Bootstrap methods for quantifying the uncertainty of binding constants in the hard modeling of spectrophotometric titration data

Equilibrium hard modeling of spectrophotometric titration data with binding parameters (ΔG° or logK values) involves nonlinear mathematical relationships and correlated experimental uncertainties. Therefore, uncertainty quantification techniques based on standard error computation substantially underestimate the true error for the calculated binding parameters. We show that the bootstrapping technique can provide accurate uncertainty quantification with no a priori knowledge of experimental error levels. Monte Carlo studies on simulated data show that bootstrapping the chemical solutions, whether on the data or residuals, handles absorbance error, transmittance error, and composition error well, producing asymmetric confidence intervals that correctly assess the true uncertainty. Additionally, stock solution error is handled well if it is present with other forms of error. Confidence interval bands for molar absorptivity curves can likewise be calculated. Analogous bootstrapping studies on real datasets confirm that the 95% confidence intervals match the variance observed from experimental replicates, though bootstrapping on the residuals should be used for smaller datasets. Bootstrapping along the titration axis should be used to estimate uncertainty whenever binding parameters are ascertained from titration datasets.