A 60-compartment quantitative systems pharmacology model of PMDD posed not as "the luteal phase floods the brain with progesterone, so lower it" but as a GAIN problem: the neurosteroid-to-affect transduction is non-monotonic (an inverted U whose peak sits inside the physiological luteal range) and its gain is set by a slow, symmetric change detector in GABA-A receptor subunit composition. Hormone concentrations are identical in the model's PMDD and control phenotypes — only three parameters differ.

PMDD is a cyclical affective disorder confined to the luteal phase of the ovulatory cycle, remitting within days of menses onset, affecting roughly 1.6–5.5% of reproductive-age women. Five findings about it are awkward together, and any model of PMDD has to survive all five at once:

1. Luteal E2, P4 and allopregnanolone (ALLO) concentrations in PMDD are indistinguishable from those of asymptomatic controls. A level-based model therefore has no disease variable at all.
2. Yet the ovarian steroids are causal. Ovarian suppression abolishes the symptoms, and blinded add-back of estradiol or progesterone reinstates them in PMDD while doing nothing in controls (Schmidt 1998, PMID 9435325).
3. Lowering ALLO helps — but only a lot of lowering. Dutasteride 2.5 mg blocks the luteal ALLO rise and improves symptoms; 0.5 mg does neither (Martinez 2016, PMID 26272051).
4. Blocking ALLO at its GABA-A site also helps. Sepranolone (isoallopregnanolone), a neurosteroid-site antagonist, reduces symptoms (Bixo 2017, PMID 28319848).
5. And SSRIs, which RAISE brain ALLO, are the best-evidenced treatment — working in 1–2 days rather than the 2–4 weeks they need in depression. They shift 3α-HSD toward the reductive direction (Griffin & Mellon 1999, PMID 10441766).

A monotone "more ALLO is worse" model explains 3 and 4 and gets 5 backwards. A monotone "more ALLO is better" model gets 3 and 4 backwards. Neither can explain 1 and 2 at all, because in a monotone model the only way a normal hormone level can be pathogenic is if the level is not normal.

(1) The transduction is non-monotonic. The affective drive produced by effective neurosteroid load L at GABA-A is unimodal:

NS_DRIVE = SENS · (L/KP) · exp(1 − L/KP)          ← peaks at L = KP

Low-to-moderate ALLO is anxiogenic and dysphoric through extrasynaptic α4βδ receptors; high load is sedative and anxiolytic, exactly as pregnanolone and progesterone behave in humans (the bimodal mood association, Andréen 2006, PMID 16368261). The disease parameter is KP — where the peak sits relative to the physiological luteal range — not the range itself. In the PMDD phenotype KP = 5 nM, inside the luteal ALLO range; in the control phenotype KP = 13 nM, above it.

(2) The gain is a slow, symmetric change detector. GABA-A subunit composition moves on a timescale of days while ALLO turns over in minutes:

• DELTA (δ-subunit abundance) follows the ALLO exposure history and is tolerance-like — its gain GAMMA_D is negative. Sustained exposure makes the system less reactive, as chronic-progesterone pseudopregnancy models show.
• ALPHA4 (α4-subunit abundance) follows the rate of change of neurosteroid and total progestogen tone and is sensitising — its gain GAMMA_A4 is positive. This is the withdrawal-induced α4 upregulation of Smith 1998 (PMID 9572737).
• The detector is symmetric: the onset of exposure drives it as well as the withdrawal, which is why the add-back experiment behaves the way it does.

The whole difference between a PMDD phenotype and an asymptomatic control in this model is three numbers: KP (5 vs 13 nM), GAMMA_A4 (1.50 vs 0.25) and GAMMA_D (−0.35 vs −0.05). Their hormones are byte-identical.

Every number below is printed by python3 pmdd_python_twin.py. The falsified column is the same model with MONOTONE = 1, RATE_OFF = 1 and both plasticity gains set to zero — a pure level detector, scaled so that it reaches the same peak drive on an untreated cycle, so the comparison cannot be won on scale.

Two of these deserve spelling out.

[P2] is the flat top of the inverted U. At L = KP the derivative d(NS_DRIVE)/dL is exactly zero. Dutasteride 0.5 mg (31% SRD5A1 inhibition at the simulated steady state of ~51 ng/mL) drops the luteal load from 5.9 to 4.1 nM and the position term barely moves — 0.986 to 0.983. Dutasteride 2.5 mg (69% inhibition, ~255 ng/mL) drops it to 2.0 nM and falls off the peak onto the low limb. The dose threshold is not a potency threshold; it is a geometry threshold. A level model has no flat region and so predicts a graded response, which is what the falsification run does.

[P3] is the reason the SSRI story is not a contradiction. In a non-monotonic system the sign of ∂symptoms/∂ALLO depends on where you are on the curve. Raising ALLO helps if you are above the peak and hurts if you are below it. The model therefore predicts that the same neurosteroid analogue should improve PMDD at a sedative dose and worsen it at a sub-sedative one — which is also the cleanest available explanation of why brexanolone and zuranolone treat a neurosteroid-withdrawal depression by giving more neurosteroid (PMID 29910040, PMID 34190962). In this model the SSRIs' own ALLO-raising arm (brain ALLO peak 5.15 → 6.58 nM) is close to sign-neutral at the late-luteal symptom peak, and their benefit is carried by the serotonergic arm; switching the transduction to a level detector makes the ALLO rise unambiguously harmful and cuts the simulated sertraline effect from +56.5% to +32.9%.

[P5] is Schmidt 2017 in equations. Symptoms are triggered by the change in ovarian steroid levels and not by continuous stable levels (PMID 28427285). A symmetric change detector reproduces that directly: constant add-back on top of ovarian suppression produces a flare while the signal is moving and then adapts away, even though the hormone input never changes again. The same add-back leaves the control phenotype asymptomatic (core luteal increase −1%).

DRSP-11 is the sum of the eleven modelled DSM-5 domains, each scored 1–6, so 11 means no symptoms and 66 is the maximum. The DSM-5 ≥30% luteal-versus-follicular criterion is evaluated on the five core affective domains (irritability, depressed mood, anxiety, affective lability, anhedonia), which is where the diagnostic weight actually sits.

Effect = % reduction of the luteal DRSP-11 burden above the floor of the scale, the model analogue of the primary endpoint of PMDD trials, on the fifth cycle.

Placebo response is deliberately not modelled, so these numbers should be compared with the active-minus-placebo differences of trials, not with raw responder rates.

1. Predisposition — cellular sensitivity, not hormone level (ESC/E(Z), ESR1×COMT, SRD5A/AKR1C variants, GABRA4/GABRD, heritability)
2. HPO-axis cycle engine (KNDy → GnRH → FSH/LH → follicle → ovulation → corpus luteum → luteolysis → menses)
3. Ovarian steroids, binding proteins, and the two withdrawal windows
4. Neurosteroidogenesis: P4 → 5α-DHP → allopregnanolone, plus isoallopregnanolone, pregnanolone, THDOC, PregS/DHEAS
5. GABA-A receptor pharmacology — synaptic α1/γ2 versus extrasynaptic α4βδ, the neurosteroid site, the missing benzodiazepine site, KCC2/chloride
6. GABA-A subunit plasticity — the exposure memory, the withdrawal signal, and the time-constant mismatch that creates the lag
7. The non-monotonic transduction — ascending limb, flat top, descending limb, and where KP sits in cases versus controls
8. Serotonergic system — the fast (irritability) and slow (depressive) branches
9. Corticolimbic gain — amygdala, dACC, dlPFC, OFC, insula, ventral striatum
10. HPA axis and the blunted stress response of PMDD
11. Autonomic, sleep and circadian
12. Somatic symptom generation — RAAS/aldosterone/bloating, mastalgia, prostaglandins, craving, menstrual migraine, calcium-PTH
13. The eleven DSM-5 symptom domains and DRSP scoring
14. SSRI pharmacology — the two mechanisms and the three dosing strategies
15. Ovulation suppression — 24/4 versus 21/7, GnRH analogues, add-back, surgery
16. Neurosteroid-directed pharmacology — sepranolone, dutasteride 0.5 vs 2.5 mg, exogenous analogues, alprazolam
17. Adjunctive and non-pharmacological treatment
18. Clinical endpoints, safety, and the falsification test itself

PK is parameterised from published values (sertraline t½ 26 h, fluoxetine 4 d / norfluoxetine 9 d, drospirenone 31 h, dutasteride ~35 d, alprazolam 12 h), and each drug attaches to a specific mechanistic node rather than to a generic "effect" term: dutasteride to SRD5A1, sepranolone to the neurosteroid site, drospirenone to gonadotropin suppression and the mineralocorticoid receptor and the progestogen-tone detector, leuprolide through a flare-then- downregulation pituitary state, SSRIs to SERT and to 3α-HSD.

Two parameters are fitted rather than taken from the literature: KI_ISO (to the sepranolone effect size) and W_SHT_AMY (to the sertraline effect size). Everything else is either published PK or is pinned by the physiological ranges asserted in the twin's check table.

python3 pmdd_python_twin.py          # 30 scenarios, 38 checks — no dependencies
python3 pmdd_python_twin.py --csv out   # per-scenario time courses as CSV
dot -Tsvg pmdd_qsp_model.dot -o pmdd_qsp_model.svg
dot -Tpng -Gdpi=150 -Gsize=26,17 pmdd_qsp_model.dot -o pmdd_qsp_model.png

library(mrgsolve); library(dplyr); library(shiny)
mod <- mread("pmdd_mrgsolve_model.R")
out <- PMDD_simulate_scenarios(mod)   # helper defined at the bottom of the file
PMDD_endpoint_table(out)
runApp("pmdd_shiny_app.R")            # 12-tab dashboard

The Python twin implements the identical 60-state system with a fixed-step RK4 integrator and the Python standard library only — no numpy, no scipy, no R — and asserts 38 checks covering the cycle physiology, all five predictions, every treatment effect quoted above and the safety readouts. All 38 pass; if a parameter is edited, the failures say exactly which claim broke.

Patient profile · cycle engine · neurosteroids · the inverted U with the patient's own luteal trajectory drawn on it · receptor plasticity · drug PK · the eleven DRSP domains · clinical endpoints · scenario comparison · the five predictions with a live falsification toggle · safety and organ systems · model notes. The two presets (PMDD / control) change nothing but KP and the two gains, which is the fastest way to see what the model is claiming.

• An educational and research model. Not validated against patient-level data and not for clinical use.
• The cycle engine is a compact ODE oscillator tuned to reproduce the E2/P4/ALLO landmarks, not a full HPO model in the Röblitz sense (PMID 23206386).
• Placebo response, adherence, comorbid depression and the perimenopausal transition are out of scope.
• KP is a phenotype knob, not a measurable quantity. Its testable content is the pattern of predictions [P1]–[P5], not its numerical value.
• The neurosteroid load L lumps allopregnanolone, pregnanolone, THDOC and exogenous analogues into one pool; the model does not distinguish their receptor-subtype selectivities.

Disclaimer. This model is for education and research only. It has not been independently validated or certified, and must not be used for clinical decisions, prescribing, or regulatory submission. Parameters and assumptions are illustrative approximations that would require fitting and qualification against real patient data before any applied use.