# Fact-check summary: what the old AI got right, wrong, and uncertain

This summary reconciles three independent reviews:

1. **Claude fact-check agent** (`research/fact-check.md`, ~5000 words)
2. **GPT/codex fact-check agent** (`research/fact-check-codex.md`, run via the codex CLI in a separate tmux session)
3. **Published-model literature scan** (`research/published-pk-models.md`)

Verdicts where both fact-checkers agreed are marked **★** (high confidence).
Where they disagreed, I describe the disagreement.

---

## Headline errors (load-bearing, fix in any model built on top)

### ❌ SHBG-E2 Kd = 1 nM (the old AI's binding equation)

**Wrong by 10–30×.** The 1 nM number is the SHBG Kd for *DHT*. For estradiol the Kd is **10–30 nM** (Hammond et al.; Avvakumov 2010, PMC8144348). ★ Both fact-checkers caught this.

This matters because it propagates: free-fraction calculations get the wrong shape, "buffering" by SHBG is overstated, and downstream models of pregnancy free E2 are wrong.

**Used in v3 model**: SHBG_Kd_E2 = 20 nM.

### ❌ ESTHER (Canonico 2007) reported oral E2 VTE OR = 2×

**Wrong.** ESTHER reported **adjusted OR = 4.2** for current oral estrogen users, and 0.9 for transdermal users, vs non-users (Canonico et al. 2007, *Circulation*; PMID 17309934). ★ Both fact-checkers caught this.

The "≈2×" figure comes from later pooled meta-analyses (Mohammed/Scarabin 2015 ≈1.48; Vinogradova 2019 ≈1.7), which dilute the ESTHER signal. The 4.2 vs 0.9 contrast is the actually striking ESTHER result.

### ❌ "Lindberg 2003" SHBG paper

The correct citation is **Lindberg et al. 2005**, *JCEM* 90:3431 (or "Ropponen et al. 2005" for a similar SHBG-rise reference; the codex agent flagged Ropponen specifically). The +67–171% SHBG-on-oral-E2 numbers are right; the year is one of those AI-misremembered details.

### ⚠️ Postmenopausal endogenous E1 from adipose ≈ 80 µg/day

**Probably ~2× too high.** Wikipedia's E1S production table (citing Longcope 1986 / Grodin 1973) gives postmenopausal E1 production around **40 µg/day**, with substantial variation by adiposity. The 80 µg/day value used in the old AI's v3 likely came from premenopausal early-luteal data being mis-applied to postmenopause.

**Used in v3 model**: 40 µg/day.

### ⚠️ Pregnancy E1S anchor "≈ 50,000 pg/mL"

**About 2× low.** Wikipedia's pregnancy-trimester table gives third-trimester E1S ≈ 105 ± 22 ng/mL = **100,000 ± 22,000 pg/mL**. The old anchor underestimates by a factor of 2.

**Used in v3 model**: anchor = 100,000 pg/mL. (Model output for pregnancy is ~54,000 — still off by ~2×, which the v3 documents as a known limitation; capturing pregnancy E1S accurately would need explicit modeling of placental sulfotransferase activity, which we don't do.)

### ⚠️ "Free E2 = 50 pg/mL in cycling women"

**Mislabeled.** 50 pg/mL is *total measured serum E2*. *Free* E2 in cycling follicular women is ~1 pg/mL (~2% of total). The old AI consistently labeled cycling-phase anchors as "free E2" when they meant total — confusing for anyone trying to interpret the SHBG buffering effects on top.

**Used in v3 model**: all anchors are explicitly **total measured serum**, and free E2 is computed as a *derived quantity* from total × free-fraction(SHBG).

### ⚠️ "Sublingual Tmax = 30 min"

**Slightly off.** Doll et al. 2022 (Endocr Pract 28:237) reports LC-MS/MS Tmax of **1–2 hours**, not 30 min. The 30-min number may be from older RIA studies that over-read very low E2, or from the first detectable rise rather than the peak. ★ Both fact-checkers flagged this.

The corrected value matters for the absorption rate constant in the model:
ka_sublingual = ln2 / (45 min) is now used in v3 (was 15 min in v2).

### ⚠️ "Bioavailability of oral E2 = 5%" — true but ambiguous

The 5% number is correct for **unconjugated plasma E2 AUC**. But the old AI used it without specifying which compartment, which led to confusion downstream:

- F(free E2 AUC) ≈ 2–5%
- F(total estrogen exposure incl. E1, E1S, conjugates) ≈ 20–40%
- F(hepatic exposure) is *higher than 100%* relative to systemic, because of portal-vein first-pass

So when the old AI said "5% bioavailable" while discussing why oral E2 has hepatic effects similar to a much larger transdermal dose, that's only coherent if you understand that the "5%" applies to the systemic free-E2 compartment but the liver sees much more than 5% in concentrated form during absorption.

**Used in v3 model**: F_oral_E2 = 4% (reaching systemic as E2), but F_oral_E1 = 30% and F_oral_E1S = 32% are tracked separately to capture the full first-pass fate of an oral dose.

---

## Most fragile load-bearing claims (cite cautiously)

### 🤷 Hepatic ER-α Kd = 0.25 nM (Yager 1989)

**Number is in the paper, but the assay is rat hepatocyte not human, and the downstream Hill-curve model the old AI built on top of it isn't directly published anywhere.** ★ Both fact-checkers raised concerns.

- Yager & Williams 1989 (*Cancer Res* 49:6605, PMID 2573415) does report Kd ≈ 0.25 nM for [³H]-E2 in rat hepatocyte nuclear/cytosolic ER. Codex disputed whether the exact paper supports this; my read agrees with Claude's that the value is in the paper but is a rat assay.
- 0.25 nM is in the textbook ER-α range (0.05–1 nM). It's not an outlier.
- But the **effective EC50 for SHBG mRNA induction** in HepG2 cells (Selva & Hammond 2009) is closer to **1–10 nM**, much higher than the receptor Kd. The discrepancy is because SHBG induction requires sustained ER-α transcriptional activity, not just transient binding.

**Used in v3 model**: ER-α Kd = 0.25 nM is kept for receptor-occupancy plots only (illustrative). The SHBG induction curve uses a *separate, much higher* EC50 of ~1500 pg/mL free hepatic E2, with the note that this is calibration-based.

### 🤷 Cytoplasmic [E1]/[E2] = 11 (from NAD⁺/NADH × Keq)

**Arithmetic is right; both input numbers are shaky.** ★ Both fact-checkers flagged.

- NAD⁺/NADH cytosolic ratio ≈ 700 (Williamson, Lund, Krebs 1967, PMID 4291787) is the canonical *rat liver fed-state* value, often quoted as universal. In starved rats it's 528, in alloxan-diabetic 208. Real cytosolic ratios in human hepatocytes vary 2–5× with metabolic state.
- E°' for the E1/E2 couple ≈ −0.265 V used by the old AI is **not a directly measured value**. The number that propagates in textbooks for secondary-alcohol/ketone is −0.16 to −0.20 V at pH 7. The −0.265 V might be from analogous steroid couples or estimated to match observation.
- The arithmetic [E1]/[E2] = Keq × NAD⁺/NADH = 0.016 × 700 = 11 is correct given the inputs, but qualifies as **plausible model** not **measured fact**.

The qualitative point — that hepatocytes oxidatively convert most E2 to E1 — is right. The number "11" should be quoted as "~5–20-fold E1 predominance, roughly consistent with plasma E1/E2 ≈ 5 in oral E2 patients."

### 🤷 "Below the hepatic ER Kd → no hepatic effect" rule

**Not defensible as stated.** Both fact-checkers (especially codex) flagged this. Hepatic estrogen effects are graded, not binary, and depend on portal vs systemic concentrations, time integration, metabolite contributions (E1 also activates hepatic ER), and probably distinct genes' responses. The transdermal-vs-oral VTE divergence is real, but the mechanistic explanation isn't as crisp as a Kd threshold.

---

## Things the old AI got right (high confidence)

★ All confirmed by both fact-checkers, with primary citations in the published-models doc:

- CA II reaction and ~10⁶–10⁷ rate enhancement (textbook)
- HSD17B2 = oxidative (liver/gut/endometrium), NAD⁺-dependent
- HSD17B1 = reductive (placenta/ovary), NADPH-dependent
- SULT1E1 has the lowest Km of any human SULT for any substrate (~5–20 nM for E2)
- SULT1E1 substrate inhibition exists (real, well-documented)
- UGT regioselectivity: 1A1/1A3/1A8/1A10 for C3, UGT2B7 for C17
- UGT1A8/1A10 are gut-specific (intestinal first-pass)
- STS reverses sulfation; expressed in many tissues including breast
- Oral E2 free bioavailability ~5%, EE bioavailability ~45%
- Free E2 fraction ~2% at baseline (drops in pregnancy due to SHBG rise)
- Free E2 half-life ~1–2 h; E1S half-life ~10–12 h
- Apparent oral E2 half-life 13–20 h (E1S reservoir reactivation)
- MCRs (1300–1700 / 2000–2700 / 80–170 L/d for E2 / E1 / E1S) — within textbook range
- Plasma E1S is the most abundant circulating estrogen (5–25× E1)
- Sulfamate-CA II prodrug strategy and the E2MATE → EC508 narrative (well-supported)
- The conceptual sulfation/desulfation cycle (SULT1E1 ↔ STS) as a tissue-switching mechanism
- Pregnancy VTE risk gradient (~3× antepartum, ~9× third trimester, ~20× postpartum)
- COC VTE RR ≈ 3.5× (BMJ 2013 network meta-analysis)
- Transdermal HRT VTE essentially baseline; oral HRT elevated

---

## Things genuinely uncertain (no good primary data either way)

- **Whether sublingual E2 carries similar VTE risk to oral E2.** Bar et al. 2024 found decreased free protein S on sublingual (a procoagulant biomarker shift), Cirrincione 2021 showed substantial E1 production (hepatic exposure marker). But no clinical VTE outcomes study exists. The old AI's revised conclusion (sublingual ≈ oral on hepatic effect) is plausibly correct but **biomarker-based, not outcome-based**.
- **Exact hepatic [E2] during oral first-pass.** Calculated to be 50–500× systemic; varies enormously depending on absorption rate. Old AI assumed ~5000 pg/mL; v3 model uses a portal-vein amplifier ~50× systemic which is a coarse approximation.
- **In vivo Hill coefficient for hepatic ER-α → SHBG induction.** No paper has fitted this. n ≈ 1 is the default assumption; the actual value could be 0.7–1.5.

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## What changed in the v3 model as a result

| Parameter | Old AI v3 | New v3 | Reason |
|---|---|---|---|
| MCR_E2 (L/day) | 1400 | 1500 | Within textbook scatter |
| MCR_E1 (L/day) | 2200 | 2200 | Unchanged |
| MCR_E1S (L/day) | 150 | 150 | Unchanged |
| f(E2→E1) | 0.30 | 0.20 | Closer to Longcope 1968 ρ = 0.15 |
| f(E2→E1S) | 0.30 | 0.50 | Ruder 1972 ρ_E2→E1S ≈ 0.57 |
| f(E1S→E1) | 0.10 | 0.21 | Ruder 1972 ρ_E1S→E1 = 0.21 |
| f(E1S→E2) | 0 | 0.014 | Ruder 1972 ρ_E1S→E2 = 0.014 |
| F_oral_E1 | 0.18 | 0.30 | To reproduce Kuhl 2005 oral E1/E2 ≈ 5 |
| Postmenopausal E1 (µg/d) | 80 | 40 | Wikipedia E1S table; fact-checker correction |
| SHBG_Kd_E2 (nM) | 1 | 20 | Hammond; fact-checker correction (was DHT Kd) |
| Albumin_Kd_E2 (nM) | n/a | 12,000 | Plowchalk/Mendel; gives correct 2% free fraction |
| Pregnancy E1S anchor (pg/mL) | 50,000 | 100,000 | Wikipedia third-trimester table |
| Sublingual Tmax | 30 min | 45 min | Doll 2022 LC-MS/MS |
| F_sublingual_E2_direct | 0.25 | 0.05 | To match Doll 2022 AUC ratio |
| SHBG induction model | binary "induces 10×" | dynamic ODE with τ=3d, Hill on hepatic free E2 | More realistic time dynamics |