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

Abstract

Monte Carlo simulations on UV‐vis titration data quantify how the precision of binding constant calculation deteriorates in strong binding regimes. For 1:1 binding, global analysis is reliable when K[H]o < 1000, a significant improvement over previous recommendations. Initial concentration error generates the majority of the error in the calculated binding constant. We derive a novel experimental design formula to maximize binding constant precision over both strong and weak binding regimes and validate it through Monte Carlo simulations.

Properly handling negative values in the calculation of binding constants by physicochemical modeling of spectroscopic titration data

“…Individual simulated datasets were constructed by choosing a “true” binding constant with a set of composition profiles for the total (preequilibrated) concentrations of H and G (referred to as [ H ] 0,j and [ G ] 0,j for the j th chemical solution) over the course of the simulated titration. Two distinct sets of preequilibration composition profiles were employed as in previous work . Both involve 51 solutions and start with only host in solution #1.…”

“…Two distinct sets of preequilibration composition profiles were employed as in previous work. 49 Both involve 51 solutions and start with only host in solution #1. The first, "dilution′ profiles, start with 100% H in solution #1 and add guest titrant solution (with concomitant dilution of H) until solution #51 has two equivalents of guest.…”

A reliable algorithm for calculating stoichiometry parameters in the hard modeling of spectrophotometric titration data

“…As a direct result of the slopes in Figure 1B, the stoichiometric ratio should be well defined in the presence of experimental errors, while the nuclearity may not be. Figure 2 uses Monte Carlo simulations to investigate the optimal ratio and nuclearity values for a 1:1 reaction in the presence of moderate absorbance error (AE), transmittance error (TE), and concentration error (CE) (AE = 0.0003, TE = 0.0003, CE = 0.1%) 41 . The optimal stoichiometry model is determined through exhaustive grid searching of the RMSE surface and therefore does not depend on the choice of optimization algorithm.…”

“…It is well known that AE from the detector, TE from stray light, composition error from imprecise stock solutions or addition amounts, and spectrometer baseline shifts can introduce both stochastic noise and systematic bias into spectrophotometric titrations 50 . These sources of uncertainty preclude accurate estimation of binding constants outside of a given sensitivity range 24,41 . Consequently, it is imperative to show that the stoichiometry ratio calculations remain accurate and precise even under reasonable levels of experimental error.…”

“…Figure 2 uses Monte Carlo simulations to investigate the optimal ratio and nuclearity values for a 1:1 reaction in the presence of moderate absorbance error (AE), transmittance error (TE), and concentration error (CE) (AE = 0.0003, TE = 0.0003, CE = 0.1%). 41 The optimal stoichiometry model is determined through exhaustive grid searching of the RMSE surface and therefore does not depend on the choice of optimization algorithm. We see that the calculated nuclearity values exhibit two orders of magnitude more spread, resulting in almost 50% relative error and a large amount of bias.…”