Nucleosome Positions Alone Can Be Used to Predict Domains in Yeast

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Direct PNAS Board. a is article This interest.y of conflict no research, declare performed authors The research, paper.y designed the wrote C.A.B. and and data, analyzed D.M., O.W., contributions: Author owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom To ulooepstoigadgnm euaina h large the at 3D regulation between scale. the genome link and impacts direct positioning a nucleosome spacing to pointing nucleosome results organization, Our chromosome irregular level. this bound- how at domain determined reveal eukaryotes) largely are higher input, locations in ary an (unlike as that information implying positioning domains nucleosome observed only yeast. experimentally using in the formation reproduces domain model Our investigate com- to use play of we simulations Here to mechanisms puter understood. the fully thought Yet not are are regulation. formation gene domain and in humans role important to an species bacteria more in are from observed been which ranging have genome Domains the self-interact. to orga- of likely further Regions are domains: which into chromosomes, nized into packaged is DNA Significance nti ae euecmue iuain ae npoly- on based simulations computer use we paper this In y tti ihrrslto,Hsieh resolution, higher this At cerevisiae. 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BIOPHYSICS AND COMPUTATIONAL BIOLOGY organization to a high degree of accuracy—most notably the of DNA–nucleosome–DNA beads this acts as a freely rotating locations of domain boundaries. Surprisingly, we find that a joint. We do not include any interactions between nucleosomes model with a more detailed DNA–nucleosome geometry does or between nucleosomes and DNA, other than simple excluded not in fact show significant differences or improved agreement volume. A schematic of the model is shown in Fig. 1A, and full with the data. This suggests that the information which encodes details of all interaction potentials and parameters are given in for 3D domain structure is already present within the map of SI Appendix. In the past, several different coarse-grained models nucleosome positions. More specifically, we find that it is the for chromatin have been used to study the yeast genome. Some irregular spacing of nucleosomes in yeast chromatin which leads have resolved individual nucleosomes (20–24), while others have to boundary formation. Although nucleosome mapping data studied nuclear organization with much lower-resolution repre- showing this irregular spacing have been available for some time, sentations of the chromatin fiber, allowing whole nuclei to be the textbook picture of a regular fiber is still prevalent. To better simulated (25, 26). The level of detail considered in this work sits understand how nucleosome spacing genome-wide differs from between that of these 2 previous approaches. This allows us to a regular fiber we examine the distribution of linker lengths at simulate large chromosome regions spanning multiple domains, domain boundaries and in different genomic environments (i.e., while resolving their internal structure. Importantly, and unlike within active and inactive genes). We find that the linker-length most previous work, we also include realistic nucleosome spac- distribution shows peaks at short, medium, and long ranges, and ing, which, as we detail below, plays a key role in determining these are distributed differently in active and inactive regions. By domain features. analyzing our simulated chromatin structures, we find that the To simulate a specific genomic region, we use MNase diges- local compaction of fibers with irregular spacing, such as those tion followed by sequencing (MNase-seq) data (15) to infer constituting the yeast genome, is highly heterogeneous and very the nucleosome positions and linker lengths. Like the MicroC much unlike that of regular fibers such as those reconstituted protocol, these experiments use micrococcal nuclease to digest in vitro. any DNA which is not protected by nucleosomes, but rather than interaction data they provide a genome-wide map show- Results ing nucleosome coverage within a population of cells (Fig. 1C, A Simple Nucleosome-Level Model for Chromatin. We start with the Top). Although in reality the exact nucleosome positions will vary simplest possible model for chromatin which resolves individual from one cell to the next, here for simplicity we considered a nucleosomes and linker DNA. Using a bead-and-spring polymer single set of “most likely” nucleosome positions (although see modeling approach, DNA is represented as a semiflexible poly- Discussion and SI Appendix for details of simulations which do mer where 2.5-nm beads correspond to ∼8 bp of DNA. This is treat cell-to-cell variation in nucleosome positions). To extract a well-studied model (17–19) and uses simple phenomenolog- the nucleosome positions from the MNase data we used a soft- ical interaction potentials to give the correct bending rigidity ware tool called NucPosSimulator (16) as detailed in SI Appendix for DNA in vivo. Specifically the DNA has a persistence length (other tools give similar results; SI Appendix and SI Appendix, lp = 50 nm (this is a measure of the bending stiffness, defined as Fig. S2). In Fig. 1C these positions are shown with blue lines the distance along the molecule over which correlations in back- under the plot; the mean nucleosome spacing is consistent with bone orientation decay). Nucleosomes (including both histone that quoted previously in the literature (SI Appendix, Fig. S2C). proteins and wrapped DNA) are represented by 10-nm beads. Importantly these are the only data which are used as an input to A chromatin fiber is then modeled as sections of DNA (link- the model. ers) interspersed with nucleosome beads. For simplicity we do We use the LAMMPS molecular dynamics software (27) to not include any orientational or bending constraints between perform Langevin dynamics simulations (see SI Appendix for full linkers and nucleosomes; i.e., where there is a connected chain details). We selected 8 regions of between 15 and 43 kbp long

A B

Fig. 1. A simple chromatin model using nucleosome positions as input. (A) Schematic showing the bead-spring polymer model for a chromatin ﬁber. DNA is represented as a chain of 2.5-nm beads connected by springs, and we include a bending rigidity to give a persistence length lp = 50 nm. Nucleosomes (including both histone proteins and wrapped DNA) are represented by 10-nm spheres. (B) Typical snapshots from simulations (shown at different zoom levels). (Left) Simulation of region chrIV:1254937–1287938 of the yeast genome (SacCer3 build). (Right) Simulation of region chrXI:86225–108599. (C) Data used as an input to the model. (Top) Pile-up of reads from yeast MNase data (from ref. 15) for the indicated genomic region. Blue lines under the plot show the positions of nucleosomes determined using the NucPosSimulator software (16); to aid visualization these are shown in 2 rows with alternating nucleosomes on the top/bottom row. Red bars show genes. Similar plots for other genomic regions are shown in SI Appendix, Fig. S1.

2 of 9 | www.pnas.org/cgi/doi/10.1073/pnas.1817829116 Wiese et al. Downloaded by guest on October 2, 2021 Downloaded by guest on October 2, 2021 nuainsgasw n orlto coefficient correlation a find given we a of signals MicroC sides and insulation simulated of opposite the comparing on measure Appendix ); quanti- (SI regions nucleosome local which between signal,” more interactions “insulation fies A the is sim- correct). interactions of than chromatin 76.0% were (i.e., less boundaries boundaries is additional ulation 31 the agreement predicted that gener- of also find randomly but we level size to this mean this same for comparing the of with by 83.2% domains 119; of ated positions of 2 the (99 (Fig. predict boundaries kbp correctly found 240 simulations not of the ably total are a which regions, cover simulated 8 boundaries which all simulations to 3 analysis the this additional Extending boundaries, experimentally. an predicted (64%). correctly predict these the of also 11 as of well our location boundaries; As the 17 show predict data correctly MicroC simulations the (see region more boundaries this to In calling details). Second, by diagonal. we domains experiments, the the identified with to simulations between close the similarity compare especially visual quantitatively as striking maps, same the the 2 note is we the reads First, of data). number the total in the 2A, that Fig. such constructed in is 11 ref. 1B, from data Fig. 2A, in Fig. simulation in shown shows results is map interaction region a nucleosome–nucleosome this of The snapshot for a conformation (chrIV:1254937–1287938); typical genome yeast the of nucleosome short-range of features 3D. it in many detail contacts sufficient predict and as captures correctly it shape, nucleosomes that to by find disk-like we mediated treats surprisingly realistic interactions tails, it histone internucleosome more complex as a the simple, ignores than is rather Domains. model spheres, Interaction this Chromosomal Although Predicts Spacing Nucleosome output. the predic- an is as truly MicroC used a simulated are is and data this positioning input, data simulations, nucleosome MicroC the 1D to where the model input since tive com- an that is as note used (as not we coordinates are pair Importantly base Hi-C). at in in means shown not mon are This and maps level simulations. interaction nucleosome the all a stated) in otherwise map as (unless and same positions that the data nucleosome using nucleosomes the of of take pair set specific simu- we a the to data, interaction compare experimental each To the detail datasets. with we the below lations and between we here, differences so data similar some respec- MicroC very are 11, to datasets and comparisons 2 10 these present refs. domains of from terms data in XL tively; MicroC and maps MicroC these with compare We given interactions. are details nucleosome–nucleosome full interacting; be in to deemed are nucleosome ino hi eaain hsfnto nldsalength-scale a func- a includes is function which This probability a separation. parameter with random their contact mimics at in of picked which be tion are to algorithm nucleosomes said stochastic are 2 a and short, In using experiment: done the is MicroC This simulated a map. generate we conformations chromatin lated S3). Fig. Appendix Appendix, (SI population ensemble representa- a equilibrium Here a the in is of find resulting we sample region, which tive region, each per configurations for 2,000 times of 20 this repeat region. 50 each for further conformations a chromatin 122-τ of a after set (Typically a obtain representative to ics a cover simulations get our total to ∼240 In regions. chromosomes chromatin genic yeast of sample different 6 across is tal. et Wiese i.2A Fig. IAppendix SI τ b.Atrsial qiirto,w vletedynam- the evolve we equilibration, suitable After kbp. stesmlto ieui,euvln o80 to equivalent unit, time simulation the is o uldtis)Te,fo ahpplto fsimu- of population each from Then, details.) full for hw eut rmasmlto fa3-b region 33-kbp a of simulation a from results shows l c ×10 efcieyti este3 eaaina hc 2 which at separation 3D the sets this (effectively n eo) pcfial hsgnrtsampof map a generates this Specifically below). and 3 pe triangle Upper τ n aecngrtoseey250 every configurations save and qiirto iuain esmlt for simulate we simulation, equilibration oe triangle Lower n h orsodn MicroC corresponding the and ,w n htremark- that find we B), 10 tesmltdmap simulated (the −11 IAppendix SI ; IAppendix), SI µs—see r p 0 = τ value We . Left. . for 62 SI for 2. Fig. .Oemgtcnie htsneMicroC since that consider might One S6A). Fig. Appendix, SI link- average boundary on regions much are simulated be ers the to nucleo- (within tends the average boundaries than at Indeed larger lengths) interactions. linker (or act nucleosome One spacing could to some nucleosomes scale. boundary spaced this widely a at of they as pair interactions data a that chromatin that input conclude of expect we might only driver positions, major the nucleosome a Since are are simplicity. model the its to given performs model well our maps, surprising contact between agreement visual ing to bound- for increases only S5B). signal correlation Fig. Appendix, insulation the the consider aries, we If S5A). Fig. (p experi- the in boundary a of in nucleosome boundary map. 1 a mental within sim- as being the defined map in is simulated found prediction” the were “correct data A the maps. in interaction present ulated not regions. boundaries 30 simulated additional 8 an all across boundaries domain Overall of number in the shown is showing data XL MicroC and in tions input for in as plots shown used Similar are data red, green). regions in in simulated boundaries boundaries 8 simulation experimental all shows shows row row (upper lower plot and called the above were orienta- marks boundaries gene tick Domain (see bars; arrowheads). map (red each black plot from with the indicated below is shown tion are nucleosomes) nearest triangle coordinates nucleo- between at interactions square to corresponding somes the reads of MicroC num- color of number are The the 1. region from the starting within bered Nucleosomes chrIV:1254937–1287938. region B A nsmay ntrso onaypeito n h strik- the and prediction boundary of terms in summary, In < ( cerevisiae. S. 10 i %o onaiswr orcl rdce ytesimulations; the by predicted correctly were boundaries of ∼83.2% and hoai brsmltosacrtl rdc irCinteractions MicroC predict accurately simulations fiber Chromatin −10 hw iuainrsls h oain fgns(apdt the to (mapped genes of locations The results. simulation shows j . sn h pamnrn correlation; rank Spearman the using oe triangle Lower a hwn neatosbtenncesmsin nucleosomes between interactions showing Map A) IAppendix SI ∼117 oprsnbtensimula- between comparison A S1. Fig. Appendix, SI p oprdto compared bp, hw irCdt rmrf 1 while 11, ref. from data MicroC shows o eal) n hs r niae with indicated are these and details), for IAppendix SI ihteMNase the with S4, Fig. Appendix, SI r NSLts Articles Latest PNAS 0 = endiagram Venn (B) S9. Fig. , ∼28 .76 pfrallinkers; all for bp (p IAppendix, SI < 10 i , j −10 indicates | Upper f9 of 3 ; SI

BIOPHYSICS AND COMPUTATIONAL BIOLOGY implicitly gives only interaction information from nucleosomes, AB then the observation of boundaries at large linkers (NDRs, where there is no MicroC signal) could be an artifact. To check that this is not the case we generate a contact map where interactions are sorted into regularly sized bins (SI Appendix, Fig. S7 A and B) and normalized for variation of nucleosome occupancy (i.e., taking NDRs into account). Further, since our simulations give the full chromatin configuration (including nucleosomes and linker DNA), we can generate a map which includes contacts from all regions of the fiber (SI Appendix, Fig. S7C). Both of these maps show domains, confirming there is a real effect of C D increased self-interaction within those regions. Examining the boundaries found in the simulations in more detail, we find that the 20 “missing” boundaries (i.e., those present in the MicroC data but not found in simulations) tend to be at more closely spaced nucleosomes (short linkers, on average ∼25 bp; SI Appendix, Fig. S6B). Using data for histone modifications and protein binding (from refs. 28 and 29, respectively) we find that the correctly predicted boundaries tend to be flanked by nucleosomes enriched in marks associated with gene acti- Fig. 3. MicroC XL data show similar domains, but how the number of reads decays as a function of genomic separation differs. (A) Plot showing interac- vation (H3K9, H3K18, and H3K56 acetylation and H3K4me3; ◦ SI Appendix, Fig. S6C), consistent with the findings of refs. 10 tion maps (rotated through 45 and cropped) for the same region of chrXV and 11. Interestingly, the missing boundaries lack any signifi- for MicroC (Top) and MicroC XL (Bottom) data from refs. 10 and 11, respectively. The same domains appear in both plots, but the level of interactions cant enrichment of these marks (i.e., they do not display the differs for larger separations (Bottom map shows darker colors toward the features found at most boundaries), and they tend to be weaker top). (B) Plot showing how, on average, the number of interaction reads (see SI Appendix for details of boundary strength quantification). between nucleosomes scales with their genomic separation for the 2 exper- Together this suggests that the missing boundaries might not imental datasets (measured in nucleosomes; i.e., a separation of 1 means in fact be real boundaries, but rather incorrect calls which the neighboring nucleosomes). A straight line on a log−log plot indicates a simulations correctly fail to reproduce. power law, and exponents in different regions are indicated. The points The 31 “extra” boundaries which are present in simulations represent an average over all simulated regions. (C) Interaction maps from but not found in the MicroC data were found to be flanked by simulations of the same genome region as in A. The 2 maps are obtained nucleosomes depleted in most “active” histone modifications, from the same set of simulations, but a different “cross-linking” length scale lc is used to generate the map. Values of lc = 11.25 nm and lc = 26.25 nm but enriched in H3K36me3 (SI Appendix, Fig. S6C). It was give the best fit to the MicroC and MicroC XL data, respectively (SI noted in ref. 10 that H3K36me3 is highly depleted at MicroC Appendix). (D) Mean reads vs. separation plot from simulations (average boundaries—together with the results presented here this sug- over all simulated regions). Each line is obtained from interaction maps with gests that this mark is associated with a mechanism which pro- different values of lc (lc = 7.5, 15, 22.5, 30, 37.5, 45, 52.5, and 60 nm). motes nucleosome–nucleosome interactions across a long linker (or NDR) which would otherwise act as a boundary. In yeast, dimethylation and trimethylation of H3K36 have been associ- plots from other experimental methods often show a power-law ated with transcription (30), and the Set2 enzyme responsible relationship (mean number of reads ∼ s−α over several decades for generating these marks is thought to interact with RNA in s), which is indicated by a linear relationship on a log−log PolII in a way which is consistent with cotranscriptional H3K36 plot. Here both the MicroC and MicroC XL data show linear methylation (31). While ∼82% of MicroC boundaries within the regions, although interestingly, there seem to be different power- simulated regions are at, or near to, gene promoters, ∼77% law regimes for short-range (separation s ≈ 2 to 10 nucleosomes) of the extra boundaries are within gene bodies (none are at and long-range (s ≈ 10 to 100 nucleosomes) interactions. The promoters). Together this suggests that transcription is another difference between the regimes is much stronger for the MicroC important determinant of boundaries: Long linkers (which are than for the MicroC XL data, and both datasets show a sim- normally associated with promoters) are natural boundaries, ilar slope in the 10- to 100-nucleosome range (Fig. 3B shows except when they occur within a gene body, in which case active experimental data for the genomic regions we simulated; a dis- transcriptional elongation appears to abrogate the boundary. cussion of the genome-wide scaling is given in SI Appendix and SI Appendix, Fig. S8 A and B). Effect of Cross-Linker Length on Interaction Maps. Although the The main difference between the MicroC and MicroC XL pro- MicroC data published in ref. 10 revealed a short length-scale tocols is the length of the cross-linkers; we reasoned that this interaction domain pattern, the method could not recapitulate could be accounted for in our simulated interaction maps by higher-order features observed in conventional Hi-C (e.g., cen- changing the length-scale lc which controls how the map is built tromere or telomere interactions characteristic of the Rabl con- from the simulated chromatin configurations (one can think of figuration). It was later found that the discrepancy arises because this as a “cross-linker length scale”). Fig. 3D shows that indeed the cross-linking agent formaldehyde is able to cross-link nucle- by increasing lc we go from a curve which is closer to the MicroC osomes only at a very short distance, and an improved version of data to one which is closer to the MicroC XL data (SI Appendix, the method, named MicroC XL, using 2 different, longer, cross- Fig. S8 C and D). Importantly the positions of the domain bound- linkers was developed (11). Data from MicroC XL experiments aries remain largely unaffected (SI Appendix, Fig. S9); using a showed both domains and higher-order chromatin interactions; value of lc which results in a reads vs. separation curve which while the domain pattern is largely unaffected, a striking differ- best fits the MicroC XL data, we find that ∼84% of boundaries ence between MicroC and MicroC XL data is in how the number found in the MicroC XL data were also present in the simulations of interactions depends on the genomic separation, s. This is evi- and ∼69% of simulation boundaries were correct (SI Appendix, dent in the interaction maps (Fig. 3A) and can be shown explicitly Fig. S9H). via a plot of the mean number of interactions for a given (nucle- The universal scaling exponents for the power-law decay of osomal) separation (Fig. 3B and SI Appendix, Fig. S8). Similar polymer interaction probability as a function of contour length

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BIOPHYSICS AND COMPUTATIONAL BIOLOGY ABlonger (about 12% of linkers are between 50 and 200 bp), which presumably correspond to NDRs, such as are found at gene promoters. (We assume most linkers greater than 200 bp are arti- facts due to unmappable regions of the genome.) Typically the nucleosome repeat length for yeast is quoted as 165 bp (40, 41), which corresponds to a linker length of 18 bp. From the distribution shown in Fig. 5A, the mean linker length is ∼28.7 bp (and this decreases to ∼18 bp if only those linkers which are ≤100 bp are considered). In Fig. 5 B–D we examine the linker-length distribution more closely by separating out different types of genomic region. CDSpecifically we look at linker lengths 1) within genes, 2) within regions 500 bp upstream of genes (promoters)∗, and 3) in nongenic regions. To unambiguously identify linkers within gene bodies, we limit the analysis to genes of length ≥1 kbp in cate- gories 1 and 2, but consider all annotated genes when determining linkers in category 3. We find that linkers within genes and in nongenic regions show a similar size distribution (although there are more short, <3-bp linkers within gene bodies: ∼30% compared to ∼25%). As expected, in the promoter regions there are also many long (50 to 200 bp) linkers (∼40%) and a lower proportion of short- and medium-length linkers. Fig. 5D confirms that genome-wide, boundaries tend to be at long linkers (with EFthe adjacent linkers tending to be short or medium in length). In Fig. 5 E and F we further separate active and inactive genes using PolII binding data (39) as a proxy for transcriptional activity (we take genes with PolII binding levels below and above the 10th and 90th percentiles, respectively). This reveals that the bodies of active genes have more very short linkers and fewer medium (4 to 50 bp) linkers than those of inactive genes (Fig. 5E). This is consistent with previous work (42) which found a correlation between gene activity and nucleosome den- sity within coding regions (suggesting that, perhaps surprisingly, nucleosome crowding strongly facilitates transcription elongation) and proposed that transcriptional plasticity (the variation of gene expression as a result of environmental changes) may Fig. 5. Linker lengths have a multimodal distribution. Plots show the be facilitated by chromatin remodelers which alter nucleosome linker-lengths distribution based on nucleosome positions generated by NucPosSimulator (using MNase-seq data from ref. 15). (A) The genome-wide spacing. Other recent work (43) revealed a correlation between distribution (red dashed line) is shown alongside that for the 8 simulated nucleosome crowding (i.e., closely spaced or even overlapping regions (green solid line). (B) Separate distributions are shown for nucle- nucleosomes) and increased nucleosome turnover, which itself is osomes within genes (including all annotated genes of length ≥1 kbp), associated with gene activity (44). The promoter regions of the within the 500 bp upstream of gene transcription start sites (TSS) (the same active genes also showed slightly more short linkers than their set of genes is used), and in nongenic regions of the genome. (C) The same inactive counterparts, as well as more long linkers (Fig. 5F). plot as in B is shown on log-linear axes. (D) The distribution of linker lengths To check that the linker-length distribution present in our found at domain boundaries (found genome-wide using the same method simulation is not an artifact of the specific experimental tech- as described above) is shown alongside the “within gene” and “upstream nique used to generate the data (MNase-seq) or the method of gene” distributions. (E) Distributions for nucleosomes within active and inactive genes are shown separately. (Activity is inferred from ChIP-on-chip used to extract nucleosome positions from the MNase data, in data for PolII, obtained from ref. 39.) Inset shows the proportion of linkers SI Appendix (also SI Appendix, Fig. S12) we present a simi- with length less than 200 bp which fall into the 3 indicated length ranges, lar analysis of linker lengths obtained from site-directed DNA with error bars showing SEs. Nonoverlapping error bars indicate a statisti- cleavage experiments, which offer higher-resolution data than cally significant difference. (F) Similar plot to that in E but for linkers of MNase-seq (45). nucleosomes in the 500 bp upstream of gene TSS. Chromatin Conformations with Irregular (Realistic) Nucleosome Spac- ing Are Heterogeneous and Differ from Regular Fibers. We now use Fig. 5A shows the distribution of linker lengths across the 8 our simulations to examine some of the properties of 3D struc- simulated regions; also shown is the genome-wide distribution tures formed by fibers with irregularly spaced nucleosomes, by (nucleosome positions generated using the NucPosSimulator comparing these to fibers of similar length with regularly spaced software as before). First, we note the concordance between nucleosomes (Fig. 6A). First, we ask how nucleosome spacing these distributions, indicating that the simulated regions are rep- affects the volume taken up by the chromatin fiber. Fig. 6B shows resentative. Second, we note that the distribution is far from how the radius of gyration (Rg , a measure of the size of the fiber) what would be expected for either regularly or randomly spaced varies as a function of fiber length for the 2 cases. We calculate nucleosomes. In the former case, one would expect a Gaussian this by finding Rg for the first L beads of the fiber (treating DNA distribution around a mean value; in the latter case, if nucleo- and nucleosome beads on the same footing), then beads 2 to somes were positioned by a Poisson process, one would expect an exponential distribution. In fact, the distribution is multimodal, with a large number of very short linkers (about 25% of linkers *Note that in some cases the region 500 bp upstream of a gene overlaps with the 50 genome-wide have length 1 to 3 bp) and a broad peak centered end of the adjacent gene on the same strand or the promoter region of an adjacent on ∼16 bp. Interestingly there are many linkers which are much divergent gene.

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BIOPHYSICS AND COMPUTATIONAL BIOLOGY or maintenance of nucleosome-depleted regions, and this in level of variation between nucleosome positions provided the turn forms a boundary. Our model also incorrectly predicted best agreement with the MicroC data (SI Appendix, Fig. S15), that boundaries would be present at some long linkers within suggesting that for yeast, the nucleosome positions are highly gene bodies—this failure is, however, itself informative, since conserved across a population of cells. It would be interesting it suggests that transcription through NDRs can counter their to study this further in the future, as single-cell experimen- boundary-forming potential. Overall these results suggest that tal measures of nucleosome occupancy develop (48). Another since the domains observed in the MicroC data occur as a con- important question is how nucleosome positions are determined sequence of nucleosome positions, they are a “signature” of reg- in the first place. While our simulations involved nucleosomes ulatory mechanisms (domains follow function); this is different at fixed positions, in reality they are likely to be more dynamic, from the current understanding of the larger domains in higher with factors such as DNA sequence, the action remodeling com- eukaryotes, which are thought to control chromatin interactions plexes and histone chaperones, and transcription and replication to regulate expression (function is driven by domains). playing important roles. These are active areas of research, In light of the important role of nucleosome spacing in and it would be interesting to see whether there is any link chromatin interactions, we next examined the linker-length dis- with domains. tribution in more detail (using both positions generated from In higher eukaryotes the family of H1 linker histone pro- MNase data and other experimental methods—SI Appendix). teins, which have been shown to induce folding of regularly The surprising number of very closely spaced or even overlapping spaced nucleosomal arrays into 30-nm fibers in vitro, is highly nucleosomes and the high abundance of these within (particu- abundant and found across the genome, particularly in het- larly the most active) gene bodies suggest that this has a role in erochromatin [to the contrary, the yeast homologue HHO1p has transcription elongation (42). been found not to be present through most of the genome, Finally, we used our simulations to study how the irregu- but rather only at restricted locations (49)]. Our simulation larity of linker lengths affected the 3D polymer properties of snapshots showing irregularly spaced nucleosomes are strikingly chromatin fibers. We found that a chromatin fiber made from reminiscent of recent imaging experiments in human cells (50) irregularly spaced nucleosomes leads to an overall reduction in which revealed spatially heterogeneous groups of nucleosomes the size of the polymer compared to a regularly spaced fiber known as “clutches.” It would be of interest to study irregular of the same length. By examining the local compaction of a nucleosome spacing in that context—how it varies in different region of the chromatin fiber as a function of the position along genomic regions and what the implications are for higher-order it, we found that irregular spacing leads to wide variation of fiber folding—particularly since H1 is thought to control nucleo- 3D size compared to the regularly spaced nucleosomes case. In some repeat length and is found to be depleted near active genes our model, this variation closely followed the number of nucle- and promoters. Similarly, it would be interesting to understand osomes within the region. Unexpectedly, we found a nonlinear whether linker length plays a role in domain boundary formation relationship between the number of nucleosomes within a region at larger length scales in higher organisms—although chromatin and its 3D size—for a small number of nucleosomes the size looping and interactions between regions with similar histone reduces compared to a region with linker DNA only, whereas modifications have been implicated there (51), long linkers might if many nucleosomes are present the 3D size is larger. Since the lead to kinks or distortions in the chromatin fiber which promote entry/exit angle of the linker DNA (which is not constrained in certain loops (52), or they might provide a natural barrier to the our simple model) is also likely to have an effect, it would be (1D and 3D) spread of histone modifications (53). This may pro- of interest to study this with a more detailed simulation scheme vide a mechanical link from DNA sequence, through nucleosome in future. positioning, to higher-order chromosome organization. In summary, our simulations have revealed a close link between nucleosome positioning and chromatin interactions Materials and Methods in 3D in yeast. Although genome-wide data on nucleosome In this work we perform Langevin dynamics simulation of a chromatin fiber positions have been available for several years, the striking irreg- modeled as a bead-and-spring polymer using the LAMMPS software (27). ularity in nucleosome spacing is often overlooked. It will be of In brief, a fiber which resolves individual nucleosomes is represented by a chain of 2 species of spherical beads. Small (2.5 nm diameter) beads interest to study how this affects the 3D structure of chromo- represent linker DNA, while larger (10 nm diameter) beads represent nucle- somes at larger length scales (46)—for example, future models osomes. We use a common model for DNA (17–19) which correctly captures could investigate the effect of the torsional rigidity of DNA, its bending stiffness and includes steric interactions. LAMMPS integrates which controls the relationship between linker length and the the Langevin equation for each bead in the simulation using a velocity- relative orientation of adjacent nucleosomes. One must also Verlet algorithm, where an implicit solvent provides a thermostat which bear in mind that there are still many challenges in obtaining results in a constant NVT ensemble. Full details of the model and sim- nucleosome positions, and the maps generated to date rely on ulation scheme are given in SI Appendix. For the simulations presented information from a population of cells—it is still unclear what in Fig. 4 the nucleosomes are instead represented as a rigid body com- posed of 5 smaller beads, arranged to approximate a 10-nm × 5-nm disk, the nucleosome landscape is like within a single cell (47). In where linker DNA forms an entry/exit angle of 72◦; full details are given in the simulations detailed above we considered a set of “most SI Appendix. likely” nucleosome positions for each region. In SI Appendix We compare our simulations to MicroC and MicroC XL data obtained we present some simulations which take cell-to-cell variation from refs. 10 (GEO:GSE68016) and 11 (GEO:GSE85220), respectively; these of nucleosome occupancy into account (SI Appendix, Figs. S14 were aligned to the S. cerevisiae genome (SacCer3 build) following the and S15). This was done by using a different set of nucle- methods discussed in those references. We further map the MicroC data osome positions based on the same MNase data in each of onto the set of most likely nucleosome positions obtained from MNase-seq 20 simulations of the same region. As one might expect, the data (from ref. 15, GEO:GSM53721), using the NucPosSimulator software level of agreement between the simulations and the MicroC (16). Full details are given in SI Appendix. data depends on the level of variability between the differ- ACKNOWLEDGMENTS. We acknowledge the European Research Council for ent input sets of positions. Interestingly input with only a low funding (Consolidator Grant THREEDCELLPHYSICS, Ref. 648050).

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