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

Equilibrium constants are essential\nfor understanding and predicting\nthe behavior of chemical systems across various scientific disciplines.\nTraditionally, these constants are computed via nonlinear regression\nof reaction isotherms, which show the dependence of the unreacted\nfraction of one reactant on the total concentration of another reactant.\nHowever, while these equilibrium constants can be precise (with small\nrandom errors), they may also be grossly inaccurate (with large systematic\nerrors), leading to potential misinterpretations. Although some statistical\nmethods exist for assessing the accuracy of nonlinear regression,\ntheir limited practicality for molecular scientists has resulted in\ntheir neglect by this research community. The objective of this work\nis to develop a practical method for quantitatively assessing the\naccuracy of equilibrium constants that could be easily understood\nand immediately adopted by researchers routinely determining these\nconstants. Our approach integrates error-propagation and regression-stability\nanalyses to establish the accuracy confidence interval (ACI)a\nrange within which the true value of the computed parameter lies with\na defined probability. In a proof-of-principle study, we applied this\napproach to develop a workflow for determining the ACI of the equilibrium\ndissociation constant (<i>K</i><sub>d</sub>) of affinity\ncomplexes from a single binding isotherm. We clearly explained how\nthe input parameters for this workflow can be determined, and finally,\nwe have implemented this workflow in a user-friendly web application\n(https://aci.sci.yorku.ca) to facilitate its immediate adoption by molecular scientists, regardless\nof their mathematical and computer proficiency. We further conducted\nthree case studies exemplifying the use of the ACI in the context\nof simultaneous assessment of precision and accuracy of determined <i>K</i><sub>d</sub> values. By understanding the ACI of equilibrium\nconstants and other parameters computed through nonlinear regression,\nresearchers can avoid misconceptions that arise from relying solely\non precision.