The olfactory transduction switch
The olfactory cascade ends in the same all-or-none R19 flip as vision, discontinuous past the spinodal. The cubic −s³ (cooperativity order 3) makes it a step, ≈229× steeper than a graded control. CNGB1 γ = 1.4357 is byte-identical to rod vision — the switch is shared.
Each transduction gene's R19 field flips discontinuously past its spinodal; the cubic −s³ (order 3) is necessary, ≈229× steeper than a graded control. CNGB1 γ = 1.4357 matches rod vision byte-for-byte — a shared, not analogous, switch.
All-or-none: the flip is discontinuous past the spinodal
The olfactory cascade (odorant → OR → Golf/GNAL → ADCY3/cAMP → CNG channel → ANO2) ends in the same R19 flip as vision. Settled from rest, each gene's field stays dark below its spinodal h* and snaps on above it with a finite, discontinuous jump.
| gene | γ | h* = spinodal | s @ 0.90 h* | s @ 1.10 h* | jump |
|---|---|---|---|---|---|
| GNAL | 1.4109 | 0.64505 | -0.8560 | +1.3866 | +2.2425 |
| ADCY3 | 1.5435 | 0.73809 | -0.8953 | +1.4503 | +2.3456 |
| CNGA2 | 1.2935 | 0.56624 | -0.8196 | +1.3276 | +2.1472 |
| CNGA4 | 1.4016 | 0.63868 | -0.8531 | +1.3820 | +2.2351 |
| CNGB1 | 1.4357 | 0.66213 | -0.8634 | +1.3987 | +2.2622 |
| ANO2 | 1.3500 | 0.60374 | -0.8373 | +1.3563 | +2.1936 |
On the principal CNG subunit CNGA2 the discontinuity is sharp: at 1.00·h* the field is still off (s = -0.6725), and one further quantum of drive at 1.01·h* flips the whole switch on (s = +1.2971). Less than a quantum does nothing.
The cooperativity is the cubic −s³, and it is necessary
The restoring term is third-order, so the cooperativity order is n = 3 — this is where olfaction's "Hill ≈ 2–3" comes from, the cubic, not a fit. A structural control with the cubic struck out (ds/dt = −γ·s + h) loses the threshold, the basin, and the jump.
Across the fold the cubic switch slope is ≈ 177.2 while the graded control is ≈ 0.773 — a ratio of ≈ 229×. Removing the cubic makes the response a smooth proportional curve; the cubic makes it a step.
The switch is genuinely shared across senses
CNGB1, the CNG channel β subunit, is literally the same gene in rod vision and olfaction. Its olfactory γ = 1.4357 is byte-identical to the independently measured rod-vision value 1.4357 — the transduction switch is reused, not paralleled.
Ordered by threshold the cascade reads CNGA2 → ANO2 → CNGA4 → GNAL → CNGB1 → ADCY3. Whether this spinodal order matches the real biochemical sequence (Golf → ADCY3 → cAMP → CNG → ANO2) is an open empirical question — it needs the measured cascade kinetics and is not assumed. The absolute odorant→drive→firing (Hz) scale is a separate calibration [O].