From DNA: Master Genes, Stacking Stability, and the R19 Switch

The cardiorespiratory dynamics descend from DNA: the master genes NKX2-5 (heart) and NKX2-1 (lung) carry measured stacking stabilities γ read from the 4D-DNA gene-clock, and that one number sets each organ's R19 bistable switch and its FitzHugh–Nagumo oscillator. Ascending γ gives the developmental order (an [interpretation], superseded: order is open [O], dna §RB). Grades [code output] readout and [consistency] substrate.

Gene → γ → R19 switch → oscillator: heart γ(NKX2-5) = 1.513 and lung γ(NKX2-1) = 1.509 are the measured DNA inputs; the switch barrier γ²/4 and the FHN cubic follow, and ascending γ orders the organs. [code output]/[consistency]; order [O].

The chain: gene → γ → R19 switch → oscillator

The cardiorespiratory dynamics in this volume descend from DNA, not from a hand-built model. Each organ begins at a master gene — NKX2-5 for the heart, NKX2-1 for the lung — whose promoter stacking stability γ is read from the 4D-DNA gene-clock.

That single number γ fixes the organ's R19 bistable switch (barrier B = γ²/4, spinodal h* = 2(γ/3)^1.5), and the switch's cubic is exactly the fast nonlinearity of the FitzHugh–Nagumo relaxation oscillator. So the heartbeat and the breath are two settings of one DNA-anchored oscillator, separated only by the slow recovery time.

[code output] In the reproduction code both oscillators run with γ = 1.0 (repro/cardioresp/repro/_engine/vp_car_engine.py, _fhn_rate_arb). The measured γ values set each gene's switch threshold (spinodal, barrier) but do not enter the computed rhythms; the heart/lung difference comes only from the chosen recovery times τ_s = 18 and 95. The sentence below that different γ values would move the recovery-time ratio and breathing rate is therefore an [interpretation] the current code does not implement.

Heart γ(NKX2-5) = 1.513 and lung γ(NKX2-1) = 1.509 are the measured inputs; everything downstream is derived from them with no further fitting.

Why γ is an input, not a fit

The no-tuning rule is strict: γ is a measured property of the gene, never a knob turned to hit a target. This is what separates a grounded emergence from a curve fit — the same γ that orders the organs also sets the switch barrier and the oscillator, with one value doing all three jobs.

Because the inputs are fixed by DNA, the dynamics are falsifiable: if the measured γ values were different, the recovery-time ratio, the breathing rate, and the carcinogen low-dose slope would all move together in the predicted direction.

Developmental order is a γ readout

Ordering the two organs by ascending γ gives lung → heart. The emergence order is owned by the DNA gene-clock and read out here; the identity and the order are established results of the 4D-DNA volume, which this volume builds upon directly.

Reading rule: this order is an [interpretation] and is superseded; order comes from regulatory-cascade depth and building is open [O] (dna §RB). [observation] In the human embryo the heart tube begins to beat at about day 22 (Carnegie stage 10), while the lung bud appears at about day 28 (stage 12) (Moore, Persaud & Torchia, The Developing Human, 11th ed., 2020). The observed sequence is therefore heart before lung, the reverse of the ascending-γ order.

What this volume establishes on top of DNA

From the DNA-anchored oscillator this volume derives the functional layer: the breathing rate, the apnea threshold, respiratory sinus arrhythmia, the Cheyne–Stokes period, baroreflex regulation, and a shared carcinogen dose–response. Each result is regenerated by a deterministic engine and graded; the grade ledger and the open items are collected in §9.