A Practical Approach to Quantitatively Assessing Equilibrium-Constant Accuracy from a Single Binding Isotherm

Abstract

Equilibrium constants are essential for understanding and predicting the behavior of chemical systems across various scientific disciplines. Traditionally, these constants are computed via nonlinear regression of reaction isotherms, which show the dependence of the unreacted fraction of one reactant on the total concentration of another reactant. However, while these equilibrium constants can be precise (with small random errors), they may also be grossly inaccurate (with large systematic errors), leading to potential misinterpretations. Although some statistical methods exist for assessing the accuracy of nonlinear regression, their limited practicality for molecular scientists has resulted in their neglect by this research community. The objective of this work is to develop a practical method for quantitatively assessing the accuracy of equilibrium constants that could be easily understood and immediately adopted by researchers routinely determining these constants. Our approach integrates error-propagation and regression-stability analyses to establish the accuracy confidence interval (ACI)─a range within which the true value of the computed parameter lies with a defined probability. In a proof-of-principle study, we applied this approach to develop a workflow for determining the ACI of the equilibrium dissociation constant (K_d) of affinity complexes from a single binding isotherm. We clearly explained how the input parameters for this workflow can be determined, and finally, we have implemented this workflow in a user-friendly web application (https://aci.sci.yorku.ca) to facilitate its immediate adoption by molecular scientists, regardless of their mathematical and computer proficiency. We further conducted three case studies exemplifying the use of the ACI in the context of simultaneous assessment of precision and accuracy of determined K_d values. By understanding the ACI of equilibrium constants and other parameters computed through nonlinear regression, researchers can avoid misconceptions that arise from relying solely on precision.