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A PRACTICAL APPROACH TO QUANTITATIVELY ASSESSING EQUILIBRIUM-CONSTANT ACCURACY FROM A SINGLE BINDING ISOTHERM
Sergey Krylov1
1York University, Toronto, Canada

PAPER: 415/Physical/Regular (Oral) OS
SCHEDULED: 13:20/Wed. 23 Oct. 2024/Marika B1

ABSTRACT:

Equilibrium constants are essential for understanding and predicting the behavior of chemical systems across various scientific disciplines [1]. 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 [2]. 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 and loss of R&D effectiveness in various areas including development of drugs and diagnostics [3, 4]. Although some statistical methods exist for assessing the accuracy of nonlinear regression [5, 6], 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, which 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 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 Kd 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.

REFERENCES:
[1] Mosher, M.; Kelter, P. Chemical Equilibrium. In An Introduction to Chemistry; Springer: Cham, 2023; pp 641–692. https://doi.org/10.1007/978-3-030-90267-4_14.
[2] Schuck, P.; Minton, A. P. Methods for the Determination of Equilibrium Binding Constants of Biomolecular Interactions. Annu. Rev. Biophys. Biomol. Struct. 1996, 25, 563-585. 10.1146/annurev.bb.25.060196.003051.
[3] Wang, T.Y.; Ji, W.; Evetron, D.; Le, A.T.H.; Krylova, S.M.; Fournier, R.; Krylov, S.N. Fundamental Determinants of the Accuracy of Equilibrium Constants for Affinity Complexes. Anal. Chem. 2023, 95(42), 15826–15832. DOI: 10.1021/acs.analchem.3c02726.
[4] Krylov, S.N. Underestimation of the Complexity of Kd Determination: Causes, Implications, and Ways to Improve. ACS Meas. Sci. Au 2024, 4(3), 231–232. DOI: 10.1021/acsmeasuresci.4c00022.
[5] Kazmierczak, N. P.; Chew, J. A.; Vander Griend, D. A. Bootstrap methods for quantifying the uncertainty of binding constants in the hard modeling of spectrophotometric titration data. Anal. Chim. Acta 2022, 1227, 339834. DOI: 10.1016/j.aca.2022.339834.
[6] Nguyen, T. H.; Rustenburg, A. S.; Krimmer, S. G.; Zhang, H.; Clark, J. D.; Novick, P. A.; Branson, K.; Pande, V. S.; Chodera, J. D.; Minh, D. D. Bayesian analysis of isothermal titration calorimetry for binding thermodynamics. PLoS One 2018, 13 (9), e0203224. DOI: 10.1371/journal.pone.0203224.