Monte Carlo simulation of error propagation in the determination of binding constants from rectangular hyperbolae. 1. Ligand concentration range and binding constant

Rectangular hyperbolae have been used both to estimate equilibrium constants and to describe chemical processes dictated by equilibria. The propagation of error from the experimental measurements to the estimated constants, however, has not been well understood. In this paper, simulated experiments are used in a Monte Carlo analysis to compare the distributions of binding constants estimated by various calculation methods under different experimental conditions. The necessity of matching the range of additive (ligand) concentrations to the binding constant of the chemical interaction is demonstrated. It is shown that the relative error in the binding constant estimate is lower when the additive concentrations cover the central to upper portion of the binding isotherm (i.e., where the fraction of analyte complexed is above 0.5). The difference in the slope of the binding isotherm at the lowest and highest additive concentration used for the measurements is a good indicator of the reliability of the binding constant estimated under a specific set of conditions.