Modulated contact frequencies at gene-rich loci support a statistical helix model for mammalian chromatin organization
© Court et al.; licensee BioMed Central Ltd. 2011
Received: 31 March 2011
Accepted: 10 May 2011
Published: 10 May 2011
Despite its critical role for mammalian gene regulation, the basic structural landscape of chromatin in living cells remains largely unknown within chromosomal territories below the megabase scale.
Here, using the 3C-qPCR method, we investigate contact frequencies at high resolution within interphase chromatin at several mouse loci. We find that, at several gene-rich loci, contact frequencies undergo a periodical modulation (every 90 to 100 kb) that affects chromatin dynamics over large genomic distances (a few hundred kilobases). Interestingly, this modulation appears to be conserved in human cells, and bioinformatic analyses of locus-specific, long-range cis-interactions suggest that it may underlie the dynamics of a significant number of gene-rich domains in mammals, thus contributing to genome evolution. Finally, using an original model derived from polymer physics, we show that this modulation can be understood as a fundamental helix shape that chromatin tends to adopt in gene-rich domains when no significant locus-specific interaction takes place.
Altogether, our work unveils a fundamental aspect of chromatin dynamics in mammals and contributes to a better understanding of genome organization within chromosomal territories.
Within the interphasic cell nucleus, the mammalian genome, packed into the chromatin, is spatially restrained into specific chromosomal territories [1, 2] and is distributed in at least two spatial compartments: one enriched in active genes and open chromatin [3–7] and the other containing inactive and closed chromatin [4, 7, 8]. It was recently proposed that, at the megabase (Mb) scale, chromosome territories consist of a series of fractal globules . However, below that scale, and beyond the simple nucleosomal array, the basic structural landscape of the chromatin in living cells remains enigmatic.
At the supranucleosomal level (approximately 10 to 500 kb), it is largely accepted that one essential determinant in relation to gene expression and other chromosomal activities is chromatin looping . However, because of technological limitations, access to this level of chromatin organization remains problematic . From this perspective, the advent of the Chromosome Conformation Capture (3C) assay [11, 12] represents a decisive technological and scientific breakthrough since it permits the identification of long-range cis and trans chromatin interactions in their native genomic context. Subsequently, several 3C-based methods have been developed that allow the unbiased large-scale identification of such interactions [4, 7, 13–16]. Noticeably, the use of a population-based approach like the 3C-real-time quantitative PCR (qPCR) protocol [17, 18], combined with appropriate algorithms for accurate data normalization , provides a powerful quantitative method that allows high-resolution analysis (on the kilobase scale) of the average contact frequencies between distant genomic regions within a locus. This information is particularly interesting as contact frequencies essentially depend on constraints that the chromatin may undergo at that scale. Constraints resulting from locus-specific interactions are easily identified in 3C-qPCR experiments since they appear as local peaks where the interaction frequency is at least four to five times higher than the surrounding collision levels [17, 19]. Furthermore, they are detected only in some experiments targeting specific regulatory sequences within a given locus. On the contrary, intrinsic constraints, resulting from fundamental characteristics of the chromatin (compaction, flexibility, basic non-linear shape), are expected to have a similar impact on contact frequencies at many sites and numerous loci.
Here, using a 3C-qPCR approach , we determined random collision frequencies within interphase chromatin at several mouse loci. We demonstrate that, in the absence of significant locus-specific interactions, several gene-rich domains of the chromatin display modulated contact frequencies in both mouse and human, thus revealing the existence of an unexpected intrinsic constraint. We propose that this constraint results from a preferential non-linear shape that the chromatin tends to adopt and show that the observed modulations can be described by polymer models as if, at these loci, the chromatin was statistically shaped into a helix.
Several mouse gene-rich loci display modulation of contact frequencies
To assess this periodicity, we needed to examine random collision frequencies for larger site separations. This was made possible by adding a primer extension step to the 3C protocol (see Materials and methods). We then repeated experiments at the anchor site F1 of the Usp22 locus and investigated a novel genomic site (F-28) located one potential modulation away (91.3 kb upstream from site F1 and 109.9 kb from site F7) (Figure 1a). These experiments validated our observations in two separate biological samples (embryonic day 16.5 and adult mouse liver) for site separation distances as far as 340 kb, revealing three consecutive modulations with a periodicity of about 90 to 100 kb (Additional file 1). Noticeably, as expected, site F-28, located 90 to 100 kb (one modulation) upstream of sites F1 and F7, displays a similar modulation in contact frequencies, confirming, once again, that this phenomenon is unlikely to result from site-specific interactions.
We conclude that several gene-rich mouse loci display an unexpected 90-kb modulation that affects contact frequencies over large genomic distances. To simplify further statistical analyses, we decided to describe this 90-kb modulation as consecutive supranucleosomal domains encompassing separation distances where random collision frequencies alternate between high and low values (Figure 2a).
Contact frequencies at a mouse gene-desert locus
Previous 3C studies in yeast  and human  indicated strong differences for chromatin dynamics between GC-rich and AT-rich/gene-poor loci . To assess whether such differences also exist in the mouse, we investigated four genomic sites (anchors) located within a gene-desert/AT-rich region of the 11qA5 chromosomal band (Figure 2b). Consistent with previous work in human , we found that random collision frequencies decrease dramatically for short site separations, reaching very low basal random collision levels for sites separated by only 5 to 6 kb. Opposite to gene-rich regions, however, no significant increase was observed for large site separations. We conclude that chromatin dynamics in gene-desert domains is radically different from that observed in intergenic portions of gene-rich domains, with random collisions frequencies noticeably decreasing much more rapidly for shorter genomic distances.
Modulated contact frequencies at gene-rich loci are conserved in human chromatin
To assess whether modulated contact frequencies of gene-rich domains could be detected in human chromatin, we used published 'Chromosome Conformation Capture Carbon Copy' (5C) data obtained at the human β-globin locus  from experiments where only residual (very weak) locus-specific interactions were detected. Statistical analysis revealed a significant increase of random collision frequencies for site separations around 100 kb (P = 0.022, Mann-Whitney U-test) followed by a very significant decrease for larger site separations (P = 0.0003, Mann-Whitney U-test) (Additional file 2). Therefore, the 90-kb modulation observed for random collision frequencies at several mouse gene-rich loci appears to be conserved at the human β-globin locus.
Genomic consequences of modulated contact frequencies
Interestingly, recent genome-wide mapping of chromosomal interactions in human by Hi-C experiments also provides direct experimental validation of our proposal. Indeed, these data confirm that long-range interactions in Giemsa-negative bands, containing gene-rich regions, are favored for site separations around 90 kb (domain III) relative to Giemsa-positive bands, which are gene-poor regions (Figure 3b). Therefore, both bioinformatic analyses and genome-wide Hi-C experiments support the predicted consequences of a 90-kb modulation and suggest that this phenomenon underlies the chromatin dynamics of a significant number of gene-rich loci in mammals.
The statistical helix model
We reasoned that the modulations of contacts frequencies observed at several gene-rich loci may reflect a preferential statistical shape that the chromatin tends to adopt when no strong locus-specific interactions take place. Since this constraint appears to be independent of the genomic position at all five gene-rich loci investigated, this preferential non-linear shape should possess a long-range translational symmetry. This led us to postulate that this statistical shape may correspond to a simple helix organization.
where D is the diameter of the helix (in nm) and P its step (in nm). In the above equations, S is the length of the Kuhn's statistical segment in kb, which is a measure of the flexibility of the chromatin, and k is the crosslinking efficiency, which reflects experimental variations. The linear mass density L is the length of the chromatin in nm that contains 1 kb of genomic DNA.
This work reveals that some gene-rich regions of the mouse and human genomes display modulation of their contact frequencies. Several lines of evidence indicate that this modulation arises from an intrinsic constraint rather than from locus-specific constraints. Firstly, for a given locus, a similar 90-kb modulation is observed at several genomic sites assayed. For example, at the Dlk1 locus it occurs at site F3 and sites F5 (9 kb away from F3) and F14 (62.7 kb away); at the Usp22 locus, it takes place at site F-28 as well as sites F1 (91.4 kb away) and F7 (109.9 kb away). Secondly, this 90-kb modulation was found at five distinct gene-rich loci located on four different mouse chromosomes. Finally, using published 5C data , we found a very similar modulation at the human β-globin locus in cells where very weak interactions were found. Interestingly, this modulation was not revealed in previous 3C experiments that we, and many others, performed in mouse or human. There are at least two reasons why this phenomenon went unnoticed. Firstly, the amplitude of the modulation is very weak and could only be significantly revealed when a relatively large number of experimental points were obtained from a highly quantitative method and combined together into a single graph after accurate normalization of the data . Secondly, at many gene-rich loci (see, for example, ), strong locus-specific interactions (above four times the local random collision level) take place, which very likely perturb this modulation. However, as observed in this work (outliers in Figure 4) or in GM06990 cells for the human β-globin locus  (Additional file 2), modulation can be perceived despite some residual and weak locus-specific cis- or trans-interactions (below three to four times the local random collision level). Interestingly, this modulation is not a simple consequence of gene expression per se since RT-qPCR analysis indicated that, in the samples investigated (30-day-old mouse liver), some loci are completely repressed (Dlk1 locus), or display very low expression levels (Emb and Lnp loci), while others contain expressed genes (UspP22 and Mtx2 loci) (Additional file 4). However, according to our modeling, the statistical helix would be in a slightly more 'open' configuration at the expressed loci (with a diameter D of about 303.92 ± 6.55 nm and a step P of 177.38 ± 12.05 nm), compared to silent loci (D = 278.83 ± 7.65 nm and P = 149.20 ± 13.67 nm) (Additional file 5). Nevertheless, these differences are minor and the statistical helix model is valid in both situations.
To what extent does this phenomenon apply to substantial parts of mammalian genomes? Our work suggests that gene-rich regions of the mammalian chromatin display modulated contact frequencies while no modulation could be evidenced in gene-poor regions (Figure 2b). As previously discussed, direct experimental detection of such modulations requires finding cellular systems where no strong locus-specific interactions occur. This is an important caveat that is particularly difficult to circumvent at many gene-rich loci that we may wish to investigate. In this work, the modulation could be observed at only five mouse and one human loci. Therefore, it remains difficult to speculate on whether such a phenomenon may apply to a substantial part of gene-rich domains, or whether it is rather limited to few loci. Clearly, however, both bioinformatic analyses and genome-wide mapping of chromatin interactions  indicate that this phenomenon may underlie the dynamics of a significant number of locus-specific interactions in gene-rich domains of mammalian chromatin (Figure 3).
As previously mentioned, one consequence of modulated contact frequency is that long-range interacting cis-regulatory sequences will undergo constraints that will tend to accumulate them within specific supranucleosomal domains where the collision dynamics is fundamentally the most appropriate for contacts. This property may explain the peculiar arrangements of genes and cis-regulatory elements observed at several important mammalian loci, such as the 'global control region' (GCR) at the mouse Hoxd (Homeobox d) locus, which is located at one or two modulations away from the genes that it regulates. It was suggested that 'the GCR would have concentrated, in the course of evolution, several important enhancers, due to an intrinsic property to work at a distance' . The modulation of contact frequencies revealed in this work represents one such intrinsic property that may contribute to enhancer clustering in mammals.
Our work suggests that modulated contact frequencies arise from an intrinsic constraint that applies to the chromatin. This led us to wonder about the nature of this constraint and to propose that it may result from a preferential statistical shape that the chromatin tends to adopt in gene-rich regions when no strong locus-specific interactions take place. This hypothesis is supported by the finding that modulated contact frequencies can be described by polymer models as if, in these regions, the chromatin was statistically shaped into a helix (Figure 4). Interestingly, by using 3C data obtained in the yeast Saccharomyces cerevisiae , we showed that the statistical helix model may also be valid for GC-rich (but not AT-rich) domains of the yeast genome (Additional files 6 and 7).
One consequence of folding the chromatin into a helix-shaped structure is that the volume it occupies increases dramatically. This increase can be estimated by calculating the volumetric mass density (Vs) of the statistical helix. In mammals, Vs = 1.02 × 105 ± 0.05 × 105 nm3/kb (or 0.0098 ± 0.0005 bp/nm3; estimated from Equation 6 given in the Materials and methods section and best fit parameter shown in Figure 4). This can be compared to the estimated volumetric mass density V of the postulated 30-nm chromatin fiber: V = 6.8 × 103 nm3/kb (calculated from Equation 6 with D = 30 nm; 〈R〉 = 9.6 nm and s = 1 kb). Therefore, the folding of a putative 30-nm chromatin fiber into a statistical helix would result in a 15.00 ± 0.73-fold increase (Vs/V) of the volume that it occupies. Finally, if the entire diploid genome had a helical chromatin organization as shown in Figure 5, it would occupy a volume of about 610 μm3 (the volume occupied by such a helix encompassing two times 3 × 109 bp), which is higher than the volume of a regular mammalian nucleus (approximately 520 μm3 for a nuclear diameter of 10 μm). Therefore, in addition to the helix-shaped organization described above, other types of dynamic folding should exist that achieve higher levels of chromatin compaction. This hypothesis is supported by our finding showing that the dynamics of random collisions in gene-desert regions is completely different to that observed in gene-rich domains.
The pioneering work of Ringrose et al.  demonstrated that chromatin behaves like a linear polymer at short distances. This work was based on quantitative comparison of in vivo recombination events and was limited to short site separation distances (less than 15 kb). Our work suggests that the upper limit for such linear polymer models may occur, in gene-rich regions, for separation distances around approximately 35 kb (supranucleosomal domain I; Figure 4). For higher genomic distances, spanning at least 340 kb (Figure 4), the statistical helix polymer model describes accurately the dynamics of the chromatin. What is the upper limit of validity for this model? We know that, at a larger scale, the chromatin is confined within the limited space of the chromosome territory [2, 29]. This 'chromosomal territory constraint' will necessarily impact on the accuracy of the statistical helix polymer model to describe chromatin dynamics. Cell imaging techniques have suggested that polymer models are incompatible with spatial distance measurements obtained for genomic separations over 4 Mbp [30, 31]. Therefore, the upper limit should lie somewhere between 340 kb and 4 Mbp. Based on the biophysical parameters provided in Figure 4, we calculated how, in interphasic cells, the spatial distances should vary as a function of genomic site separations and compared the resulting values to those measured in fluorescence in situ hybridization (FISH) experiments. For separation distances below 1 Mb, spatial distances predicted from the statistical helix model (red curve in Additional file 8) are fully compatible with the distances measured in FISH experiments (data points in Additional file 8) . However, above 1 Mb, the statistical helix model does not fit with the experimental data and, therefore, the upper limit of validity of this model appears to reside at separation distances around 1 Mb. This suggestion is in agreement with the recent comprehensive mapping of chromosomal interactions in the human genome (Hi-C experiments) showing that, above the megabase scale, the chromatin adopts a 'fractal globule' conformation . In line with modeling approaches pioneered by Dekker and colleagues [11, 24], our work suggests that, below the megabase scale, chromatin dynamics within such globules can be accurately described by appropriate polymer models. We can reasonably expect that the increasing sensitivity of both cell imaging and 3C-derived techniques will soon help us to assess the validity of this approach, thus enlightening one of the last remaining 'mysteries' of mammalian genome organization.
In this work, we have discovered an unexpected 90- to 100-kb modulation of contact frequencies at gene-rich loci of mammalian chromatin. We show that this modulation has important implications for genome evolution and we provide an original model that suggests that the modulation may result from a fundamental statistical helix shape that the chromatin tends to adopt when no significant locus-specific interactions are taking place. Altogether, our work contributes to a better understanding of the fundamental dynamics of mammalian chromatin within chromosomal territories.
Materials and methods
All experimental designs and procedures were in agreement with the guidelines of the animal ethics committee of the French 'Ministère de l'Agriculture'.
The 3C-qPCR assays were performed as previously described  with a few important modifications that increased the efficiency of the 3C assays four-fold, thus allowing real-time PCR quantifications of 3C products using the SybGreen technology instead of TaqMan probes used in previous work [17, 19]. The 3C-qPCR method  was modified as follows. Step 2: 5 × 106 nuclei were crosslinked in 1% formaldehyde. Step 8: added 5 μl of 20% (w/v) SDS (final 0.2%). Step 10: added 50 μl of 12% (v/v) Triton X-100 diluted in 1 × ligase buffer from Fermentas (40 mM Tris-HCl pH7.8, 10 mM MgCl2, 10 mM DTT, 5 mM ATP). Step 13: added 450 U of restriction enzyme (EcoRI for the Dlk1 locus or HindIII for the other loci). Step 16: incubated 30 minutes at 37°C; shake at 900 rpm. Step 34: additional digestions were performed using BamHI for the Dlk1 locus and StyI for the other loci. Step 39: adjusted 3C assays with H2O to 25 ng.μl-1. 3C products were quantified (during the linear amplification phase) on a LighCycler 480 II apparatus (Roche, Basel, Switzerland); 10 minutes at 95°C followed by 45 cycles 10 s at 95°C/8 s at 69°C/14 s at 72°C) using the Hot-Start Taq Platinum Polymerase from Invitrogen (Carlsbad, California, USA) (10966-34) and a standard 10 × qPCR mix  where the usual 300 μM dNTP were replaced with 1,500 μM of CleanAmp dNTP (TEBU 040N-9501-10). Standards curves for qPCR were generated from BACs (Invitrogen) as previously described : RP23 55I2 for the Usp22 locus; RP23 117C15 for the Dlk1 locus; and a subclone derived from RP23 3D5 for the gene-desert region. For 3C-qPCR analyses of site F-28 at Usp22 locus, a PCR product encompassing 733 bp around site F-28 was generated from genomic DNA (FA4 gccatactcagccacagggac and RA2 cctgatctcacgaatcaccctc). This PCR product (0.1 μg) was mixed with 3.4 μg of the RP23 55I2 BAC before HindIII digestion and ligation to generate standard curves. Data obtained from these experiments are included in Additional file 9 (gene-rich loci) or Additional file 10 (gene-desert locus). 3C-qPCR primer sequences are given in Additional file 11. The number of sites analyzed in each experiment were as follows: Usp22 locus, for anchor sites F1 and F7, 34 and 40 sites, respectively; Dlk1 locus, for anchor sites F14/F5 and F3, 23/17 and 9 sites, respectively; Emb locus, for anchor sites R4 and R7, 31 and 30 sites, respectively; Lnp locus, for anchor sites R41 and R46, 27 and 25 sites, respectively; Mtx2 locus, for anchor sites R2 and R56, 52 sites for each anchor; and for the gene-desert locus, for anchor sites R9/F25/F35 and F48, 36/40/40 and 38 sites, respectively.
For each biological sample and each extension primer (1F, cagtccagtgagacacatggttg; FA1, gttaaacccacagggcaagagc), six reactions were performed, pooled, purified with a QiaQuick PCR purification kit and diluted in H2O at 12.5 ng.μl-1. Each reaction was done as follows: 0.1 μM of extension primer was added to a 10-μl reaction containing 1 × qPCR mix  and 1 μl of highly concentrated 3C assay (containing about 200 to 300 ng of genomic DNA). Primers were extended by the Hot-Start Taq Platinum polymerase (Invitrogen) in a LightCycler apparatus (3 minutes at 95°C followed by 45 cycles 1 s at 95°C/5 s at 70°C/15 s at 72°C). Amplified 3C products were quantified by qPCR as explained above. Data obtained from these experiments are included in Additional file 9.
Supranucleosomal domains (D.I to D.VI) were defined from statistical analyses (Mann-Whitney U tests) performed on data shown in Figure 2a. They encompass separation distances where random collision frequencies are alternatively lower and higher: 0 to 35 kb (domain I), 35 to 70 kb (domain II), 70 to 115 kb (domain III), 115 to 160 kb (domain IV), 160 to 205 kb (domain V) and 205 to 250 kb (domain VI).
Finally, the β term given in Equation 5 can be used in Equation 1 to provide a model that describes random collisions within a circular helix polymer. (Note that, for P = 0, Equation 5 describes a circularized polymer of size D and when both P = 0 and D tend to infinity the equation is able to describe a linear polymer). The length of one turn on the statistical helix Sh was calculated from the best-fit curve (Figure 4) by applying the second derivative method.
where 〈R〉 corresponds to Equation 4c.
Best-fit analyses were implemented under the R software . We used the 'nls object' (package stats version 2.8.1), which determines the nonlinear (weighted) least-squares estimates of the parameters of nonlinear models.
Bioinformatics and statistical analyses
Contact frequencies at the human β-globin locus in the EBV-transformed lymphoblastoid cell line GM06990 were downloaded from  (Supplemental Tables 6 and 7). These 5C data were normalized using our previously published algorithm  and compiled into a graph (Additional file 2).
Co-expressed genes were selected from the READ Riken Expression Array Database , which contains the relative expression levels of 16,259 transcripts in 20 mouse tissues. Housekeeping genes, which tend to accumulate in clusters  and are co-expressed but do not necessarily share cis-acting regulatory elements, have been excluded. According to the criteria defined by Ferrari and Aitken , housekeeping genes were considered as those having a P-value > 0.5. The resulting database contained 11,701 genes. We then retained only genes for which expression data were available for at least 15 tissues and selected gene pairs separated by less than 400 kb. This database, containing 6,619 genes, was used for identification of clustered co-expressed gene pairs and randomizations (see below).
where t is the t-student variable as read in the Student's table for a degree of freedom of 29 and an alpha risk factor of 0.5 (t = 2.04), μ is the mean number of counts, σ is the standard deviation and N is the number of randomizations performed (here 30). Error bars represent the 95% confidence interval for counts in each domain.
Hi-C data used in Figure 3b are from published experiments : Gene Expression Omnibus accession numbers [GSM455137] (sequencing of [GM06990] cells-lane1), [GSM455138] (sequencing of [GM06990] cells-lane2), [GSM455139] (sequencing of K562 cells-lane1) and [GSM455140] (sequencing of K562 cells-lane2). For each of the four datasets, we selected all the pairs of sequence tags located on the same chromosome and removed those located on distinct chromosomes (that is, we removed trans-interactions). Pairs of sequence-tags were classified by chromosome. We extracted the positions of all HindIII and NcoI sites from the human genome (hg18). Restriction fragments were numbered and, for each restriction fragment, we specified the positions of the 5' and 3' ends. The downloaded positions of the tags were replaced by the position of the corresponding restriction site. For this operation we used the restriction fragment numbers provided in the downloaded files. Direction '0' corresponds to a restriction site located at the 3' end of the restriction fragment (sense reading of the sequence-tag) while direction '1' corresponds to the 5' end (antisense reading of the sequence-tag). We then assembled datasets generated from lanes 1 and 2 of each experiment. We extracted from the UCSC server the positions of chromosomal bands (Giemsa-negative and Giemsa-positive; hg18). We selected all pairs of sequence-tags for which both partners are located within the same chromosomal band (to remove long-range/inter-band interactions). Data were pooled into two separate sets: a first set corresponding to all pairs of sequence-tags located in Giemsa-negative bands and a second one corresponding to pairs of sequence tags located in Giemsa-positive bands (threshold above 50, that is, g-pos-100, g-pos-75 and g-pos-50; see UCSC server). For each set, we selected interactions that are represented by at least four pairs of sequence tags (multiple pairs of sequence tags for identical interaction partners) and calculated for each interaction the separation distance between the restriction sites (using the positions previously calculated as described above). In each set (Giemsa-negative and Giemsa-positive), the number of interactions were counted in each supranucleosomal domain (as defined in Figure 2a) and this number was normalized to the total number of interactions counted in all domains (D.I to D.VI). Data are presented in a histogram (Figure 3b) that provides, for each domain, a comparison between the counts of interactions in Giemsa-negative and Giemsa-positive sets.
Chromosome Conformation Capture
bacterial artificial chromosome
fluorescence in situ hybridization
real-time quantitative polymerase chain reaction.
We thank Annie Varrault, Luisa Dandolo, Laurent Journot, Georges Lutfalla, Jean-Marc Victor, Jacques Piette and Jean-Marie Blanchard for stimulating scientific discussions and the staff from the animal unit at the IGMM for technical assistance. This work was supported by the Association pour la Recherche contre le Cancer (ARC), the Centre National de la Recherche Scientifique (PIR Interface 106245) and the Agence Nationale de la Recherche (ANR-07-BLAN-0052-02) to TF. The CEFIC-Long-range Research Initiative (LRI-EMSG49-CNRS-08) to MW. FC was supported by a fellowship from the Ligue Nationale contre le cancer (Ardèche section). The funders had no role in study design, data collection, analysis and interpretation, decision to publish or writing of the manuscript.
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