Carcinogenesis as R19 barrier lowering

A carcinogen is a sustained aberrant drive on the same R19 cell-fate switch; it lowers the barrier out of the healthy basin, and the malignant-crossing rate is Kramers/Arrhenius over that barrier. The tilted double well gives barrier = γ²/4 at zero drive, falling to zero at the spinodal, so relative risk RR(dose) = exp(Δbarrier/D). Grade [F].

Health and malignancy are the two basins of V(s) = ¼s⁴ − (γ/2)s² − hs. A carcinogen drive h lowers the escape barrier ΔE_b, which equals γ²/4 at h=0 and vanishes at the spinodal |h| = 2(γ/3)^1.5; the crossing rate, hence RR, is Arrhenius in ΔE_b.

One switch, two basins

Cell fate is the shared R19 switch. Its potential is a double well; the healthy and malignant states are the two minima separated by a barrier ΔE_b = γ²/4 at rest.

A carcinogen tilts the well

A sustained carcinogen drive h tilts the potential, shrinking the healthy basin toward its spinodal and lowering the escape barrier. The barrier is computed exactly as V(saddle) − V(healthy minimum) from the three steady-state roots, falling to zero precisely at |h| = 2(γ/3)^1.5, beyond which the healthy basin disappears (barrierless).

The malignant-crossing rate is Arrhenius in the barrier, so RR(dose) = exp([ΔE_b(0) − ΔE_b(dose)]/D). The next two sections instantiate this single kernel for renal and hepatic cancer and test it against cited epidemiology.