Repair Fidelity as a Control Parameter Linking Cancer Resistance and Longevity: a bistable order-repair hypothesis inspired by the bowhead whale

Abstract

The bowhead whale resists cancer without adding tumour-suppressor barriers — its fibroblasts are in fact easier to transform than human fibroblasts. What its cells have instead is more accurate DNA repair. This work asks what follows if repair fidelity is treated not as one more cancer defence but as a parameter controlling whether multicellular tissue remains in a stable cooperative state at all. A single order parameter I describes tissue integrity, maintained by self-amplifying repair and eroded by stress: dI/dtau = mu(I)(1 - I) - rho I, with mu(I) = mu0 (1 + beta I^h/(K^h + I^h)). The equilibrium condition inverts exactly, so the bifurcation diagram follows from a sweep of I with no integration and no fitting. Bistability is assumed rather than discovered; the question the model answers is what moves the threshold. Under uniform scaling the relation is exact. A repair multiplier alpha cancels from the fold condition, so the fold sits at the same tissue order for every alpha and the tipping point is precisely proportional to it. Computed independently at 64 values of alpha from 0.25 to 8, rho_c/alpha is constant to a relative deviation of 3e-16 and the fold position varies by 1e-16 -- both at machine precision. This holds for every value of mu0, beta, K and h. The direction is robust; the magnitude is not. Across 17,583 randomly drawn bistable parameter sets, raising alpha raised the tipping point in 100% of cases under all three ways repair enhancement can enter the model. The three differ by nearly twofold in how much: doubling alpha multiplies the threshold by 2.00 under uniform scaling, 1.89 under feedback-only enhancement, and only 1.10 under constitutive-only enhancement. Enough constitutive repair removes the cliff rather than moving it. Above alpha = 2.60 at the baseline parameters the two folds annihilate in a cusp, rho(I) becomes monotone, and the tissue's stress response changes character — from all-or-nothing collapse to graded decline with no threshold at all. The hypothesis concerns repair fidelity — accurate restoration — and explicitly not repair capacity or speed; error-prone end-joining can itself generate the variants that drive transformation. Every result is a structural consequence of an assumed feedback, not a fitted or validated biological prediction, and the order parameter has no established experimental counterpart. No experimental data were generated or used.