Deterministic Error Propagation in Kinetic K_d Determination: General Theory with Application to Surface-Based Assays

Accurate determination of equilibrium dissociation constants (K_d) from kinetic measurements requires understanding of how systematic errors in concentration and signal propagate into errors in rate constants k_on and k_off and further in the resulting K_d computed as k_off/k_on. Here, we present a deterministic, platform-independent framework for error propagation that applies to any kinetic method in which a reversible 1:1 binding between a ligand (L) and a target/analyte (T) is monitored through time-resolved traces under pseudo-first-order conditions, where the total concentration of T (T₀) remains effectively constant during the association phase. The analysis yields closed-form expressions for the relative error in K_d and reveals a triphasic dependence of |ΔK_d/K_d| on T₀/K_d, including a low T₀/K_d regime in which K_d is intrinsically robust to systematic error. Because these features arise from the structure of the kinetic equations, they are general to both solution- and surface-based assays, regardless of detection modality. In this framework, the measured signal is proportional to the amount of LT complex (C) formed, and the maximal proportional response S_max corresponds to the signal that would be observed if all binding sites of L were fully occupied by T. To illustrate how the general theory manifests in practice, we apply it to surface-based measurements in which S_max is established independently and show that accurate k_on, k_off, and K_d can be obtained from time-resolved traces acquired at T₀ values far below the true K_d. We further show that, when full multiconcentration titrations are impractical, constraining S_max independently can enable more robust kinetic K_d determination from minimal data while preserving compatibility with established strategies such as reference binding partners, off-rate screening, and benchmark multiconcentration fitting. We also outline practical limitations, including the requirement that k_on and k_off be resolvable from the measured traces, and discuss how the theoretical conclusions relate to established experimental strategies such as reference binding partners, off-rate screening, and software-based correlation diagnostics. This work provides a general theoretical foundation for understanding accuracy constraints in kinetic K_d determination and clarifies how these principles apply when implemented in practical surface-based measurements widely used for molecular interaction analyses.