Fig 1.
The toy model of a chromosome with a hierarchical energy landscape.
(A) The energy landscape with three levels of hierarchy considered here. (B) Pairwise contact energy landscape for the toy model of a chromosome of length 500. (C) Illustration of the effect of annealing on the mean-first passage time (MFPT) between the states. (D) Optimization of the metastability index results in profiles, revealing three levels of hierarchy corresponding to three hub sets , and
, respectively. (E, top) A network representation of the toy chromosome interactions with nodes colored according to the partitions associated with the hub set
; (E, bottom) reduced network constructed from the partitions associated with the hub set
, with links depicting effective interactions between partitions calculated via Eq 11 in Materials and methods.
Fig 2.
Analysis of human chromosome 17 using a MSM-based computational framework.
(A) Pairwise contact energy landscape of human chromosome 17. (B) 1D projection of the chromosome 17 energy landscape. (C) Effect of annealing on the mean-first passage time (MFPT) between loci. (D) Optimization of the metastability index under different annealing conditions (β = 1 to 9). (E) Partitioning of chromosome 17 determined by the hub set
(left, visualization obtained by the Fruchterman-Reingold visualization algorithm implemented in Gephi [60]) and schematic illustration of the effective interactions between 12 observed partitions (right).
Fig 3.
Architecture of the chromosome 17 at three levels of structural hierarchy.
(A-C) Graph representation of three levels of structural hierarchy. The nodes represent partitions, the node sizes scale with partition sizes, and pie charts in nodes indicate the euchromatin/heterochromatin composition of corresponding partitions obtained from the Giemsa staining (with red denoting the centromere). The color gradient (25, 50, 75, and 100%) corresponds to heterochromatic bands with corresponding degrees of compactness. The width of edges indicates the effective interaction strength, which is obtained from the effective interaction matrices at each level of hierarchy (D-F). Partitions are labelled at each level to reflect the strict hierarchy: partition 1 contains sub-partitions 1.1 and 1.2, partition 1.2 contains sub-partitions 1.2.1, 1.2.2, 1.2.3, and 1.2.4, and so on. Weak interaction edges are omitted for clarity (see Materials and Methods for details). (G) Band representation of partitioning at the three levels of hierarchy (). Partition boundaries observed at the lowest level persist in higher levels of hierarchy, indicating the presence of a strict hierarchy in the chromosome structural organization. To guide the eye on how the different types of chromatin packing are distributed across partitions, Giemsa staining bands are also shown on top of the partition diagrams for all levels of hierarchy.
Fig 4.
Distribution of epigenetic factors in partitions of chromosome 17 at the third level of structural hierarchy.
Partitions are represented as pie-charted nodes depicting the presence of eu- and heterochromatin (on the basis of Giemsa-staining) within the partition. The node sizes are set according to the partition size or Z-scored density of the factor in the corresponding partitions (see scales in corresponding panels). Edge widths correspond to effective interaction strengths, while node sizes in each panel represent the (A) partition size, and factors’ Z scores for (B) CTCF, (C) H3K9ac, and (D) DNase-Seq epigenetic factors. Visual legends show how the values corresponding to each partition scale with the node size.
Fig 5.
Matrix of whole-genome effective interactions between 539 partitions.
Effective interactions between partitions, calculated according to Eq 12 (see Materials and Methods) and plotted on a logarithmic color scale. Massive interactions are formed by chromosomes 14–20, 22, and 1 (clusters of dark pixels), whereas chromosomes 4, 5, 9, 21, and X are not involved in many interactions (lighter pixels). To construct a representation of inter-chromosomal interactions via partitions of comparable sizes, we used partitions of the third level of hierarchy in chromosomes 1–12 and X, second level in chromosomes 13–21, and first level in chromosome 22.
Fig 6.
The major cluster in whole-genome partition interactions.
The nodes represent (A) partition sizes and (B) CTCF Z-scores. Tight sub-clusters of partitions show chromosomal territories, which are differentiated by the node colors characteristic for different chromosomes. Black edges between nodes represent scaffold-layer interactions, and grey edges, layer 1 interactions (see also S4 Fig and corresponding explanations on the classification of effective interaction strengths in “Data sets, processing, and visualization” of the Materials and Methods). The chromosomes that are not shown here form only single-chromosome clusters that do not strongly interact with chromosomes of the major cluster.
Fig 7.
Matrix of the whole-genome affinity between 539 partitions.
A color gradient from white to blue is used to show the affinity change from low to high.
Fig 8.
High-affinity clusters enriched in various histone modifications.
Node sizes represent the factor Z scores, and edge widths represent affinity values. The following histone modifications are considered; (A) H3K9ac, (B) H3K9me3, (C) H3K27ac, (D) H3K27me3, (E) H3K4me1, and (F) H3K4me3. In each case, only partitions with factor Z-scores above 2 and only edges connecting partition pairs with high affinity C > 2 are shown.