Four-dimensional chromosome reconstruction elucidates the spatiotemporal reorganization of the mammalian X chromosome

Chromosomes are segmented into domains and compartments, but how these structures are spatially related in three dimensions (3D) is unclear. Here, we developed tools that directly extract 3D information from Hi-C experiments and integrate the data across time. With our “4DHiC” method, we use X chromosome inactivation (XCI) as a model to examine the time evolution of 3D chromosome architecture during large-scale changes in gene expression. Our modeling resulted in several insights. Both A/B and S1/S2 compartments divide the X chromosome into hemisphere-like structures suggestive of a spatial phase-separation. During the XCI, the X chromosome transits through A/B, S1/S2, and megadomain structures by undergoing only partial mixing to assume new structures. Interestingly, when an active X chromosome (Xa) is reorganized into an inactive X chromosome (Xi), original underlying compartment structures are not fully eliminated within the Xi superstructure. Our study affirms slow mixing dynamics in the inner chromosome core and faster dynamics near the surface where escapees reside. Once established, the Xa and Xi resemble glassy polymers where mixing no longer occurs. Finally, Xist RNA molecules initially reside within the A compartment but transition to the interface between the A and B hemispheres and then spread between hemispheres via both surface and core to establish the Xi.

CBCR: A Curriculum Based Strategy For Chromosome Reconstruction

In this paper, we introduce a novel algorithm that aims to estimate chromosomes’ structure from their Hi-C contact data, called Curriculum Based Chromosome Reconstruction (CBCR). Specifically, our method performs this three dimensional reconstruction using cis-chromosomal interactions from Hi-C data. CBCR takes intra-chromosomal Hi-C interaction frequencies as an input and outputs a set of xyz coordinates that estimate the chromosome’s three dimensional structure in the form of a .pdb file. The algorithm relies on progressively training a distance-restraint-based algorithm with a strategy we refer to as curriculum learning. Curriculum learning divides the Hi-C data into classes based on contact frequency and progressively re-trains the distance-restraint algorithm based on the assumed importance of each curriculum in predicting the underlying chromosome structure. The distance-restraint algorithm relies on a modification of a Gaussian maximum likelihood function that scales probabilities based on the importance of features. We evaluate the performance of CBCR on both simulated and actual Hi-C data and perform validation on FISH, HiChIP, and ChIA-PET data as well. We also compare the performance of CBCR to several current methods. Our analysis shows that the use of curricula affects the rate of convergence of the optimization while decreasing the computational cost of our distance-restraint algorithm. Also, CBCR is more robust to increases in data resolution and therefore yields superior reconstruction accuracy of higher resolution data than all other methods in our comparison.

4D chromosome reconstruction elucidates the spatial reorganization of the mammalian X-chromosome

Chromosomes are segmented into domains and compartments; yet, how these structures are spatially related in 3D is unclear. Here, by directly integrating Hi-C capture experiments and 3D modeling, we use X-inactivation as a model to examine the time evolution of 3D chromosome architecture during substantial changes in gene expression. First, we show that gene expression A/B compartments are consistent with phase separation in 3D space. Second, we show that residuals of smaller scale structures persist through transitions, despite further large-scale reorganization into the final inactive configuration, comprising two “megadomains”. Interestingly, these previously hidden residual structures were not detectable in 2D Hi-C maps or principal component analyses. Third, time-dependent reaction-diffusion simulations reveal how Xist RNA particles diffuse across the 3D X-superstructure as it reorganizes. Our 4DHiC pipeline helps satisfy the growing demand for methodologies that produce 3D chromosome reconstructions directly from 2D datasets, which are consistent with the empirical data.

The use of simulated annealing in chromosome reconstruction experiments based on binary scoring.

We present a method of combinatorial optimization, simulated annealing, to order clones in a library with respect to their position along a chromosome. This ordering method relies on scoring each clone for the presence or absence of specific target sequences, thereby assigning a digital signature to each clone. Specifically, we consider the hybridization of oligonucleotide probes to a clone to constitute the signature. In that the degree of clonal overlap is reflected in the similarity of their signatures, it is possible to construct maps based on the minimization of the differences in signatures across a reconstructed chromosome. Our simulations show that with as few as 30 probes and a clonal density of 4.5 genome equivalents, it is possible to assemble a small eukaryotic chromosome into 33 contiguous blocks of clones (contigs). With higher clonal densities and more probes, this number can be reduced to less than 5 contigs per chromosome.