Figure 2. Hierarchical clustering and the detailed structural analysis of traced Segment 1.

(A) The dendrogram representation of the hierarchical clustering of Segment 1 (chr21 29.37–31.32 Mb for IMR90 and K562 of Bintu et al., 2018), where $1-Q$ is used as the distance between two structures. The clustering reveals three main clusters: closed dumbbell, open dumbbell, and highly dense structures. Further analysis of Cluster 1 reveals the presence of sub-clusters labeled 1a–1d that represent the gradual opening of the closed dumbbell. Representative traced structures are shown for each of the clusters and sub-clusters. The population-averaged contact maps for the closed and open structure clusters are shown respectively in (B) and (C), where 330 nm is used to define a contact between two 30 kb loci. (D) The distribution of the radius of gyration (top), the corresponding potential of mean force (center), and the distributions of radius of gyration for Cluster 1 and Cluster 2 (bottom) are shown for the traced structures of Segment 1 of IMR90 and K562. The distribution exhibits a heavy tail to the right of the average value, indicating the existence of open, elongated structures. (E) The UCSC Genes track is plotted along the genomic positions of Segment 1 using the Genome Browser (Kent et al., 2002). Figure 2—figure supplement 1 shows the contact maps for the experimentally traced segments of chromatin. Figure 2—figure supplement 2 shows the distributions of the radius of gyration for the sub-clusters of closed dumbbell structures obtained experimentally using tracing. Figure 2—figure supplement 3 shows the hierarchical clustering and detailed structural analysis of the experimentally traced Segment 2.

Figure 2—figure supplement 1. Contact maps for the experimentally traced segments of chromatin.

The contact maps for the chromatin structures obtained from super-resolution imaging (Bintu et al., 2018) for (A) IMR90 Segment 1 (chr 21 29.37–31.32 Mb), (B) IMR90 Segment 2 (chr 21 20.0–21.9 Mb), and (C) K562 Segment 1 (chr 21 29.37–31.32 Mb) are shown. For a given chromatin structure, two loci i and j are spatially proximal when the cartesian distance between them, $r_{ij}$, is less than or equal to a cutoff distance d—we define a contact using $d=0.248\mu m$. This allows us to define a label $c_{ij}$ for a pair of loci that equals one when loci i and j are in contact and 0 when they are not: $c_{ij}=\{\begin{array}{c}1\text{ if }{r}_{ij}\le d\\ 0\text{ if }{r}_{ij}>d\end{array}$. The variance of the contact frequency over the mean contact frequency (Fano Factor) $F=\left(1-⟨c_{ij}⟩\right)$ is plotted for each of the respective chromatin segments in (D), (E), and (F), where the angular brackets denote averaging over the structural ensemble. A Fano factor of $F=0$ indicates zero variability, $0<F<1$ indicates that the process is under-dispersed and characterized by a binomial distribution, and $F=1$ is characteristic of a Poisson process. Segment 1 for IMR90 and K562 both have globular domains at the head and tail of the chromatin segment. On the other hand, Segment 2 has no loop domains and the only observable feature in its contact map is the decay of the contact probability as a function of genomic distance.

Figure 2—figure supplement 2. Distribution of radius of gyration for sub-clusters of closed dumbbell structures obtained experimentally using tracing.

Sub-clusters of Cluster one in Figure 2 are denoted as 1a, 1b, 1 c, and 1d. The sub-clusters of Cluster one characterize the gradual opening of the closed dumbbell structures.

Figure 2—figure supplement 3. Hierarchical Clustering and the detailed structural analysis of traced Segment 2.

(A) The dendrogram representation of the hierarchical clustering of Segment 2 (chr 21 20.0–21.9 Mb for IMR90 of Bintu et al., 2018), where $1-Q$ is used as the distance between two structures. The dendrogram highlights 10 clusters—representative structures are shown for each of the featured clusters. Cluster 1 bears a close relation to the closed dumbbell structures observed for Segment 1 (Figure 2). Cluster 8 captures the highly dense chromatin structures that are attributed to experimental artifact; analogous to Cluster three in Figure 2. The additional clusters capture the gradual opening of Segment 2. However, a striking difference from the structures of Segment 1 occurs due to the lack of loop domains in Segment 2; as a result, the globular domains at the head and tail of the segment observed for Segment 1 do not exist. The lack of loop domains and domain boundaries leads to disordered structures that deviate from the open dumbbell structures observed for Segment 1. (B) The distribution of the radius of gyration (top) and the corresponding potential of mean force (bottom) are shown for the traced structures of Segment 1 and Segment 2 of IMR90. Both distributions exhibit a heavy tail to the right of the average value, indicating the existence of open, elongated structures.

Figure 2—figure supplement 4. The positioning of genes along traced Segment 1 and Segment 2.

The UCSC Genome Browser (Kent et al., 2002) is used to plot the UCSC Gene Track for (A) traced Segment 1 and (B) traced Segment 2. The positioning of the genes along Segment 1 appears primarily in the linker region sandwiched between the globular domains that are at the head and tail of the chromatin segment. Segment 2, which has no loop domains, also coincidentally has an apparent absence of genes.