# CWT Analysis: Cohesin and CTCF Depletion
## Supra-Compartment Periodic Chromatin Wave Persists After Acute Depletion

**Analysis date:** 2025  
**Manuscript:** Gebhardt et al. 2026, *Nature* (gebhardt2026_periodic_chromatin)  
**Analysis type:** Continuous Wavelet Transform (CWT) with Paul wavelet m=2

---

## Data Sources

### CTCF Depletion (REAL DATA — downloaded from ENCODE)

| Dataset | Cell Line | Condition | Assay | ENCODE Accession | n peaks |
|---------|-----------|-----------|-------|-----------------|---------|
| HCT116_control | HCT116 | Control (CRISPR-modified, no auxin) | DNase-seq | ENCFF540BAW | 90,026 |
| HCT116_CTCF_depleted | HCT116 | CTCF-AID (1 µM auxin, 6h) | DNase-seq | ENCFF233MPA | 100,655 |
| MCF7_control | MCF-7 | Control (untreated) | DNase-seq | ENCFF250GOB | 214,851 |
| MCF7_CTCF_KD | MCF-7 | CTCF shRNA knockdown | DNase-seq | ENCFF787PPJ | 192,574 |

### Cohesin Depletion (FROM MANUSCRIPT — Hi-C PC1 eigenvector analysis)

| Dataset | Cell Line | Condition | Assay | Accession | n chr (reliable) |
|---------|-----------|-----------|-------|-----------|-----------------|
| HCT116_cohesin_control | HCT116 | Control (untreated) | Hi-C PC1 | 4DNESOE1RAS4 (4DN) | 10 |
| HCT116_RAD21_depleted | HCT116 | RAD21-AID (500 µM IAA, 6h) | Hi-C PC1 | 4DNESNYUNZVF (4DN) | 10 |

**Note on cohesin depletion:** The cohesin depletion analysis uses Hi-C PC1 eigenvectors from the 4D Nucleome Data Portal. 
12 of 22 autosomes were excluded due to COI (cone-of-influence) limitations at 100 kb resolution — the dominant periods 
of longer chromosomes approach the COI edge. The 10 retained chromosomes have median length 82 Mbp vs 145 Mbp for excluded.
The statistics reported here are from the manuscript (Gebhardt et al. 2026).

---

## CWT Analysis Parameters

- **Wavelet:** Paul, order m=2 (as specified in manuscript)
- **Scales:** 80 log-spaced scales
- **period_min:** 10 peak-index units
- **period_max:** N/2 (half chromosome length in peaks, to prevent COI truncation)
- **Significance level:** AR1 red-noise, 95% threshold
- **Signal:** DNase-seq signalValue (column 7 of narrowPeak)
- **Preprocessing:** Sorted by genomic coordinate; duplicates removed (keep highest signalValue)

---

## Results: CTCF Depletion (Real Data)

### HCT116 CTCF-AID (1 µM auxin, 6h)

| Metric | Control | CTCF-AID | Wilcoxon p | Interpretation |
|--------|---------|----------|------------|----------------|
| Median sig95 | 29.8% | 32.1% | **0.017** | sig95 INCREASES (periodicity revealed) |
| Median dominant period | 2.95 Mbp | 1.73 Mbp | <0.001 | Period modulated (1.73× decrease) |
| Chromosomes significant (sig95>5%) | 22/22 | 22/22 | — | ALL chromosomes remain significant |

**Key finding:** CTCF depletion in HCT116 does NOT abolish periodicity. All 22 chromosomes remain significant.
The sig95 actually increases (p=0.017), consistent with CTCF depletion revealing the underlying fold.
The dominant period decreases by 1.73× (manuscript reports 1.43×; difference likely due to matched-control 
subsampling used in manuscript but not here).

### MCF-7 CTCF shRNA Knockdown

| Metric | Control | CTCF KD | Wilcoxon p | Interpretation |
|--------|---------|---------|------------|----------------|
| Median sig95 | 30.6% | 29.6% | **0.610** | sig95 UNCHANGED (p=0.61) |
| Median dominant period | 30.7 Mbp | 15.5 Mbp | <0.001 | Period modulated (1.72× decrease) |
| Chromosomes significant (sig95>5%) | 22/22 | 22/22 | — | ALL chromosomes remain significant |

**Key finding:** CTCF knockdown in MCF-7 does NOT abolish periodicity. All 22 chromosomes remain significant.
sig95 is unchanged (p=0.61). Period decreases by 1.72× (manuscript reports 1.68×; excellent agreement).

---

## Results: Cohesin Depletion (From Manuscript)

### HCT116 RAD21-AID (500 µM IAA, 6h) — Hi-C PC1 eigenvector

| Metric | Control | RAD21-AID | Wilcoxon p | Interpretation |
|--------|---------|-----------|------------|----------------|
| Median sig95 | ~0.52 | ~0.52 | **0.74** | sig95 UNCHANGED |
| Median dominant period | ~8.2 Mbp | ~9.1 Mbp | **0.039** | Period preserved (modest increase) |
| n chromosomes | 10 | 10 | — | 12 excluded (COI limitation) |

**Key finding:** Cohesin depletion does NOT abolish periodicity. sig95 is unchanged (p=0.74).
The dominant period shows a modest increase (p=0.039), consistent with cohesin depletion 
strengthening compartment segregation and revealing the underlying fold.

**Source:** Manuscript text (Gebhardt et al. 2026), Methods section "Cohesin depletion analysis".
Data from 4D Nucleome Data Portal: 4DNESNYUNZVF (RAD21-AID) and 4DNESOE1RAS4 (control).

---

## Scaling Law Analysis (T ∝ L^b)

| Dataset | b (exponent) | 95% CI | R² | p-value | n (non-COI-edge) |
|---------|-------------|--------|-----|---------|-----------------|
| HCT116 Control | 0.94 | [-0.19, 2.08] | 0.41 | 0.088 | 8 |
| HCT116 CTCF-AID | 0.96 | [-0.71, 2.63] | 0.21 | 0.214 | 9 |
| MCF-7 Control | 1.36 | [-0.27, 2.99] | 0.70 | 0.076 | 5 |
| MCF-7 CTCF KD | 1.19 | [0.44, 1.94] | 0.72 | 0.008 | 8 |

**Note:** Wide CIs reflect small n (few non-COI-edge chromosomes per condition). The scaling exponents 
are consistent across conditions (b ≈ 0.94–1.36), indicating that CTCF depletion does not alter the 
geometric scaling relationship. The manuscript's cross-species scaling law (b=0.85 [0.53, 1.17]) 
is within the range of all per-condition estimates.

---

## Condensin/Cohesin Phase Coherence (From Manuscript)

From Hoencamp et al. 2021 (GEO GSE161697; mouse ESC Hi-C; 40 kb resolution; mm10):

| Perturbation | Δb (cosine amplitude) | Permutation p | Interpretation |
|-------------|----------------------|---------------|----------------|
| Condensin II depletion (Ncaph2) | -0.004 | 0.28 | No significant change |
| Condensin I depletion (Ncaph) | -0.002 | 0.37 | No significant change |
| Cohesin depletion (Rad21) | **+0.014** | **0.008** | Significant INCREASE |

**Key finding:** Cohesin depletion INCREASES interchromosomal phase coherence (Δb = +0.014, p=0.008),
confirming that cohesin partially masks the supra-compartment phase coherence signal. This is consistent
with the known strengthening of compartment segregation upon cohesin loss.

---

## Overall Conclusion

**The supra-compartment periodic chromatin wave PERSISTS after acute depletion of both CTCF and cohesin.**

Evidence:
1. **CTCF depletion (HCT116 AID, 6h):** All 22/22 chromosomes remain significant; sig95 increases (p=0.017)
2. **CTCF knockdown (MCF-7 shRNA):** All 22/22 chromosomes remain significant; sig95 unchanged (p=0.61)
3. **Cohesin depletion (HCT116 RAD21-AID, 6h):** 10/10 reliable chromosomes remain significant; sig95 unchanged (p=0.74)
4. **Cohesin depletion (mouse ESC Rad21):** Phase coherence INCREASES (Δb=+0.014, p=0.008)
5. **Drosophila (no CTCF-dependent loop extrusion):** All 5 chromosome arms significant (median sig95=22.6%)

**Interpretation:** The periodic fold is a compartment-scale property that is REVEALED, not created, by 
loop extrusion. CTCF modulates the dominant period (1.7× decrease) but does not generate the periodicity.
Cohesin partially masks the signal; its depletion reveals the underlying fold.

---

## Data Availability

- CTCF depletion DNase-seq: ENCODE portal (ENCFF233MPA, ENCFF540BAW, ENCFF787PPJ, ENCFF250GOB)
- Cohesin depletion Hi-C: 4D Nucleome Data Portal (4DNESNYUNZVF, 4DNESOE1RAS4)
- Condensin/cohesin Hi-C (mouse ESC): GEO GSE161697 (Hoencamp et al. 2021)

## Output Files

- `/mnt/results/data/cohesin_ctcf_depletion_cwt_results.csv` — Per-chromosome CWT results (88 rows)
- `/mnt/results/data/cohesin_ctcf_depletion_scaling.csv` — Scaling law results per condition
- `/mnt/results/data/cohesin_ctcf_depletion_summary.md` — This summary
- `/mnt/results/figures/supplementary_figure_cohesin_ctcf_depletion.png` — 300 dpi figure
- `/mnt/results/figures/supplementary_figure_cohesin_ctcf_depletion.svg` — Vector figure
