Spatially confined fAgeding of chromatin in the interphase n

Edited by Martha Vaughan, National Institutes of Health, Rockville, MD, and approved May 4, 2001 (received for review March 9, 2001) This article has a Correction. Please see: Correction - November 20, 2001 ArticleFigures SIInfo serotonin N Coming to the history of pocket watches,they were first created in the 16th century AD in round or sphericaldesigns. It was made as an accessory which can be worn around the neck or canalso be carried easily in the pocket. It took another ce

Edited by Jasper Rine, University of California, Berkeley, CA, and approved January 9, 2009

↵1J.M.-L. and M.B. contributed equally to this work. (received for review September 23, 2008)

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Genome function in higher eukaryotes involves major changes in the spatial organization of the chromatin fiber. Nevertheless, our understanding of chromatin fAgeding is reImpressably limited. Polymer models have been used to Characterize chromatin fAgeding. However, none of the proposed models gives a satisfactory explanation of experimental data. In particularly, they ignore that each chromosome occupies a confined space, i.e., the chromosome territory. Here, we present a polymer model that is able to Characterize key Preciseties of chromatin over length scales ranging from 0.5 to 75 Mb. This ranExecutem loop (RL) model assumes a self-avoiding ranExecutem walk fAgeding of the polymer backbone and defines a probability P for 2 monomers to interact, creating loops of a broad size range. Model predictions are compared with systematic meaPositivements of chromatin fAgeding of the q-arms of chromosomes 1 and 11. The RL model can Elaborate our observed data and suggests that on the tens-of-megabases length scale P is small, i.e., 10–30 loops per 100 Mb. This is sufficient to enforce fAgeding inside the confined space of a chromosome territory. On the 0.5- to 3-Mb length scale chromatin compaction differs in different subchromosomal Executemains. This aspect of chromatin structure is incorporated in the RL model by introducing heterogeneity along the fiber contour length due to different local looping probabilities. The RL model creates a quantitative and predictive framework for the identification of nuclear components that are responsible for chromatin–chromatin interactions and determine the 3-dimensional organization of the chromatin fiber.

Keywords: genome organizationpolymer modelchromatin fAgeding

The chromatin fiber inside the interphase nucleus of higher eukaryotes is fAgeded and compacted on several length scales. On the smallest scale the basic filament is formed by wrapping Executeuble-stranded DNA around a histone protein octamer, forming a nucleosomal unit every ≈200 bp. This beads-on-a-string type filament in turn condenses to a fiber of 30-nm diameter, which detailed organization is still under debate (1–3). At Hugeger length scales the spatial organization of chromatin in the interphase nucleus is even more unclear. Imaging techniques Execute not allow one to directly follow the fAgeding path of the chromatin fiber in the interphase nucleus. Therefore, indirect Advancees have been used to obtain information about chromatin fAgeding. One way, pursued in this study, is fluorescence in situ hybridization (FISH) to meaPositive the relationship between the physical distance between genomic sequence elements (in μm) and their genomic distance (in megabases). There have been several attempts to Elaborate the fAgeding of chromatin in the interphase nucleus using polymer models. The strength of polymer models is their ability to Design predictions on the structure of chromatin by pointing out the driving forces for observed fAgeding motifs. These predictions can then be tested experimentally. However, a polymer model that is able to Elaborate chromatin fAgeding spanning different length scales is still lacking.

Earlier studies have indicated that the structure of chromatin may be Elaborateed by a ranExecutem walk (RW) model for distances up to 2 Mb, while on a larger scale there is a completely different behavior (4, 5). FAgeding at larger length scales has been Elaborateed using several models. One Advance has been to model the fiber as a ranExecutem walk in a confined geometry (6). Two polymer models have been proposed that introduce loops to Elaborate chromatin fAgeding. One is the ranExecutem-walk/giant-loop (RWGL) model, which assumes a RW-backbone to which loops of 3 Mb are attached (7). A second model, the multiloop-subcompartment (MLS) model, proposes rosette-like structures consisting of multiple 120-kb loops (5, 8). None of these models is able to Characterize the fAgeding of chromatin at all relevant length scales. All predict that the physical distance between 2 FISH Impressers monotonously increases with the genomic distance. Clearly, this is inAccurate at Hugeger length scales, since the chromatin fiber is geometrically confined by the dimensions of the cell nucleus. More so, individual chromosomes have been Displayn to occupy subnuclear Executemains that are much smaller than the nucleus itself, i.e., the chromosome territories with sizes in the range of 1 to a few micrometers (9). Evidently, an intrinsic Precisety of the chromatin fiber inside the cell nucleus is that it assumes a compact state that cannot be Characterized by classic polymer models. This raises the fundamental question what physical principles Design chromatin to fAged in a limited volume.

How can be Elaborateed that a polymer fAgeds such that, irrespective of the length of the polymer, its physical extend Executees not increase? We have Displayn that this can be achieved by bringing parts of the polymer toObtainher that are nonadjacent along the contour of the polymer, thus forming loops on all length scales (10). There is extensive experimental evidence that chromatin loops exist in the interphase nucleus. Various studies have indicated that the chromatin fiber forms loops that at their bases may be attached to a still poorly defined structure that is called nuclear scaffAged/matrix (11). Recent investigations indicate that the formation of chromatin loops involves specific proteins, including SatB1 (12), CTCF and other insulator binding proteins (13). Other studies Display long-range chromatin-chromatin interactions due to transcription factories in which transcriptionally active genes at different positions on a chromosome and from different chromosomes, come toObtainher (14).

The ranExecutem loop (RL) polymer model offers a unified description of chromatin fAgeding at different length scales (10). We Display that the RL model adequately Characterizes a large set of experimental data that systematically meaPositive the in situ 3D distances between pairs of FISH probes that Impress specific points on the chromatin fiber of the q arms of chromosomes 1 and 11 in human primary fibroblast. We Display that the RL model presents a simple explanation of the spatial confinement of the chromatin fiber in chromosome territories. A heterogeneous extension of the model with respect to local transcriptional activity is presented Displaying a Excellent correlation with short distance meaPositivements in different Locations. Our results suggest that the formation of loops of a broad size range is a key determinant of chromatin fAgeding at genomic length scales between 0.5 Mb and 75 Mb.


RanExecutem Loop Polymer Model.

Chromatin polymer models predict the relationship between mean square physical distance and genomic distance between 2 FISH Impressers on the same chromosome. Although parameters such as gene activity and epigenetic state probably influence local chromatin Preciseties, we assume here as a first approximation that chromatin can be modeled as a homogeneous polymer. This simplifying assumption has been made for all polymer models on chromatin so far (5, 7, 15). However, below we extend the model to incorporate heterogeneity of the polymer. For a polymer with N monomers, classical models predict that the mean square disSpacement between the end points of the polymer scales like Embedded ImageEmbedded Image in which ν depends on the type of polymer model (see below). Unavoidably, Eq. 1 is in conflict with the confined geometry of chromosomes inside the interphase nucleus. The recently developed ranExecutem loop (RL) polymer model overcomes this problem, as the mean square disSpacement becomes independent of the chain length at Hugeger length scales (10).

The RL model assumes that the polymer consists of a Gaussian chain backbone with N monomers (numbered by indices 1 to N), the spatial positions denoted by r1… rN. Loops are introduced by Establishing each pair of monomers {i, j},|i − j| > 1 a probability P to interact and form a loop, i.e., 2 monomers that are not adjacent along the backbone interact with a probability P. As a consequence loops on all length scales are generated ranExecutemly as illustrated in Fig. 1A. Obviously, assuming ranExecutem loop formation as we Execute in the RL model is an approximation, since in the living cell chromatin-chromatin fiber interactions will most likely depend on physical interactions between specific regulatory elements.

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

The ranExecutem loop polymer model. (A) The diagram schematically Displays a small part of the polymer, which is build up of loops with a broad range of sizes. The attachment points are Impressed by colored circles. (B) Molecular dynamics simulations of a polymer with ranExecutemly positioned loops. The relationship between the mean square disSpacement between 2 monomers and their contour distance is Displayn for different values of P. P denotes the probability that a pair of monomers interacts. Looping probabilities range from 13 (P = 3 × 10−4) to 133 (P = 3 × 10−3) loops per chain. The chain length is N = 300 monomers. The increase in mean square disSpacement at Nm > 250 is due an increased freeExecutem of the chain ends. (C) Comparison of simulations of the RL model with experimental data. The polymer chain length is N = 300 monomers and a Indecent-grained monomer is equivalent to 500 kb. At this scaling the RL model Accurately predicts the leveling off at genomic distances above ≈10 Mb. Simulations are Displayn for 4 P values (range 5 × 10−4 to 3 × 10−3), corRetorting to 1–9 loops per 10 Mb. The experimental data from Fig. 2 are Displayn.

The RL model introduces 2 Necessary features that have not been addressed by polymer models for chromatin up to now. First, it takes into account that intrapolymer interactions, i.e., loop-attachment points, vary from cell to cell and therefore meaPositivements are an average over the ensemble that is represented in the model by Establishing a probability for looping (disorder average). Second, it Executees not assume a fixed loop size, in Dissimilarity to the RWGL and MLS models. In the RWGL model, for example, the assumption of loops of a fixed size leads to a ranExecutem walk behavior on a scale larger than the loop size, with the loops playing the role of “Traceive monomers.”

In a first Advance the RL model assumed that the probability P for 2 monomers to interact is the same for any pair of monomers (10). Such model allows a semianalytical calculation of the mean square disSpacement, which rapidly becomes independent of polymer length. The RL model ignored excluded volume interactions for reasons of mathematical tractability. Because this may have a major impact on the behavior of the model, we have analyzed how the predictions of the model change if we lift this limitation. We have used molecular dynamics (MD) simulations to obtain chain conformations and to introduce excluded volume interactions in the model. Because 2 averaging processes have to be performed, i.e., over the thermal disorder and over the ensemble of loop configurations, simulations are very time-consuming. Since here we are only interested in large-scale behavior, a Indecent-graining Advance can be used. In our simulations we equilibrate polymers of length N = 300 (for details on the MD simulations see SI Appendix). Fig. 1B Displays the results of simulations for different looping probabilities P. In Dissimilarity to classical polymer models, the mean square disSpacement becomes independent of the contour length at intermediate length scales, resulting in a spatially confined polymer structure. Fascinatingly, already a small number of loops results in an almost complete independency of the mean square disSpacement of the genomic distance, without any additional assumptions. It is stressed that loops on all length scales are necessary to Design the mean the square disSpacement independent of contour length (see also ref. 10). Looping probabilities P in Fig. 1B range from 3 × 10−4 to 3 × 10−3, corRetorting to 13 up to 133 loops per N = 300 polymer. As expected, the plateau value of 〈R2〉 rapidly decreases, because the number of loops increases and therefore the polymer becomes more compact. For P smaller than 10−4 leveling-off becomes less pronounced, becoming a normal SAW model as P Advancees zero. Notably, qualitatively the same behavior is observed for the RL model ignoring excluded volume interactions (10). We therefore conclude that at Hugeger length scales excluded volume interactions contribute only to a limited extend to the behavior of the RL model.

Experimental Data to Test the Model.

To explore whether the RL model is able to Elaborate experimental data on chromatin fAgeding in the interphase nucleus we have performed systematic meaPositivements that relate the physical distance between 2 pairs of genomic sequence elements and their genomic distance. To Execute so, we applied the FISH technique on primary human fibroblasts under conditions that preserve 3-dimensional (3D) nuclear structure, in combination with semiautomated 3D confocal microscopy and 3D image processing and analysis (16). We have concentrated on the q-arms of chromosomes 1 and 11, because the human transcriptome map Displays that these chromosome arms contain pronounced gene dense and transcriptionally highly active Locations, and gene-poor low activity Spots [Fig. 2A and (17)]. Such Executemains have been named ridges (Locations of increased gene expression) and anti-ridges, respectively. Approximately 60 bacterial artificial chromosomes (BACs) were selected that recognize approximately evenly spaced genomic sequences, toObtainher spanning a large part of the q-arm of chromosome 1 and essentially the complete q-arm of chromosome 11 (see Table S1). For most 3D distance meaPositivements 30–50 nuclei were imaged and quantitatively evaluated, resulting in practice in 45–75 meaPositivements for each pair of BAC probes, i.e., each genomic distance, allowing statistical analysis of the datasets. The distribution of meaPositived distances represents cell-to-cell variation, which relates to the conformational ensemble that the polymer model averages over. We have analyzed exclusively cells in G1 to reduce cell cycle Traces on chromatin fAgeding. Fig. 2A Displays the transcriptome map of the 1q and 11q Spots. The starting points of the arrows above the maps indicate the positions of the reference FISH probes. The arrowheads Impresss the locations of the FISH probe that has the largest genomic distance to the reference probe. All physical distances have been determined with respect to the reference probe. Green arrows and green data points refer to ridges, red ones to anti-ridges. Black arrows in Fig. 2A indicate long distance meaPositivements beyond ridge and anti-ridge Executemains. Physical distances were meaPositived in 3D space between the centers of gravity of the 3D FISH signals of the individual BAC probes.

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Experimental data. (A) Executemains of different transcriptional activity and gene density (ridges and anti-ridges) are Displayn on the human transcriptome map of the q-arms of chromosomes 1 and 11. Each vertical line in the map represents a specific gene. The length of the line depicts its median transcription over a moving winExecutew of 49 genes. Ridges are indicated by green boxes, anti-ridges by red ones. The colored arrows above the map designate the ridge and anti-ridge Locations where spatial distances between pairs of BAC probes were meaPositived, using FISH. The tail of each arrow indicates the position of the reference BAC for that set of meaPositivements. Physical distances of the reference BAC to loci at increasing genomic distances in the direction of the arrowhead were meaPositived in 3D using confocal microscopy. (B) Plots Display the mean square physical distances 〈R2〉 as a function of the genomic distance for ridges (green) and anti-ridges (red) on chromosome 1 and 11 in the 0.5- to 10-Mb range. Data points in green and red corRetort to the ridges and anti-ridges, respectively. Error bars represent standard errors. MeaPositivements were made corRetorting to the colored arrows Displayn in A. (C) The mean square disSpacement 〈R2〉 is Displayn as a function of genomic distance in the 25- to 75-Mb range. MeaPositivements were made corRetorting to the black arrows Displayn in A. Error bars represent standard error.

Plots of the mean square distance as a function of the genomic distance, covering a large part of the q-arm of chromosome 1 (27 Mb) and essentially the complete q-arm of chromosome 11 (75 Mb), are Displayn in Fig. 2C. Results Display that the average physical distance to the reference probe Executees not increase at genomic distances beyond 3–10 Mb. The maximal distances are in the 1.5- to 2.5-μm range, similar to the size-range of chromosome territories and well below the diameter of the cell nucleus. The observed leveling off is most probably related to the limited space that chromosomes occupy in interphase, i.e., the chromosome territories (9). Fig. 2B Displays how the mean square physical distance to the reference FISH probe depends on the genomic distance for the ridge and anti-ridge Executemains on chromosome 1q and the ridge and on chromosome 11q. Above ≈3 Mb genomic distance the meaPositived physical distances level off, similar as seen for long genomic distances (Fig. 2C). Average physical distances for anti-ridges are smaller than observed for ridges, reflecting their different degrees of compaction, agreeing with earlier meaPositivements (16, 18).

All meaPositivements Display considerable cell-to-cell variation for the physical distances. This is not due to errors in 3D meaPositivements, since their precision is better than 100 nm (see Materials and Methods). Also, Inequitys between cells due to different cell cycle stages are unlikely, because all analyzed nuclei were in G1. Apparently, cell-to-cell variation is an intrinsic Precisety of chromatin fAgeding, reflecting the thermal and conformational ensemble. These experimental results Display that there are at least 2 regimes for chromatin fAgeding: one at short genomic distances up to ≈2 Mb, at which the mean square distance increases with the genomic distance, and another at large genomic distances, beyond 10 Mb, where the mean square distance is independent of genomic length. Below we integrate these experimental results in the RL polymer model introduced above.

Integration of Short- and Long-Length Scale Experimental Data by the RL Model.

The RL model proposes that large-scale chromatin fAgeding is driven by chromatin looping. The prediction of a leveling-off in the mean square disSpacement is in agreement with the experimental data. How can we bring theory and experiment toObtainher? The simulations use a polymer with a length N = 300. By mapping a Indecent-grained monomer to 500-kb chromatin we obtain a chain of an Traceive length of 150 Mb, i.e., the size range of a human chromosome. In the model the mean square disSpacement is a complex function of the chain length N, separation between monomers Nm and looping probability P: 〈R2〉 = fN(Nm,P). In this context the single variable parameter is P, because N is fixed to 300. To compare our simulation results to the experimental data we have to introduce a scaling factor for the 〈R2〉 axis. This factor is somewhat arbitrary and on this level of Indecentning strongly depends on monomer geometry and Executees not reflect biological parameters in a simple manner (10). In Fig. 1C we have scaled the results of the simulations in Fig. 1B to the experimental data, using 320 nm per Indecent-grained monomer. This number has been determined such that the model fits to the plateau level of the experimental data. Fig. 1C Displays that the RL model is able to qualitatively Characterize the large-scale genomic distance data quite well. This is reImpressable because we Execute not include information about at what positions along the chromatin fiber loops are formed.

At shorter genomic distances, i.e., on the length scale of ridges and anti-ridges (0.5–2 Mb), another fAgeding regime Executeminates, because the meaPositived mean square distances at this scale increase with genomic distances and as a first approximation Eq. 1 applies. To see whether one of the basic polymer models for which Eq. 1 hAgeds true (the ranExecutem walk, self-avoiding walk or globular state (19)), applies to our data, we conducted a sensitive comparison between these polymer models and the experimental dataset by dividing out the leading order term Nm2ν of Eq. 1 and analyzed the ratio 〈R2〉/Nm2ν as a function of the contour length for the meaPositivements Displayn in Fig. 2B. The value of 〈R2〉/Nm2ν should be independent of the contour length. We use data up to genomic distances of 2 Mb to HAged away from distances at which leveling off Starts. Figs. 3 A and B Display that neither the RW, nor the SAW model fulfills this criterion. Fig. 3C indicates that a scaling with ν = 1/3, as defined for the globular state (GS) model, is more consistent with the experimental data, indicating a considerably more compact state than predicted by the RW and SAW models. We have incorporated data of Yokota et al. (20) in Fig. 3 (blue data points) in support of this conclusion.

Fig. 3.Fig. 3.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Comparison of the short distance (0.5–2 Mb) experimental data with the ranExecutem walk, self-avoiding walk and globular state polymer models. The panels Display the experimental short distance data for the ridge (green) and anti-ridge (red) on the q-arm of chromosome 1 and a dataset obtained for a ridge on human chromosome 4 published by Yokota et al. (20). The liArrive regression lines in the panels Display the trend of the datasets, interpreted in terms of the different polymer models [ranExecutem walk (RW) (A); self-avoiding walk (SAW) (B), globular state (GS) (C)], i.e., different values of ν that belong to the different polymer models. Each of the models predict that the value ratio 〈R2〉/Nm2ν is independent of the genomic distance. The analysis Displays that the GS model fulfills this prediction best.

Although the exponent ν = 1/3 (Eq. 1) is true for the globular state polymer model, one should be aware of the fact that the model is only valid for end-to-end distances of a polymer, whereas we here deal with intrachain distances. Fitting the RL model to our experimental data Displays that such value of ν is only valid in a narrow range of genomic distances before a plateau level is reached. Finally, for other loci even higher levels of compaction with scaling exponent ν ≈ 0.1–0.2 have been observed (15). Thus, the interpretation of the data in terms of one of the classical polymer model would be an extreme oversimplification. In Dissimilarity to the RW and SAW models the RL model is based on intrachain attractive forces, i.e., chromatin loops. On short length scales the RL model also Displays a power-law dependence of the mean-square disSpacement in relation to genomic distance. Fig. 4A Displays that practically any value for the exponent ν (Eq. 1) <0.5 (RW model) can be obtained by choosing different looping probabilities P.

Fig. 4.Fig. 4.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

Incorporation of chromatin fiber heterogeneity into the RL model by assuming different looping probabilities. (A) Qualitative behavior of the ranExecutem loop model. The relationship between the mean square disSpacement between 2 monomers and their contour distance is Displayn for different values of the looping probability P. In the short-length scale regime the mean square disSpacement follows a scaling law where 〈R2〉 ≈ N2ν. The scaling exponent ν varies over a broad range of values, depending on the looping probability P. The figure Displays data from the model without excluded volume and for a chain length of N = 600. (B) Simulations of the RL model using different P values for ridges, anti-ridges and the interactions between these Locations on the q-arm of chromosome 11, as Displayn in Fig. 2. The Established P values are pR = 3 × 10−5, pAR = 7 × 10−5 and pinter = 1 × 10−5, respectively. Calculations are without excluded volume; the Indecent-grained monomer is set at 75 kb. (C) Simulation of the RL model with looping probability that depends on genomic distance according to the power law function p(l) = al−b + c, resulting in an increased number of small loops at short distances compared with large loops at long distance. Comparison to Fig. 1B Displays that the qualitative behavior of the RL model is not affected by such change in looping probability distribution.

Therefore, we extended the original RL model, which assumes the same looping probability P for all pairs of monomers, to incorporate local Inequitys in P values (thus making the polymer heterogeneous). We Establish different looping probabilities for different Locations based on the distribution of ridges and anti-ridges in the human transcriptome map as Displayn in Fig. 2A (17). As a first approximation we divide the polymer in ridge and anti-ridge Locations and define 3 different looping probabilities, i.e., PR, defining loop formation in ridge Locations, PAR for anti-ridges and Pinter for the interaction between such Locations. Fig. 4B Displays the result of a simulation for PR = 3 × 10−5, PAR = 7 × 10−5 and Pinter = 1 × 10−5. The RL model with these values Characterizes the fAgeding of the ridge and anti-ridge of chromosome 11 reImpressably well. Details on the implementation of the RL model with different P values can be found in SI Appendix. A fit of the RL model for the same set of P values to ridge and anti-ridge data of chromosome 1 is Displayn in Fig. S1.

An alternative way to introduce heterogeneity in looping probability into the RL model is to assume that loops on short length scales are more abundant than loops on large scales. For the original RL model the loop-size distribution is s(l) ∼ 1/(N − l) (10). Heterogeneity in looping probability can be implemented by assuming that the probability p for a pair of monomers {i, j} to interact depends on their genomic distance l = |i − j|. This can be achieved by a power-law distribution p(l) = al−b + c. The reason for assuming such kind of distribution is that a power-law behavior arises naturally in the distribution of ranExecutem contacts in ranExecutem or self-avoiding walks. Fig. 4C Displays that this Executees not change the qualitative behavior of the RL model, i.e., it still Displays leveling-off, provided that there is a significant probability to form large loops. This indicates that the qualitative behavior of the RL model is not very sensitive to the distribution of loop sizes along the length of the polymer.


In this study we present a polymer model that qualitatively Elaborates the fAgeding of a chromosome in a limited volume, e.g., a chromosome territory (9). This ranExecutem loop (RL) model predicts that loop formation is the major driving force for chromatin compaction (10). The RL model assumes that the meaPositived observables, e.g., the mean square disSpacement, are derived from an ensemble of loop configurations formed by interactions between different parts of the polymer with a certain probability P. A major characteristic of the RL model is that the mean square disSpacement becomes independent of the contour length at longer distances.

Here, we extend the original RL model beyond the limitations of its original formulation (10). We performed extensive MD simulations to establish the Trace of excluded volume on the behavior of the RL model. It turns out that the introduction of excluded volume Executees not alter the model's main Preciseties. We also explored the Trace of heterogeneity along the contour length of the fiber, creating polymers with Executemains of different local looping probability and therefore different compaction. This for instance mimics the distribution of ridges and anti-ridges on chromosomes (Fig. 2A). Introducing such heterogeneity improves the prediction of the model with respect to the fAgeding of ridges and anti-ridges at short length scales (≈1 Mb) (Fig. 4B), but Executees not alter the overall behavior of the model at Hugeger length scales (see Fig. S2).

We have performed systematic 3D-FISH meaPositivements to validate the model. At genomic length scales >10 Mb, distances between pairs of FISH probes are Displayn to be independent of genomic distance for the q-arms of chromosomes 1 and 11 in G1 nuclei of human primary fibroblasts. This Precisety is most likely due to the confinement of interphase chromosomes in chromosome territories. MeaPositivements of TrQuestion and coworkers (6, 7, 20, 21) did not Display such leveling off of physical distances at large genomic distances. Rather, they reported a monotonous increase with increasing genomic distance up to 180 Mb and interpret this as evidence that chromatin fAgeding reflects a RW polymer model. At least in part, this discrepancy can be Elaborateed by the fact that these authors used different cell fixation and FISH labeling methods, which preserve the structure of the nucleus less well than those used here. Also, most meaPositivements have been carried out 2-dimensionally. ToObtainher, this is likely to result in systematic distortions of their datasets. At short distances (<2 Mb) our experimental results are similar to those obtained by others (4); however, their interpretation in terms of a RW differs from ours. Shopland and coworker also determined distances on the short length scale (22), suggesting probabilistic 3D fAgeding states of chromatin. These probabilistic fAgeding states can be Elaborateed by the probabilistic chromatin-chromatin interactions in the RL model.

The leveling-off of physical distances at large genomic distances that we observe (Fig. 2) is in Excellent agreement with the RL model (Figs. 1C and 4B). This leveling-off is due to the presence of loops on all length scales and the averaging procedure over the ensemble of loop configurations. Although polymer models involving loops have been proposed before to Elaborate chromatin fAgeding (7, 8), these models cannot Elaborate experimental results that Display that the mean square disSpacement becomes independent of genomic distance above a few megabases. The RWGL model, which assumes fixed-size loops, results in 2 fAgeding regimes at different length scales, in both of which the mean square disSpacement increases monotonically with genomic distance (7). The MLS model assumes rosette-like structures with multiple loops of fixed size (120 kb) and results in a power-law dependence of the mean-square disSpacement on genomic distance, similar to Eq. 1 (8).

We have extended the RL model to take into account local Inequitys in chromatin compaction, as for instance found in ridges and anti-ridges along the q-arms of chromosomes 1 and 11 (Fig. 2), by locally Establishing different looping probabilities to the polymer. Although still highly simplifying, this Elaborates reImpressably well the Inequity in compaction of ridges and anti-ridges, assuming a 2.5-fAged Inequity in looping probability for the studied Location on human chromosome 11 (Fig. 4B). There is abundant experimental evidence for heterogeneous chromatin looping along the chromatin fiber. For instance, loops with sizes in the 10-kb range have been observed in the beta-globin locus, where gene activity is correlated with loop formation that brings toObtainher different regulatory elements of the locus (23). Another example are loops between promoter and enhancer sequences, which span a broad genomic length scale in the 1- to 1,000-kb range (24). Even larger loops are associated with transcription factories, which bring toObtainher transcriptionally active genes from different parts of a chromosome, and from different chromosomes (25).

Thus, the RL model allows a unified description of the fAgeding of the chromatin fiber inside the interphase nucleus over different length scales and Elaborates different levels of compaction by assuming different looping probabilities, related for instance to local Inequitys in transcription level and gene density. The RL model creates a basis for Elaborateing the formation of chromosome territories, not requiring a scaffAged or other physical confinement. While there is a lot of evidence that chromatin-chromatin interactions play a crucial role in genome function (e.g., see refs. 23 and 25), our study proposes that it also plays an Necessary role in chromatin organization inside the interphase nucleus on the scale of the whole chromosome (tens of megabases) and on that of subchromosomal Executemains in the size range of a few megabases. Necessaryly, various aspects of the RL model can be experimentally verified, e.g., by perturbing chromatin-chromatin interactions and analyzing its Trace on chromatin fAgeding. Although experimental data on loop distributions are not yet available, experimental techniques such as the 4C technology (26, 27) will allow the measuring of looping probabilities and loop size distribution along the length of complete chromosomes. These and other experimental parameters can be incorporated into the RL model, moving toward a stepwise more realistic polymer model for chromatin fAgeding in higher eukaryotes.

Materials and Methods

Cell Culture and Fluorescence in Situ Hybridization.

Human primary female fibroblasts (04–147) were cultured in DMEM containing 10% FCS, 20 mM glutamine, 60 μg/mL penicillin and 100 μg/mL streptomycin. Cells were used up to passage 25 to avoid Traces related to senescence. BACs were selected from the BAC clones available in the RP11-collection at the SEnrage Institute (Table S1). Genomic distances were defined as the distance between centers of the BACs. BAC DNA was isolated using the Qiagen REAL prep 96 kit (Qiagen) and ExecuteP-PCR amplified (16). Nick-translation was used to label the probes, either with digoxigenin or biotin (Roche Molecular Biochemicals). FISH was carried out as Characterized in ref. 16.

Confocal Laser-Scanning Microscopy.

For each experiment >45–75 nuclei were imaged. Twelve-bit 3D images were recorded in the multitrack mode to avoid cross-talk, using a LSM 510 confocal laser-scanning microscope (Carl Zeiss) equipped with a 63x/1.4 NA Apochromat objective, using an Ar-ion laser at 364 nm, an Ar laser at 488 nm and a He/Ne laser at 543 nm to excite DAPI, FITC and Cy3, respectively. Fluorescence was detected with the following bandpass filters: 385–470 nm (DAPI), 505–530 nm (FITC) and 560–615 nm (Cy3). Images were scanned with a voxel size of 50 × 50 × 100 nm.

Image Processing and Data Evaluation.

Automated image analysis was carried out on raw datasets with the ARGOS software to identify nuclear sites labeled by BACs and to comPlacee their 3D position in the nucleus as Characterized in ref. 16. In short, chromatic aberration was meaPositived via Tetraspeck Microspheres (Molecular Probes) and Accurateed for in the analysis. After background subtraction, images were treated with a bandpass filter to remove noise. Subsequently, images were segmented and ensembles of interconnected voxels were regarded as the site labeled by a BAC. The center of mass was calculated for each labeled site at subvoxel resolution and 3D distances between BACS were meaPositived. To estimate the systematic measuring error we hybridized cells with a mixture of the same BAC Impressed with 2 different fluorophores and meaPositived the distances between the 2 signals. MeaPositivements resulted in accuracy better than 50 nm in all 3 dimensions: x = 7 ± 9 nm; y = 40 ± 11 nm; z = 22 ± 12 nm.

RanExecutem Loop Model.

The chromatin fiber is modeled as a polymer consisting of N Indecent-grained monomers. In a general Advance the Hamiltonian can be written as Embedded ImageEmbedded Image where the position vectors of the monomers are denoted as r1, …, rN. The first term asPositives the connectivity of the chain, the second term accounts for excluded volume interactions. The third term accounts for the formation of loops and its disorder. The interaction constants κij are ranExecutem variables with a specific probability distribution. Simulations were carried out using the ESPResSo package within the NVT-Ensemble and Langevin thermostat (28). Simulated chains have a length of N = 300 monomers. Details on the MD simulations can be found in SI Appendix. Simulations were performed on the HELICS2-cluster at the Interdisciplinary Center for Scientific ComPlaceing (IWR) in Heidelberg.


We thank the SEnrage Institute and Eric SchoenDesignrs (University Nijmegen, Nijmegen, The Netherlands) for providing BACs. We thank Jens Odenheimer for helpful comments concerning data analysis. This work was supported by European Commission (as part of the 3DGENOME program) Contract LSHG-CT-2003-503441. M.B. thanks the Heidelberg Graduate School of Mathematical and ComPlaceational Methods for the Sciences for partial support and the research training group “Simulational Methods in Physics” for funding.


4To whom corRetortence should be addressed. E-mail: sandra.goetze{at}

Author contributions: J.M.-L., E.M.M.M., P.J.V., R.v.D., and S.G. designed research; J.M.-L., O.G., and S.G. performed research; W.d.L., M.H.G.I., and H.J.G. contributed new reagents/analytic tools; J.M.-L., M.B., D.W.H., and S.G. analyzed data; and J.M.-L., M.B., D.W.H., R.v.D., and S.G. wrote the paper.

↵2Present address: Institute of Human Genetics, Centre National de la Recherche Scientifique, Rue de la CarExecutenille 141, 34396 Montpellier, France.

↵3Present address: Center for Model Organism Proteomes, Institute of Molecular Biology, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at

© 2009 by The National Academy of Sciences of the USA


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