In a competitive menin-binding scaffold with assumed rates, the drug exposure needed scales with menin relative to the fusion-menin Kd, and whether recovery after a lapse lags collapse is governed by the drug's residence time - a conditional counter-lead to the pulsed-dosing premise, not a prediction
also called program loop simulation · menin occupancy required exposure · residence time and hysteresis model
We built a small computer model of the loop that keeps this leukaemia's growth program switched on, and of a drug that competes with the fusion protein for the same grip on menin. Almost every number in it is a guess within a wide range, so it does not predict any patient. What it does show is which guesses matter. The more menin the cell holds relative to how tightly the fusion grips it, the more drug is needed, and how fast the program comes back after a missed dose depends mostly on how long the drug stays stuck to menin once it lands.
The same thing, for a scientist
A mean-field ODE with a single-cell tau-leap layer: pharmacokinetics with 12-hourly dosing, competitive drug binding to free menin with an explicit residence time, fusion MBM1-menin binding at fast equilibrium (checked against the full mass-action ODE: half-equilibrium in about 4 s at an assumed kon), an H3K79me2-like mark with deposition proportional to recruitment and loss by dilution and replacement, a Hill transcription response and mRNA turnover. 3,000 Latin-hypercube samples over assumed ranges; every control passed (stationary untreated state, no-effect drug, bounds, a dummy parameter with rank correlation near zero, stochastic mean within 12.6% of the ODE mean). Closed form, confirmed in the full model: the peak free drug needed to bring the program to 30% of untreated is about 5.5, 10.9, 30, 85 and 276 times Ki when menin/Kd is 1, 3, 10, 30 and 100, so exposure scales roughly with menin/Kd and a Ki increase of f divides the peak-to-Ki ratio by f. Recovery after a lapse was slower than collapse in 15.7% of the assumed space; the up/down time ratio correlates with drug residence time at +0.94 and with menin excess at -0.76. Ki is non-identifiable by parametrisation (drug strength is peak/Ki). The MBM1-menin Kd is swept 10-100 nM; the abstract of PMID 20961854 supports only about 10 nM for the two-motif fragment.
What was built and what the controls were
The loop is menin-fusion binding, a chromatin mark and a transcriptional program, driven by a drug that competes for the menin pocket 1. Controls were asserted in code and had to pass before any result was written: the untreated cell stays exactly at 1, a drug of negligible strength changes nothing, occupancy and the mark stay in bounds, the fast-equilibrium assumption for the fusion step matches the mass-action ODE, a parameter the model never uses shows near-zero rank correlation, and the stochastic mean tracks the ODE. The stochastic control passed narrowly (12.6% against a 15% limit) 1.
The exposure requirement
With a competitive drug on free menin and menin far above the fusion's sites, recruitment of the fusion relative to untreated is (Mt+Kd)/(Mt+Kd(r+1)) where r is peak free drug over Ki. Setting the program to 30% gives the table in the summary, which the full model reproduces 1. Two consequences depend on this structure and on the unmeasured nuclear menin and fusion-menin Kd: higher menin or tighter fusion binding raises the exposure needed roughly in proportion, and a pocket substitution that raises Ki by a factor f is equivalent to dividing r by f 13. The Kd range is anchored loosely: the abstract of the cited biochemical paper gives a two-motif fragment Kd near 10 nM and names the critical residues 2.
Hysteresis, and why this is a counter-lead
The corpus hypothesis that menin-inhibitor effect is hysteretic, with the program collapsing faster than it recovers, motivates intermittent dosing. In this scaffold recovery was slower than collapse in 15.7% of the assumed parameter space and faster in the rest, because only a modest fraction of menin has to be freed to restore fusion binding when menin exceeds Kd. The ratio is governed by the drug's residence time on menin and by menin excess 1. A kinetic effect of the same kind exists on the target side: the G331D mutant slows MLL1 dissociation from menin 3. So the premise of pulsed dosing holds mainly for long-residence compounds at low menin excess, and compound residence time is the number to measure.
| script | analyses/q205-program-loop-simulation/program_loop.py |
|---|---|
| output | analyses/q205-program-loop-simulation/results.json |
| samples | 3000 |
| seed | 7 |
| share recovery slower than collapse | 0.157 |
| parameters assumed | true |
required peak over Ki for program 30pct — the numbers behind the chart
{
"3": 10.9,
"10": 30.1,
"30": 84.8,
"100": 276.4,
"menin/Kd=1": 5.5
}prcc hysteresis ratio — the numbers behind the chart
{
"drug_residence_time": 0.94,
"menin_nM": -0.76,
"peak_over_Ki": 0.533,
"half_activation": 0.524,
"Kd_mbm1": 0.517,
"mrna_half_life": -0.399
}controls
[ "untreated stationary at 1", "no-effect drug", "bounds", "dummy parameter", "QSS vs mass action", "tau-leap vs ODE (12.6% of 15%)", "closed form vs full model" ]
- Reading the hysteresis premise as settled would put an intermittent schedule on a compound whose residence time is short, where this scaffold says recovery is fast; the result could be rebound in the troughs of a drug that was supposed to be spared.
- A trough-guided dose chosen from the exposure table is only as good as the unmeasured menin concentration: if nuclear menin is higher than assumed, the same dose under-treats, and if lower, over-treats an infant.
- A drug engineered for a long residence time would help the hysteresis argument and also lengthen the time to recover from toxicity, which matters for the tissue effects already in the corpus.
- What is the drug residence time on menin for each clinical compound? It is the number the hysteresis ratio is most sensitive to.
- What is the nuclear menin concentration relative to the fusion-menin Kd in an infant KMT2A::AFF1 cell? It sets the exposure requirement.
- Is the trough free drug at the 12-hourly dosing interval above the required multiple of Ki in children? PK in infants is not in this model.
- Does a fusion-specific recruitment readout agree with the model's recruitment variable, unlike menin displacement (the pharmacodynamic proxy risk already in the corpus)?
- E1weak confidence 2 of 5: Preliminary, small, indirect, or not yet peer reviewed.database
In a stochastic, ODE-based scaffold of the menin-fusion program loop with assumed rate ranges, the peak free drug needed to bring the program to 30% of untreated is about 5.5, 10.9, 30, 85 and 276 times Ki at menin/Kd of 1, 3, 10, 30 and 100; recovery after a lapse was slower than collapse in 15.7% of 3,000 sampled parameter sets, with the up/down ratio correlating with drug residence time (+0.94) and menin excess (-0.76).
analyses/q205-program-loop-simulation/program_loop.py and results.json, run 2026-10-14 (3,000 Latin-hypercube samples, seed 7) · this repository 2026What this evidence cannot show
Almost every rate is an assumed range, not a measurement. The prior is wide on purpose (peak drug up to 3,000 times Ki), so shares and quantiles describe the ranges, not patients. Ki cancels by parametrisation. The competitive-binding structure assumes the drug binds only free menin and that fusion sites are far fewer than menin. The mark is a single lumped state. The stochastic layer was run at one midpoint where the drug is over-dosed, so cell-to-cell heterogeneity there is uninformative.
Evidence that argues against this (1)
- If nuclear menin is limiting, or the fusion sites are not far below menin, the exposure table changes. And if real compounds have long residence times, recovery would lag collapse and the corpus hysteresis premise would hold more often than in this prior.
- E2moderate confidence 3 of 5: One strong study, or several smaller consistent ones.paper
MLL interacts with menin with nanomolar affinity (Kd about 10 nM) through two motifs, MBM1 and MBM2, within the N-terminal 43 amino acids; MBM1 is the high-affinity motif and the hydrophobic residues Phe9, Pro10 and Pro13 are most critical for binding.
Molecular basis of the mixed lineage leukemia-menin interaction: implications for targeting mixed lineage leukemias · Grembecka J, Belcher AM, Hartley T, Cierpicki T · J Biol Chem 2010What this evidence cannot show
Abstract read only (2026-10-14). The abstract does not give the 53 nM, 72 nM or 1,400 nM values the corpus attributes to this paper; those could not be checked because the full text could not be retrieved, and they are logged as an open question on the MBM1 interface entry.
Evidence that argues against this (1)
- A peptide Kd in vitro is not an affinity in a cell: the fusion's avidity on chromatin, from other contacts, may make the effective affinity tighter, which would raise the exposure the model says is needed.
- E3moderate confidence 3 of 5: One strong study, or several smaller consistent ones.paper
Menin patient mutants occur adjacent to the MLL1 binding site without affecting MLL1 binding, they generate steric clash with menin inhibitors, and G331D results in very slow dissociation of MLL1 from menin.
Drug-resistant menin variants retain high binding affinity and interactions with MLL1 · Ray J, Clegg B, Grembecka J, Cierpicki T · J Biol Chem 2024What this evidence cannot show
Abstract read only (2026-10-14). In vitro measurements on an N-terminal MLL1 fragment.
Evidence that argues against this (1)
- A slow off-rate in vitro does not show a change in cellular occupancy or in drug response; the model's use of residence time is a hypothesis about drugs, not a result from this paper.
conditional counter-lead: recovery is faster than collapse in most of the assumed space
the Kd the model sweeps; quantitative values unverified from the abstract
the model's recruitment variable versus a menin-displacement readout
- related to →MEN1 drug-interface mutations — the first proof that a chromatin drug can drive Darwinian escape in patients
a Ki increase of f divides the peak-to-Ki ratio by f; G331D slows dissociation
atlas modes FM-001, FM-011 and FM-130, modelled under assumed ranges