Schematic depiction of the method. Our method relies on the 4C procedure by using cross-linking, two rounds of alternating restriction enzyme (RE) digestion (6 bp-cutter RE1 for the 3C-step digestion and 4 bp-cutter RE2 for the 4C-step digestion) and intra-molecular ligation. At step 7, each circle contains the 6 bp restriction enzyme recognition site originally used to link the two interacting partner sequences (RE1). Diverging from 4C, we re-linearize the circles using RE1, then sequentially insert two sets of adaptors, one of which permits digestion with a type IIS or type III restriction enzyme (such as Ecop15I). Following Ecop15I digestion, fragments are produced that incorporate interacting partner sequence at either end, which can be rendered suitable for deep sequencing (see ).

Validation of the assay. a, Graph showing an inverse relationship between interaction frequency and genomic distance (20kb or larger, excluding self-ligations and adjacent ligations) separating interacting restriction fragments (either HindIII or EcoRI) in each of four experimental but none of five control libraries. Note, the five lines representing the five control libraries are very close to each other. b, The fraction of instances that each HindIII site along chromosome I was engaged in an intra-chromosomal interaction was highly correlated between two independently derived experimental H-Mp (HindIII-MspI) libraries (designated A and B, left panel) but was not correlated between experimental and non-cross linked control H-Mp libraries (right panel). c, Two-dimensional heat maps demonstrating broad reproducibility of interaction patterns within chromosome I for two independently derived H-Mp libraries. The chromosomal positions of mappable (green hatches) and un-mappable (black hatches) HindIII fragments are indicated. The binary interaction matrix of all interactions with an FDR threshold of 1% has been smoothed with a Gaussian of width 3 kb. d. High degree of correlation between absolute interaction frequencies as determined by our method (symbols) versus relative interaction frequencies as determined by conventional 3C using cross-linked (dark bars) and uncross-linked (light bars) libraries. Results for 10 potential long-range intra-chromosomal interactions are depicted, of which 6 passed (circles) and 4 did not pass (triangles) an FDR threshold of 1%. Error bars denote standard deviations over three experiments. Interaction sites are as follows. A: Chr III position 11811; B: Chr III position 290056; C: Chr III position 15939; D: Chr III position 314440; E: Chr I position 26147; F: Chr I position 191604; G: Chr I position 204567; H: Chr VI position 12007; I: Chr VI position 243206; J: Chr VI position 249743; K: Chr II position 238203; L: Chr II position 502988; M: Chr II position 512024; N: Chr IV position 236977; O: Chr IV position 447899; P, Chr IV position 239805; Q, Chr IV position 461284.

Folding patterns of chromosomes III (a, b) and XII (c, d). The heat maps (a, c) and Circos diagrams (b, d) were generated using the intra-chromosomal interactions identified from the HindIII libraries at an FDR threshold of 1%. In the heat maps (a, c), the chromosomal positions of centromeres (dashed pink lines), telomeres (pink hatches), mappable (green hatches) and un-mappable (black hatches) HindIII fragments are indicated. Circos diagrams (b, d) depict each chromosome as a circle. Each arc connects two HindIII fragments and represents a distinct interaction. The shade of each arc, from very light grey to black, is proportional to the negative log of the p-value of the interaction. The chromosomal positions of centromeres (red hexagon), telomeres (red colored area), tRNA genes (blue outer thatches), mappable (green inner hatches) and un-mappable (black inner hatches) HindIII fragments are indicated. Black outer hatches and numbers mark genomic positions. Note that the two ends of chromosome XII (c, d) exhibit extensive local interactions but very little interaction with each other. Separating the ends of chromosome XII are 100–200 rDNA repeats, of which only two copies are depicted here (from coordinates 450 to 470 kb). Additional heat maps and Circos diagrams for all chromosomes are shown in .

Inter-chromosomal interactions. a, Circos diagram showing interactions between chromosome I and the remaining chromosomes. All 16 yeast chromosomes are aligned circumferentially, and arcs depict distinct inter-chromosomal interactions. Bold red hatch marks correspond to centromeres. To aid visualization of centromere clustering, these representations were created using the overlap set of intra-chromosomal interactions identified from both HindIII and EcoRI libraries at an FDR threshold of 1%. Additional heat maps and Circos diagrams are provided in . b, Circos diagram, generated using the intra-chromosomal interactions identified from the HindIII libraries at an FDR threshold of 1%, depicting the distinct interactions between a small and a large chromosome (I and XIV, respectively). Most of the interactions between these two chromosomes primarily involve the entirety of chromosome I, and a distinct region of corresponding size on chromosome XIV. c, Inter-chromosomal interactions between all pairs of the 32 yeast chromosomal arms (the 10 kb region starting from the midpoint of the centromere in each arm is excluded). For each chromosome, the shorter arm is always placed before the longer arm. Note that the arms of small chromosomes tend to interact with one another. The color scale corresponds to the natural log of the ratio of the observed versus expected number of interactions (see ). d, Enrichment of interactions between centromeres, telomeres, tRNA genes, early origins of replication, and chromosomal breakpoints. To measure enrichment of strong interactions with respect to a given class of genomic loci, we use receiver operating curve (ROC) analysis.

Three-dimensional model of the yeast genome. Two views representing two different angles are provided. Chromosomes are colored as in (also indicated in the upper right). All chromosomes cluster via centromeres at one pole of the nucleus (the area within the dashed oval), while chromosome XII extends outward toward the nucleolus, which is occupied by rDNA repeats (indicated by the white arrow). After exiting the nucleolus, the remainder of chromosome XII interacts with the long arm of chromosome IV.