In the last decade, our view of genome organisation started to greatly change once again with the realisation that the spatial arrangement of eukaryotic chromosomes inside cells is not random. Such arrangement was called the nuclear architecture by Cremer and Cremer, who showed that during interphase, chromosomes seem to occupy distinct territories with preferential locations relative to the nuclear center 1 . Spatial proximity between genetic elements situated at distant positions along the genome or even on different chromosomes is known to be important for gene expression. For instance, transcription seems to be localised within discrete regions that have been called "transcription factories" 2 3 . Those are multifunctional supercomplexes able to process several, often distally located genes. More recently, spatial proximity was shown to also correlate with translocation frequencies in somatic cells, including across different chromosomes 4 . This work provided evidence that chromosome territories may intermingle.

Taking this observation one step further, we ask here whether chromatin interactions are correlated with genomic rearrangements that are conserved throughout evolution. We detected breakpoint regions (Figure 1) resulting from evolutionary rearrangements which occurred since the split of the human and mouse lineages using a method we previously developed 5 . We obtained a set of region pairs that are genomically distant in the human lineage, but adjacent in the mouse linage. We refer to these human genomic regions as breakpoint pairs.

To study the spatial (3D) proximity of these regions in the human lineage, we used the first and so far only whole-genome proximity map available for human cells 6 . These maps were obtained using Hi-C, a method that identifies chromatin interactions across an entire genome by coupling proximity-based ligation with massively parallel sequencing. While Hi-C is a complex experimental procedure, it can be thought of as a means to quantitatively sequence pairs of DNA fragments that were in close 3D proximity in live cells (for more details, see 6 ).

Our purpose in comparing these two datasets is to test whether loci which are genomically distant in the human genome but adjacent in mouse, tend to be brought close to each other through 3D chromatin folding in human cells. This would argue in favour of a conservation of spatial proximities over large evolutionary distances and support the notion of spatial synteny. Moreover, this would also give evidence of a conservation of spatial proximities across cell types since we are using a proximity map which was established in a lymphoblastoid cell line while the rearrangements we study occurred in the germline and a affected all cell lines.

In the first part of this paper, we ask whether pairs of loci containing breakpoint-region pairs are more frequently observed to be in spatial proximity than other locus pairs at a similar genomic distance in human. We then check if the lineage of origin of a breakpoint pair or its evolutionary re-use has an influence on the 3D proximity of the pair. For all these questions, we controlled for both biological and methodological confounding factors. Finally, and more generally, we show that the method used to map short reads to repetitive regions of a genome has to be chosen with extreme caution when dealing with Hi-C data, as this may lead to an over-estimation of the frequency of interaction of distant loci containing repeats.

In this analysis, we divided the human genome in non overlapping windows (or loci) of 1 Mb and compared the three-dimensional (3D) proximity of pairs of loci containing or not a breakpoint pair. As suggested in 6 , we used the number of Hi-C read pairs between two 1-Mb genomic loci as a proxy for their 3D proximity. We detected breakpoints on the human genome using the software Cassis 7 , and grouped them by pairs such that each distant pair in the human genome corresponds to adjacent loci in the mouse genome (see Figure 1 and Methods). As a consequence, human locus pairs containing a pair of breakpoints constitute a subset of the human genome that is genomically distant in human and genomically close in mouse. We obtained 294 locus pairs containing at least one breakpoint pair. Among them, 126 are inter-chromosomal and 168 are intra-chromosomal.

In this paper, we used whole-genome chromatin contact data from the Hi-C technology 6 to study the spatial behaviour of evolutionary breakpoints. We were able to show that loci which are distant in the human genome but adjacent in mouse are observed significantly more often in close proximity in the human nucleus than expected. This result holds for loci located on a same chromosome regardless of the genomic distance separating them.

Similar correlations were previously observed with other types of rearrangement events. Cancer and somatic translocations, as well as radiation-induced rearrangements depend on spatial proximity and intermingling within chromosome territories 4 16 17 . These correlations were explained by a mechanistic hypothesis suggesting that DNA sequences in close proximity are more likely to be part of a rearrangement (for a review see 18 ). In mammals, experimental studies have shown that Double Strand Breaks (DSBs) are not mobile in the nucleus 19 20 . This argues in favour of a contact-first model where the loci involved in a rearrangement must be in spatial proximity before a mismatch repair between DSBs can happen.

The mechanistic scenario is able to explain the 3D proximity in the time immediately following a rearrangement. However, it is not sufficient to explain the conservation of spatial proximity over a longer period of time. In our case, we observe 3D proximity between loci that were rearranged at some point in the course of evolution since the last common ancestor of human and mouse, that is, potentially up to 80 million years ago. Although it had been previously reported that spatial organisation of the genome inside the nucleus is not random and that preferential interactions exist 1 21 , our result not only confirms this previous report but also suggests that the time scale of the conservation may be much larger than anticipated.

Our result therefore also suggests that some 3D proximities are conserved across cell-types, as previously noticed 22 23 . Indeed, we observe a correlation between evolutionary events which happened in germline cells and the current 3D organisation in a lymphoblastoid cell line. The signal we detect is therefore indirect. In order to be maintained throughout evolution, these 3D proximities, or at least the information encoding these 3D proximities, had to be passed to the next generation, that is, had to be present in the germline. Establishing whether the 3D proximity itself, or only its encoding, is present in the germline would require to have a Hi-C dataset obtained in the germline. Since no such dataset is available, we cannot give a clear answer to this point. We could however argue that, under the contact-first model, since the loci had to be in close contact for the break to occur, it is more parsimonious to assume that they have been kept in contact ever since in the germline.

We observe that the time of conservation of the spatial proximity may be different depending on whether the break occurred in the human lineage or in the mouse lineage, as shown in Figure 5. If the rearrangement occurred in the human lineage (two genomically adjacent loci broke apart in the human lineage), it implies that the two loci were genomically close to each other in the ancestor and therefore also close in 3D. In order to explain the observed pattern, we need to invoke that the spatial proximity was maintained since the break. On the other hand, if the rearrangement occurred in the mouse lineage, the two loci were most likely not genomically close to each other in the ancestor. They are however observed today genomically close in mouse, and spatially close in human nuclei. If the parsimony principle applies, proximity was present in the ancestor. However, in this case, the proximity was not genomic, it was spatial. Overall, the spatial proximity in this case was conserved over more than 80 million years (from the speciation to human, and from the speciation to the break in mouse, see Figure 5).

In this study, we were able to observe the correlation of 3D proximities with intra-chromosomal breakpoint pairs only. The lack of signal for inter-chromosomal loci could be explained by the overall lower number of inter-chromosomal reads (5 reads on average per locus pair), which reduces the power of statistical analyses. Alternatively, inter-chromosomal interactions could be less conserved through evolution or cell-types. The notion of chromosome territories corroborates this hypothesis since intra-chromosomal proximities are constrained inside a defined territory. In addition, chromosome territories are found in different cell-types and species but their arrangement with respect to each other seems to differ between cell-types and species 24 .

The function of long-range chromatin interactions and the mechanisms responsible for their maintenance are still mostly unknown and go beyond the scope of this paper. We may however observe that several hypotheses can be formulated to address this point. We can for instance mention the participation of loci to the same transcription factory 22 25 26 , their synchronisation during replication 27 , or the fact that they bind to a common protein, such as CTCF 28 . Although it does not enable to clearly favour one of these hypotheses, our result sheds a new light on this field by bringing evidence that long-range chromatin interaction loci are enriched in evolutionary breakpoints. In the case of a rearrangement separating two loci, 3D proximity could represent a functional compensation for the loss of genomic synteny. Indeed, the arrangement of genes and of functional regions is not random along the chromosomes, and positional changes due to rearrangements may have serious consequences on the fitness of an organism. If the two separated loci need, for instance, to be co-expressed, the rearrangement will probably not be selected, unless the loci can be brought next to each other in the cell by another means, for instance through chromatin interactions at transcription factories. We therefore suggest the existence of a spatial synteny, which is another level of organisation of the genes, in addition to genomic synteny. The fact that we found a stronger correlation in gene-rich and open-chromatin regions argues at least for a gene or transcription-dependent mechanism maintaining 3D proximities. Indeed, if 3D proximities are driven by active gene and transcription factories, we can expect the signal to be stronger in gene-rich regions.

In this paper, we were able to show that some 3D proximities may be maintained over a long period of time. We also show that the loci which are maintained in contact lie within open-chromatin, gene-dense regions, and contain breakpoint pairs. These 3 features are therefore all related to the conservation of the spatial arrangement of loci, but it remains an open question which of these features, if any, is the driver. We were able to rule out gene density and DNaseI sensitivity as possible confounding factors in our analysis and showed that taking into account these factors, breakpoint pairs are still closer in 3D than other locus pairs. However, we may have missed another unknown genomic feature which could also explain the close proximity of breakpoints. Nevertheless, even if spatial proximity was not directly a cause or a compensation for the rearrangement, it remains to be explained why rearrangements occur in these specific regions, and why these regions are maintained close in 3D through evolution.

Finally, on the methodological side, we outlined a point related to the treatment of repetitive sequences which has been crucial in the analysis and goes much beyond the context of this paper. We showed that the mapping method used in the Hi-C publication over-estimates the 3D proximity of distant loci when at least one locus contains a repetitive sequence. Our own way of compensating for these repetitive sequences might be too conservative and under-estimate the interaction between distant loci containing repeats. Although weaker, the correlation between breakpoints and 3D proximities was still significant after our correction and would only benefit from a more specific correction method. However, it may be that the conclusions w.r.t. the origin of the breakpoint could change if we are indeed under-estimating the true interaction intensity between distant copies. Dedicated methods and/or technologies that enable to deal with the mainly methodological-related difficulties of handling such regions are therefore needed.

In this paper, we analysed the spatial proximity in the nucleus of loci involved in a rearrangement between human and mouse. We considered breakpoints resulting from any type of evolutionary rearrangement, which we detected with a method that we previously developed. We showed that two loci distant in the human genome but adjacent in the mouse genome are significantly more often observed in close proximity in the human nucleus than expected, and this result holds for loci located on the same chromosome regardless of the genomic distance separating them. These findings strongly suggest that part of the 3D organisation of chromosomes may be conserved across very large evolutionary distances. To characterise this phenomenon, we propose to use the notion of spatial synteny which generalises the notion of genomic synteny to the 3D case.

AV collected the data from 6 while CL prepared the data on breakpoint rearrangements using Cassis 5 7 . AV, CL and VL conducted the computational analyses described in the paper. All authors contributed equally to conceiving the experiments and writing the manuscript. All authors read and approved the final manuscript.