Master-Gene Dosage Dysplasias as a Forced Crossing Cliff

Halving a master gene's dosage is a haploinsufficiency: it drops the organ's R19 switch drive below the spinodal, so the switch fails to cross from the OFF basin and development is delayed or incomplete. With WT occupancy 1.00, the heterozygote collapses to 0.10 — reproducing the documented dysplasias of RUNX2, SOX9 and TBX5 loss. The crossing CLIFF at ⅔ of WT drive is FORCED by the substrate [F].

The WT master drives its switch at 1.5× its spinodal; a 0.5 dosage halving lands it at 0.75× spinodal, below the γ-independent crossing cliff at dosage ≈ 0.667. Occupancy is monotone in dosage, so the defect scales with loss; below the cliff the switch never crosses (latency undefined). Mechanism [V]; threshold shift [F]; absolute developmental timing/morphology [O].

The cleanest test of the γ-switch claim

The package's central claim is that each organ is an R19 bistable switch governed by its MEASURED master-gene γ. The sharpest human falsification is a Mendelian haploinsufficiency: halve the master's effective dosage and the switch should fail to cross on schedule, reproducing the documented developmental defect. The severity is CITED (heterozygous loss = 0.5 dosage), never fitted.

A forced crossing cliff

In the kit, a successfully developing organ is driven at 1.5× its spinodal s* = 2(γ/3)^3/2. Scaling the drive by dosage x gives x·1.5·s*; this stays above the spinodal only while x > 1/1.5 = ⅔. The critical dosage cliff is therefore ≈ 0.667 and — remarkably — independent of γ: it is the same for every master. A 0.5 haploinsufficiency sits below it, so the heterozygous switch cannot release from the OFF basin: occupancy collapses from 1.00 (WT) to 0.10 and the crossing latency becomes undefined.

Three master genes, three dysplasias

RUNX2 → cleidocranial dysplasia (open fontanelles, clavicular hypoplasia, supernumerary teeth as ‘incomplete crossing’); SOX9 → campomelic dysplasia (hypoplastic, bowed cartilage template); TBX5 → the limb component of Holt-Oram (radial-ray / appendicular reduction; the cardiac component is OUT of class and routed to the cardiovascular sibling). T7d (MYOD1) is reported as a SECONDARY, weaker case [V?] — human MYOD1 LoF disease is rare and recent — and is excluded from the hard gate, though it passes the same cliff.

What is NOT claimed

The DIRECTION (failed/partial crossing) and the forced threshold shift are the result. The absolute developmental calendar and the precise morphology (how many millimetres of clavicle, which fontanelle, when) are NOT fixed by the substrate and stay [O]: occupancy is a switch-state proxy, not a morphogenetic geometry.