Optimal experimental design for precise parameter estimation in competitive cross-reaction equilibria

Precise and accurate determination of equilibrium constants in chemical systems plays a crucial role in understanding their behavior, predicting reactions, and optimizing processes, leading to advancements in materials science, pharmaceuticals, and environmental studies. Various procedures, such as the mole ratio method, continuous variation, and titration, are commonly employed to investigate equilibrium systems and calculate equilibrium constants involving host–guest complexes. However, the impact of different experimental designs on the accuracy and precision of the fitted parameters has not been extensively explored. In this study, we focus on the role of experimental design in monitoring chemical equilibria and its influence on model parameter estimation. The indicator displacement assay and guest displacement assay are investigated as typical monitoring methods, and the optimal experimental design approach is introduced to identify suitable probe systems. The global analysis is also explored to improve parameter estimation by simultaneously fitting multiple datasets. Furthermore, non-regular procedures are examined, demonstrating the potential for robust model fitting with minimal measurements and providing insights into selecting appropriate probe systems. The results indicate that with appropriate design for monitoring equilibrium positions in competitive reactions, the probe equilibrium can differ by several orders of magnitude (more than 3 units) from the target equilibrium constant. Yet, accurate and precise determination of the equilibrium constant can still be achieved. The findings shed light on the importance of optimal experimental design for accurately determining thermodynamic parameters and binding affinities in complex chemical systems.