as it is far above the persistence length.The simulations for short loop formation were done on 100-nucleosome chains with a repeat of 168bp.

Fig.3shows a 1.6Mbp chromatin conformation with a large 167kbp long loop.Another loop conformation in a regular chromatin ?ber can be found in Fig.4.

Most of the probabilities presented in this work are given under the condition that the chromatin ?ber has at least one loop,and hence are denoted as conditional probabilities in the following.All unlooped ?bers are left out in these cases.

RESULTS

In a previous work,Bystricky et al.(2)reconciled high-reso-lution FISH data from intervals of 14–100kbp along single chromatids with measurements of whole chromosome arms

(122–623kbp in length),monitored in intact cells through the targeted binding of bacterial repressors fused to GFP derivatives.The results are interpreted with a ?exible polymer model and suggest that interphase chromatin exists in a compact,higher-order conformation with a persis-tence length of 170–220nm and a mass density of z 110–150bp/nm.These values are equivalent to 7–10nucleosomes per 11nm within a 30-nm-like ?ber structure.To analyze chromatin compaction ratios in interphase nuclei,investigators have generally applied FISH using differentially derivatized probes.Bystricky et al.(2)deter-mined end-to-end distances for a range of genomic intervals by using unique techniques for high-resolution FISH (50,51)and live GFP-fusion imaging based on repressor binding to chromosomally integrated,nonampli?ed lac or tet operator arrays (52).This process combined with immuno?uores-cence allowed them to examine chromatin folding over small distances in intact yeast cells.They also compared arm length measurements with distances separating different repressor array insertions.The WLC model then allowed them to deter-mine both the persistence length and the mass density of chromatin from these end-to-end distance values.

Our simulations show that the regular chromatin ?bers have a diameter of ~33nm and a persistence length of 280nm,whereas the disturbed ?bers have a persistence length of only 140nm and thus are much more ?exible (44).Nevertheless,one must take care in applying the concept of persistence length to ?bers with H1and nucleo-some depletion.Although the persistence length is still on the order of 100nm,?ber parts can come very close together due to the nucleosome depletion,although they are only a few NRLs apart along the ?ber axis,i.e.,they are still in a region where one would expect the ?ber to be too stiff to bend if the persistence length were used as a measure of stiffness.Moreover,chromatin ?bers in the cell nucleus that are larger than a few hundred kilobasepairs are no longer unconstrained and start to feel the presence of the biological

environment.

FIGURE 3Loop conformation in a chromatin ?ber modeled by the E2A model.Two ?ber parts must (by de?nition of the interaction radius r max )come closer together than 35nm to form a loop.Chromatin loops on small scales play a very impor-tant role in gene regulation because enhancer/silencer and promoter regions of the DNA have to be in close proximity to actually work.The length of these loops is typically on the order of a few kilobasepairs,although there are some exceptions;therefore,the loop shown in this ?gure is a large one with a length of 167kbp.

loop #

p r o b a b i l i t y [%]

Loop Number Distribution

FIGURE 4Example of a regular chromatin conformation with a small loop.The chain has a total length of 160kbp.The loop length is z 10kbp.Biophysical Journal 99(9)2995–3001

2998Diesinger et al.

We sampled the large chains without depletion effects to exclude the possibility that the differences of the loop distri-butions would disappear if we changed the ?ber length.Fig.5shows the scaling of the spatial versus the genomic nucleosome separation together with experimental results from two-color FISH measurements (2).The ?gure does not contain any ?ts,but shows absolutely determined values for the regular and disturbed chromatin ?bers.It is clear that the graph for the disturbed ?bers matches the experimental data much better than the graph of the regular ones,albeit not perfectly.The remaining difference results from the fact that in the experiment chromatin melts were examined,whereas in our simulations only one chromatin ?ber was generated at a time (i.e.,we examined a very dilute chro-matin solution).Flory (53)showed that polymers in melts behave as if their monomers have zero volume (Gaussian statistics).Hence,the actual distance graph for chromatin melts would de?nitely lie below the curves presented in Fig.5.Furthermore,the chromatin ?bers in the experiment experience the con?nement of the cell nucleus,whereas those in the computer simulation do not.These effects would further decrease the graph of the disturbed chromatin ?bers toward the experimental data.The graphs of Fig.5provide at least a suitable upper bound for the actual behavior of chromatin in the cell nucleus.

Fig.6shows a comparison of the loop number probability distribution for regular and disturbed chromatin ?bers.One can clearly see that regular ?bers have much fewer loops (0.31on average)than the disturbed ?bers (with an average of 25.5loops per ?ber).Furthermore,these (normalized)distributions are independent of ?ber length (see Fig.S9)because three-dimensional random walks are recurrent and

thus the probability to actually form a loop decreases very rapidly with increasing loop length.

As pointed out above,the mere loop number is not suf?-cient to describe the loop statistics.The distribution of the loop length is highly important as well.It is displayed in Fig.7for regular and disturbed chromatin ?bers together with 5C data for random chromatin contacts (1).The loop length distribution of the regular ?bers shows a completely different shape than the experimentally determined distribu-tion.They show no loops at all at the important small scale in the kilobasepair regime,and therefore their genes would probably be less expressed,since promoter/enhancer contacts are formed less easily.This kind of chromatin might resemble the transcriptionally inactive heterochromatin.In contrast to the regular chromatin ?bers,the disturbed ones show a qualitatively completely different loop length distribution that much more strongly resembles the experi-mentally found values.The disturbed chromatin ?bers

genomic nucleosome separation Δ [kbp]

a v e r a g e s p a t i a l n u c l e o s o m e d i s t a n c e [n m ]

Spatial Nucleosome Distance versus Genomic Separation

FIGURE 5Comparison of the scaling of spatial versus genomic nucleo-some separation.The data show results from two-color FISH experiments (2).One can see that the disturbed chromatin ?bers are much closer to the experimentally determined points.The remaining differences come from the fact that in the simulations only one chromatin ?ber was simulated at a time (dilute chromatin),whereas the experiments were done in a crowded environment that furthermore had the con?nement of the cell nucleus.

genomic distance [kbp]

(c o n d i t i o n a l ) i n t e r a c t i o n p r o b a b i l i t y [%]Frequency of Physical Interactions depending on Genomic Distance between Interacting Fragments

= l P

FIGURE 6Probability distribution of the loop number within regular and disturbed chromatin ?bers.The distributions are independent of the ?ber length because the self-avoiding walk is recurrent in three-dimensional space (cf.Supporting Material ).Disturbed chromatin ?bers show many more loops compared to regular chromatin ?bers.The regular ?bers have an average loop number of 0.31and the disturbed chromatin ?bers have an average loop number of 25.5.

FIGURE 7Comparison of the loop length distributions of regular and disturbed chromatin ?bers with experimental data from 5C experiments on a gene desert (1).The regular chromatin ?bers show a completely different loop distribution because they are too stiff to have loops on small length scales.The persistence length of these ?bers is 280nm,which corre-sponds to a length along the contour of 13.5kbp.One can clearly see that this is the region where the looping starts in the regular ?bers.The disturbed chromatin ?bers show a qualitatively similar-shaped graph compared to the 5C data.In contrast to the regular ?bers,they have loops on the small scales that are very important for gene regulation.

Biophysical Journal 99(9)2995–3001

Chromatin Looping by Depletion Effects 2999

indeed show the chromatin contacts on the kilobasepair scale that are so important for gene regulation in genetically active euchromatin.

The distribution for ?bers without depletion effects resem-bles the loop distribution of an ordinary (self-avoiding)random walk.Small loops are unlikely because the ?ber is too stiff to bend on the short length scales.The persistence length of 280nm corresponds to a ?ber contour length of z 13.5kbp.One can see that this is approximately the region where the loop probability starts to https://www.wendangku.net/doc/4a18519583.html,rge loops are unlikely,too,since the random walk is transient in three dimensions.

The loop distribution of the chromatin ?bers with deple-tion effects looks completely different,and small loops are very likely in this case.The depletion effects give the ?ber much more ?exibility and thus facilitate loop formation on the kilobasepair scale.In particular,nucleosome depletion allows the ?bers to bend even on small length scales.

The ?ber length does not have a recognizable effect on the loop distribution on this small length scale (cf.Figs.S9and S10).The difference between the 160kbp ?ber without depletion effects and the corresponding 10-fold larger ?ber stems from the normalization,since the ?ber length limits the maximal loop length.Furthermore,one has to keep in mind that there is a cutoff for the minimal loop length at ~5.9kbp.

Finally,simulations of short (100-nucleosome)chromatin ?bers with and without linker histones show that the proba-bility for formation of short loops deviates signi?cantly from that for a WLC.For a semi?exible chain with homoge-neous elasticity,the loop formation probability has a maximum for a chain length of ~3.3L p (Fig.8).For the simulated chromatin ?bers,it is clear that the broad maximum is at a much smaller contour length (about two

persistence lengths;the strong increase in j at short distances is an artifact,since an end-to-end distance of <20nm is taken as an interaction).Thus,chromatin chains have an intrinsic tendency to form tight bends with a higher proba-bility than predicted from the theory for a homogeneous elastic chain.This can be seen as analogous to the behavior of B-DNA,for which it was recently shown that short frag-ments bend more easily into circles than predicted from WLC theory (54),and that the bending potential deviates from a Hookean spring potential for very tight bends (39).CONCLUSIONS

We have shown that histone depletions can have functional roles in gene regulation and are not only ?ber defects.Histone depletion may even be crucial for gene regulation mechanisms,such as enhancer and silencer regions.Methyl-ation,acetylation,phosphorylation,and other histone modi-?cations facilitate these histone depletion effects,as well as DNA methylation,and thus contribute indirectly to gene regulation.On the other hand,methylation decreases linker histone and nucleosome depletion,and therefore leads to regular chromatin ?bers,which (like the heterochromatin)are probably more inactive.

The simulation data of the chromatin ?bers with depletion effects match the experimental FISH data (2)and the 5C data (1)much better than the simulation data of the regular ?bers.Furthermore,only the loop length distribution of the disturbed chromatin ?bers can explain the shape of the exper-imental loop length distribution.Together with the fact that even ordered chromatin ?bers can bend easily into very tight loops,this is a strong indication that chromatin ?bers in vivo may be far from perfectly ordered 30nm ?bers.SUPPORTING MATERIAL

Two ?gures are available at https://www.wendangku.net/doc/4a18519583.html,/biophysj/supplemental/S0006-3495(10)01034-9.

We thank Job Dekker for many fruitful discussions.

REFERENCES

1.Dostie,J.,T.A.Richmond,.,J.Dekker.2006.Chromosome confor-mation capture carbon copy (5C):a massively parallel solution for mapping interactions between genomic elements.Genome Res.16:1299–1309.

2.Bystricky,K.,P.Heun,.,S.M.Gasser.2004.Long-range compaction and ?exibility of interphase chromatin in budding yeast analyzed by high-resolution imaging https://www.wendangku.net/doc/4a18519583.html,A.101:16495–16500.

3.Chakravarthy,S.,Y .J.Park,.,K.Luger.2005.Structure and dynamic properties of nucleosome core particles.FEBS Lett.579:895–898.

4.van Holde,K.1989.Chromatin.Springer-Verlag,New York.

5.van Holde,K.,and J.Zlatanova.1995.Chromatin higher order struc-ture:chasing a mirage?J.Biol.Chem.270:8373–837

6.6.van Holde,K.,and J.Zlatanova.1996.What determines the folding of the chromatin ?ber?https://www.wendangku.net/doc/4a18519583.html,A.

93:10548–10555.

FIGURE 8Loop closure probability (j -factor)as a function of the contour length for a 30nm chromatin ?ber with (blue x)and without (red t)linker histones.The red and blue vertical lines correspond to the persistence length of the ?bers as calculated from the mean-squared end-to-end distance.

Biophysical Journal 99(9)2995–3001

3000Diesinger et al.

7.Schalch,T.,S.Duda,.,T.J.Richmond.2005.X-ray structure of a tet-

ranucleosome and its implications for the chromatin?bre.Nature.

436:138–141.

8.Bednar,J.,R.Horowitz,.,C.Woodcock.1998.Nucleosomes,linker

DNA,and linker histone form a unique structural motif that directs the higher-order folding and compaction of chromatin.Proc.Natl.Acad.

https://www.wendangku.net/doc/4a18519583.html,A.95:14173–14178.

9.Woodcock,C.L.,S.A.Grigoryev,.,N.Whitaker.1993.A chromatin

folding model that incorporates linker variability generates?bers resembling the native https://www.wendangku.net/doc/4a18519583.html,A.90: 9021–9025.

10.Schiessel,H.,W.M.Gelbart,and R.Bruinsma.2001.DNA folding:

structural and mechanical properties of the two-angle model for chro-matin.Biophys.J.80:1940–1956.

11.Dorigo,B.,T.Schalch,.,T.J.Richmond.2004.Nucleosome arrays

reveal the two-start organization of the chromatin?ber.Science.306: 1571–1573.

12.Thoma,F.,T.Koller,and A.Klug.1979.Involvement of histone H1in

the organization of the nucleosome and of the salt-dependent super-structures of chromatin.J.Cell Biol.83:403–427.

13.Finch,J.T.,and A.Klug.1976.Solenoidal model for superstructure in

https://www.wendangku.net/doc/4a18519583.html,A.73:1897–1901.

14.Widom,J.,and A.Klug.1985.Structure of the300A chromatin

?lament:X-ray diffraction from oriented samples.Cell.43:207–213.

15.Depken,M.,and H.Schiessel.2009.Nucleosome shape dictates chro-

matin?ber structure.Biophys.J.96:777–784.

16.Schiessel,H.2003.Topical review:the physics of chromatin.J.Phys.

Condens.Matter.15:R699–R774.

17.Richmond,T.J.,and C.A.Davey.2003.The structure of DNA in the

nucleosome core.Nature.423:145–150.

18.Jenuwein,T.,and C.D.Allis.2001.Translating the histone code.

Science.293:1074–1080.

19.Kornberg,R.D.,and Y.Lorch.1999.Twenty-?ve years of the nucleosome,

fundamental particle of the eukaryote chromosome.Cell.98:285–294.

20.Wyrick,J.J.,F.C.Holstege,.,R.A.Young.1999.Chromosomal

landscape of nucleosome-dependent gene expression and silencing in yeast.Nature.402:418–421.

21.Lia,G.,E.Praly,.,T.Owen-Hughes.2006.Direct observation of

DNA distortion by the RSC complex.Mol.Cell.21:417–425.

22.Widom,J.1986.Physicochemical studies of the folding of the100A

nucleosome?lament into the300A?lament.Cation dependence.

J.Mol.Biol.190:411–424.

23.Fan,Y.,T.Nikitina,.,A.I.Skoultchi.2005.Histone H1depletion in

mammals alters global chromatin structure but causes speci?c changes in gene regulation.Cell.123:1199–1212.

24.Routh,A.,S.Sandin,and D.Rhodes.2008.Nucleosome repeat length

and linker histone stoichiometry determine chromatin?ber structure.

https://www.wendangku.net/doc/4a18519583.html,A.105:8872–8877.

25.Widom,J.1992.A relationship between the helical twist of DNA and

the ordered positioning of nucleosomes in all eukaryotic cells.Proc.

https://www.wendangku.net/doc/4a18519583.html,A.89:1095–1099.

26.Aumann,F.,J.Shnel,.,S.Diekmann.2010.Rigid assembly and

Monte Carlo models of stable and unstable chromatin structures:the effect of nucleosomal spacing.Theor.Chem.Acc.125:217–231. 27.Dekker,J.2003.A closer look at long-range chromosomal interactions.

Trends Biochem.Sci.28:277–280.

28.Liu,Z.,and W.T.Garrard.2005.Long-range interactions between three

transcriptional enhancers,active V k gene promoters,and a30boundary sequence spanning46kilobases.Mol.Cell.Biol.25:3220–3231.

29.Murrell,A.,S.Heeson,and W.Reik.2004.Interaction between differ-

entially methylated regions partitions the imprinted genes Igf2and H19 into parent-speci?c chromatin loops.Nat.Genet.36:889–893.

30.Palstra,R.J.,B.Tolhuis,.,W.de Laat.2003.The b-globin nuclear

compartment in development and erythroid differentiation.Nat.Genet.

35:190–194.31.Spilianakis,C.G.,and R.A.Flavell.2004.Long-range intrachromoso-

mal interactions in the T helper type2cytokine locus.Nat.Immunol.

5:1017–1027.

32.Tolhuis,B.,R.J.Palstra,.,W.de Laat.2002.Looping and interaction

between hypersensitive sites in the active b-globin locus.Mol.Cell.

10:1453–1465.

33.Dekker,J.2006.The three‘C’s of chromosome conformation capture:

controls,controls,controls.Nat.Methods.3:17–21.

34.Simonis,M.,J.Kooren,and W.de Laat.2007.An evaluation of3C-

based methods to capture DNA interactions.Nat.Methods.4:895–901.

35.Mateos-Langerak,J.,M.Bohn,.,S.Goetze.2009.Spatially con?ned

folding of chromatin in the interphase nucleus.Proc.Natl.Acad.Sci.

USA.106:3812–3817.

36.Yokota,H.,G.van den Engh,.,B.J.Trask.1995.Evidence for the

organization of chromatin in megabase pair-sized loops arranged along

a random walk path in the human G0/G1interphase nucleus.J.Cell

Biol.130:1239–1249.

37.Grosberg,A.,and A.Khokhlov.1994.Statistical Physics of Macromol-

ecules.AIP Press,New York.

38.Rippe,K.,P.H.von Hippel,and https://www.wendangku.net/doc/4a18519583.html,ngowski.1995.Action at

a distance:DNA-looping and initiation of transcription.Trends Bio-

chem.Sci.20:500–506.

39.Wiggins,P.A.,T.van der Heijden,.,P.C.Nelson.2006.High?ex-

ibility of DNA on short length scales probed by atomic force micros-copy.Nat.Nanotechnol.1:137–141.

40.Wedemann,G.,and https://www.wendangku.net/doc/4a18519583.html,puter simulation of the

30-nanometer chromatin?ber.Biophys.J.82:2847–2859.

41.Aumann,F.,https://www.wendangku.net/doc/4a18519583.html,nkas,.,https://www.wendangku.net/doc/4a18519583.html,ngowski.2006.Monte Carlo simula-

tion of chromatin stretching.Phys.Rev.E Stat.Nonlin.Soft Matter Phys.73:041927.

42.Kepper,N.,D.Foethke,.,K.Rippe.2008.Nucleosome geometry and

internucleosomal interactions control the chromatin?ber conforma-tion.Biophys.J.95:3692–3705.

43.Diesinger,P.M.,and D.W.Heermann.2006.Two-angle model and

phase diagram for chromatin.Phys.Rev.E Stat.Nonlin.Soft Matter Phys.74:031904.

44.Diesinger,P.M.,and D.W.Heermann.2009.Depletion effects

massively change chromatin properties and in?uence genome folding.

Biophys.J.97:2146–2153.

45.Diesinger,P.M.,and D.W.Heermann.2008.The in?uence of the

cylindrical shape of the nucleosomes and H1defects on properties of chromatin.Biophys.J.94:4165–4172.

46.Bednar,J.,R.A.Horowitz,.,C.L.Woodcock.1995.Chromatin

conformation and salt-induced compaction:three-dimensional struc-tural information from cryoelectron microscopy.J.Cell Biol.

131:1365–1376.

47.Metropolis,N.,A.Rosenbluth,.,E.Teller.1953.Equations of state

calculations by fast computing machines.J.Chem.Phys.21:1087–1092.

48.Binder,K.,and D.Heermann.2002.Monte Carlo Simulations in Statis-

tical Physics.Springer,New York.

49.Segal,E.2008.Average nucleosome occupancy for the whole yeast

genome.

50.Gotta,M.,https://www.wendangku.net/doc/4a18519583.html,roche,.,S.M.Gasser.1996.The clustering of telo-

meres and colocalization with Rap1,Sir3,and Sir4proteins in wild-type Saccharomyces cerevisiae.J.Cell Biol.134:1349–1363.

51.Heun,P.,https://www.wendangku.net/doc/4a18519583.html,roche,.,S.M.Gasser.2001.The positioning and

dynamics of origins of replication in the budding yeast nucleus.

J.Cell Biol.152:385–400.

52.Straight,A.F.,A.S.Belmont,.,A.W.Murray.1996.GFP tagging of

budding yeast chromosomes reveals that protein-protein interactions can mediate sister chromatid cohesion.Curr.Biol.6:1599–1608. 53.Flory,P.1953.Principles of Polymer Chemistry.Cornell University

Press,Ithaca,NY.

54.Cloutier,T.E.,and J.Widom.2004.Spontaneous sharp bending of

double-stranded DNA.Mol.Cell.14:355–362.

Biophysical Journal99(9)2995–3001

Chromatin Looping by Depletion Effects3001