Sharp Identification Bounds for Binding Rates under Joint Calibration Uncertainty

Finite-time binding measurements constrain kinetic rates through both a reaction model and its calibration parameters. We characterize the sharp upper bound for the association rate in a three-state conformational-selection model when the dissociation rate, conformational rate, equilibrium constant and concentration scale belong to a prescribed compact joint set. The observations are calibrated bound fractions subject to finitely many closed interval constraints. We first prove that each finite-time bound fraction is strictly increasing in the initial binding-competent population. The physical feasible set at a fixed calibration is therefore an interval in that population. Let V be the calibration parameters with a nonempty physical feasible interval and let C = cl(V) within the joint calibration set. The sharp rate supremum is the reciprocal of the minimum of lambda K0 L / b on C, where L is the lower inverse threshold. Uniform finiteness is equivalent to a positive joint separation from the zero-population limiting curve on C. Explicit examples distinguish pointwise finiteness from uniform finiteness, inaccessible closed boundary points from physical limiting models, and separation by different readings from separation by one fixed reading. A continuous calibration example admits a certified sharp bound. We also state the optical conditions needed to interpret fluorescence as bound population.