ensemble  hi - c protocol to create a method to determine the contacts in an individual nucleus ( fig . 1a , supplementary information ) .
we used male , mouse , spleenic cd4 t cells , differentiated in vitro to t helper ( th1 ) cells to produce a population of cells ( > 95% cd4 ) , of which 69% have 2n genome content , reflecting mature cell withdrawal from the cell cycle .
chromatin cross - linking , restriction enzyme ( bgl ii or dpn ii ) digestion , biotin fill - in and ligation were performed in nuclei ( fig .
1a ) as opposed to ensemble hi - c where ligation is performed after nuclear lysis and dilution of chromatin complexes .
we then selected individual nuclei under the microscope , placed them in individual tubes , reversed cross - links , and purified biotinylated hi - c ligation junctions on streptavidin - coated beads .
the captured ligation junctions were then digested with a second restiction enzyme ( alu i ) to fragment the dna , and ligated to customized illumina adapters with unique 3 bp identification tags .
single cell hi - c libraries were then pcr amplified , size selected and characterized by multiplexed , paired - end sequencing .
de - multiplexed single cell hi - c libraries were next filtered thoroughly to systematically remove several sources of noise ( extended data fig .
hi - c in male diploid cells can theoretically give rise to at most two ligation products per autosomal restriction fragment end , and one product per fragment end from the single x chromosome . using bgl ii
, the total number of distinct mappable fragment - end pairs per single cell can not therefore exceed 1,201,870 ( extended data fig .
deep sequencing of the single cell hi - c libraries demonstrated that following stringent filtering our current scheme allows recovery of up to 2.5% of this theoretical potential , and has identified at least 1000 distinct hi - c pairings in half ( 37/74 ) of the cells .
deep sequencing confirmed saturation of the libraries complexity , and allowed elimination of spurious flow cell read pairings and additional biases ( extended data tables 1 - 3 ) .
based on additional quality metrics we selected ten single cell datasets , containing 11,159 - 30,671 distinct fragment - end pairs for subsequent in - depth analysis ( extended data fig .
visualization of the single cell maps suggested that despite their inherent sparseness , they clearly reflect hallmarks of chromosomal organization , including frequent cis - contacts along the matrix diagonal and notably , highly clustered trans - chromosomal contacts between specific chromosomes ( fig .
we used the same population of cd4 th1 cells to generate an ensemble hi - c library .
sequencing and analysis of 190 million read pairs produced a contact map representing the mean contact enrichments within approximately 10 million nuclei .
the probability of observing a contact between two chromosomal elements decays with linear distance following a power law regime for distances larger than 100 kb .
we found similar regimes for the ensemble , individual cells and a pool of 60 single cells ( fig .
1c ) . moreover , after normalizing the matrices given this canonical trend , comparison of intra - chromosomal interaction intensities for the pool and ensemble , by global correlation analysis of contact enrichment values at 1 mb resolution generates a highly significant correspondence ( fig .
this is emphasized by the high similarity observed in comparisons of individual chromosomes from ensemble and pooled hi - c maps ( fig .
despite different experimental procedures and sparse nature of the single cell matrices , the pooled matrix retains the most prominent properties of the ensemble map , confirming the validity of the approach and prompting us to further explore the similarities and differences among the individual cell chromosomal conformations .
a key architectural feature of ensemble hi - c datasets is their topological domain structure .
as expected 1403 domains were identified in the th1 cell ensemble hi - c map ( supplementary information table 1 , and supplementary information ) .
we used the ensemble domains to ask whether the same domain structure can be observed at the single cell level .
visual inspection of the domain structure overlaid on individual intra - chromosomal contact maps ( fig .
2a ) , and global statistical analysis of the ratios between intra- and inter - domain contact intensities in individual cells ( approximately 2-fold enrichment on scales of 100 kb to 1 mb , fig .
2a ) , both supported the idea that domains are observed consistently in the single cell maps . to test whether domain structures are variable between individual cells , we estimated the distributions of intra - domain contact enrichments across cells and compared it to the distributions derived from reshuffled maps .
we reasoned that cell - to - cell variation in intra - domain contact intensities would result in an increase of the variance of this distribution compared to the expected variance resulting from sampling contacts in uniformly ( shuffled ) intra - domain contacts .
2c ) , showed that the distributions for the intra - domain enrichments in real cells are not more varied than expected ( kolmogorov - smirnov p < 0.52 ) .
a similar observation was derived by comparison of the correlations between intra - domain contact enrichments for pairs of real and pairs of reshuffled maps ( extended data fig .
while this analysis can not quantify variability in the high - resolution internal structure of domains , the data suggests that domain intactness is generally conserved at the single cell level . visual comparison of whole chromosome contact maps ( fig .
2d ) suggested that unlike intra - domain interactions , inter - domain contacts within single cell chromosomes are structured non - uniformly .
the maps showed large - scale structures as indicated , for example , by specific insulation points separating chromosomes into two or more mega - domains in a cell - specific fashion . to rule out the possibility that this can be explained by sparse sampling of contacts in each single cell map
real or randomized ) we quantified the frequency of loci that strongly polarize the matrix into two weakly connected submatrices ( using an insulation score ; supplementary methods ) .
we confirmed that single cell maps indeed show many more such loci than reshuffled maps ( fig .
the reshuffled controls made by mixing contacts from different single cell maps , are in fact similar to sparse versions of the ensemble map , which do not show specific structure at the intra - domain level . along similar lines ,
the correlation in contact intensities between domains on the same chromosome in pairs of single cell maps is lower compared to reshuffled controls ( fig 2f ) . taken together , these data show that domains form a robust and recurrent conformational basis that is evident in each of the single cells
. however , inter - domain contacts are highly variable between individual cells , suggesting large - scale differences in higher - order chromosome folding that are obscured in ensemble maps , averaged over millions of such structures .
to determine whether the single cell hi - c data is consistent with unique chromosome conformations we developed a modeling approach to reconstruct the conformations of the single - copy , male x chromosome .
we used intra - chromosomal contacts as distance restraints and calculated structural models using a simulated annealing protocol to condense a particle - on - a - string representation of individual chromosomes from random initial conformations ( supplementary information ) , to produce both fine - scale and low - resolution models , with backbone particles representing either 50 or 500 kb of the chromosome , respectively . for fine - scale calculations ,
each intra - chromosomal contact restrained its precise position on the chromosome , while low - resolution calculations combined contacts into larger bins . tests of our simulation protocol demonstrated that restraint density was the most important parameter for modeling ( extended data fig .
hence , from the ten high - quality single cell datasets , we selected six with the largest numbers of intra - chromosomal x contacts , plus one with a lower number of contacts ( cell-9 ) for contrast .
repeat calculations starting from random positions generated 200 x chromosome models for each cell at both scales .
the fine - scale models displayed very low numbers of restraint violations ( extended data fig .
we introduced an estimated average unit dna distance length to approximate packaging of chromatin fibers ( ~0.15 m/50 kb ) ( supplementary information ) .
this resulted in models with a mean x chromosome territory diameter of 4.3 m ( range 3.3 - 5.9 m ) , in good agreement with x chromosome paint fish in th1 cells ( fig .
we confirmed that the restrained points in a single cell are indeed close in the structures calculated from them ( extended data fig .
interestingly , the single cell distance matrix demonstrates how the network of contacts in a model imparts further structural information beyond the directly observed contacts ( extended data fig .
comparison of the low - resolution models demonstrated convergence toward a single conformation for each single cell dataset ( fig .
hierarchical clustering revealed 4 - 5 that were most representative of the data ( fig .
4a , b ) . highlighting four regions of the x chromosome showed large - scale conformational differences between cells ( fig .
models created by shuffling hi - c contacts , or combining contacts from two cells resulted in structures smaller and more compact than observed chromosome territories ( extended data fig .
4c , d ) with many restraints stretched toward or exceeding their upper bounds ( extended data fig .
these results reaffirm that the variation in single cell contacts is not the result of partial sampling of a single underlying structure .
we next asked whether despite their cell - to - cell variability , x chromosome structures share common folding properties that could be tested in real cells .
one such important property , which is often consistent within a cell population , and with multiple potential functional implications , is localisation within the chromosomal territory relative to its surface . to predict loci with consistent positions within their chromosome territory we calculated the structural density along the x chromosome ( supplementary information ) and identified regions with consistently high or low structural density ( fig .
we chose five such regions ( p1-p5 ) with predicted positions near the surface ( p1 , p2 , p5 ; low structural density ) or inside ( p3 , p4 ; high structural density ) the model x chromosome territories using the 1200 models from the six cells ( extended data fig .
we then performed double label dna fish with x chromosome paints and p1-p5 bac probes ( fig .
the distances between dna fish signals and edge of the chromosome territory in over one hundred th1 cells showed that probes p1 , p2 and p5 were indeed found predominantly outside or toward the edge of the chromosome territory , whereas signals for probes p3 and p4 were found at internal positions ( fig .
these data show that despite highly variable inter - domain structure of the x chromosomal territory , some of its key organisational properties are robustly observed across the cell population .
overlaying data from trans - chromosomal contacts on the x chromosome models demonstrates that trans - chromosomal contacting regions are strongly enriched toward the inferred surface of the models ( fig .
these observations prompted us to further explore the structural characteristics of interfaces between chromosomal territories , and the relationships between such interfaces and the domain structure of the territory itself .
we found that trans - chromosomal contact enrichments of domains vary across cells ( fig .
4a ) , showing a significant difference between the mean contact enrichment per domain in the real and reshuffled maps ( p < 1.2e-9 , kolmogorov - smirnov test ) .
the higher variance of the distribution for the real data suggests some domains are more likely to contact elements on other chromosomes .
previous work has suggested that active genomic regions on the sub - domain scale often loop out of their chromosome territories , which might imply less defined local domain structures and disassociation from their chromosome territory .
however , our analysis shows that trans - contacting domains retain domain organisation , as demonstrated by the intra - domain contact probabilities within them ( fig .
trans - contacting domains show slightly reduced contact intensity to other domains on the same chromosome ( fig .
5c , d ) , consistent with localisation on the interfaces of their territories rather than dissociation from them .
analyses of ensemble hi - c data have previously shown that active marks correlate with enrichment of trans - chromosomal contacts . using the single cell maps combined with annotation of domains based on their enrichment for histone h3 lysine 4 tri - methylation ( h3k4me3 ) hotspots ( fig .
4d ) , we tested whether this correlation is the result of low frequency re - localisation of active domains to other chromosome territories ( looping out ) , or from frequent localisation of active domains on territory interfaces . as shown in fig .
4e , domains with high trans- to cis - chromosomal contact ratios ( excluding intra - domain ) are highly correlated with h3k4me3 enrichment in all cells . however , the data show that domains ( including active ones ) retain their association with the territory in almost all cases .
very few domains with strong trans - contacts were found to lack association with their own territory ( i.e. , upper left points in graphs in fig .
4e ) . some of this lack of perfect territory re - localisation can be explained by having two copies of each autosomal domain , but the overall reduction with territory association for trans - contacting domains is much smaller than the 50% expected by this explanation ( reduction estimated at 15 - 20% and 10% for contacts across 1 - 5 mb and 10 mb , respectively , fig .
4c ) . comparison of active domain localization shows that different active domains are highly trans - contacting in each cell ( extended data fig .
5e ) . together , these data show that preferential localisation of active domains to territory interfaces is a hallmark of chromosome organisation in all cells .
active domains maintain their intra - domain organisation , and only partially lose intra - chromosomal contacts with other domains .
our data are consistent with the concept that chromosomal territories are maintained robustly despite the trans - chromosomal contacts between active domains .
interestingly , domains associated with lamin - b1 , which are thought to be primarily inactive regions , are also found toward the surface of the models ( fig .
3h ) . however , these domains are highly anti - correlated with h3k4me3 domains ( spearman s correlation = 0.73 ) and typically depleted of trans - chromosomal contacts ( extended data fig .
superposition of h3k4me3 , lamin - b1 enriched domains and trans - chromosomal contacts on the x chromosome models illustrates spatial partitioning of the active , trans - contacting regions from those that are lamin - associated , although both types of domains tend toward the surface of the chromosome territory , supporting the above descriptions of differential positioning of domains ( extended data fig .
ensemble hi - c maps generate a highly complex view of chromosomal contacts , including low intensity contacts between all possible chromosomal pairings . in contrast
, years of single cell analyses by microscopy have suggested that individual cells have much simpler and discrete chromosome structures involving a limited number of interfaces between spatially constrained chromosomal territories .
our single cell maps bridge the gap between the genomic and imaging techniques , showing cell - specific clusters of trans - chromosomal contacts associating some pairs of chromosomes , and a lack of contacts between other chromosome pairs ( fig .
5a , red ) confirming it is not a consequence of sparse contact sampling ( extended data fig .
trans - chromosomal contact clusters bring pairs of domains together , as shown by comparing the enrichment in trans - contacts between pairs of elements connecting the same two domains and pairs connecting one domain with two different domains ( fig .
such synergistic contacting preferentially brings together pairs of active domains , with interaction between active and inactive domains being underrepresented ( fig .
although inactive domains are depleted as a group from trans - chromosomal interactions ( fig .
4e ) , inactive domains that engage in trans - contacts are more likely to interact with other inactive domains .
interestingly , analysis of interacting pairs of domains suggests that the number of chromosomes contacted by each chromosome is relatively constant ( less than 30% difference ) despite the > 3-fold change in chromosome size , the total number of trans - chromosomal contacts in the map , or a number of other factors ( fig .
we note that even though the total number of chromosome - chromosome interfaces per single cell is bounded , the detailed interface between chromosome pairs can involve multiple domain - domain contacts reflecting higher order organization ( extended data fig .
overall , these results indicate that each chromosome contacts a discrete and fairly constant number of other chromosomes in a single cell , with little dependency on the chromosome size . at the single cell level both
the microscopic and genomic observations therefore indicate highly defined territory structures , which can be hypothesised to harbor much of the chromosome within the territory , and expose a limited , relatively constant surface area engaged in chromosome - to - chromosome interfaces .
since these interfaces are highly variable among different cells , their averaging by ensemble hi - c contributes toward the relatively uniform trans - chromosomal contact matrices previously reported .
we have presented a new experimental strategy to create hi - c contact maps from single cells .
the approach allows for characterization of thousands of simultaneous contacts occurring in individual cells , and provides unique insights into hi - c technology and 3d chromosomal architecture ( supplementary videos 3 and 4 ) .
single cell contact maps reflect conservation of domain structure that was recently characterized , but show that inter - domain and trans - chromosomal contact structure is highly variable between individual cells .
genome - wide statistical analysis and reconstruction of the single copy x chromosome models gave us the opportunity to quantify key features of chromosomal architecture .
for example , active domains tend to locate on the boundaries of their chromosomal territories in the majority of nuclei , while maintaining associations with other domains on the same chromosome
. our results do not exclude chromosome territory intermingling , but argue against domains becoming completely immersed in other territories . coupled with previous observations of small and large - scale chromatin mobility a highly dynamic view of chromosomal organization ermerges , where territories are continuously being remodeled , while maintaining some key local ( domain ) and global ( depth from surface ) organisational features .
male th1 cells were fixed and subjected to modified hi - c , in which nuclei were maintained through restriction enzyme digestion , biotin fill - in labelling and ligation .
single nuclei were isolated and processed to prepare single cell hi - c libraries for paired - end sequencing .
sequences were mapped to the mouse genome , and abnormal read pairs were discarded . read pairs that occurred only once ( without duplication ) in the library sequencing were removed .
we chose 10 single cell datasets for further in - depth analyses based on several quality criteria ( see supplementary information ) . to validate the single cell hi - c procedure , we pooled the single cell hi - c datasets and compared them to ensemble hi - c dataset prepared from approximately 10 million cells essentially as described .
we created reshuffled datasets by randomly redistributing contacts of the analyzed single cells to create the same number of cells with the same number of contacts in each cell as a control to statistically analyse the variation among single cell datasets .
we reconstructed three - dimensional x chromosome structure models using restrained molecular dynamics calculations employing a simulated annealing protocol .
a combination of unambiguous distance restraints from the x intra - chromosomal contacts in the single cell hi - c dataset and anti - distance restraints between regions that were found not to contact each other in the ensemble hi - c dataset was used . to assess the precision and accuracy of the structure generation process we used the protocol to generate synthetic hilbert curve structures , and explored the impact of varying the number of restraints . for pair - wise comparison of the structures ,
we calculated the root - mean - square deviation ( rmsd ) . to compare the x chromosome models to x chromosome structure in vivo , we selected five loci with consistently high or low structural density in the models , and compared distances between the loci and the x chromosome territory surface in cells ( dna fish ) .
. a , shown are the numbers of read - pairs in the original and re - sequenced runs , the number of fend - pairs in the original one , the number of fend - pairs when combining the sequences of the two runs , and the addition to fend - pairs the re - sequencing contributed .
% valid non - amplified are the percentages of singly covered fend - pairs in the original sample that were supported by more read - pairs in the re - sequenced one .
these fend - pairs were discarded as potential spurious pairs in the original run , but proved by the re - sequencing to be valid pairs .
this gives a sense of the fraction of valid pairs we discard when removing the read - pairs suspected to be sequencing pairing errors .
b , shown are fend - pair coverage contingency tables of the original and the re - sequenced runs for the five single - cells . mouse and human nuclei or single cell hi - c samples were mixed in different stages of the experiment ( group a , before fixation ; group b , before library construction [ so all the mouse and human samples in each library have the same identification tag ] ; group c , before library amplification [ so mouse and human samples in each library have different identification tags ] ) .
we created single cell ( for group a ) or human / mouse two cell ( for groups b and c ) hi - c libraries and analysed them .
the table shows the percentages of the three possible read - pairs : mouse - mouse ( mm9-mm9 ) , human - human ( hg18-hg18 ) and human - mouse ( hg18-mm9 ) .
for group a , we selected mouse cells based on morphology . in group a , all six libraries contain almost exclusively mouse - mouse read - pairs with insignificant human - human or mouse - human pairs .
each group b library has both human - human and mouse - mouse read - pairs as expected , and the number of spurious human - mouse read - pairs is extremely low . in each group
c library , which was created by amplifying the distinctly tagged human ( c1-c6 ) and mouse ( c7-c12 ) single cell samples in the same tube ( e.g. , c1 and c7 , c2 and c8 , etc . ) , the fractions of foreign pairs ( human reads with a mouse tag and vice versa ) and of spurious pairs ( human - mouse ) were consistently extremely low . to estimate the fraction of foreign and spurious pairs that could have originated simply from mapping a truly pure mouse library to a concatenated human - mouse genome , libraries from pure mouse cells ( group d ) were mapped to such a genome .
the mean percentages of both foreign and spurious fend - pairs in this lane are the same as those found in the different human - mouse mixed lanes , suggesting there is no inter - cellular contamination .
phix174 dna library was added to four lanes of single cell hi - c multiplexed libraries . in theory , no mixed mouse - phix174 read - pair is expected , but in fact a small number were detected .
shown are the fraction of phix174 dna loaded to each lane capacity , the percentage of phix174 read - ends in the lane , and the observed number of read - pairs by type .
the pairing probability was crudely estimated from these figures , and from it the number of expected spurious mouse - mouse read - pairs was calculated .
most of these spurious pairs are discarded when the unique identification tags at the beginning of each read - end are matched .
shown is the estimated number of spurious mouse pairs that coincidently have matching identification tag and are therefore not detected and removed . a , efficiency of biotin labelling at hi - c ligation junctions for two hi - c ligation products , showing 90 - 95% efficiency ( supplementary information ) .
c , discarding the missed re2 read - pairs removes a uniform  blanket  of non - specific contacts from the map .
shown is the dependency between the number of fend - pairs in a sample and the estimated number of autosomal fends covered by more than two fend - pairs under different models .
the binomial model ( grey line ) distributes fend - pairs to fends randomly without any constraint , as if sampling fend - pairs from an infinite number of chromosomes .
number of fends in each 250 kb genomic bin for bgl ii or dpn ii as re1 .
tail of bins with few fends is for bins of low mappability and near the chromosomes edges .
f , median fend length ( distance from re1 to the first upstream re2 ) in each 250 kb genomic bin for bgl ii or dpn ii as re1 .
g , information on the two restriction enzymes we used for re1 , bgl ii ( 6 cutter , which we used predominantly ) and dpn ii ( 4 cutter , only used for cell-8 ) .
fends in which their first re2 site starts a non - unique 36 bp sequence are marked as non - unique fends .
we discarded both blind and non - unique fends and used only the unique fends .
the number of actual fends in a male mouse genome , which have two copies of each autosome and a single x chromosome are shown as well as the median fragment length ( chromosomes y and mitochondrial genome were ignored throughout the analysis ) .
h , information on the ten single - cell datasets that successfully passed the quality control filters .
p - value of the number of autosomal fends with more than two covering fend - pairs was calculated from the binomial model ( panel d and supplementary information ) .
k , distribution of fend - pair coverage ( number of read - pairs that support each fend - pair ) in the ten single - cell datasets .
l , distribution of mean contacts per fend calculated for each mappable 1 mbp , normalized by the mean value in each cell , and averaged across autosomal or x chromosomes from the ten single - cells . a , ratios between intra - domain and inter - domain contact enrichments over genomic distance .
chromosomes are grouped into four groups : group 1 ( chromosomes 1 , 8 , 15 , 16 and x ) , group 2 ( chromosomes 2 , 6 , 10 , 13 and 18 ) , group 3 ( chromosomes 3 , 5 , 11 , 14 and 17 ) and group 4 ( chromosomes 4 , 7 , 9 , 12 , 19 ) .
the intra- over inter- domain enrichment is persistent in all chromosome groups and does not seem to stem from peculiar chromosomes .
b , distribution of correlations between intra - domain contact numbers of all domains from pairs of real and reshuffled controls .
c , distribution of the insulation score at each fend in nine single cell hi - c datasets ( where re1 is bgl ii ; real cells ) is shown in red .
fifty sets of reshuffled cells were produced ( see supplementary methods ) and their insulation score distribution is shown in black .
real cells have a heavier tail of highly insulating loci , which is indicative of non - uniform and cell - specific inter - domain contact structure .
a , results of structure calculations using restraints from a space - filling hilbert curve test structure with 4096 particles and four typical results of structure modelling using different numbers of restraints are shown ( upper panels ) .
structure calculations of the hilbert curve from random positions using different sets of 1024 restraints ( lower panel ) .
b , comparison of rmsd values from hilbert curve and single cell x chromosome models .
structure calculations for hilbert curves were repeated 100 times with variable numbers of restraints as shown .
the root mean square deviation ( rmsd ) values between 100 models ( precision ) using the indicated number of restrains ( mean + / sd ) are plotted in blue .
the rmsd values between the original hilbert curve and each of the 100 models ( accuracy ) for the same numbers of restraints are plotted in green ( mean + / sd ) .
rmsd values from 100 repeated calculations of fine - scale ( 50 kb backbone ) x chromosome structure from the seven single cell datasets are also plotted ( red ; mean + / sd ) .
the distances between directly restrained positions in fine - scale ( 50 kb backbone ) x chromosome models are shown .
models for the six single cell datasets ( cell-1 to cell-6 ; red ) show no values exceeding the upper bound ( dashed line ) .
calculations with six shuffled interaction maps ( created from cell-1 dataset ; blue ) show significant violations .
structure calculations performed on merged pairs of datasets ( yellow ; all possible combination of cell-1 to cell-4 ) have a few violations and are significantly closer to the upper limit .
d , comparison of structure - derived distance matrix from 200 fine - scale x chromosome models from cell-1 ( orange ) and its single cell hi - c contacts ( black crosses ) . the orange colour indicates the minimum distance between backbone particles .
e , comparison or x chromosome structural models for six cells computed using low - resolution ( 500 kb binned ) single - cell hi - c interaction data .
the bundles shown represent minimised structural alignments of five models from repeat calculations for each cell .
a , pair - wise comparison of fine - scale x chromosome structural models by rmsd analysis .
each pixel represents an rmsd value for a pair - wise comparison of two models .
the order of 200 models in each panel was determined by hierarchical clustering of the rmsd values .
numbers shown are the mean rmsd values and the standard deviations for all the comparisons for each cell calculated by comparing the hi - c contact particles .
b , cell - to - cell comparison of 200 fine - scale x chromosome structural models by rmsd analysis .
each pixel represents an rmsd value for a pair - wise comparison of two models .
c , fine - scale x chromosome structures calculated from cell-1 and cell-3 datasets , and a structure from the combined dataset .
d , typical structure calculated using a randomised dataset , where the interacting points for cell-1 have been shuffled with a pairing probability proportional to one over the square root of the sequence separation .
colours and scale as shown in c. e , distribution of measurements of depth from the surface for five loci p1 - p5 ( fig .
3e ) in 1200 x chromosome models ( 200 fine - scale models for each of the six cells ) . whiskers on box plots define 10th and 90th percentiles and the outliers are shown as individual dots . a , intra - domain contact enrichment for each quartile of trans - chromosomal contacting domains .
b , same as a but subtracting the mean quartile enrichment in each genomic distance emphasizing the differences shown in a. c , using the same sets as in a but plotting the enrichment of inter - domain contacts within the same chromosome .
d , same as c but subtracting the mean quartile enrichment in each genomic distance .
e , percentage of cells in which high and low h3k4me3 enriched domains are trans - interacting .
for each cell the domains with top 10th percentile trans intensity were defined as trans - interacting in that cell .
we then counted for each domain the fraction of cells in which that domain was trans - interacting .
shown are the distributions of these fractions for h3k4me3 enriched and non - enriched domains ( the top and bottom 25th percentiles , respectively ) .
f , distribution of the average laminb1-damid enrichment in chromosomal domains , color coded according to the enrichment value .
g , domains plotted according to their number of trans- and cis - chromosomal ( but excluding intra - domain ) contacts , color - coded as in f. the domain laminb1-damid enrichment and h3k4me3 peak density are highly anti - correlated ( spearman s correlation = 0.73 ) .
h , intra - domain contact enrichment for high vs. low quartile of domains stratified by their mean laminb1-damid enrichment . error bars indicate 95% confidence intervals . i , using the same sets as in h but plotting the enrichment of inter - domain contacts within the same chromosome
error bars as in h. j , lamin - b1 domains show a minor decrease in intra - domain contact intensities that might suggest less compacted domains , and significantly increased cis inter - domain contact , maybe due to lack of trans - chromosomal contacts .
topology of lamin b1 , h3k4me3 and trans - contacts on five - model bundles of low - resolution x chromosome models .
scale bar , 1 m . a , comparison of observed coverage of the trans - chromosomal 1 mb square bins of each cell ( red lines ) , versus predicted coverage assuming a binomial model ( random uniform distribution of contacts to bins ; black dashed line ) .
observed coverage is consistently higher than the uniform model , indicating the highly non - random distribution of trans - chromosomal contacts to genomic bins .
b , trans - chromosomal contact enrichment around observed trans contacts as a function of the contacts total distance on both chromosomes ( manhattan distance in the contact map ) . observed and expected ( by random uniform contact distribution )
number of contacts are counted around each trans contact , and their ratio is shown for the 9 real cells ( blue ; where re1 is bgl ii ) and reshuffled cells ( red ) , at two different scales .
c , left panel , trans contacts were classified according to h3k4me3 density of the domains they associate : high and low for top and bottom 25th percentiles , respectively , mid for 25th-75th percentiles . shown is the log ratio of the contingency table counts with the expected counts generated by multiplying the corresponding marginal probabilities for each group ( chi - square test ; p = 5.8e-18 ) . to make sure this phenomena is not caused by the trans enrichment of active domains and depletion of non - active ones , only the top 15th percentile trans enriched domains from each cell were used .
middle panel , similar to left panel but contacts are classified by their associated domain gene density ( chi - square test ; p = 2.3e-12 ) .
right panel , similar to left panel but using domains in the top 40th percentile of gene density , classifying by their h3k4me3 density , to test h3k4me3 enrichment beyond gene density ( chi - square test ; p = 3.6e-06 ) . in all cases active / gene - rich domains preferentially interact with each other , although active domains ( high h3k4me3 density ) interact beyond that expected by their gene density .
a , the number of interacting chromosomes per chromosome is depicted in circles sized according to the number of single cells the value was observed in , while ordering chromosomes by the number of transcription start sites ( tsss ) in each chromosome which is shown by blue bars .
spearman correlation between the number of tsss and the mean value of the number of interacting chromosomes per chromosome is 0.18 .
two chromosomes were defined as interacting when they had at least one domain - domain interaction ( see main text ) supported by two or more contacts .
however , the change is small , and the number of interacting autosomal chromosomes per chromosome ( the plotted value divided by two ) remains between 4 and 6 .
b , same as a except that chromosomes ordered by the number of active h3k4me3 domains ( the top 25th percentile h3k4me3 peak density domains ) .
c , same as a except that chromosomes are ordered by the number of non - lad basepairs in the chromosome .
the fraction of a chromosome covered by lads ranges from 31% to 53% and is correlated with chromosome size ( 0.52 spearman ) .
thus , chromosome lengths span a range of 3.2 fold change , while their non - lad fraction spans a smaller range of 2.8 fold change .
the mean number of contacts of each chromosome with others it interacts with is shown for the ten single cells , ordering chromosomes by their size .
chromosome size is correlated with the number of contacts it has , but the dynamic range of this number is small .
e , the number of interacting chromosomes per chromosome is depicted in circles sized as the number of single cells the value was observed in , while ordering the ten single cell datasets by the number of trans contacts in each dataset , shown by blue bars . only autosomes are displayed .
spearman correlations between the number of trans contacts in each dataset and the mean value of the number of interacting chromosomes per chromosome is 0.73 .
however , the change is small , and the number of interacting autosomal chromosomes per chromosome ( the plotted value divided by two ) remains between 4 and 6 .
top and bottom 30th percentiles of h3k4me3 peak density domains are marked in light pink and light grey , respectively .
note the grid - like trans contacts arrangement , and the correspondence between the two large trans contact clusters and the organisation of cis contacts in both chromosomes to large  mega domains  .
 large - scale chromosome structure and spatial nuclear arrangement have been linked to control of gene expression and dna replication and repair . 
 genomic techniques based on chromosome conformation capture assess contacts for millions of loci simultaneously , but do so by averaging chromosome conformations from millions of nuclei . 
 here we introduce single cell hi - c , combined with genome - wide statistical analysis and structural modeling of single copy x chromosomes , to show that individual chromosomes maintain domain organisation at the megabase scale , but show variable cell - to - cell chromosome territory structures at larger scales . despite this structural stochasticity , localisation of active gene domains to boundaries of territories 
 is a hallmark of chromosomal conformation . 
 single cell hi - c data bridge current gaps between genomics and microscopy studies of chromosomes , demonstrating how modular organisation underlies dynamic chromosome structure , and how this structure is probabilistically linked with genome activity patterns . 
Single cell Hi-C
Single cell and ensemble Hi-C similarity
Intra- and inter-domain contacts
3D structural modeling of X chromosomes
Domains at the interface
Online Methods
Supplementary Material