Maximizing the Accuracy of Equilibrium Dissociation Constants for Affinity Complexes: From Theory to Practical...

The equilibrium dissociation constant (K_d) is a major characteristic of affinity complexes and one of the most frequently determined physicochemical parameters. Despite its significance, the values of K_d obtained for the same complex under similar conditions often exhibit considerable discrepancies and sometimes vary by orders of magnitude. These inconsistencies highlight the susceptibility of K_d determination to large systematic errors, even when random errors are small. It is imperative to both minimize and quantitatively assess the systematic errors inherent in K_d determination. Traditionally, K_d values are determined through nonlinear regression of binding isotherms. This analysis utilizes three variables: concentrations of two reactants and a fraction R of unbound limiting reactant. The systematic errors in K_d arise directly from systematic errors in these variables. Therefore, to maximize the accuracy of K_d, this study thoroughly analyzes the sources of systematic errors within the three variables, including (i) non-additive signals to calculate R, (ii) mis-calibrated experimental instruments, (iii) inaccurate calibration parameters, (iv) insufficient incubation time, (v) unsaturated binding isotherm, (vi) impurities in the reactants, and (vii) solute adsorption onto surfaces. Through this analysis, we illustrate how each source contributes to inaccuracies in the determination of K_d and propose strategies to minimize these contributions. Additionally, we introduce a method for quantitatively assessing the confidence intervals of systematic errors in concentrations, a crucial step toward quantitatively evaluating the accuracy of K_d. While presenting original findings, this paper also reiterates the fundamentals of K_d determination, hence guiding researchers across all proficiency levels. By shedding light on the sources of systematic errors and offering strategies for their mitigation, our work will help researchers enhance the accuracy of K_d determination, thereby making binding studies more reliable and the conclusions drawn from such studies more robust.