Sensitivity limits for determining 1:1 binding constants from spectrophotometric titrations via global analysis

Abstract

The simultaneous nonlinear regression modeling of multiple wavelengths of spectrophotometric data allows binding constants to be determined with much higher precision than in previous single‐wavelength methods; however, this method of global analysis has intrinsic limitations as well. Through Monte Carlo simulations on UV‐vis titration data using various types of experimental errors, we demonstrate how the precision of binding constant calculation deteriorates under very strong binding regimes, as quantified by the product K[H]o. We show that for a 1:1 binding model, global analysis can be reliably performed when K[H]o < 1000, representing a significant improvement over previous recommendations. The relative impacts of different sources of error as well as the degree of overlap in molar absorptivity curves are quantified. Even under optimal conditions, errors in initial concentrations of the titration solutions are found to have the most impact on error in the calculated binding constant, while instrumental noise is largely weeded out by the global analysis technique. We propose experimental diagnostics indicating when the model has lost sensitivity to the binding constant and derive a novel experimental design formula for maximizing the precision of the binding constant calculation. The results imply the need to develop robust and accessible uncertainty estimation techniques competent to deal with concentration errors and asymmetric confidence intervals.