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

2 ABSTRACT: Accurate determination of equilibrium dissociation constants (Kd) from kinetic measurements requires understanding how systematic errors in concentration and signal propagate into errors in rate constants kon and koff and further in the resulting Kd computed as koff/kon. Here, we present a deterministic, platform-independent framework for error propagation that applies to any method in which reversible 1:1 binding between a ligand (L) and a target/analyte (T) is monitored through time-resolved association and dissociation 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 Kd and reveals a triphasic dependence of |ΔKd/Kd| on T0/Kd, including a low T0/Kd regime in which Kd 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 Smax 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 Smax is established independently and show that accurate kon, koff, and Kd values can be obtained from time-resolved traces acquired at T0 values far below the true Kd. We also outline practical limitations, including the requirement that kon and koff 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 softwarebased correlation diagnostics. This work provides a general theoretical foundation for understanding accuracy constraints in kinetic Kd determination and clarifies how these principles apply when implemented in practical surface-based measurements widely used for molecular interaction analyses.