Fractional occupancy needs a free concentration as well as a Kd, and nobody has measured either for a KMT2A fusion
also called occupancy arithmetic · theta = C/(C+Kd)
You cannot say how much of the time the fusion is sitting on a CpG site from a binding constant alone - you also need to know how much fusion protein is floating free in the nucleus, and nobody has measured that. The published binding constants alone already change the answer ten-thousand-fold.
The same thing, for a scientist
An existing open question in this graph asks what fraction of fusion occupancy at a CpG island is CXXC-driven, given a 44 uM affinity. The question is unanswerable as posed. Fractional occupancy theta = C/(C+Kd) requires the free nuclear concentration C of the fusion, which has never been measured for any KMT2A fusion protein, and Kd itself spans 44 uM to 33 nM across nine published measurements. The product of the two uncertainties is about seven orders of magnitude. What the arithmetic does establish is that the two endpoint values imply qualitatively different mechanisms - at any C below roughly 100 nM, a 44 uM contact gives negligible single-site occupancy while a 33 nM contact gives substantial occupancy - which is why the discrepancy mattered. Separately, equilibrium occupancy is probably the wrong observable for a scanning protein; residence time and inter-site transfer are what multivalency changes most, and neither has been measured for this contact.
The arithmetic, with both unknowns shown
Fractional occupancy of a single site by a single binder at equilibrium is theta = C / (C + Kd), where C is the free concentration of the binder. Both terms are unknown for this system, and the entry that asked this question phrased it as if only one were.
| Kd | C = 1 nM | C = 10 nM | C = 100 nM | C = 1 uM |
|---|---|---|---|---|
| 44 uM (row 1) | 0.002% | 0.02% | 0.2% | 2.2% |
| 3.5 uM (row 7) | 0.03% | 0.3% | 2.8% | 22% |
| 0.64 uM (row 8) | 0.2% | 1.5% | 14% | 61% |
| 33 nM (row 9) | 2.9% | 23% | 75% | 97% |
The table spans four orders of magnitude in the answer across the range of published Kd, and another three across any plausible range of C. No published measurement gives the free nuclear concentration of a KMT2A fusion protein in a leukaemia cell, and this project has no entry that does either.
Two corrections follow for how the question is posed.
interface-kmt2a-cxxc-cpg-dnaasks: "Given a 44 uM intrinsic affinity, what fraction of fusion occupancy at a CpG island is CXXC-driven?" That question has no answer, and not because the decomposition is hard - because both inputs are unmeasured and the Kd term alone moves the answer 1,300-fold. The question has been rewritten.- Equilibrium occupancy is probably the wrong quantity anyway. A fusion scanning chromatin is not at equilibrium with one site; what matters is residence time and the rate of transfer between sites, and those are what a multivalent tether changes most. A contact can contribute almost nothing to steady-state occupancy and a great deal to residence time, or the reverse. Nothing in this literature measures either for the CXXC contact. The measurable proxy that does exist is fluorescence recovery or single-molecule tracking of a C1188D fusion against wild type, which nobody has run.
What the arithmetic does establish, and it is worth keeping: at any free concentration below about 100 nM, a 44 uM contact gives essentially zero occupancy of any individual site, while a 33 nM contact gives substantial occupancy. The two published numbers do not merely differ in magnitude; they imply qualitatively different mechanisms, which is why the discrepancy was worth a beat and why leaving it unresolved was not an option.
One of the two unknowns has been partly measured, and it is the one nobody expected
This entry argued that residence time, not equilibrium occupancy, is the quantity a scanning protein's biology turns on, and that nothing in this literature measures it. That was almost right and is now qualified.
Liang et al. profiled the MLL1 CXXC domain on a 187-bp CpG island from the Hoxa9 gene, embedded in a 236-bp hairpin, by magnetic tweezers 3. The assay reports, along the island:
- the binding-probability and free-energy landscape at 1-bp resolution - i.e. which positions in a real CpG island the domain occupies and how strongly, which no bulk measurement can give;
- site-specific pausing times, from which the dissociation time of the domain along the island is derived;
- the rupture time of individual CXXC-CpG complexes, about 10 ms at a probing force of 12.5 pN.
What this is not. The 10 ms is a force-assisted rupture time under 12.5 pN of applied tension, not a spontaneous residence time at zero force, and it is on naked DNA with no nucleosome, no fusion protein and no competing factors. It cannot be substituted into an occupancy calculation.
What it is. The first measurement of this contact on a real CpG island rather than a designed oligonucleotide, and the first that reports dynamics at all. It also supplies the direct test of the one-dimensional-diffusion idea Cierpicki floated: the paper's own framing is that the CpG pattern in an island governs spatially dependent collaboration among CpGs, which is a positional-cooperativity model rather than free sliding, and is consistent with Erfurth's steric-exclusion stoichiometry 2.
The free nuclear concentration of the fusion remains completely unmeasured, so the occupancy table above stands unchanged as a statement of what cannot be computed.
| script | none - elementary equilibrium algebra on published constants, shown in full so it can be re-derived |
|---|---|
| status | run |
| formula | theta = C / (C + Kd) |
| result summary | Occupancy is underdetermined by roughly seven orders of magnitude - 1,300-fold from the Kd span and three to four more from the unknown free concentration. The one robust statement is that 44 uM and 33 nM imply qualitatively different mechanisms at any plausible nuclear concentration, so the discrepancy could not be left unresolved. |
| corrects | the open question in interface-kmt2a-cxxc-cpg-dna asking what fraction of fusion occupancy at a CpG island is CXXC-driven given a 44 uM intrinsic affinity |
| shown for fusion | NO - nobody has looked in any fusion. No free nuclear concentration, residence time or bound fraction has been measured for any KMT2A fusion protein. |
inputs
[ "the nine Kd values in ana-cxxc-dna-affinity-ladder" ]
unmeasured inputs
[ "free nuclear concentration of any KMT2A fusion protein - no published measurement found, and no entry in this graph carries one", "spontaneous (zero-force) residence time of the fusion on chromatin with and without a functional CXXC domain - PARTLY addressed by Liang 2021, which gives a force-assisted rupture time of about 10 ms at 12.5 pN for the isolated domain on a real Hoxa9 CpG island", "the fraction of fusion that is chromatin-bound versus free at steady state" ]
occupancy table
[
{
"kd_nM": 44000,
"theta_at_1nM": 0.0000227,
"theta_at_10nM": 0.000227,
"theta_at_100nM": 0.00227,
"theta_at_1000nM": 0.0222
},
{
"kd_nM": 3500,
"theta_at_1nM": 0.000286,
"theta_at_10nM": 0.00285,
"theta_at_100nM": 0.0278,
"theta_at_1000nM": 0.222
},
{
"kd_nM": 640,
"theta_at_1nM": 0.00156,
"theta_at_10nM": 0.0154,
"theta_at_100nM": 0.135,
"theta_at_1000nM": 0.61
},
{
"kd_nM": 33,
"theta_at_1nM": 0.0294,
"theta_at_10nM": 0.233,
"theta_at_100nM": 0.752,
"theta_at_1000nM": 0.968
}
]partially measured
{
"what": "binding-probability and free-energy landscape of the isolated CXXC domain along a 187-bp Hoxa9 CpG island at 1-bp resolution, plus site-specific pausing times and about 10 ms rupture at 12.5 pN",
"pmid": "34280370",
"limits": "force-assisted, naked DNA, isolated domain, pauses below 10 ms unresolvable"
}- A drug endpoint stated as 'displace the fusion from chromatin' presumes an occupancy model. If the operative quantity is residence time, a compound could halve residence time with no measurable change in ChIP occupancy, and the programme would read as a failure.
- If free nuclear fusion concentration is high enough that even a 44 uM contact is meaningfully occupied, then the weak-contact argument fails for a reason nobody has tested - and the measurement that would settle it has never been attempted in this disease.
- What is the free nuclear concentration of KMT2A::AFF1 in SEM or RS4;11? A calibrated fluorescence-correlation or quantitative-immunoblot measurement would make every occupancy statement in this project computable for the first time.
- What is the SPONTANEOUS residence time of the fusion on chromatin, and how much of it does C1188D remove? Liang 2021 gives a force-assisted rupture time for the isolated domain on a real CpG island; single-particle tracking of a knock-in tagged fusion is the zero-force, in-cell version and is the readout this beat most wants.
- Is the operative model equilibrium occupancy, one-dimensional sliding, or repeated capture within a condensate or a clustered site? The three predict different responses to a menin inhibitor and nothing published distinguishes them.
- E1strong confidence 4 of 5: Replicated in peer-reviewed work by more than one group.paper
Published dissociation constants for the KMT2A CXXC/MT-DNA contact span 44 uM to 33 nM across nine measurements, so any occupancy calculation inherits a 1,300-fold uncertainty from the Kd term before the free-concentration term is considered at all.
MLL protects CpG clusters from methylation within the Hoxa9 gene, maintaining transcript expression. · Erfurth FE, Popovic R, Grembecka J, et al. · Proc Natl Acad Sci U S A 2008What this evidence cannot show
The nine-measurement span is assembled in ana-cxxc-dna-affinity-ladder from five primary papers read in full this cycle; this evidence item cites the one that itself spans 3.5 to 32 uM internally and that first noted the discrepancy in print. The occupancy table is elementary algebra on those constants and is not a result from any paper - it is presented to show what the constants do and do not determine.
Evidence that argues against this (1)
- Single-site equilibrium occupancy is the wrong model for a protein that scans DNA. Cierpicki et al. observe 2- to 4-fold higher affinity at sites with multiple CpG motifs and suggest one-dimensional diffusion along DNA, under which the relevant quantities are the search rate and the residence time rather than theta at a fixed site, and a weak contact can produce long effective residence through repeated rebinding. Cierpicki T et al. 2010
- E2moderate confidence 3 of 5: One strong study, or several smaller consistent ones.paper
Cierpicki et al. observe 2- to 4-fold higher affinity for oligonucleotides with multiple CpG motifs and interpret it as possible one-dimensional diffusion along DNA, which makes residence time rather than single-site equilibrium occupancy the mechanistically relevant quantity.
Structure of the MLL CXXC domain-DNA complex and its functional role in MLL-AF9 leukemia. · Cierpicki T, Risner LE, Grembecka J, et al. · Nat Struct Mol Biol 2010What this evidence cannot show
The 2- to 4-fold figure comes from the paper's Supplementary Table 1, which is behind the Europe PMC open-access gate and was NOT read; only the authors' statement of it in the main text was verified. The one-dimensional-diffusion interpretation is explicitly offered by the authors as a possibility ('possibly indicative of'), not as a demonstrated mechanism, and no single-molecule experiment on this domain exists.
Evidence that argues against this (1)
- Erfurth's stoichiometry result cuts against a simple sliding model: a 16-mer with three CpGs binds only 1.93 domains, which the authors read as steric exclusion between adjacent sites. A domain whose footprint blocks its neighbours does not slide freely along a dense CpG island, so the multiple-CpG gain may be a local-concentration effect rather than one-dimensional diffusion. Erfurth FE et al. 2008
- E3moderate confidence 3 of 5: One strong study, or several smaller consistent ones.paper
Magnetic-tweezers profiling of the MLL1 CXXC domain on a 187-bp Hoxa9 CpG island gives a 1-bp-resolution binding-probability and free-energy landscape and site-specific pausing times, with individual CXXC-CpG complexes rupturing in about 10 ms at a 12.5 pN probing force.
Dynamics and inhibition of MLL1 CXXC domain on DNA revealed by single-molecule quantification. · Liang L, Ma K, Wang Z, et al. · Biophys J 2021What this evidence cannot show
A force-assisted rupture time under 12.5 pN of applied tension is not a spontaneous residence time at zero force and cannot be substituted into an equilibrium occupancy calculation. Naked DNA, no nucleosome, no fusion protein, no competing factors, and a chemically synthesised isolated domain whose span is in an unretrieved supplementary table. Pauses shorter than 10 ms are below the instrument's resolution, so the distribution is truncated at exactly the scale of the reported value. Full text read via the PMC HTML route (PMC8392069).
Evidence that argues against this (1)
- The measurement is of the isolated domain. In the fusion the same contact is one of several on a single polypeptide, and multivalency changes residence time far more than it changes single-site affinity - so a 10 ms isolated-domain rupture time may understate the fusion's dwell by orders of magnitude, in the direction that matters for the address argument. Grembecka J et al. 2010
Shows what the 1,300-fold Kd span does to any occupancy statement: about four orders of magnitude before the unmeasured free concentration is considered.
The entry's open question asking what fraction of occupancy is CXXC-driven given a 44 uM affinity is unanswerable: both the Kd and the free nuclear concentration are unmeasured.
The free nuclear concentration term is unmeasured for the same reason the affinity is measured only on fragments.