Phys. Biol. 13 (2016) 035006 doi:10.1088/1478-3975/13/3/035006

PAPER

Computational strategies to address chromatin structure problems

Ognjen Perišić1 andTamar Schlick2,31 Big BlueGenomics, 11000Belgrade, Serbia2 Department of Chemistry, NewYorkUniversity, NY10003,USA3 Courant Institute ofMathematical Sciences, NewYorkUniversity, NY 10012,USA

E-mail: schlick@nyu.edu

Keywords: chromatin structure,molecularmodeling,molecular dynamics, coarse grainedmodeling

AbstractWhile the genetic information is contained in double helical DNA, gene expression is a complexmultilevel process that involves various functional units, fromnucleosomes to fully formed chromatinfibers accompanied by a host of various chromatin binding enzymes. The chromatinfiber is a polymercomposed of histone protein complexes uponwhichDNAwraps, like yarn uponmany spools. Thenature of chromatin structure has been an open question since the beginning ofmodernmolecularbiology.Many experiments have shown that the chromatin fiber is a highly dynamic entity withpronounced structural diversity that includes properties of idealized zig-zag and solenoidmodels, aswell as othermotifs. This diversity can produce a high packing ratio and thus inhibit access to amajority of thewoundDNA.Despitemuch research, chromatin’s dynamic structure has not yet beenfully described. Long stretches of chromatinfibers exhibit puzzling dynamic behavior that requiresinterpretation in the light of gene expression patterns in various tissue and organisms. The propertiesof chromatinfiber can be investigatedwith experimental techniques, like in vitro biochemistry, in vivoimagining, and high-throughput chromosome capture technology. Those techniques provide usefulinsights into thefiber’s structure and dynamics, but they are limited in resolution and scope, especiallyregarding compactfibers and chromosomes in the cellularmilieu. Complementary but specializedmodeling techniques are needed to handle largefloppy polymers such as the chromatinfiber. In thisreview, we discuss current approaches in the chromatin structurefieldwith an emphasis onmodeling,such asmolecular dynamics and coarse-grained computational approaches. Combinations of thesecomputational techniques complement experiments and addressmany relevant biological problems,as wewill illustrate with special focus on epigeneticmodulation of chromatin structure.

Introduction

Celebrated as one of the highest achievements inscience, the first mapping of the human genome in thedawn of the 21st century [1, 2], raised fundamentalquestions that may take a whole century to answersatisfactorily. The human genome, and genomes of allother higher organisms, contain much less genes thanexpected, but the amount of genes expressed inmajority of tissues is higher than anticipated [3].Moreover, simpler organisms can have comparable oreven higher number of genes than human. Thesefindings suggest that the diversity of living speciesstems not only from the multitude of genes, but alsofrom many ways of their expression [3]. Althoughshort segments of RNA can have enzymatic roles, they

are not sufficient to account for the variety of cell typesand cell signaling processes. Chromatin, the fiber thatstores the genomic material in eukaryotes, holds oneof the keys to the connection between the limitednumber of genes and the complex nature of higherorganisms. Chromatin’s primary role, to compress2 m of total genomic DNA in humans into a micro-meter sized cell nucleus, is accompanied by a moreactive role, namely the control of gene expression.

The chromatin fiber is made of double helicalDNA wrapped around protein-octamer globules.Nucleosomes, chromatin’s building blocks, are builtof about 147 base pairs of DNA wrapped aroundhighly conserved, four histone proteins (H2A, H2B,H3 and H4) [4], with the addition of the dynamicallybound linker histone (LH) H1/H5. The interplay

RECEIVED

1December 2015

REVISED

11March 2016

ACCEPTED FOR PUBLICATION

8April 2016

PUBLISHED

24 June 2016

© 2016 IOPPublishing Ltd

between positively charged tails protruding from thehistone cores with DNA and neighboring nucleosomeparticles and various chromatin binding factors con-trols the level of chromatin compaction [5, 6], fromaccessible double stranded DNA to fully formed chro-mosomes. That level may determine the type of cell, itsstatus, and its future. Modern day genomics coupledwith the next generation sequencing [7–9] reveals thatthe perturbation of the gene expression patterns candisrupt cell-signaling processes and affect humanhealth [10, 11]. High throughput genome studiesaimed at deciphering the spatial connectivity of chro-mosomal genomic regions [12] are suggesting that thestructural diversity of chromosomes is related to geneexpression patterns [13] and that genes and corresp-onding regulatory elements can be, sequentially andspatially, far apart in the genome [13, 14]. Therefore,deciphering chromatin structure and dynamics is ofthe crucial importance for understanding gene expres-sion control in various organisms and tissues.

In this paper, we describe challenges associatedwith chromatin structure and the histone code, andthen outline modeling approaches to study chromatinstructure, dynamics, and the effect of epigenetic mod-ifications on chromatin structure. We end by advocat-ing code/resource sharing approaches to accelerateboth experimental and modeling research in this areaand to helpmake the necessary links between them.

Chromatin structure and the histone code

The internal organization of chromosomes and thecorresponding structure of the chromatin fiber are stillopen questions [15, 16]. The internal organization ofthe 30 nm fiber, often observed in vitro via variousoptical techniques, was for a long time a holy grail ofstructural biology [17]. Two theoretical models weredeveloped to address the 30 nm organization, one-start solenoid with bent DNA linkers [18, 19] and two-start zig-zag with straight linkers [20–22]. Zig-zagfibers are often observed under idealized experimentalconditions [23–27], withmild ionic environments thatdiscourage linker bending. Multiple experiments andsimulations showed that the chromatinfiber is a highlydynamic entity with a very pronounced structuraldiversity sharing properties of both theoretical models[15, 16, 28, 29]. For example, cryo-electron micro-scopy and synchrotron x-ray scattering experimentsobserved a fractal-like organization of chromosome inhuman mitotic HeLa cells, without prominent 30 nmfiber like structures [30]. The absence of 30 nm motifwas also demonstrated in recent cross-linking experi-ments of HeLa cells in combination with modelingthat revealed zigzag motifs associated with hierarchi-cally looped chromatin fiber in interphase and meta-phase chromatin [31]. Real-world fibers interact withvarious enzymatic particles that disrupt the simpletwo-start nucleosome ordering. They do not fold into

identically ordered structures in every cell because theentropic cost of such a folding process would beenormous [32]. Increased ion concentrations screenelectrostatic repulsion between positively chargedDNAfibers and allow their bending [28]. The naturallyoccurring variability of DNA linkers connectingsuccessive nucleosome cores introduces a diversity inthe fiber structure [28, 33, 34]. The H1/H5 LHdynamically binds to the nucleosome between twoDNA strands (entering and exiting), draws themtogether, and establishes the nucleosome stem.

Prominent sources of fiber diversity are post-translational modifications of histones and histonetails [35–39]. Histone tails are typical targets for mod-ification because they have prominent roles in inter-and intra-nucleosomal interactions and interactionswith DNA linkers [28, 35, 39–41]. Modifications ofhistone core and tails also influence the stability anddynamics of nucleosomes [36, 38, 42–46], althoughearly experiments did not observe a prominent role oftails in nucleosome stabilization [47, 48]. Therefore,histone modifications either induce partial unfoldingof the chromatin fiber (euchromatin) or stabilize atightly lockedfiber (heterochromatin).

Enzymes introducing histone modifications areusually very selective [49]. They act upon a specificresidue or a small group of selected residues. The threemajor covalent histone tail modifications are acetyla-tion, phosphorylation, and methylation, see figure 1.These chemical changes reduce the tails charges andmodify tails dynamics and thus influence their interac-tions with neighboring nucleosomes andDNA linkers.Other notable modifications with similar influencesare ubiquitylation, sumoylation, ADP ribosylation,histone tail clipping, histone proline isomerizationandβ-N-acetylglucosaminemodification [5].

The histone modifications have been a researchtopic for many years, but their importance came toprominence with the realization that the DNA con-tains much less genes than expected, and that theirexpression strongly depends on those heritable [49],albeit reversible modifications. Seemingly simple,these chemical changes produce perplexing effects,alone or in combination with other factors [5]. Acet-ylation neutralizes the positive charge of lysine and inthis manner weakens interactions between positivelycharged histones and negatively charged DNA andexposes DNA to transcription mechanisms [49–55]. Itis also involved in gene silencing [56], and DNAdamage response [57–59]. Acetylation affects numer-ous lysines on all tails (see table 1), and the high num-ber of possible sites where it may occur is an indicationof the existence of hyper-acetylated regions that aredevoid of tail charges and thus transcriptionally active[60, 61]. Phosphorylation adds a negative charge toserines, threonines and tyrosines, mostly in the his-tone N-terminal tails, but its mechanism of action isnot based on electrostatic screening only. It is a highlydynamic, site-specific modification active in mitosis,

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meiosis, transcription activation, cell death, DNArepair, DNA replication and recombination [62–67](see table 1). Phosphorylation is a strong signaling fac-tor dependent on the cell cycle, and its dysregulation ishighly correlated with cancer [66, 68]. Methylation is aphysically small modification that does not alter thecharge of a histone protein but can have a profoundeffect as a signaling factor for various cell processes. Itmodifies all histone molecules, including LHs. Methy-lation is associated with transcriptional activation,repression, silencing, euchromatin formation, andantagonistic or supportive cross-talks with othermod-ifications as well as with DNA methylations [69–73](see table 1). Ubiquitylation produces the largest phy-sical modification of all reactions mentioned herebecause it attaches ubiquitin, a 76-amino acid poly-peptide, to the lysine’s Ɛ-amino group. Ubiquitin is acell-signaling factor mostly involved in the degrada-tion of proteins [74]. Histone ubiquitylation induces achange of the overall nucleosome conformation and inturn disrupts intra and inter nucleosomal interactions,as well as interactions with DNA or with other chro-matin-binding factors. It has a role in gene silencing,meiosis, transcriptional activation and in euchromatinformation [75–77]. The same enzymes that attach ubi-quitin are involved in sumoylation [78], a reaction thatattaches small, an ubiquitin-likemodifiermolecules tohistone lysines. This chemical change antagonizesacetylations and ubiquitylations that address the samelysine side chains [79, 80], and it is primarily associatedwith the transcriptional repression, though its directphysical effects are not yet known [5, 77, 79, 81]. Bioti-nylation is a modification that covalently attaches the

vitamin biotin to a protein. Biotin is a small molecule,when compared to ubiquitin, but its binding to his-tone proteins influences gene expression, cell pro-liferation [82], transcription repression and histonedimerization [83], as well as the cell’s response toDNAdamage [84, 85]. Biotinylation may affect other his-tone modifications via crosstalk [82]. Gene expressioncan be also regulated though histone tail clipping, aprocedure that removes residues from a histone tail.The procedure is present in many systems, from yeasttomammals [86–88].

The effects of histone modifications are sequenceand context dependent. Besides directly affectingchromatin structure, they often attract factors thatinduce or remove modifications on neighboring resi-dues, or they impair access to gene promoting or sup-pressing factors [72, 89]. Biochemical andphysiological effects caused by histone modificationscannot be interpreted solely through their linear com-bination and could be perceived as a type of code thatcontrols gene expression [90]. This histone code is,therefore, complementary to the four-letter geneticcode that holds information for protein synthesis[90–92].

Chromatinmodeling

The roles of histone components and histone mod-ifications in chromatin structure formation can beaddressed using various biophysical, biochemical,genetic or epigenomic experimental techniques.These techniques offer insights into the structure, andmore importantly dynamics of chromatin fibers

Figure 1.Positions of targets formajor covalent histonemodifications (pdb ID 1KX5). The histone octamer is white andDNA is pinkand cyan. Acetylations are colored red, phosphorylation blue, ubiquitylations, sumoylations and biotinylations green, andmethylations yellow. The linker histone (PDB IDs 1HST and 1C7Y) is gray.

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Table 1. List ofmajor histone covalentmodification (A—acetylation, P—phosphorylation, U—ubiquitylation, S—sumoylation,M—methylation) listed by the histone and sequence position. The number of histonemodifying factors (9th column) represents the relativeimportance a residue haswithin a histone code.

Tail Residue A P U S B M#modify-ing factors Description

Lys26 x 1 Transcription silencing [72, 89]

Ser27 x 1 Transcription silencing, chromatin decon-densation [72, 89]

Lys48 x 1 OxidativeDNAdamage [38, 93, 94]

Arg54 x 1 Chromatin compaction, transcription [95]

H1 Lys65 x x 2 OxidativeDNAdamage [94, 96]

Lys66 x 1 OxidativeDNAdamage [94, 96]

Tyr73 x 1 Unknown [96]

Lys92 x x 2 OxidativeDNAdamage [93, 96]

Lys99 x 1 Unknown [93]

Ser1 x 1+ Mitosis, chromatin assembly, transcriptionrepression [97, 98]

Arg3 x 4 Transcription activation, transcriptionrepression [73]

Lys4 (S. cerevisiae) x 1 Transcription activation [99]

Lys5 (mammals, S.cerevisiae)

x 3 Transcription activation, unknown[50, 100, 101]

Lys7 (S. cerevisiae) x 1 Transcription activation [99, 102]

Lys9 x 1 Transcription repression [83]

Lys13 x 1 Transcription repression [83]

Lys36 x 1 Unknown [96, 103]

Arg42 x 1 Unknown [38, 96]

Lys74 x 1 Unknown [104]

Lys75 x 1 Unknown [104]

Arg77 x 1 Unknown [104]

H2A Arg88 x 1 Unknown [96]

Lys95 x 1 Unknown [104]

Gln105 x 1 Transcription [105]

Lys119 (mammals) x 1 Gene silencing [75]

Thr119 (D.melanogaster) x 1 Mitosis [106]

Thr120 (mammals) x 2 Mitosis, transcription repression [107, 108]

Ser122 (S. cerevisiae) x 1 DNA repair [64]

Lys125 x 1 Histone dimerization [83]

Lys126 (S. cerevisiae) x 1 Transcription repression [81]

Lys127 x 1 Histone dimerization [83]

Lys129 x 1 Histone dimerization [83]

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Table 1. (Continued.)

Tail Residue A P U S B M#modify-ing factors Description

Ser129 (S. cerevisiae) x 2 DNA repair [109, 110]

Ser139 (mammalianH2A.X)

x 3 DNA repair [111–113]

Thr142 (mammalianH2A.X)

x 1 Apoptosis, DNA repair [114]

Lys5 x 2 Transcription activation [50, 115]

Lys6 (S. cerevisiae) x 1 Transcription repression [81]

Lys7 (S. cerevisiae) x 1 Transcription repression [81]

Ser10 (S. cerevisiae) x 1 Apoptosis [116]

Lys11 (S. cerevisiae) x 1 Transcription activation [102]

Lys12 (mammals) x 2 Transcription activation [50, 115]

Ser14 (vertebrates) x 1+ Apoptosis, DNA repair [63, 117]

Lys15 (mammals) x 2 Transcription activation [50, 115]

Lys16 (mammals) x 2 Transcription activation [102]

H2B Lys20 x x 2 Transcription activation [50]

Lys23 x Unknown [96]

Ser33 (D.melanogaster) x 1 Transcription activation

Ser36 x 1 Transcription activation [118]

Lys43 x 1 Unknown [103]

Lys57 x 1 Unknown [96]

Arg79 x 1 Unknown [96]

Lys85 x 1 Unknown [96]

Arg99 x 1 Unknown [96]

Lys120 (mammals) x 1 Meiosis, development [76]

Lys123 (S. cerevisiae) x 1 Transcription activation, elongation,euchromatin [77]

Arg2 x 2 Transcription repression [73]

Thr3 x 2 Mitosis [119]

Lys4 (S. cerevisiae) x x x 8 Transcription activation (tri-me), geneexpression, cell proliferation, permissiveeuchromatin (di-me) [82, 99, 120–124]

Thr6 x 1 Unknown [125]

Arg8 x 3 Transcription activation, transcriptionrepression [126, 127]

Lys9 x x x 10 Transcription activation, transcriptionrepression (tri-me), genomic imprinting,histone deposition, gene expression, cellproliferation [51, 70, 71, 82, 128–131]

Ser10 x 5 Transcription activation,mitosis,meiosis,immediate-early gene activation, DNAmethylation [62, 132–135]

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Table 1. (Continued.)

Tail Residue A P U S B M#modify-ing factors Description

Thr11 (mammals) x 2 Mitosis [136]

Lys14(12) x 12 Transcription activation (elongation), DNArepair, transcription control, histonedeposition, RNApolymerase II transcrip-tion, cell growth [50, 51, 56–58, 99, 100, 120, 128, 129, 137–139]

Arg17 x 1 Transcription activation [140]

Lys18 x x 3 Transcription activation, histone deposi-tion, gene expression, cell proliferation[50, 51, 82, 140]

H3 Lys23 x 3 Transcription activation, histone deposi-tion,DNA repair [50–52, 128, 140]

Arg26 x 1 Transcription activation [73]

Lys27 x x 3 Transcription silencing, X inactivation[130, 141]

Ser28 (mammals) x 3 Mitosis, immediate-early gene activation[133, 142, 143]

Lys36 x x 1 Transcription activation (elongation)[144, 145]

Tyr41 x 1 Transcription activation [67]

Arg42 x 1 Transcription activation [146]

Thr45 x 1 Apoptosis [147]

Lys56 x x 1 Transcription activation, DNA repair, oxi-dativeDNAdamage [53, 59, 96, 148, 149]

Lys57 x 1 Unknown [150]

Arg63 x 1 Unknown [96]

Lys64 x x 2 Transcription [96, 104, 151]

Lys79 x 1 Euchromatin, transcription activation(elongation), checkpoint response[152–154]

Thr80 x 1 Mitosis [150]

Thr118 x 1 Transcription, DNA repair [103, 155, 156]

Lys122 x x 2 Transcription, DNA repair [94, 96, 157]

Arg128 x 1 Unknown [96]

Ser1 x 2+ Mitosis, chromatin assembly, DNArepair [65, 97]

Arg3 x 5 Transcription activation, transcriptionrepression [73, 126, 158]

Lys5 x 7 Transcription activation, histone deposi-tion,DNA repair[50, 57, 58, 99, 100, 115, 120, 159]

Lys8 x x 9 Transcription activation (elongation), DNArepair[50, 57, 58, 84, 85, 99, 100, 115, 137, 160]

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[22–27, 168, 169], but they cannot fully describe thechromatin structural patterns. The difficulties stemfrom the tightly packed and still not fully accessiblechromatin fiber interior and from the small size ofhistone modifications. Furthermore, laboratory pre-parations often put analyzed specimens in conditionsnot present in vivo. For example, in vitro fibers haveequally spaced nucleosomes and usually lack histonemodifications [168, 169]. In principle, systematicmodeling can help address the influence of histonemodifications on chromatin structure. This is achallenging task because the effects of histone mod-ifications cover various spatial and temporal scales,which means that different levels of chromatin fiberorganization have to be described using differenttheoretical and computational methods [6]. The first,basic level modeling has to cover is the influence ofhistone modifications on histone tails themselves. Thesecond level is the modeling of the structure andbehavior of nucleosome cores with and withoutmodifications. Next, the behavior and structure ofoligonucleosomes, with and without histone modifi-cations, has to be accurately determined. The finallevel is the modeling of longer stretches of chromatinfiber and the modeling of whole chromosomes. Allthose four levels of modeling have to apply differenttools and strategies in a selective manner, but they

have to be consistent in the interpretation of fiberbehavior.

Nucleosome and oligonucleosomemodeling

Molecular dynamics uses the atom level interpretationof molecules to model their behavior in naturalenvironments (for a detailed review see [170]). Itsnumerical complexity makes MD simulations ofbiomolecules applicable to systems with a limitednumber of atoms, usually less than ten million [171],including solvent and salt atoms [170]. The maximumtime span MD can cover is in the range of micro-seconds [171–173], or milliseconds on special archi-tectures (Anton [174]). The full atom interpretation ofa dinucleosome in explicit solvent requires 800 000atoms [39], which means that besides simulationsof individual tails only a limited number of nucleo-some related simulations have been conducted sofar (see [175] for details). Although limited inscope, those simulations provide important insightsinto the behavior of the nucleosome and itscomponents.

Many methods have been developed in attempt toimprove the efficiency of molecular dynamics (MDs)

Table 1. (Continued.)

Tail Residue A P U S B M#modify-ing factors Description

Lys12 x x 7 Transcription activation (elongation), DNArepair, histone deposition, telomericsilencing, euchromatin[50, 57, 58, 84, 85, 99, 100, 120, 159, 161]

H4 Lys16 x 7 Transcription activation, transcriptionsilencing, DNA repair [39, 56–58, 99, 100, 102, 115, 160, 162]

Lys20 x 5 Transcription activation, transcriptionsilencing (mono-me), heterochromatin(tri-me), checkpoint response [163–165]

Arg35 x Unknown [96]

Ser47 x Nucleosome assembly [166]

Arg55 x Unknown [96]

Lys59 x 1+ Transcription silencing, oxidativeDNAdamage [96, 167]

Arg67 x 1 Unknown [96]

Lys77 x x 2 Unknown [96]

Lys79 x x 2 OxidativeDNAdamage [94, 96]

Tyr88 x 1 Unknown [96]

Lys91 (S. cerevisiae) x . 2 Chromatin assembly [96, 168]

Arg92 x 1 Unknown [96, 104]

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simulations [176–184]. The most commonly methodused to reduce the numerical cost of MD is implicitsolvent. This approach reduces the number of simu-lated atoms by representing solvent as a continuousmedium, following the assumption that polar orcharged molecules stay in water [185, 186]. Thismethod is used to explore the protein folding anddynamic behavior of biological polymers, DNA, RNAand proteins. Its applicability can be limited in a tightlypacked environment of the chromatin fiber interior,in which individual water molecules may affect thebehavior of small peptides such as histone tails.

Many other methods have been developed, buttheir application to complex systems like the chroma-tinfiber remains to be shown as advantageous.

Coarse-graining interprets biological moleculesless accurately thanMD, but allows simulations of lar-ger systems and makes possible more efficient sam-pling of the configurational space. Early coarse-grained models, although simple, were able to inter-pret basic structural patterns of the chromatin fiberand approach experimental findings [187–191]. Thosemodels usually represented DNA as a worm-like-chain and nucleosomes as simple, rigid particles thatinteract via simple potentials. Advanced models usemore detailed representations of nucleosomes andapply explicit tails.

Woodcock et al applied a model of the oligonu-cleosome fiber, based on a simple representation ofrotatable nucleosome core particle (NCP) and vari-able-length DNA linkers with linker entry-exit angles,to interpret EM chromatin images [187]. A similarearly coarse-grained model by Katritch, Bustamanteand Olson was able to reproduce force-extensioncurves of real chromatin pulling experiments [192].Later on, Wedemann and Langowski modeled NCPsas oblate ellipsoids in an elastic fiber [189]. TheirMonte Carlo simulations of 100-NCP chains withelastic and electrostatic interactions reproducedexperimental properties of 30 nm fibers with mediumDNA linker lengths (they achieved a mass density of6.1 NCP per 11 nm with 32 nm wide fiber). Later on,they added various chromatin structural elements totheir model, such as the nucleosome stem [190] orirregularly spaced nucleosomes [193]. Many othergroups also developed coarse-grained models toaddress the stability of nucleosome, its response tostretching, and to analyze interactions between DNAand cylindrical particles (nucleosomes) under physio-logical conditions [194–198]. See [6] for a recent over-view of coarse-grained and multiscale modeling ofchromatin.

Our group was among the first to address the roleof histone tails in chromatin compaction using adetailed coarse-grainedmodel of the nucleosome. Themodel uses different coarse-graining techniques tomodel basic chromatin building blocks. Nucleosomes,histone tails, DNA linkers and LHs are modeled asseparate entities using appropriate theoretical models

[15, 28, 33–35, 37, 199–205]. The nucleosome core(eight histones plus wrapped DNA), without histonetails, is modeled as a rigid object with irregular surfaceinterpreted via approximately 300 charged beads[201]. The charge of each bead is assigned using thediscrete surface charge optimization algorithm devel-oped by Beard and Schlick [206] based on the Debye–Hückel approximation. The nucleosome core modelrobustly reproduces the electrostatic field of thenucleosome at physiological monovalent salt con-centrations. DNA linkers between consecutive nucleo-somes are interpreted as worm-like-chains. Theirnegative charges are modeled using Stigter’s proce-dure [202]. The core histone tails are separately mod-eled, using the Warshel–Levitt united-atom proteinmodel, with one bead per five amino-acids [35]. TheLH was initially modeled as a rigid three-bead struc-ture [15]. A recent refinement accounts for the inher-ently dynamic and disordered nature of the LH[199, 203]. The refined model includes flexible C-terminal domains and a globular head attached to thenucleosome [200]. Chromatin fiber configurations aresampled using an efficient set of Monte Carlomoves [35, 37].

Comparison with real-world experimental data hasbeen used to validate the model. For instance, themodel reproduces values of sedimentation coefficients,radios of gyration and packing ratios encountered inin vitro experiments [15, 28, 33, 34, 37, 200, 204, 205].Various applications have detailed the influence ofdynamic tails [35], variable linker lengths [207] anddivalent Mg2+ ions [15], and the LH binding affinity[205, 208] on chromatin’s structure [28]. Furthermore,fiber models share properties of both theoretical mod-els (zig-zag and solenoid) [28]. The model withimproved LH was able to explain the binding asym-metry and relate the LH condensation and nucleosomestem formation with the global condensation of chro-matin [200]. A linear relationship between the LH con-centration and the DNA linker length observedexperimentally could also be related to the formation ofa compact zig-zag fiber [209]. Forced induced unfold-ings showed that LH increases fiber’s resistance tounfolding, and that dynamic binding/unbinding of LHreduces it [204, 205]. Heterogeneous elements promotesuper beads-on-a-string configurations during stretch-ing. Those configurations are biologically advantageousbecause they selectively expose DNA as 10 nm linkersbetween super-beads. The fibers with non-uniform lin-ker lengths also exhibit smoother transitions because ofa more continuous range of similar stable configura-tions [210]. The absence of 30 nm fiberswas also shownin recent modeling work in collaboration with cross-linking experiments. Persistence of zig-zag motifswithin a new model of hierarchical looping for meta-phase chromosomes helps reconcile current models ofpolymer melts on one hand and other models thatdefine clear chromosomal boundaries [31].

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The histone tails have been a major topic of mod-eling studies due to their intrinsic disorder and theirroles in fiber compaction. The tails were addressedusing full-atom MD [45, 211] as well as coarse-grain-ing [35, 37, 39, 41]. The researchers explored the rolesof individual tails and their interactions with nucleo-somes and DNA before shifting their focus to tailmodifications. Our early studies, although lessdetailed than full-atomMD simulations, revealed thattails have multiple roles and are crucial for fiber com-paction. They delineated roles of each tail, especiallythe role of the H4 tail in mediating internucleosomalinteractions in highly compacted fibers with LHs, fol-lowed by roles of ‘H3,H2A, andH2B tails in decreasingorder of importance’ [35, 37], a result concordant withexperimental finding on the role of H4 tail in fibercondensation [54]. The nanosecond timescale MDsimulations of the nucleosome core by Roccatano andcoworkers [211] showed that at physiological salt con-centrations histone tails adopt conformations inwhich tail segments preferentially interact with majorand minor grooves of DNA and produce a slightlymore compact and solvent-protected nucleosome, aresult that contradicts experimental finding that tailsadopt a largely solvent-exposed structure at salt con-centrations above 50 mM NaCl [212]. H3 in theirsimulations exhibited the most noticeable conforma-tional changes, correlated with the increased numberof close tail-DNA contacts, while H2A domainsshowed affinity toward the DNA minor groove andhigher mobility, likely caused by the presence of theH2A’s long C-terminal tail. Roccatano and coworkersalso showed that the canonical nucleosome particle ismostly rigid under physiological conditions during thenanosecond simulation runs. Over longer time scales,however, nucleosomes exhibit conformational het-erogeneity and spontaneous unwrapping/rewrappingof nucleosomal DNA, as shown by the Langowski andWidom groups [213, 214]. MD simulations by Biswasand coworkers [45] showed that nucleosome simula-tions with truncated H2A and H3 tails produce lesscompact nucleosomes. The removal of these tails dis-rupts the electrostatic potential around the H2A his-tone, which in turn destabilizes the docking betweenthe H2A–H2B dimer and the H3–H4 tetramer. Themultiscale study of nucleosome unwrapping by theLangowski group [41], based on coarse-grained mod-eling and all-atom MD simulations, suggested thathistone tails could have an opposite effect on themononucleosome. While the attraction between theH3 tail and the ‘acidic patch’, formed on the nucleo-some surface by seven acidic residues from H2A andH2B, can trigger partial unwrapping of DNA, and pre-vent the DNA rewrapping, the attraction between theH4 tail and the patch promotes full wrapping of thenucleosome. That indicates that the H3 tails activelyparticipate in the initiation of the nucleosome remo-deling. A recent study from the same group [40], basedon replica-exchange and MDs simulations showed

that the H2B and H4 tails have a single dominantbinding configuration with DNA, while the H2B andH3 tails have multiple DNA binding configurations.However, large portions of tails were found not to bebound to DNA, which is an indirect conformation oftheir complex roles. The Rippe group studied thenucleosome’s resistance to forced unwrapping usingthe steeredMD (SMD) [215]. The analysis of SMD tra-jectories proposed a multistep process in which his-tone tails have prominent roles in the resistance tounwrapping. The authors also suggested that there aretwo main base-pair related barriers to unwrapping.However, results obtained with SMD simulations haveto be taken with precaution because SMD perturba-tions are five to six orders of magnitude faster thanexperimental techniques. The Langowski groupapplied Brownian dynamics to a coarse-grainedmodelwith a uniform, distance-dependent potential toexamine the mechanical unfolding of DNA from thetorus-like nucleosome core [216]. Their simulationssuggested a gradual unwrapping of DNA from nucleo-some and reproduced force-extension curves for thelow-force loading rate. Dobrovolskaia and Arya usedcoarse-grained models of nucleosome and DNA withexperimentally derived position-dependent freeenergy profile to address the influence of non-uniforminteractions between histone octamer and wrappedDNA on the nucleosome’s resistance to externalforce [217].

An effective modeling of histone modificationsrequires both MD and coarse-grained approaches todescribe the direct influence of modifications on thenucleosome and their influence on longer stretchesof the chromatin fiber. Yang and Arya [218] con-firmed the experimental finding [219] that the inter-actions between the H3 and H4 histone tails and thenucleosome’s acid patch play a crucial role in the reg-ulation of the nucleosome structure and may have asignificant role in the overall fiber architecture. Theysuggested that the acetylation of the lysine 16 fromthe H4 tail reduces the alpha-helix forming pro-pensity of H4 and destabilizes its binding to the acidicpatch. In a similar study, Potoyan and Papopian[220] found that the acetylation of H4K16 inducespartial ordering of the H4 histone and enhances itspropensity toward alpha-helical organization. Theordering of the intrinsically disorder protein reducesthe tail’s binding affinity toward neighboring nucleo-somes and weakens internuclosomal contacts, aresult in concordance with experimental findings[54]. The acetylation of the H4 tail, despite reducingthe positive tail charge produces a stronger attractionbetween the tail and DNA by inducing a partial col-lapse of the tail that enables it to make more hydro-phobic contacts with the surface of DNA [220]. Ourrecent multiscale study follows the path establishedby our earlier studies and addresses seven major his-tone acetylations [39]. In that study Collepardo-Gue-vara and coworkers show through combinedMD and

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coarse-grained Monte Carlo simulations of 24 oligo-nucleotides that acetylations change the overall his-tone-tail flexibility and decrease the disorder of tails.The more folded tails have reduced interaction sur-face areas that limit inter-nucleosomal interactionsin oligonucleosomes and trigger chromatin fiberopening. For instance, a H4 tail with acetylated resi-dues has a limited ability to extend and reach neigh-boring nucleosomes but has a higher affinity towardparental DNA. The results clearly underscore manyfactors that affect the chromatin compaction incooperative manner, and confirm that the hyper-acetylation is not a prerequisite for a significant struc-tural change. The acetylation of a single H4 lysine(H4K16) prohibits the formation of compact fiberand affects the formation of both higher order chro-matin structures and functional interactions betweenchromatin fiber and non-histone proteins [54, 220].

Chromatin-protein interactions are an attractiveresearch topic also. An MD study by Papamokos andcoworkers [221] suggested that the binding of a pro-tein important for the formation of the hypercon-densed mitotic chromosomes (HeterochromatinProtein 1—HP1, [6]) to the H3 tail is strongly affectedby the H3S10 phosphorylation. That study discoveredthat the phosphorylated H3S10 residue forms a saltbridge with H3R8 and thus impacts the HP1 bindingto the methylated H3K9me2/3. A similar MD basedstudy depicted the non-covalent binding of lysinespecific demethylase-1 enzyme (LSD1) with its co-repressor protein (CoREST) to chromatin [222]. Thisstudy is notable because LSD1 is one of the most pro-mising epigenetic targets for drug discovery againstcancer and neurodegenerative diseases [222]. Theauthors showed that the LSD1/CoREST complexbinds to H3 via an induced-fit mechanism, an infor-mation potentially useful in designing LSD1 inhibi-tors. The combined docking, Brownian dynamics,and normal mode analysis by the Wade group [199]showed that the LH H1/H5 can adopt various dock-ing positions near the nucleosome’s dyad axis, aresults in concordance with the latest experimentalstudies that suggests that asymmetric, on- and off-dyad, binding of the LH globular domain may leadtoward distinct higher order chromatin structures[223]. The variable LH positioning is importantbecause it allows the LH to influence the higher orderstructure of chromatin fiber in adaptable fashionthrough the modulation of entering/exiting angles ofDNA linkers [224].

Polymer and continuummodels

Polymer models are less refined than mesoscalemodels, but cover much larger spatial scales. Theyinterpret chromatin as a chain of spherical beads thatinteracts through simple harmonic and Lennard–Jones systems, where each bead represents more than

one nucleosome core. The polymer models have beendeveloped as a response to large-scale experimentalobservations by various chromatin conformationcapture techniques based on cross-linking of sequen-tially distant DNA segments. Those techniques pro-duce kilo-base (3C), mega-base (4C and 5C) andgenome-wide (Hi-C) interaction frequencies betweengenome loci in the nucleus as statistical averages overcell populations [225]. Interaction frequencies insingle cells can be analyzed via 3C [226] and fluores-cence in situ hybridization techniques [227]. Conti-nuum models, on the other hand, were developed tointerpret experimental data related to in vivo celldynamics. They primarily use analytical approaches,based on fluid dynamics, to explain the behavior oflarge segments of chromatin in the cell nucleus.

Both experimental observations and simulationsestablished the fractal model of the structural organi-zation of chromosomes (first introduced by Grosbergand coworkers [228, 229]). The model assumes globu-lar organization of chromosomes at almost all scales.In that case the contact probability of genomic loci as afunction of the genome distance (or sub-chain length)follows the same scaling law. That law is the outcomeof the self-similar polymer (chromatin) domains orga-nized into non-equilibrium hierarchical structureswith open-state and untangled topologies that rarelyinterfere with each other [230]. The Mirny lab intro-duced the fractal framework using a 20 nm bead poly-mer chain in which each bead covers six nucleosomes[231]. They were able to generate a fractal-like organi-zation of their chain with a power law contact prob-ability with the −1 exponent. However, theequilibration of that chain produced a uniform dis-tribution, incompatible with the interphase chromo-somes. Later on, they decreased the bead size to 10 nmand applied attractive and repulsive Lennard–Jonespotentials, softened at short distances to allow chaincrossing [232]. This refined model produced contactprobabilities consistent with experimental data andproposed local loop formations, without reproducibleradial positions, with the rest of their model chromo-some being in disordered state. Themodel suggested apower law dependency of contact probability on geno-mic distance with the exponential factor −0.5 forshort distances, that sharply decays with the increasein distance [232]. Barbieri and coworkers showed thatfractal organization also depends on the concentrationof protein cofactors able to bridge different genomicregions [233]. Simulations based on a polymer modelcomposed of two set of beads by the Langowski lab[234] showed that yeast chromosomes have pre-ferential positions in cell nucleus with dynamical clus-tering of functional elements of genomes. Jost andcoworkers addressed epigenetic modificationsthrough block organized chromatin model [235]. Intheir interpretation, the chromatin chain is organizedinto various blocks of identical monomers that pre-ferentially interact with other monomers of the same

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chromatin type over interactions with monomers ofother types. They applied Langevin dynamics andGaussian like potentials to sample fiber configura-tions. Their results are consistent with Hi-C dataobtained from 10 Mbp drosophila regions. The topo-logical domains they generated are related epigeneti-cally and form a multistable fiber with coiled andcollapsed microphase regions that separate differentepigenetic domains. Bruinsma and coworkers [236]produced a two-fluid analytical model (nucleoplasmas a solvent and chromatin as a solute) to interpretexperimental observation of coherent movementsbeyond single chromosomes [237]. They showed thatthe nucleus in ATP-depleted cells is characterized withpassive longitudinal thermal fluctuations, while ATP-active cells have intense transverse long wavelengthvelocity fluctuations driven by force dipoles depen-dent on ATP. Isaacson and coworkers examined thetime required to find specific DNA binding site as afunction of the chromatin density (expressed as thevolume exclusivity, a potential term that excludes adiffusing protein from a given volume filled with chro-matin) [238, 239]. Their results based on a continuummodel indicate that the time sharply decreases as theexclusivity increases and reaches a minimum valueand then slowly increases with the increase in volumeexclusivity.

Discussion

The chromatin structure problem has remained achallenge despite many recent advances in bothexperimentation and modeling. Its appeal comes notonly from the puzzling nature of chromatin architec-ture and still unknown relationship between local fiberproperties and behavior of the chromatin fiber at large,but also from the chromatin’s key role in geneexpression. And the deciphering that role has verypractical implications because the disruption of DNApackaging has serious implications on health. Indeed,chromatin structure can be easily disrupted by histonemodifications. That disruption can affect overallchromosome integrity and alter gene expression,including the aberrant regulation of oncogenes and/or tumor suppressors. However, new treatment ave-nues arise because the majority of histone modifica-tions is reversible.

The detailed modeling of histone modifications isrequired for a proper interpretation of chromatin fiberstructure and dynamics because experimentation is stilllimited in scope and resolution. The current modelingefforts addressed only general properties of chromatinfiber and described a very small number of histonemodifications. To understand the chromatin fiberstructure and its behavior, all modifications and theirinterplay have to be addressed in a systematic fashion.

Figure 2.Multiscale chromatinmodeling covers all levels ofmodeling, from atomicmodels of nucleosomes and histonemodifications, via oligomers and polymermodels to continuousmodels that interpret global chromatinmotion in cell nucleus.

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That enormous task will require MD simulations of alltail modifications, within mononucleosome and with-out it. The puzzling role and behavior of LH has to befurther examined, using docking, MD and coarse-graind simulations. Furthermore,MD simulations haveto be performed on structures larger than dinucleo-somes, with and without histone modifications. Simu-lations with four, or even more, nucleosomes arenecessary if we want to fully grasp the role of tails ininternucleosomal interactions. Those simulations haveto based on different crystal structures becausemajorityof current simulations has been based on the same highresolution structure, 1KX5 [175]. The role of DNAsequence in nucleosome positioning and fiber dynam-ics also has to be addressed in a systematic fashion. Thatwill require all atom representations of DNA linkersand, probably, combination of classical and quantumMD. The nucleosome’s mechanical resistance tounfolding has been addressed using only fast SMD[215], orders of magnitude faster that experimentalstretching.New simulations have to be performedusingmuch slower pulling on single nucleosomes with andwithout modifications, and, if possible, on equilibratedsystemswithmorenucleosome cores.

All-atom simulations are, despite recent advancesin hardware, numerically still very expensive. Thatmeans that longer stretches of fiber have to be simu-lated using coarse grained models. Current models arevery detailed, but have to be improved to include all his-tone modifications, as well as LH and nucleosome coredynamics, especially during mechanical stretching.Moreover, they have to accurately interpret the influ-ences of various binding factors and ion environments.

To facilitate research and collaboration, themodel-ing approaches should be able to record chromatinsimulation trajectories, corresponding starting config-urations, and force filed parameters in a standardized,human readable format(s) based on attribute-valuepairs. Similarly, software tools should be open sourcedand deposited in easily accessible online repositories.This can enable an approach to modeling where anappropriate algorithm can be called if necessary insemi-autonomous fashion. For instance, a coarse-grained model can invoke an atom-based model tointerpret an unusual configuration. This could, in prin-ciple, allow zooming-in and zooming-out of chromatinregions, see figure 2, because information betweenmodeling levels can be easily exchanged using a com-mon data format. In that case, the long chromatin fiberis already in energetically favorable configurationwhichmeans that only sampling on a limited scale with spatialconstraints, using local neighborhoods would have tobe performed. Such a gradual, object-oriented model-ing enables inheritance of general properties from onemodeling level to another without the burden ofincreased numerical complexity. However, it has to beapplied with caution because an apparently small mod-ification with a limited influence on a local fiber

neighborhood can have a crucial role in the behavior oflonger stretches of the chromatin fiber. Those longerstretches often exhibit puzzling dynamic behavior thatrequires a detailed interpretation in the light of geneexpression patterns in various tissue andorgans.

Chromatin structure and its relation to the histonecode remains a central question in structural/mole-cular biophysics and genetics. Addressing it fullyrequires a joint effort of experimentalist andmodelers.To facilitate these efforts, a more facile informationflow and data/program sharing between differentteams could be valuable.

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Phys. Biol. 13 (2016) 035006 OPerišić andT Schlick