Two-window deconvolution: at a typical shared promoter only 1.8% of the signal can be proved to belong to the gene it is filed under, and at IRX2's one near-positive it is 19.7%
also called shared window deconvolution · attributable fraction promoter
When two overlapping windows both report a number, the difference between them can only come from the small stretches they do not share. That difference sets a floor on how much of a gene's signal is genuinely its own. Across this dataset the floor is usually under 2%, meaning almost all of a shared-window measurement is unattributable arithmetic.
The same thing, for a scientist
The two windows at this locus differ only in two 215 bp flanks, so with no modelling at all: `(mean_IRX2 − mean_IRX2DT) × 2000 = sum(flank_IRX2) − sum(flank_IRX2DT)`, and because the second term is non-negative, **the IRX2-only flank contributes at least `Δ/mean_IRX2` of IRX2's window signal**. This is a hard lower bound on the attributable fraction and it is the only attribution this data structure permits without base-resolution coverage [E1]. Applied to the one GSE252378 sample where the locus carries appreciable signal, **p454 KMT2A-N1: IRX2 3.8119, IRX2-DT 3.0629, Δ 0.7490, so ≥19.7% of IRX2's window signal comes from sequence IRX2-DT's window does not contain** [E1]. Applied as a general statistic over every ≥50%-sharing pair in the table, in every KMT2A-N library where the larger member reaches a share of 2.0, **the median attributable fraction is 0.018 and it is below 0.10 in 82.1% of 25,880 pair × library cases** [E1]. **So in four out of five occupied shared-promoter calls, over 90% of the signal is arithmetically unattributable**, and p454's IRX2 at 0.197 sits at the **91.6th percentile** — this locus is an unusually GOOD case and is still four-fifths unattributable [E1]. The twist worth reading twice: **the 215 bp that is IRX2's alone is `chr5:2,750,677-2,750,892`, which is 785–1,000 bp INTO IRX2's gene body on the minus strand — not its promoter.** The only part of the measurement that can be attributed to IRX2 is not promoter sequence at all [E2].
The arithmetic, in full, because it is the whole method
IRX2 window chr5:2,750,677 - 2,752,677 (2,000 bp)
IRX2-DT window chr5:2,750,892 - 2,752,892 (2,000 bp)
shared chr5:2,750,892 - 2,752,677 (1,785 bp)
flank A, IRX2 only chr5:2,750,677 - 2,750,892 (215 bp)
flank B, IRX2-DT only chr5:2,752,677 - 2,752,892 (215 bp)
mean_IRX2 * 2000 = sum(shared) + sum(A)
mean_IRX2DT * 2000 = sum(shared) + sum(B)
---------------------------------------------
(mean_IRX2 - mean_IRX2DT) * 2000 = sum(A) - sum(B)
Two equations, three unknowns. The shared term cannot be recovered, which is precisely the attribution failure. What can be recovered is the difference of the two flanks, and since sum(B) >= 0, a positive difference is a lower bound on sum(A).
The quantity reported is max(0, Δ) / mean_IRX2 — the fraction of the window's own mean that is provably not shared. It is conservative in two ways: it ignores any signal in flank B (which would raise sum(A)), and it says nothing about the shared 1,785 bp, which may or may not be IRX2's.
Every GSE252378 sample with any signal at this locus
KMT2A-N1 arm, within-sample shares:
| sample | fusion | IRX2 | IRX2-DT | Δ | flank-sum difference | ≥ this fraction is IRX2-only |
|---|---|---|---|---|---|---|
p454 | AFF1 | 3.8119 | 3.0629 | +0.7490 | 1,498 | 0.197 |
TB051939 | AFF1 | 0.6195 | 0.0168 | +0.6027 | 1,205 | 0.973 |
148752 | ENL | 0.2663 | 0.2251 | +0.0413 | 83 | 0.155 |
152985 | ENL | 0.9845 | 1.0403 | −0.0557 | −111 | 0 (IRX2-DT side) |
p186 | ENL | 0.2328 | 0.2433 | −0.0105 | −21 | 0 (IRX2-DT side) |
R3595 | EPS15 | 0.0252 | 0.0358 | −0.0106 | −21 | 0 (IRX2-DT side) |
A89691, A93949, R3652, p279 | — | equal | equal | 0 | 0 | 0 |
TB051939 is the striking row: 97.3% of a small IRX2 window signal is in the 215 bp flank, i.e. essentially all of it sits in IRX2's first intron and none of it near either TSS. p454, the near-positive that q151 reported honestly, is 19.7%. Neither reaches the occupancy gate, so this changes no call — it changes what a call would have meant.
Three samples put the excess on the IRX2-DT side. With n = 10 informative libraries and no direction pre-specified, the sign is not a finding.
The null, and why 0.018 is the number that travels
Over all 1,563 ≥50%-sharing pairs, in every KMT2A-N library where the larger member reaches a share of 2.0 (n = 25,880 pair × library):
| statistic | value |
|---|---|
| median attributable fraction | 0.018 |
| interquartile range | 0.000 – 0.068 |
| below 0.10 | 82.1% |
| p454 IRX2's 0.197 | 91.6th percentile |
A median of 1.8% is the headline. For a typical occupied shared-promoter window in this deposit, 98% of the signal is in sequence two genes own jointly. That is not a threshold artefact and not a property of any particular locus — it is what a 2 kb mean does to a 200 bp offset.
| script | analyses/q153-can-an-irx2-promoter-measurement-be-attributed/q153_deconv.py |
|---|---|
| status | run |
| result summary | Exact two-window arithmetic gives a hard lower bound on the attributable fraction. Median 0.018 over 25,880 shared-pair cases; p454 IRX2 0.197 at the 91.6th percentile; the attributable 215 bp is gene body, not promoter. |
| identity | (mean_a - mean_b) * 2000 = sum(flank_a) - sum(flank_b); sum(flank_b) >= 0 so the bound is one-sided and conservative |
measurements — the numbers behind the chart
[
{
"quantity": "min_attributable_fraction",
"subject": "IRX2's 2 kb window signal in p454 KMT2A-N1, fraction provably from sequence IRX2-DT's window does not contain",
"value": 0.197,
"units": "fraction of the window mean",
"n": 1,
"universe": "p454 KMT2A-N1 of GSE252378; IRX2 share 3.8119, IRX2-DT share 3.0629; 215 bp unique flank each side of a 1,785 bp shared core",
"null": 0.018,
"note": "null is the median over 25,880 pair x library cases at >=50%-sharing pairs; 91.6th percentile, so this locus is an unusually GOOD case and is still four-fifths unattributable"
},
{
"quantity": "min_attributable_fraction",
"subject": "median across all >=50%-sharing promoter pairs in libraries where the larger window reaches a share of 2.0",
"value": 0.018,
"units": "fraction of the larger window's mean",
"n": 25880,
"universe": "1,563 pairs x up to 54 KMT2A-N libraries, restricted to cases where max(share) >= 2.0",
"null": null,
"note": "IQR 0.000-0.068; below 0.10 in 82.1% of cases. In four of five occupied shared-promoter calls, over 90% of the signal is arithmetically unattributable"
},
{
"quantity": "min_attributable_fraction",
"subject": "IRX2's window signal in TB051939 KMT2A-N1",
"value": 0.973,
"units": "fraction of the window mean",
"n": 1,
"universe": "TB051939 KMT2A-N1; IRX2 share 0.6195, IRX2-DT share 0.0168",
"null": 0.018,
"note": "almost all of a SMALL signal sits in the 215 bp IRX2-only flank, i.e. in IRX2's first intron, not at either TSS. Well below the 2.0 occupancy gate, so it changes no call"
}
]- The bound is one-sided, so it can only ever say a signal IS partly attributable, never that it is not. An intervention programme cannot use it to clear a target - a 0.018 median means 'we could not prove attribution', which is exactly the state in which a wrong gene gets nominated and nothing in the analysis objects.
- Can the shared term be recovered with a third window? A window centred between the two TSSs, or a set of tiled 200 bp windows across chr5:2,750,677-2,752,892, would turn two equations into many and could localise the summit - and it needs the bigWig, which this beat was instructed not to download.
- Is the flank excess at TB051939 and p454 a real intronic feature or coverage noise at a window edge? A 215 bp mean from a single library has no error bar here, and none was computed.
- Does the median attributable fraction of 0.018 depend on the 2.0 share cutoff used to define 'occupied enough to attribute'? The statistic was computed at one cutoff and its sensitivity was not tested.
at least 19.7% of IRX2's p454 window signal is from IRX2-only sequence - and that sequence is gene body, not promoter
the caveat on the p454 near-positive is the deconvolution bound: at best one fifth attributable
the gene-body interval separates IRX2 from IRX2-DT, so the attribution question q153 posed is answerable at this scale