Open Research Index

A two-reaction counterexample to the gross-amplification affinity bound

Michael Mislan

Palomar Registrypalomar/PALOMAR-2026-10-01-000001Oct 1, 2026q-bio.MNscore 0

Despons, De Decker and Lacoste (https://arxiv.org/abs/2306.02366, conjecture following Eq. (33)) proposed that the affinity at maximum production flux is bounded below by the logarithm of the gross amplification ratio in seed-dependent autocatalytic networks. A two-species reversible mass-action counterexample is given by X ⇌ Y with forward/reverse rates (3, 2) and 2Y ⇌ 2X + Y with rates (7, 6). On the positive Y-stationary set, the production current has its unique global maximum at (X, Y) = (1, 1). At this point the exponential of the overall affinity is 7/4, strictly below the gross…

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