Fig 1.
Overall properties of the chromosome model.
(A) Density of states (microcanonical entropy) of the radius of gyration for both excluded volume potentials. (B) Relation between the radius of gyration and the size of the X chromosome.
Fig 2.
Inferential structure determination of the mouse X chromosome from single-cell data.
(A) Pooled histogram of all distances involved in an experimentally observed contact. The left peak corresponds to experimental contacts between consecutive beads that are neighbors in the chromosome fiber. The red dashed line marks the contact distance dc. (B) Cis-chromosomal contacts from single-cell Hi-C and (C) distance matrix obtained with the Lennard-Jones potential. (D) Model evidence for both excluded volume potentials without and with FISH data shown as a function of the replica temperature. (E) Distribution of the radius of gyration for the Lennard-Jones prior without and with FISH data. (F) Matrix of standard deviations of pairwise distances reflecting the spread of the sampled X-chromosome conformations. Shown is the result for the Lennard-Jones potential with additional FISH data. The color palette ranges from black to yellow indicating small to large standard deviations.
Fig 3.
Distance based modeling of the X chromosome.
(A) Histogram of sampled distance scale estimates γ. (B) Average distance matrix for the Gaussian error model with a flat plateau (upper diagonal) and for the lognormal model (lower diagonal). (C) Log evidence log Pr(D|I) for different data weighting parameters λ (the inverse temperature λ is varied from 10−4 to 1 in a replica exchange simulation to facilitate sampling of the posterior distribution).
Fig 4.
X-chromosome structure ensemble at 500 kb resolution.
(A) Four principal conformers representing the posterior ensemble. Top: Trace plots showing all members of each cluster. The color palette indicates chromosome position ranging from centromere (blue) to telomere (red). Bottom: “Sausage representation” with the tube thickness indicating the local precision of bead positions. Unmappable beads 1–10 (1–5 Mb) and 48–66 (24–33 Mb) have been omitted for clarity. (B) Root mean square fluctuations (RMSF) within each cluster of the ISD ensemble and within clusters of the ensemble from the original single-cell Hi-C publication. (C) Three-dimensional feature maps for the first structural cluster. Regions involved in trans-chromosomal contacts are shown as red density. Lamin-B1 enriched regions are shown in yellow. H3K4me3 enriched regions are shown as blue volume. The overall shape of the cluster is shown in mesh representation. The orientation of the maps shown on the left is identical to the orientation of the ensemble shown in panel (A). The maps shown on the right are rotated by 180° about a vertical axis.
Fig 5.
X-chromosome structure at 50 kb resolution.
(A) Representative structure of the X chromosome at 50 kb resolution where the tube thickness and color encodes the local packing density (dense packing: red, thick; low packing: blue, thin). (B) Representative structure of the X chromosome with beads involved in trans-chromosomal contacts highlighted as red spheres. (C) Contact probability between beads in the ISD ensemble as a function of the genomic distance s. Predictions made by various polymer models are shown as dashed lines: s−3/2 ideal chain/equilibrium globule, s−1 fractal globule.
Fig 6.
Inference of chromosome 1 structure.
(A) Distance violations in a probabilistic calculation using a single copy of chromosome 1. The contact distance is shown as dashed red line. (B) Distances of contacting beads in copy 1 against distances in copy 2. (C) Experimental contacts classified into restraints formed in both copies (green) and contacts seen only in one of the two copies (dark blue: copy 1, light blue: copy 2). (D, E) Average structures of both copies of chromosome 1. (F) Average distance matrix with upper half showing the first copy of chromosome 1 and the lower half showing the second copy.
Fig 7.
Coarse-grained chromosome model.
(A) The chromatin fiber is composed of beads representing 500 kb of chromatin. Every bead is modeled as a spherical shape of size a. Configurations with overlapping beads are penalized using a nonbonded force field accounting for volume exclusion. The beads are arranged as a linear chain where the spacing between the beads is chosen such that two neighboring beads touch each other in the equilibrium configuration. (B) Effective potential between consecutive beads along the chromatin fiber. The dashed vertical line indicates the size of the spherical bead a = 430 nm.
Fig 8.
Comparison of ISD to existing methods for chromosome structure inference from single-cell Hi-C data.
ShRec3D, MBO and the simulated annealing procedure (SA) by Nagano et al. (two versions of SA were tested: a long version based on the default annealing protocol and a short version with ten-fold faster annealing). (A): Accuracy (RMSD to ground truth) achieved with all four methods. (B): Precision (spread of structural ensemble) for MBO, SA and ISD (ShRec3D produces only a single model, therefore it is not possible to assess the precision of the ShRec3D model). Both accuracy and precision are quantified by RMSDs and increase when the RMSDs decrease.