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Analysis of high-resolution 3D intrachromosomal interactions aided by Bayesian network modeling

  1. Arthur D. Riggsa,1
  1. aDepartment of Diabetes Complications and Metabolism, Diabetes and Metabolism Research Institute, City of Hope, Duarte, CA
  1. Contributed by Arthur D. Riggs, October 2, 2017 (sent for review December 16, 2016; reviewed by Peter N. Cockerill and Leonid A. Mirny)

  1. Fig. 2.

    TSS activity affects interaction strength. (A) Heatmap showing that TSS activity within the two interacting anchors is positively associated with interaction strength. The color gradient represents the average interaction strength. Tss level is in units of rpkm. (B) Interaction strength affects the chance to observe Tss–Tss interactions. y axis represents the relative chance of observing the TSS activity (<mml:math><mml:mrow><mml:mo>></mml:mo><mml:mrow><mml:mpadded width="+3.3pt"><mml:mn>5</mml:mn></mml:mpadded><mml:mtext>rpkm</mml:mtext></mml:mrow></mml:mrow></mml:math>>5rpkm) at one anchor given the corresponding interaction strength (x axis) and Tss (<mml:math><mml:mrow><mml:mo>></mml:mo><mml:mrow><mml:mpadded width="+1.7pt"><mml:mn>5</mml:mn></mml:mpadded><mml:mtext>rpkm</mml:mtext></mml:mrow></mml:mrow></mml:math>>5rpkm) in the other anchor. (C) Interaction strength between two anchors with at least one occupied by a TF decreases if no TSS activity is associated with these anchors. W/O_Tss: without Tss. W_Tss: with Tss. P values were calculated by a Kolmogorov–Smirnov test. The “random” sample had a similar “distance” distribution to the target sample but was sampled randomly from the whole population.

  2. Fig. 3.

    MNs of Ebf1 variable node, separated into left and right anchors. (A) Extended MN of the Ebf1 left variable in the BN derived from the chr1 unrestricted dataset. (B) Same as in A, for Ebf1 right. (C) Visualization of a trivariate interaction between Ebf1, Rad21, and Znf143 variables, left anchor. (D) Same as in C, right anchor. See Fig. 1B and SI Appendix, section 5, Tables S1 and S2 for general BN designations and principal variable descriptions. Note that dependency strength is shown as a number (proportional to the likelihood ratio, see text for details) next to the corresponding edge in the network. Only edges above 40,000 in strength are shown in Fig. 3 C and D for easier network readability.

  3. Fig. 4.

    Orientation of convergent CTCF–cohesin complexes affects interaction strength. F: The CTCF–cohesion complex is in the forward orientation. R: The CTCF–cohesin complex is in the R orientation. (A) Convergent CTCF–cohesin pairs (F_R) interact more strongly compared with the other orientations. In_loop: The two anchors (containing CTCF–cohesin complexes) of an interaction are in the same loop. Crs_loop: The two anchors cross the loop boundaries. (B) Genome-wide, convergent CTCF–cohesin complex pairs that are within loops (8) are more frequent than the other orientation combinations. Overall, if Hi-C loops are not selected, the four categories of ctcf pairs occur in about equal numbers: F–R, 23,836, 24%; R–F, 25,935, 26%; F–F, 24,709, 25%; R–R, 24,283, 25%.

  4. Fig. 5.

    CTCF–cohesin complexes affect the distribution and direction of high-intensity intrachromosomal interactions. (A)The probability profile for 5-kb segments neighboring CTCF–cohesin complexes containing the anchors of high-intensity interactions. The y axis has the same meaning in A–C. (B) The probability profile for 5-kb segments neighboring the CTCF–cohesin complexes with F motifs containing the left or right anchors of a high-intensity interaction. (C)The probability profile for 5-kb segments neighboring the CTCF–cohesin complexes with R motifs containing the left or right anchors of a high-intensity interaction. (D) The formation of an asymmetrical distribution in B can be explained by a DNA-reeling/extrusion model. In this model, reeling and loop formation initiated downstream will be terminated by an F CTCF–cohesin complex.

  5. Fig. 6.

    CTCF–cohesin complexes affect EP interactions. (A) The genome-wide occurrence of upstream enhancers (En left) and downstream enhancers (En right) within the 5-kb segments neighboring CTCF–cohesin complexes with F motifs. (B) The Same as in A but with the R CTCF–cohesin complex. Note that upstream and downstream follow the standard chromosomal base-numbering convention relative to the interacting promoters, not related to the transcription direction. A similar finding is obtained by targeting the high-intensity interactions crossing loop boundaries (SI Appendix, section 3 and Fig. S3 A–C).

  6. Fig. 7.

    Convergent CTCF–cohesin complex pairs affect interaction strength via a “reduced distance” (RD) effect. (A) An example to show the principle of RD. The genomic anchors i and j are separated by a pair of CTCF–cohesin complexes with convergent direction. If the loop is formed between a and b, the distance between i and j changes from d to d1 + d2. (The calculation of the RD is shown in detail in SI Appendix, section 4). (B) The interactions that are affected by the RD have higher interaction strength than average.

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